when loaded with iron rods a lorry has mass of 12000kg. if the mass of iron rods is there times that of the empty lorry . find the mass or iron.

Answers

Answer 1

Complete Question

When loaded with iron rods a lorry has mass of 12000kg. if the mass of iron rods is three times that of the empty lorry, find the mass of iron.

Answer:

3000kg

Step-by-step explanation:

Let us represent

Mass of lorry = x

Mass of iron rods = y

x + y = 12000kg..... Equation 1

x = 12000kg - y

We are told that:

If the mass of iron rods is three times that of the empty lorry, find the mass of iron.

x = 3y

We substitute 3y for x in Equation 1

x = 12000kg - y

3y = 12000kg - y

Collect like terms

3y + y = 12000kg

4y = 12000kg

Divide both sides by 4

y = 12000kg/4

y = 3000kg

Note that:

Mass of iron rods = y

Hence, Mass of iron rods = 3000kg


Related Questions

The
sum of three numbers is 94. The thors number is 10 less than the
first. The second number is 2 times the third. What are the
numbers?

Answers

The three numbers are 31, 42 and 21.

Given that the sum of three numbers is 94, and the third number is 10 less than the first and the second number is 2 times the third.

We need to find the three numbers.

Let's represent the three numbers as x, y, and z.

First number = x Second number = y Third number = z

As per the given statement, we have the following equations:x + y + z = 94z = x - 10y = 2z

Substitute the value of y and z in the first equation.x + y + z = 94x + 2z + z = 94x + 3z = 94

Now, substitute the value of z in terms of x in the above equation.

x + 3(x - 10) = 94x + 3x - 30 = 94

Simplify the above equation

4x = 94 + 30 = 124x = 31

Thus, the first number is 31.

The third number is 10 less than the first.

So, the third number is 31 - 10 = 21.

Second number = 2z = 2 × 21 = 42

Therefore, the three numbers are 31, 42, and 21.

#SPJ11

Let us know more about sum of numbers:https://brainly.com/question/16740360

Construct a continguency table and find the indicated probability. 8) Of the 91 people who answered "yes" to a question, 12 were male. Of the 48 people that answered "no" to the question, 14 were male. If one person is selected at random from the group, what is the probability that the person answered "yes" or was male? Round your answer to 2 decimal places.

Answers

The probability that the person answered "yes" or was male 1

We have a contingency table with rows corresponding to the Yes and No answers, and columns corresponding to the Male and Female respondents:  

               Yes         No          

Male         12           12

Female    79           34

The sum of all the entries is 139.

The probability that a randomly selected person answered "yes" is the sum of the probabilities of a male who answered "yes" and a female who answered "yes".

This is(12 + 79)/139 = 91/139

The probability that a randomly selected person is a male is the sum of the probabilities of a male who answered "yes" and a male who answered "no".

This is(12 + 14)/139 = 26/139

The probability that a randomly selected person answered "yes" or was male is the sum of the probabilities of a male who answered "yes", a female who answered "yes", a male who answered "no", and a female who answered "no".

This is(12 + 79 + 14 + 34)/139 = 139/139 = 1.00 (rounded to two decimal places).

Therefore, the probability that a randomly selected person answered "yes" or was male is 1.00.

To learn more about probability

https://brainly.com/question/13604758

#SPJ11

Brady caught f fly balls at baseball practice today. Mark caught two more than Brady. If Mark caught nine fly balls at practice, which of the following equations could be used to find how many fly balls Brady caught?

f - 2 = 9
f + 2 = 9
f = 9 + 2
2 f = 9

Answers

None, it doesn’t have an answer without substitution

the tables shows the charges for cleaning services provided by 2 companies

question below​

Answers

a) The range of values of n when it is cheaper to obtain the cleaning service from Company A is < 3 hours.

b) The range of values of n when it is cheaper to obtain the cleaning service from Company B is >3 hours.

How the ranges are computed?


The ranges can be computed by equating the alegbraic expressions representing the total costs of Company A and Company B.

The result of the equation shows the value of n when the total costs are equal.

Company   Booking Fee   Hourly Charge

A                        $15                     $30

B                       $30                     $25

Let the number of hours required for a home cleaning service = n

Expressions:

Company A: 15 + 30n

Company B: 30 + 25n

Equating the two expressions:

30 + 25n = 15 + 30n

Simplifing:

15 = 5n

n = 3

Thus, the range of values shows:

When the number of hours required for home cleaning is 3, the two company's costs are equal.

Below 3 hours, Company A's cost is cheaper than Company B's.

Above 3 hours, Company B's cost is cheaper than Company A's.

Learn more about the range at https://brainly.com/question/24326172.

#SPJ1

Label the following statements as being true or false. (a) The rank of a matrix is equal to the number of its nonzero columns. (b) The product of two matrices always has rank equal to the lesser of the ranks of the two matrices.

Answers

(a) The rank of a matrix is equal to the number of its nonzero columns - False.

(b) The product of two matrices always has rank equal to the lesser of the ranks of the two matrices - false.

What is the rank of a matrix?

(a) The rank of the matrix refers to the number of linearly independent rows or columns in the matrix.

So based on the definition of rank of a matrix, we can conclude that the rank of the matrix is the number of linearly independent rows or columns in the matrix and NOT equal to the number of its nonzero columns.

(b) The rank of the product of two matrices can be at most the lesser of the ranks of the two matrices, but it can also be smaller.

So the product of two matrices does not always has rank equal to the lesser of the ranks of the two matrices.

Thus, the two statements about rank of matrices are FALSE.

Learn more about ranks of matrix here: https://brainly.com/question/31397722

#SPJ4

Solve the IVP: y" + 4y = = = { t, if t < 1 11, if t >1' y(0) = 2, y'(0) = 0

Answers

To solve the initial value problem (IVP) y" + 4y = f(t) with the given piecewise function f(t), we need to consider two cases: t < 1 and t > 1. Let's solve the IVP step by step.

Case 1: t < 1

In this case, the function f(t) is equal to t. To solve the differential equation, we assume a solution of the form y(t) = A(t) + B(t), where A(t) is the solution to the homogeneous equation y" + 4y = 0, and B(t) is a particular solution to the non-homogeneous equation.

The homogeneous equation y" + 4y = 0 has characteristic equation r^2 + 4 = 0, which yields the complex roots r = ±2i. Therefore, the homogeneous solution is A(t) = c1*cos(2t) + c2*sin(2t), where c1 and c2 are constants.

For the particular solution B(t), we assume B(t) = Ct, where C is a constant to be determined. Substituting B(t) into the differential equation, we get:

2C + 4Ct = t

6Ct + 2C = t

Comparing the coefficients, we have 6C = 0 and 2C = 1. Solving these equations, we find C = 0 and C = 1/2, respectively.

Therefore, the particular solution for t < 1 is B(t) = (1/2)t.

Combining the homogeneous and particular solutions, we have y(t) = A(t) + B(t) = c1*cos(2t) + c2*sin(2t) + (1/2)t.

To find the constants c1 and c2, we use the initial conditions y(0) = 2 and y'(0) = 0. Substituting t = 0 into the equation, we get:

y(0) = c1*cos(0) + c2*sin(0) + (1/2)*0 = c1 = 2

y'(0) = -2c1*sin(0) + 2c2*cos(0) + (1/2)*1 = 2c2 + (1/2) = 0

From the second equation, we find c2 = -1/4.

Thus, the solution for t < 1 is y(t) = 2*cos(2t) - (1/4)*sin(2t) + (1/2)t.

Case 2: t > 1

In this case, the function f(t) is equal to 11. The differential equation y" + 4y = 11 has a constant right-hand side, so we assume a particular solution of form B(t) = D, where D is a constant. Substituting B(t) into the equation, we have:

0 + 4D = 11

D = 11/4

Therefore, the particular solution for t > 1 is B(t) = 11/4.

The general solution for t > 1 is the homogeneous solution, which is the same as in Case 1, plus the particular solution B(t):

y(t) = A(t) + B(t) = c1*cos(2t) + c2*sin(2t) + 11/4

Since we have no additional initial conditions for t > 1, we can leave the constants c1 and c2 unspecified.

In conclusion, the solution to the IVP y" + 4y =

f(t) with y(0) = 2 and y'(0) = 0 is:

For t < 1: y(t) = 2*cos(2t) - (1/4)*sin(2t) + (1/2)t

For t > 1: y(t) = c1*cos(2t) + c2*sin(2t) + 11/4

Here, c1 and c2 are arbitrary constants, and the particular solutions take different forms depending on the value of t.

To know more about the differential equation, click here;

https://brainly.com/question/32538700

#SPJ11

In a school there are 26 teachers and administrative members. The school management wants to forma committee of 3 administrative members and 5 teachers or 2 administrative members and 6 teachers. How many ways can be formed this committee?

Answers

In this scenario, the number of ways to form the committee is 325 * 23,725 = 7,725,125. In total, the number of ways to form the committee is 170,734,400 + 7,725,125 = 178,459,525.

we need to consider two scenarios: forming a committee of 3 administrative members and 5 teachers, or forming a committee of 2 administrative members and 6 teachers.

Scenario 1: Committee of 3 administrative members and 5 teachers

The number of ways to choose 3 administrative members from a group of 26 is given by the combination formula:

C(26, 3) = 26! / (3! * (26-3)!) = 26! / (3! * 23!) = (26 * 25 * 24) / (3 * 2 * 1) = 2600

Similarly, the number of ways to choose 5 teachers from a group of 26 is:

C(26, 5) = 26! / (5! * (26-5)!) = 26! / (5! * 21!) = (26 * 25 * 24 * 23 * 22) / (5 * 4 * 3 * 2 * 1) = 65,780

Therefore, in this scenario, the number of ways to form the committee is 2600 * 65,780 = 170,734,400.

Scenario 2: Committee of 2 administrative members and 6 teachers

Similarly, the number of ways to choose 2 administrative members from a group of 26 is:

C(26, 2) = 26! / (2! * (26-2)!) = 26! / (2! * 24!) = (26 * 25) / (2 * 1) = 325

The number of ways to choose 6 teachers from a group of 26 is:

C(26, 6) = 26! / (6! * (26-6)!) = 26! / (6! * 20!) = (26 * 25 * 24 * 23 * 22 * 21) / (6 * 5 * 4 * 3 * 2 * 1) = 23,725

The number of ways to form the committee is 325 * 23,725 = 7,725,125.

In total, the number of ways to form the committee is 170,734,400 + 7,725,125 = 178,459,525.

Learn more about combination here:

https://brainly.com/question/30469166

#SPJ11

arrange the steps in order to produce a proof that if n is a composite integer, then n has a prime divisor less than or equal to

Answers

The proof starts by assuming n is a composite integer and proceeds to show that there must exist a prime divisor of n that is less than or equal to √n by contradiction.

To produce a proof that if n is a composite integer, then n has a prime divisor less than or equal to √n, the steps should be arranged in the following order:

Assume n is a composite integer.

Express n as a product of its prime factors.

Suppose all prime factors of n are greater than √n.

Take the product of all prime factors of n.

The product obtained in step 4 is greater than n.

This contradicts the fact that n is a composite integer.

Therefore, the assumption made in step 3 is false.

There must exist at least one prime factor of n that is less than or equal to √n.

Hence, if n is a composite integer, then n has a prime divisor less than or equal to √n.


To learn more about prime numbers click here: brainly.com/question/29629042

#SPJ11

the half life of radium is 1690 years. if 90 grams are present now, how much will be present in 500 years?

Answers

Approximately 70.79 grams of radium will be present in 500 years.

To determine the amount of radium that will be present in 500 years, we can use the concept of radioactive decay and the half-life of radium.

The half-life of a radioactive substance is the amount of time it takes for half of the initial quantity to decay. In this case, the half-life of radium is given as 1690 years.

To calculate the amount of radium that will be present in 500 years, we can divide the elapsed time by the half-life and then use the exponential decay formula:

N(t) = N₀ * (1/2)^(t / T),

where N(t) represents the amount of radium present at time t, N₀ represents the initial amount of radium, T represents the half-life, and t represents the elapsed time.

Given that the initial amount of radium is 90 grams, the half-life is 1690 years, and we want to find the amount present in 500 years, we have:

N(500) = 90 grams * (1/2)^(500 / 1690).

To calculate this expression, we can use a calculator or a computer software. Evaluating the expression, we find:

N(500) ≈ 90 grams * (1/2)^(0.2959) ≈ 90 grams * 0.7866 ≈ 70.79 grams.

Therefore, approximately 70.79 grams of radium will be present in 500 years.

It's important to note that radioactive decay is a random process, and the half-life represents the average time it takes for half of the substance to decay. The actual amount of radium present in 500 years may vary due to the random nature of radioactive decay.

By using the exponential decay formula and the given half-life of radium, we can estimate the amount of radium that will be present in 500 years as approximately 70.79 grams.

Learn more about radium here

https://brainly.com/question/29018436

#SPJ11

Mahidol University Wisdom of the Land Exercise If X, and X, are independent random variables with = 4,₂= 2, 0₁-3, O₂ = 5, and Y = 4X₁-2X₂, determine the following. ▪ E(Y) ▪ V(Y) ▪ E(2Y) ▪ V(2Y) 53

Answers

E(Y) = 12, V(Y) = 20, E(2Y) = 24, V(2Y) = 80 for given independent random variables X₁ and X₂.

Given:

E(X₁) = 4

V(X₁) = 0₁ (variance of X₁)

E(X₂) = 2

V(X₂) = 5 (variance of X₂)

We are asked to find:

E(Y) = E(4X₁ - 2X₂)

V(Y) = V(4X₁ - 2X₂)

E(2Y) = E(2(4X₁ - 2X₂))

V(2Y) = V(2(4X₁ - 2X₂))

E(Y):

E(Y) = E(4X₁ - 2X₂)

= 4E(X₁) - 2E(X₂) (since expectation is linear)

= 4(4) - 2(2) (substituting given values)

= 16 - 4

= 12

Therefore, E(Y) = 12.

V(Y):

V(Y) = V(4X₁ - 2X₂)

= 4²V(X₁) + (-2)²V(X₂) (since variances add for independent variables)

= 4²(0₁) + (-2)²(5) (substituting given values)

= 16(0) + 4(5)

= 0 + 20

= 20

Therefore, V(Y) = 20.

E(2Y):

E(2Y) = 2E(Y)

= 2(12) (substituting E(Y) = 12)

= 24

Therefore, E(2Y) = 24.

V(2Y):

V(2Y) = (2²)V(Y)

= 2²(20) (substituting V(Y) = 20)

= 4(20)

= 80

Therefore, V(2Y) = 80.

Learn more about the independent random variables at

brainly.com/question/29461549

#SPJ4

You deposit $2500 in a bank account. Find the balance after 3 years for an account that pays 2.5% annual interest compounded monthly. Round to the nearest dollar.
pls help test today!!

Answers

After 3 years, the balance in the account would be approximately $2,708.

To find the balance after 3 years for an account that pays 2.5% annual interest compounded monthly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A is the final balance

P is the principal amount (initial deposit)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

In this case:

P = $2500

r = 2.5% = 0.025 (as a decimal)

n = 12 (monthly compounding)

t = 3 years

Plugging in these values into the formula, we get:

A = $2500(1 + 0.025/12)^(12*3)

A = $2500(1.00208333333)^(36)

Using a calculator, we can evaluate the expression inside the parentheses and calculate the final balance:

A ≈ $2500(1.083282498) ≈ $2708.21

Therefore, after 3 years, the balance in the account would be approximately $2,708.

for such more question on annual interest

https://brainly.com/question/14768591

#SPJ8

Let W1,W2⊂VW1,W2⊂V be finite-dimensional subspaces of a vector space VV. Show

dim(W1+W2)=dimW1+dimW2−dim(W1∩W2)dim⁡(W1+W2)=dim⁡W1+dim⁡W2−dim⁡(W1∩W2)

by successively addressing the following problems.

(a) Prove the statement in the cases W1={0}W1={0} or W2={0}W2={0}.

Hence, we may and will assume that W1,W2≠{0}W1,W2≠{0}. To this aim, we start from a basis of W1∩W2W1∩W2, which will later be completed to a basis of W1+W2W1+W2.

(b) Let S⊂W1∩W2S⊂W1∩W2 be a basis of W1∩W2W1∩W2. Show the existence of sets T1,T2⊂VT1,T2⊂V such that S∪T1S∪T1 is a basis of W1W1 and S∪T2S∪T2 is a basis of W2W2.

(c) Show that U:=S∪T1∪T2U:=S∪T1∪T2 spans W1+W2W1+W2.

(d) Show that UU is linearly independent, and deduce the claimed identity.

Answers

By addressing each step, we establish the validity of the identity dim(W1+W2) = dim(W1) + dim(W2) - dim(W1∩W2) for finite-dimensional subspaces W1 and W2 of a vector space V.

To prove the identity dim(W1+W2) = dim(W1) + dim(W2) - dim(W1∩W2), we address the problem in several steps.

(a) If either W1 or W2 is the zero subspace {0}, then the statement holds trivially since the dimension of the zero subspace is zero.

(b) Assuming W1 and W2 are non-zero subspaces, we start with a basis S of the intersection W1∩W2. Then, we find sets T1 and T2 such that S∪T1 is a basis of W1 and S∪T2 is a basis of W2. This can be done by adding vectors from V to S in a way that they span W1 and W2 respectively.

(c) We show that the union U = S∪T1∪T2 spans W1+W2. Since T1 and T2 span W1 and W2 respectively, any vector in W1+W2 can be expressed as a linear combination of vectors from U.

(d) We demonstrate that U is linearly independent, meaning no non-trivial linear combination of vectors in U equals the zero vector. This ensures that the vectors in U are independent. From this, we conclude that dim(W1+W2) = dim(W1) + dim(W2) - dim(W1∩W2).

Therefore, by addressing each step, we establish the validity of the identity dim(W1+W2) = dim(W1) + dim(W2) - dim(W1∩W2) for finite-dimensional subspaces W1 and W2 of a vector space V.

Know more about Validity here:

https://brainly.com/question/29808164

#SPJ11

As the manager of a local cinema, you are interested in understanding the preferences of customers to different film genres. You recently conducted a survey of 477 customers and found that 71 of them enjoy horror films. Use the survey results to estimate, with 93% confidence, the proportion of customers who enjoy horror films. Report the upper bound of the interval only, giving your answer as a percentage to two decimal places

Answers

With 93% confidence, the upper bound of the interval for the proportion of customers who enjoy horror films is estimated to be 17.73%. This means that we can be 93% confident that the true proportion lies below 17.73%.

To estimate the proportion of customers who enjoy horror films with 93% confidence, we can use the formula for the confidence interval for a proportion. The upper bound of the interval can be calculated as:

Upper Bound = Sample Proportion + (Z * Standard Error)

where Z is the z-value corresponding to the desired confidence level, and the Standard Error is calculated as the square root of [(Sample Proportion * (1 - Sample Proportion)) / Sample Size].

In this case, the sample proportion is 71/477 = 0.1487. The sample size is 477.

To compute the z-value for a 93% confidence level, we need to find the z-value that leaves 3.5% in the upper tail of the standard normal distribution. By looking up the z-value in the standard normal distribution table, we find that the z-value is approximately 1.81.

Plugging in the values, we have:

Upper Bound = 0.1487 + (1.81 * sqrt[(0.1487 * (1 - 0.1487)) / 477])

Calculating this expression, we find that the upper bound of the interval is approximately 0.1773, or 17.73% (rounded to two decimal places).

Therefore, with 93% confidence, we can estimate that the proportion of customers who enjoy horror films is no more than 17.73%.

To know more about confidence level refer here:

https://brainly.com/question/22851322#

#SPJ11

A random sample of 16 statistics examinations from a large population was taken. The average score in the sample was 78.6 with a standard deviation of 8. We are interested in determining whether the average grade of the population is significantly more than 75. The test statistic is: 3.6 045

Answers

A random sample of 16 statistics examinations from a large population was taken. The test statistic (t) for this hypothesis test is 1.8.

To determine whether the average grade of the population is significantly more than 75, we can perform a hypothesis test using the given sample data. We'll set up the null and alternative hypotheses as follows:

Null Hypothesis (H 0): The average grade of the population is not significantly more than 75.

Alternative Hypothesis (Ha): The average grade of the population is significantly more than 75.

To conduct the hypothesis test, we can use the t-test since the population variance is unknown. Here, we'll assume the sample is representative and the Central Limit Theorem applies.

To calculate the test statistic for this hypothesis test, we will use the t-distribution since the population standard deviation is unknown. The formula for the t-test statistic is as follows:

t = (sample mean - hypothesized mean) / (sample standard deviation / √(sample size))

Given the information:

Sample mean (x) = 78.6

Hypothesized mean (μ) = 75

Sample standard deviation (s) = √(variance) = √(64) = 8

Sample size (n) = 16

Let's calculate the test statistic using the formula:

t = (78.6 - 75) / (8 / √(16))

t = 3.6 / (8 / 4)

t = 3.6 / 2

t = 1.8

To learn more about Test statistic here;  https://brainly.com/question/30458874

#SPJ11

Complete Question:

A random sample of 16 statistics examinations from a large population was taken. The average score in the sample was 78.6 with a variance of 64. We are interested in determining whether the average grade of the population is significantly more than 75. Assume the distribution of the population of grades is normal.

How do you get the test statistic?

Consider the linear program minimize f(x) = cTx subject to Ax >= b. (i) Write the first- and second-order necessary conditions for a local solution. (ii) Show that the second-order sufficiency conditions do not hold anywhere, but that any point x. satisfying the first-order necessary conditions is a global minimizer. (Hint Show that there are no feasible directions of descent at xx, and that this implies that x, is a global minimizer.)

Answers

Tthe first-order necessary conditions are sufficient to guarantee global optimality in linear programming, even though the second-order sufficiency conditions may not hold.

The first- and second-order necessary conditions and the second-order sufficiency conditions are important concepts in optimization theory.

In the context of the linear program minimize f(x) = cTx subject to Ax >= b, we can derive these conditions to determine local solutions and global minimizers.

(i) The first-order necessary condition for a local solution in linear programming is that the gradient of the objective function, c, must be orthogonal to the feasible region defined by the constraints Ax >= b.

Mathematically, this condition can be expressed as c - ATλ = 0, where λ is the vector of Lagrange multipliers.

The second-order necessary condition for a local solution states that the Hessian matrix of the Lagrangian function, which combines the objective function and constraints, must be positive semi-definite.

In other words, the eigenvalues of the Hessian matrix must be non-negative.

(ii) In linear programming, the second-order sufficiency conditions do not hold anywhere.

This means that the Hessian matrix is not positive definite, and it is possible to have points that satisfy the first-order necessary conditions but are not global minimizers.

However, if a point x satisfies the first-order necessary conditions, it is guaranteed to be a global minimizer.

This is because the absence of feasible descent directions at that point implies that there are no neighboring points that can improve the objective function value while satisfying the constraints.

Therefore, any point that satisfies the first-order necessary conditions in a linear program is also a global minimizer.

In summary, the first-order necessary conditions are sufficient to guarantee global optimality in linear programming, even though the second-order sufficiency conditions may not hold.

Learn more about Lagrange multipliers here:

https://brainly.com/question/32544889

#SPJ11

olve the problem. Find C and D so that the solution set to the system is {(-4, 2)}. Cx - 2y = -16 2x + Dy = -16 Select one: O a. C = -4: D = -3 O b. C = -4: D = 3 Oc. C= 3: D = -4 O d. C = -3; D = 4

Answers

The solution set {(-4, 2)} is satisfied when C = 3 and D = -4. Hence, the correct answer is option C.

To find the values of C and D that satisfy the given system of equations, we substitute the coordinates of the solution set {(-4, 2)} into the equations and solve for C and D.

Substituting x = -4 and y = 2 into the first equation, we have:

C(-4) - 2(2) = -16

-4C - 4 = -16

-4C = -12

C = 3

Next, substituting x = -4 and y = 2 into the second equation, we have:

2(-4) + D(2) = -16

-8 + 2D = -16

2D = -8

D = -4

Therefore, the values of C and D that satisfy the system of equations and yield the solution set {(-4, 2)} are C = 3 and D = -4. Thus, the correct answer is option c: C = 3, D = -4.

Learn more about the Substitution method here: brainly.com/question/14763562

#SPJ11

whats 2+2?
A) frog
B) 4
C) 8028402848
D)urmom

Answers

The sum of the numbers 2 and 2 using the addition principle is 4.

Using the addition concept

Addition lets us count two or more numbers in order of magnitude.

Given the values :

2 and 2

The addition sign is represented as '+'. Addition of positive numbers can be done irrespective of the value on the left or right hand side.

Therefore, the solution to the expression 2+2 is 4.

Learn more on addition : https://brainly.com/question/24536701

#SPJ1

At Timberland High School, it was found that 61% of students are taking a political science class, 72% of students are taking a French class, and 54% of students are taking both.

Find the probability that a randomly selected student is taking a political science class or a French class. You may answer with a fraction or a decimal rounded to three places if necessary.

Answers

The probability that a randomly selected student is taking a political science class or a French class is 0.79 or 79%.

What is the formula to calculate the present value of an investment?

To find the probability that a randomly selected student is taking a political science class or a French class, we can use the principle of inclusion-exclusion.

First, we know that 61% of students are taking a political science class and 72% of students are taking a French class.

However, if we simply add these two percentages together, we would be counting the students who are taking both classes twice.

To correct for this, we subtract the percentage of students taking both classes (54%) from the sum of the individual percentages (61% + 72%).

This accounts for the double counting and gives us the probability that a student is taking either political science or French or both.

So, the probability is calculated as follows:

Probability(Political Science or French) = Probability(Political Science) + Probability(French) - Probability(Both)

= 61% + 72% - 54%= 79%

Therefore, the probability is 0.79 or 79%.

Learn more about political science

brainly.com/question/14346467

#SPJ11

a) There exists a simple graph with 6 vertices, whose degrees are 2,2,2,3,4,4. b) There exists simple graph with 6 vertices whose degrees are 0,1,2,3,4,5 c) There exists simple graph with degrees 1,2,2,3 d) A graph containing an Eulerian circuit is called an Eulerian graph. If 61 and 62 Are Eulerian graph, and we add the following edges between them, then resulting graph is Eulerian: 6

Answers

No simple graph with six vertices and the above degrees exists.Graph with 6 vertices with degrees 0, 1, 2, 3, 4, 5.For a simple graph, the sum of the degrees of all vertices must be even.The resulting graph is also an Eulerian graph.

a) There exists a simple graph with 6 vertices, whose degrees are 2,2,2,3,4,4.

The given degrees 2, 2, 2, 3, 4, 4 sum up to 17, which is an odd number.

A simple graph with six vertices whose degrees are all even must have a sum of degrees of 6 × 2 = 12, which is even.

Therefore, no simple graph with six vertices and the above degrees exists.

b) There exists a simple graph with 6 vertices whose degrees are 0, 1, 2, 3, 4, 5.

The sum of degrees of vertices in a graph is twice the number of edges, so there are a total of 2 × (0 + 1 + 2 + 3 + 4 + 5) = 30 degrees in this graph.

For the graph to be simple, there can be a maximum of one vertex of degree 5 and one vertex of degree 0.

The graph may be formed by starting with a vertex of degree 5, and joining it to the vertices of degrees 4, 3, 2, 1, and 0 in turn.

The resulting graph is shown in the following figure:Graph with 6 vertices with degrees 0, 1, 2, 3, 4, 5

c) There exists a simple graph with degrees 1, 2, 2, 3.

The degree sequence has an odd sum, so no simple graph can have that degree sequence.

This is because, for a simple graph, the sum of the degrees of all vertices must be even.

d) A graph containing an Eulerian circuit is called an Eulerian graph.

If 61 and 62 Are Eulerian graph, and we add the following edges between them, then the resulting graph is Eulerian:6For 6 to be added as an edge to both 1 and 2, they must have even degree.

Since they were originally Eulerian graphs, each vertex already had even degree.

After 6 is added as an edge to both vertices, it becomes possible to start at one vertex and traverse the graph by using edges that have not been used before and eventually return to the starting vertex.

Hence, the resulting graph is also an Eulerian graph.

Know more about Eulerian circuit here,

https://brainly.com/question/30681808

#SPJ11

Suppose that (a,n) : = if and only if 1. Prove that a¹ = a^(mod n) b = c(mod ord,(a)).

Answers

We have proved that a^1 ≡ a^(mod n) and b ≡ c (mod ordₙ(a)).

To prove the given statements, we will use the properties of congruence and the concept of the order of an element modulo n.

Statement 1: a^1 ≡ a^(mod n)

Let's consider a positive integer k such that k ≡ 1 (mod φ(n)), where φ(n) represents Euler's totient function. By Euler's theorem, we know that a^φ(n) ≡ 1 (mod n). Therefore, we can rewrite k as k = 1 + mφ(n), where m is an integer. Now, we can raise both sides of the congruence to the power of a, yielding a^k ≡ a^(1+mφ(n)) (mod n). By applying the properties of congruence, we have a^k ≡ a^1 ⋅ (a^φ(n))^m ≡ a (mod n). Hence, a^1 ≡ a^(mod n).

Statement 2: b ≡ c (mod ordₙ(a))

Let ordₙ(a) denote the order of a modulo n. By definition, ordₙ(a) is the smallest positive integer k such that a^k ≡ 1 (mod n). Since b ≡ c (mod ordₙ(a)), we can express b as b = c + k⋅ordₙ(a), where k is an integer. Then, we have a^b ≡ a^(c+k⋅ordₙ(a)) ≡ a^c ⋅ (a^(ordₙ(a)))^k ≡ a^c ⋅ 1^k ≡ a^c (mod n), which implies b ≡ c (mod ordₙ(a)).

In conclusion, we have proved that a^1 ≡ a^(mod n) and b ≡ c (mod ordₙ(a)).

Know more about Integer here:

https://brainly.com/question/490943

#SPJ11







in Q. 4. (a) Find the minimal polynomial and the degree of 72 over Q(V2). (b) Find the splitting field of x² +1 over Zz.

Answers

The minimal polynomial of 72 over Q(√2) is (x - 72), with a degree of 1. The splitting field of x² + 1 over Zz is the field of complex numbers, C.

(a) To determine the minimal polynomial and degree of 72 over Q(√2), we need to determine the polynomial that is satisfied by 72 and has coefficients in Q(√2).

Since 72 is not a perfect square, it is an irrational number. Thus, it is not an element of Q(√2). Therefore, the minimal polynomial of 72 over Q(√2) is the polynomial of minimal degree with coefficients in Q(√2) that is satisfied by 72.

The minimal polynomial of 72 over Q(√2) is the polynomial of the form (x - 72), as this is the simplest polynomial with coefficients in Q(√2) that has 72 as a root.

Hence, the minimal polynomial of 72 over Q(√2) is (x - 72), and its degree is 1.

(b) To determine the splitting field of x² + 1 over Zz, we need to find the field extension in which the polynomial x² + 1 completely factors into linear factors.

The polynomial x² + 1 does not have any roots in Zz, the ring of integers. However, it does have roots in the field of complex numbers, denoted by C.

The splitting field of x² + 1 over Zz is the smallest field extension that contains Zz and all the roots of x² + 1. In this case, the splitting field is the field of complex numbers, C, because it contains the roots of x² + 1, namely ±i.

Therefore, the splitting field of x² + 1 over Zz is the field of complex numbers, C.

To know more about minimal polynomial refer here:

https://brainly.com/question/30452357#

#SPJ11

Solve the boundary value problem Au = 0, 0 < x < R, 0 < a < 27, u(R, 6) = 4+3 sin 0, 0 << 27. =

Answers

Solution: Given boundary value problem is Au = 0, 0 < x < R, 0 < a < 27, u(R, 6) = 4+3 sin 0, 0 << 27. = Using separation of variables let the solution be: u(x,θ) = X(x)Θ(θ)

Now, we need to solve the equation Au = 0 by using the method of separation of variables. Let us first start with Θ(θ) part. Let Θ(θ) = A sin(mθ) + B cos(mθ), Where A, B are constants and m is a constant to be determined, and let the boundary condition at θ = 6 be u(R, 6) = 4 + 3sin(0)∴ 4 + 3sin(0) = X(R)Θ(6)= X(R) (A sin(6m) + B cos(6m))…

(1)Next we need to determine the value of m. For this we will use the boundary condition that u(0,θ) = 0, which gives usΘ(θ) = A sin(mθ) + B cos(mθ)= 0, θ ≠ 6⇒ B cot(m6) = -A …

(2)Hence we obtainΘ(θ) = A sin(m(θ - 6)) + B cos(m(θ - 6))Now let us move to the X(x) part which satisfies: X''(x)/X(x) = - λLet λ = m² + k²  …

(3)⇒ X(x) = C₁ cos(mx) + C₂ sin(mx) ...

(4)Hence the general solution to the equation Au = 0 is u(x,θ) = (C₁ cos(mx) + C₂ sin(mx))(A sin(m(θ - 6)) + B cos(m(θ - 6))) ...

(5). Now let us apply the boundary condition u(R, 6) = 4 + 3 sin(0) to get C₁ = 0, C₂ = 3/Θ(R) = A sin(6m) + B cos(6m)= 4 + 3sin(0)⇒ A = 3cos(6m) and B = 4/sin(6m). Now we have the expression for Θ(θ), hence substituting the values of A and B in the expression of Θ(θ), we getΘ(θ) = 3cos(m(θ - 6)) + 4sin(m(θ - 6))/sin(6m). Thus the solution to the boundary value problem is given by: u(x,θ) = C sin(mθ) (3cos(m(θ - 6)) + 4sin(m(θ - 6))), where C = 4/3π(1 - cos(6m)) and m is given by (3). Therefore, u(x,θ) = 4/3π(1 - cos(6m)) sin(mθ) (3cos(m(θ - 6)) + 4sin(m(θ - 6))).

Thus the solution to the boundary value problem is given by u(x,θ) = 4/3π(1 - cos(6m)) sin(mθ) (3cos(m(θ - 6)) + 4sin(m(θ - 6))) and m is given by (3).

To know more about equation refer to:

https://brainly.com/question/27893282

#SPJ11

1. What is a virtue? 2. What are the cardinal virtues? Describe them briefly. 3. According to C. S. Lewis how can the moral life be compared to a fleet of ships? 4. How is it that human sexual activit

Answers

Virtues are positive qualities guiding behavior. Cardinal virtues - prudence, justice, temperance,fortitude.

C.S. Lewis compares moral life to ships. Committed marriage fosters best experience of human sexual activity.

What is the explanation for the above?

Virtues are positive moral qualities guiding behavior,including prudence, justice,   temperance, and fortitude.

C.S. Lewis uses the metaphor of a fleet of ships to illustrate the moral life. Human sexual activity is best experienced within a committed married relationship, promoting trust and emotional intimacy.

Virtues and a strong moral foundation guide individuals in making wise choices and living a fulfilling and virtuous life.

Learn more about virtue at:

https://brainly.com/question/26183268

#SPJ4

Full Question:

Although part of your question is missing, you might be referring to this full question:

1. What is a virtue?

2. What are the cardinal virtues? Describe them briefly.

3. According to C. S. Lewis how can the moral

life be compared to a fleet of ships?

4. How is it that human sexual activity is best experienced within a committed married relationship?

Olivia was asked to factor the following expression completely:
x^3-x+3x^2y=3y
x(x^2-1)+3y(x^2-1)
(x+3y)(x^2-1)
How can you check Olivia’s work to show the answer is or is not correct. If Olivia is not correct, explain to Olivia where her mistake is and how to fix it.

Answers

Step-by-step explanation:

To check Olivia's work, we can multiply the factors she obtained to see if they result in the original expression. Let's perform the multiplication:

(x + 3y)(x^2 - 1) = x(x^2 - 1) + 3y(x^2 - 1)

Distributing the terms:

= x * x^2 - x * 1 + 3y * x^2 - 3y * 1

= x^3 - x + 3yx^2 - 3y

As we compare this with the original expression:

x^3 - x + 3x^2y = 3y

We can see that Olivia's factored expression, (x + 3y)(x^2 - 1), does not match the original expression. Olivia made a mistake in the step where she distributed the terms.

To correct the mistake, we need to distribute the terms correctly. Let's go through the factoring process again:

Starting with the original expression: x^3 - x + 3x^2y = 3y

Rearranging the terms: x^3 + 3x^2y - x - 3y = 0

Now, we can factor by grouping:

x^2(x + 3y) - 1(x + 3y) = 0

Notice that we have a common factor of (x + 3y). Factoring it out:

(x + 3y)(x^2 - 1) = 0

Now we have the correct factored expression.

Answer:

Olivia's work is not correct.

The correct factorization of the expression is: (x-1)(x+1)(x+3y)

Step-by-step explanation:

In order to check Olivia's work, we can expand the two factors she gave:

x(x^2-1)+3y(x^2-1)

x^3-x+3x^2*y-3xy

This is not equal to the original expression, so Olivia's factorization is incorrect.

To help Olivia find the correct factorization, we can first factor out a common factor of x from the first two terms:

x(x^2-1)+3y(x^2-1)

x(x^2-1)+3y(x^2-1)

Now, we can factor the quadratic expression x^2-1:

x(x-1)(x+1)+3y(x-1)(x+1)

Finally, we can factor out a common factor of (x-1)(x+1) from the two terms:

(x-1)(x+1)(x+3y)

This is the correct complete factorization of the expression.

Use Propositional logic to prove whether the following is a theorem: q (p&q) →→P)

Answers

The expression q (p ∧ q) → P is not a theorem in propositional logic.

To prove whether a given expression is a theorem in propositional logic, we need to determine if it is logically valid, meaning it holds true for all possible truth assignments to its propositional variables.

Let's analyze the expression q (p ∧ q) → P using a truth table:

p q (p ∧ q) q (p ∧ q) q (p ∧ q) → P

T T T T ?

T F F F ?

F T F F ?

F F F F ?

In the truth table, we see that for the row where p is false and q is false, the expression q (p ∧ q) → P is undetermined, denoted by "?". This means that the expression does not have a definite truth value for all possible truth assignments.

Since the expression does not hold true for all truth assignments, it is not a theorem in propositional logic.

Learn more about propositional logic here:

https://brainly.com/question/13104824

#SPJ11

You want to obtain a sample to estimate a population mean. Based on previous evidence, you believe the population standard deviation is approximately 36.7. You would like to be 90% confident that your estimate is within 2 of the true population mean. How large of a sample size is required?

Answers

a sample size of 177 is required.

When obtaining a sample to estimate a population mean, the sample size formula is given as follows:n = ((z-score)^2 * σ^2) / E^2

Where,σ = population standard deviation

E = margin of error

z-score is obtained from the level of confidence.

To find the sample size required to estimate a population mean, with a 90% confidence level and a margin of error of 2, the following formula can be used:

n = ((1.645)^2 * 36.7^2) / 2^2= 176.3769 ≈ 177

Therefore, a sample size of 177 is required.

To know about sample size visit:

https://brainly.in/question/26985448

#SPJ11

for the circle with equation (x-2)2 (y 3)2 = 9, what is the diameter?

Answers

The diameter of the given circle is 6 units.

We can rewrite the given equation of the circle in standard form as below

x² + y² - 4x - 6y + 13 = 0

We can find the center of the circle by equating the equation to zero as below:x² + y² - 4x - 6y + 13 = 0(x-2)² + (y-3)² = 3²

The center of the circle = (2, 3)

The radius of the circle is 3 units. The diameter is twice the radius.

diameter = 2 × 3 = 6 units

Therefore, the diameter of the given circle is 6 units.

To know more about the equation of the circle visit:

https://brainly.in/question/16747480

#SPJ11

Suppose a patient has a 1% chance of having a disease, and that he is sent for a diagnostic test with a 90% sensitivity (detects true positives) and 80% specificity (detects true negatives). What is the post test probability of having the disease if the patient is tested +ve? What is it if the patient is tested -ve? Please draw a decision tree for this question.

Answers

The post-test probability of not having a disease if the patient is tested -ve is approximately 99.8% is the answer.

Given that a patient has a 1% chance of having a disease and is sent for a diagnostic test with 90% sensitivity and 80% specificity. We need to find the post-test probability of having a disease if the patient is tested +ve and if the patient is tested -ve. Post-test probability is the probability of a patient having the disease after the diagnostic test.

We can find it using Bayes’ theorem.

Prior probability = 1% = 0.01Sensitivity = 90% = 0.9Specificity = 80% = 0.8False Positive Rate = 1 - Specificity = 0.2False Negative Rate = 1 - Sensitivity = 0.1

The decision tree for the problem is as shown below:  [tex]P(A) = 0.01[/tex][tex]P(\lnot A) = 0.99[/tex][tex]P(B|A) = 0.9[/tex][tex]P(\lnot B|A) = 0.1[/tex][tex]P(\lnot B|\lnot A) = 0.8[/tex][tex]P(B|\lnot A) = 0.2[/tex]

Using Bayes' theorem, we can find the post-test probability of having a disease if the patient is tested +ve and -ve.If the patient is tested +ve, we need to find the probability of having a disease.[tex]P(A|B)=\frac{P(B|A)P(A)}{P(B|A)P(A)+P(B|\lnot A)P(\lnot A)}[/tex][tex]=\frac{0.9*0.01}{0.9*0.01+0.2*0.99}[/tex][tex]\approx 0.043[/tex]

The post-test probability of having a disease if the patient is tested +ve is approximately 4.3%.

If the patient is tested -ve, we need to find the probability of not having a disease.[tex]P(\lnot A|\lnot B)=\frac{P(\lnot B|\lnot A)P(\lnot A)}{P(\lnot B|\lnot A)P(\lnot A)+P(\lnot B|A)P(A)}[/tex][tex]=\frac{0.8*0.99}{0.8*0.99+0.1*0.01}[/tex][tex]\approx 0.998[/tex]

The post-test probability of not having a disease if the patient is tested -ve is approximately 99.8%.

know more about Bayes’ theorem.

https://brainly.com/question/29598596

#SPJ11

You have 4 flower pots in your home one at a balcony, one at a kitchen window, one on the kitchen floor and one on the table in the living room. Your local store has 11 different kinds of flowers for pots. Suppose you want to buy flowers for all your pots so that each pot has a different kind of flower. How many different ways are there to do it? Show your work. What if you decide to move all the flower pots into the kitchen, so it doesn't matter which type of flower is in which pot - how many different choices of four different flower types do you have now? Show work.

Answers

There are two scenarios to consider:

If each pot must have a different kind of flower and they are placed in different locations (balcony, kitchen window, kitchen floor, living room table).

If all the pots are moved into the kitchen and it doesn't matter which type of flower is in which pot.

Scenario 1: Each pot in a different location:

For the first pot, there are 11 options. For the second pot, since it must have a different kind of flower, there are 10 options remaining. Similarly, for the third and fourth pots, there are 9 and 8 options respectively. Therefore, the total number of ways to choose flowers for the pots is 11 * 10 * 9 * 8 = 7,920.

Scenario 2: All pots in the kitchen:

In this case, we only need to choose four different flower types out of the 11 available. This can be calculated using combinations. The number of ways to choose four different flower types out of 11 is denoted as C(11, 4) and can be calculated as C(11, 4) = 11! / (4! * (11-4)!) = 330.

Therefore, if the pots are moved into the kitchen, there are 330 different choices of four different flower types.

Learn more about balcony click here;

https://brainly.in/question/5629555

#SPJ11

If you covered confidence intervals for differences between population proportions in the homework of the previous lesson, continue on to complete the rest of those problems here. Continuing with the sample data from the previous problem, let's find a confidence interval for the difference between the proportions of wives and husbands who do laundry at home. Use technology to compute a 99% confidence interval for the difference in population proportions, P.-P.

Answers

With 99% confidence, the difference between the proportions of wives and husbands who do laundry at home is between 23.8% and 56.2%.

Given that we are given a sample data from the previous problem, let's find a confidence interval for the difference between the proportions of wives and husbands who do laundry at home. We are supposed to use technology to compute a 99% confidence interval for the difference in population proportions, P.-P.

For a random sample from two populations, the confidence interval for the difference in population proportions is given by:

P(wives doing laundry) = p1= 0.60N1=100P(husbands doing laundry) = p2 = 0.20N2=100

We can find the standard error (SE) as:

SE = sqrt{ [p1(1-p1) / n1 ] + [ p2(1-p2) / n2 ] }

SE = sqrt{ [0.6(0.4) / 100] + [0.2(0.8) / 100] }

SE = sqrt{0.0024 + 0.0016}

SE = sqrt(0.004)

SE = 0.063

For a 99% confidence interval, we will have alpha level of 1 - 0.99 = 0.01 / 2 = 0.005 on each tail of the distribution. So, the z-critical value will be:

z-critical = inv Norm(0.995)

z-critical = 2.576

Finally, we can calculate the confidence interval as follows:

CI = (p1 - p2) ± z-critical * SE

CI = (0.60 - 0.20) ± 2.576 * 0.063

CI = 0.40 ± 0.162

CI = (0.238, 0.562)

Hence, the 99% confidence interval for the difference in population proportions of wives and husbands doing laundry at home is (0.238, 0.562).

Therefore, we can conclude that with 99% confidence, the difference between the proportions of wives and husbands who do laundry at home is between 23.8% and 56.2%.

Learn more about confidence interval here:

https://brainly.com/question/32546207

#SPJ11

Other Questions
how did civil rights begin. Was it something that happened all over the country, or was it one act by one person? * The following function represents the production cost f(x), in dollars, for x number of units produced by company 1:f(x) = 0.05x2 7x + 300The following table represents the production cost g(x), in dollars, for x number of units produced by company 2:x g(x)0.6 899.580.8 899.521 899.501.2 899.521.4 899.58Based on the given information, determine which company has a lower minimum and find the minimum value. f(x) at (1, 899.50) g(x) at (70, 55) f(x) at (70, 55) g(x) at (1, 899.50) Solve the following recurrence relations (a) [6pts] an = 3an-2, Q1 = 1, 42 = 2. b) [6pts] an = an-1 + 2n 1,01 = 1, using induction (Hint: compute the first few terms, = pattern, then verify it). Indicate whether each of the following transactions represents an increase in net exports, a decrease in net exports, an increase in net capital outflow, or a decrease in net capital outflow for the United States. Transaction Net Exports Net Capital Outflow Increase Decrease Increase Decrease The Japanese car manufacturer Nissan builds a factory in Ohio. A German citizen buys an Apple computer. An American buys a Sony TV. An American fashion company opens up an outlet in the U.K. Neurotransmitters that open Na+ channels and trigger action potentials in receiving cells are calleda. Inhibitoryb. Cross-linkedc. Excitatoryd. Blockede. Obligatory aved Which of the following is NOT an example of deformation? O faults O folds O foliation O stratification wildlife biologists believe that the weights of adult trout can be described by a normal model with a standard deviation of 1.2 pounds. if only 7% of adult trout weigh more than 5 pounds what is the mean weight (in pounds) of adult trout? stock prices gave a realized return of 4%, 4%, 10%, and 10% over four successive quarters. what is the annual realized return for for the year? State the name of the property illustrated. 2 + (6 + 4) = (2 + 16 + 74 () A Associative O Distributive Commutative o Both associative and commutative True or false? President Franklin Roosevelt was sworn in after President Kennedy's assassination Help me please ASAP I need help before month-end adjustments are made, the february 28 trial balance of bridgeports enterprise containsrevenue of $11,000 and expenses of $8,900. Adjustments are necessary for the following items:Depreciation for February is $1,200.Revenue earned but not yet billed is $2,800.Accrued interest expense is $900.Revenue collected in advance that is now earned is $2,500.Portion of prepaid insurance expired during February is $500.Calculate the correct net income for Cole's Enterprise for the month end.Net income $______ What happen on Black Tuesday in October 1929 A random sample of elementary school children in New York state is to be selected to estimate the proportion p who have received a medical examination during the past year. An interval estimate of the proportion p with a margin of error of 0.06 0.06 and 99% 99 % confidence is required. HelPP pleaseee !!!!!Which of the following were characteristics of the Great Depression? (Check all that apply)Dramatic drops in stock market valuevalue of money dropsbreadlines where people lined up to get something to eatmany lost their jobsmany lost homesSchools closed.there was a shortage of oil Windsor, Inc. purchased a delivery truck for $32,000 on January 1, 2022. The truck has an expected salvage value of $4,000, and is expected to be driven 100,000 miles over its estimated useful life of 8 years. Actual miles driven were 16,600 in 2022 and 13,100 in 2023. (a1) Calculate depreciable cost per mile under units-of-activity method. (Round answer to 2 decimal places, e.g. 0.50.) Depreciable cost Project: Introducing your Argument. I don't get this project at all I need help. True or false: On average, eta-squared, partial eta-squared, and R-squared are all measures of effect size that refer to the proportion of variance explained within a study. A sphere has a radius of 9 feet. A second sphere has a radius of 6 feet. What is the difference of the volumes of the spheres? The volume of the larger sphere is cubic feet greater than the volume of the smaller sphere. A duopoly faces the inverse demand curve p = 50 - Q. Firm i 's total cost function is Ci(qi) = 10q; for i = 1, 2. In a Stackelberg equilibrium, a. the leader chooses quantity 20 and the follower chooses quantity 15. b. both the leader and the follower choose quantity 40 3 C. the leader chooses quantity 10 and the follower chooses quantity 5. d. the leader chooses quantity 20 and the follower chooses quantity 10.