7. Suppose Pr(A) = 0.36 and Pr(B) = 0.46, where A and B are mutually exclusive. Find Pr(AUB). Pr(AUB) = (Simplify your answer. Type an integer or a decimal.)

Answer:8 cars

Step-by-step explanation:

to find the least amount of cars dived 30/4 which equilds 7.5

Since there are 2 remaining students, an additional car will be needed bringing the total to 8 cars.

The time it takes for the principle to triple in value is t = 18.792 years.

To determine how long it would take for a principal of $10,000 to triple in value at an interest rate of 3.75% compounded semi-annually, we can use the compound interest formula. By rearranging the formula and solving for time, we can find the answer.

The compound interest formula can be expressed as A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of compounding periods per year, and t is the time in years.

In this case, we have P = $10,000, r = 3.75% (or 0.0375 as a decimal), and n = 2 since compounding occurs semi-annually.

We want to find the time it takes for the principal to triple, so A = 3P. Substituting the known values into the compound interest formula, we have:

3P = P(1 + r/n)^(nt)

Canceling out the common factor of P on both sides, we get:

3 = (1 + r/n)^(nt)

Taking the natural logarithm (ln) of both sides to isolate the exponent, we have:

ln(3) = nt ln(1 + r/n)

Now, we can solve for t by dividing both sides of the equation by n ln(1 + r/n) and simplifying:

t = ln(3) / (n ln(1 + r/n))

Substituting the given values of r = 0.0375 and n = 2, we can calculate the value of t.

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Answer:

If you are looking at a graph then yes it will have a y-axis

Step-by-step explanation:

Answer:

True.

Step-by-step explanation:

A horizontal line goes on infinitely on both ends will eventually cross the y-axis, making a y-intercept.

Answer: Joe earns a monthly salary of 250 plus a commission on his total sales. Last month his total sales were $7,289 and he earned a total of $1,275. What is his commission rate?

Step-by-step explanation:  

250 + $7,289 + $1,275 = 8814

Answer:

151.2

Step-by-step explanation:

7x12=84

84/3=28

28x5.4=151.2

Answer:

a ≤ 9

Step-by-step explanation:

Closed circle means ≤ or ≥

Shading to the left means left direction < or ≤

The inequality sign that has both is: ≤

a ≤ 9

Answer:

The answer is C

Step-by-step explanation:

I took the test and I got it right

The coefficient matrix is a square matrix with dimensions equal to the number of variables in the system of equations.

The coefficient matrix is a matrix of the coefficients of the variables in a system of linear equations.

Now, we arrange these coefficients in a matrix format by placing them row-wise. This gives us the coefficient matrix:

[tex]2x + 3y + 3x3 = 20[/tex]

[tex]3x + 5y + 2x3 = 9[/tex]

[tex]-x + 3y + 5x3 = 4[/tex]

Each row of the coefficient matrix corresponds to an equation in the system, and each column represents the coefficients of a specific variable (x₁, x₂, x₃).

In summary, the coefficient matrix for the given system of equations is:

[tex]| 2 3 3 |[/tex]

[tex]| 3 5 2 |[/tex]

[tex]|-1 3 5 |[/tex]

This matrix provides a compact representation of the coefficients in the system, which can be further used for various operations and calculations.

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Answer:

d

Step-by-step explanation:

integer is a whole number

imagine the sum of the first set of 3 integers = 4 + 5 + 6

product = 4 x 5 x 6 = 120

imagine the sum of the 2nd set of 3 integers = 6 + 7 + 8 = 21

6 x 7 x 8 = 3364

The volume of the oblique cylinder is calculated as: B. 96π units³.

Volume = πr²h, where h is the height and r is the radius of the given cylinder.

Given the following:

Volume = πr²h = π(4²)(6)

Volume = 96π units³ (option B)

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Answer:

85

Step-by-step explanation:

425 divided by 8= 85

Answer:

He as 85 race cars.

Step-by-step explanation:

Just divide 425 by 5 and you have your answer.

Answer:

c because 3.3.3.3 is 3 to the 4th power expanded

Given that the probability of event A is Pr(A) = 1/3 and the probability of the union of event A and event B, namely AUB, is Pr(AUB) = 5/6. The probability of event B is Pr(B) = 2/3.

Suppose that event A and event B are disjoint.

The probability of event B is Pr(B) = 1/2.

To find the probability of event B.

For disjoint events A and B, we know that A ∩ B = Φ (empty set).

Thus, we can express the union of A and B as: AUB = A + B, where A and B are disjoint.

In general, the probability of the union of two events can be expressed as: P(AUB) = P(A) + P(B) - P(A ∩ B).

For disjoint events, the intersection of the events is always an empty set.

Thus, P(A ∩ B) = 0.

Using this information, we can write:

P(AUB) = P(A) + P(B) - P(A ∩ B)

= P(A) + P(B) - 0

= P(A) + P(B)

Given P(A) = 1/3 and P(AUB) = 5/6, we can solve for P(B) as follows:

5/6 = P(A) + P(B)

=> P(B) = 5/6 - P(A)

=> P(B)  = 5/6 - 1/3

=> P(B)  = 2/3

Thus, the probability of event B is Pr(B) = 2/3.

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Therefore, the probability of exactly one card being jack when a hand of four cards is drawn from a standard deck of playing cards with replacement is 0.073 or 7.3%.

Suppose a hand of four cards is drawn from a standard deck of playing cards with replacement, the probability of exactly one card being jack can be determined using the following steps:Step 1: Determine the total number of possible outcomes when four cards are drawn from a standard deck of 52 cards with replacement. The total number of possible outcomes = 52 × 52 × 52 × 52 = 7,311,616.Step 2: Determine the total number of ways in which exactly one card can be a jack. There are four jacks in a standard deck of 52 cards, so the total number of ways in which exactly one card can be a jack = 4 × 48 × 48 × 48 = 53,333,632.Step 3: Determine the probability of exactly one card being jack. Probability of exactly one card being jack = Total number of ways in which exactly one card can be a jack / Total number of possible outcomes= 53,333,632/ 7,311,616 = 7.28 ≈ 0.073 or 7.3%.Therefore, the probability of exactly one card being jack when a hand of four cards is drawn from a standard deck of playing cards with replacement is 0.073 or 7.3%.

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The test value for this hypothesis is 3.0.

The test value for this hypothesis can be calculated using the formula for a one-sample t-test:

test value = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Calculating the test value:

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Answer:

the blue one but not sure

Answer:

the third one i think

Step-by-step explanation:

Answer: 5/4

Step-by-step explanation: That should be right because I have big brain. Mark brainlist please :)

(a) `dy/dx = (2y - 2x)/(3y - 2x)`.

(b) The slope of the tangent line at points where x = 6 is 0.

(c) the curve has a vertical tangent line when x = (3/2)y.

(a) To show that `dy/dx = (2y - 2x)/(3y - 2x)`, we need to find the derivative of `y` with respect to `x`. We can do this by implicitly differentiating the given equation.

Differentiating both sides of the equation with respect to `x`, we get:

4x(dx/dx) + 6y(dy/dx) - 4[(dx/dx)y + x(dy/dx)] = 0

Simplifying the equation, we have:

4x + 6y(dy/dx) - 4xy - 4xy - 4x(dy/dx) = 0

Rearranging the terms and combining like terms, we get:

(6y - 4x)(dy/dx) = 8x - 8xy

Dividing both sides by (6y - 4x), we obtain:

dy/dx = (8x - 8xy)/(6y - 4x)

Simplifying further, we have:

dy/dx = (2x(4 - 4y))/(2(3y - 2x))

Canceling out the common factors, we get:

dy/dx = (2y - 2x)/(3y - 2x)

Therefore, `dy/dx = (2y - 2x)/(3y - 2x)`.

(b) To find the slope of the tangent line at the points where x = 6, substitute x = 6 into the expression we found for `dy/dx` in part (a):

dy/dx = (2(6) - 2(6))/(3y - 2(6))

      = 0/(3y - 12)

      = 0

The slope of the tangent line at points where x = 6 is 0.

(c) To find the value of x at which the curve has a vertical tangent line, we need to find the point(s) where the slope `dy/dx` is undefined. In other words, we need to find the values of x where the denominator of `dy/dx` becomes zero.

Setting the denominator equal to zero and solving for x:

3y - 2x = 0

2x = 3y

x = (3/2)y

So, the curve has a vertical tangent line when x = (3/2)y.

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It's 12 because if you divide 6 by 0.5 you should get 12, so basically use the opposite operation.

Hope that helps!

The expected value E(X) of a binomial random variable X can be calculated as n * p, and the variance Var(X) can be calculated as n * p * (1 - p). These formulas can be generalized for any values of p and n, and the value of p that minimizes the variance can be found by setting the derivative of Var(X) with respect to p equal to zero.

a. In part (a), we are given specific values for n (3) and p (3/4). The expected value E(X) of a binomial random variable X can be calculated as n * p, which gives us:

3 * 3/4

= 2.25.

The variance Var(X) can be calculated as n * p * (1 - p), which gives us:

3 * 3/4 * (1 - 3/4)

= 0.5625.

b. In part (b), we generalize the calculation of E(X) and Var(X) for any value of p and n. Using the binomial theorem, we can expand (p + (1 - p))ⁿ and differentiate it to find the coefficients for E(X) and Var(X).

c. To find the value of p that minimizes the variance Var(X), we can take the derivative of Var(X) with respect to p binomial, set it equal to zero, and solve for p. This will give us the value of p that minimizes the variance.

d. For any t > 0, we can calculate E(e^(tx)) using the binomial theorem by substituting e^t for p in the expansion of (p + (1 - p))ⁿ. This will give us the expected value of the exponential of tx.

Therefore, the expected value E(X) of a binomial random variable X can be calculated as n * p, and the variance Var(X) can be calculated as n * p * (1 - p). These formulas can be generalized for any values of p and n, and the value of p that minimizes the variance can be found by setting the derivative of Var(X) with respect to p equal to zero.

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Answer:

7/20

Step-by-step explanation:

Given function is { x) = {0, if 0 < x < 1/2, 1, if 1/2 < x < 1}.

Step-by-step explanation: Given function is { x) = {0, if 0 < x < 1/2, 1, if 1/2 < x < 1}.

The function is an even function because the function is symmetric with respect to the y-axis (i.e.) { -x) = {x). So, the Fourier series has only cosine terms. Therefore, the Fourier cosine series of the given function is given by:

f(x) = a0/2 + Σ an cos(nπx/L),

where L is the period of the function.

Since the function is even, the Fourier series reduces to  f(x) = a0/2 + Σ an cos(nπx/L) ...(1) , where a0 = 1/L ∫f(x)dx, an = 2/L ∫f(x)cos(nπx/L)dx for n = 1, 2, 3, ..., n. Let L = 1,

then a0 = 1/1 ∫0^1 f(x)dx = 1/2 an = 2/1 ∫0^1 f(x)cos(nπx)dx for n = 1, 2, 3, ..., n.
a1 = 2 ∫1/2^1 cos(nπx)dx = 1/nπ sin(nπx) from 1/2 to 1
= [1/nπ sin(nπ/2) - 1/nπ sin(0)]
= 2/nπ sin(nπ/2)

Hence, the Fourier cosine series is given by f(x) = 1/2 + 2/π ∑[sin(nπ/2)/n] cos(nπx) ...(2)for n = 1, 2, 3, ...Similarly, the Fourier sine series of the given function is given by: f(x) = Σ bn sin(nπx/L)where L is the period of the function. Since the function is even, there are no sine terms in the Fourier series. So, the Fourier sine series is zero, i.e., bn = 0 for n = 1, 2, 3, ....Hence, the full Fourier series is the same as the Fourier cosine series, which is given byf(x) = 1/2 + 2/π ∑[sin(nπ/2)/n] cos(nπx) ...(3)for n = 1, 2, 3, ...The Fourier series converges pointwise to f(x) for x in (0, 1/2) U (1/2, 1).The Fourier series does not converge at x = 0 and x = 1/2 because the function is not continuous at these points.

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The positive constant b is 0. This is obtained by setting the coefficient of the xy^2 term to zero in the equation derived from equating the integral of the joint probability density function to 1.

To compute the positive constant b, we need to calculate the integral of the joint probability density function (pdf) over the entire probability space and set it equal to 1 since it represents a valid probability density.

∫∫ f(x, y) dx dy = 1

Since the joint pdf is defined as:

f(x, y) = 5 - bcx * cb - bzycb

And it is zero otherwise, we can set up the integral as follows:

∫∫ (5 - bcx * cb - bzycb) dx dy = 1

To solve this integral, we need to determine the limits of integration. Since the joint pdf is not specified outside of the equation, we assume it is defined for all real values of x and y.

∫∫ (5 - bcx * cb - bzycb) dx dy = ∫∫ 5 - bcx * cb - bzycb dx dy

Integrating with respect to x first:

∫ (5x - bcx^2/2 * cb - bzy * cb) ∣∣ dy = 1

Now integrating with respect to y:

(5xy - bcxy^2/2 * cb - bzy^2/2 * cb) ∣∣ dy = 1

Since this equation holds for all real values of x and y, we can ignore the limits of integration.

Next, we can solve for b by equating the integral to 1 and simplifying:

(5xy - bcxy^2/2 * cb - bzy^2/2 * cb) = 1

Simplifying further:

5xy - bcxy^2/2 - bzy^2/2 = 1

Now, we can compare the coefficients of the terms on both sides of the equation:

- bc/2 = 0 (since there is no xy^2 term on the right-hand side)

Solving for b:

bc = 0

Since we are looking for a positive constant b, we can conclude that b = 0.

Therefore, the positive constant b is 0.

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The velocity of the train after 4 hours is 20 miles per hour.

To find the velocity of the train after 4 hours, we need to differentiate the given function s(t) with respect to t.

Velocity is the derivative of position with respect to time.

That is,v(t) = ds(t)/dtTo differentiate s(t) = –13 + 3t² – 4t – 4, we differentiate each term separately.v(t) = d/dt(-13) + d/dt(3t²) - d/dt(4t) - d/dt(4)v(t) = 0 + 6t - 4

The velocity of the train after 4 hours is given by substituting t = 4 in the above equation.v(4) = 6(4) - 4 = 20

The velocity of the train after 4 hours is 20 miles per hour.To sum up, the velocity of the train after 4 hours is 20 miles per hour.

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The school is not justified to make this claim because of the reasons defined.

The following is a statement that might be made about the high school to justify its claim No, because the z-score of Z = 1.06 is not uncommon because it does not fall within the range of a typical event, namely within 2 standard deviations of the sample mean.

It has been given to us that:

μ = 511

σ = 119

Sample size (n) = 55

and

s = 119 / √55

= 16.046

As we all know,

Only when z > 2 then, the high school's allegation is valid and warranted.

To locate,

Z's value is

So,

Z = ( X - μ )/σ

by applying the Central Limit Theorem to the values,

z = ( 528 - 511 ) / 16.046

= 1.06

Since, z < 2, as a result, the allegation is unjustified.

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Correct question:

The average math SAT score is 511 with a standard deviation of 119. A particular high school claims that its students have unusually high math SAT scores. A random sample of 55 students from this school was​ selected, and the mean math SAT score was 528. Is the high school justified in its​ claim? Explain. ▼ No Yes ​, because the​ z-score ​( nothing​) is ▼ unusual not unusual since it ▼ does not lie lies within the range of a usual​ event, namely within ▼ 1 standard deviation 2 standard deviations 3 standard deviations of the mean of the sample means. ​(Round to two decimal places as​ needed.)

Answer:

x = -8 and y = -7

Step-by-step explanation:

I will solve your system by substitution.

(You can also solve this system by elimination.)

8x−12y=20;4x−4y=−4

Step: Solve8x−12y=20for x:

8x−12y+12y=20+12y(Add 12y to both sides)

8x=12y+20

8x

8

=

12y+20

8

(Divide both sides by 8)

x=

3

2

y+

5

2

Step: Substitute

3

2

y+

5

2

forxin4x−4y=−4:

4x−4y=−4

4(

3

2

y+

5

2

)−4y=−4

2y+10=−4(Simplify both sides of the equation)

2y+10+−10=−4+−10(Add -10 to both sides)

2y=−14

2y

2

=

−14

2

(Divide both sides by 2)

y=−7

Step: Substitute−7foryinx=

3

2

y+

5

2

:

x=

3

2

y+

5

2

x=

3

2

(−7)+

5

2

x=−8(Simplify both sides of the equation)

Answer:

I THINK it would be B.

Step-by-step explanation:

I’m very sorry if I’m wrong.

Answer:

16.3%

Step-by-step explanation:

21.5 times 0.163= 3.5

Answer:

60 degrees

Step-by-step explanation:

Each triangle needs to add up to 180 total degrees.  70+50=120,

180

-

120

___

60

Answer:

960

Step-by-step explanation:

Let P, R and T denote principal amount, rate of interest and time period.

Principal amount of loan (P) = 4,000

Time period (T) = 4 years

Rate of interest (R) = 6%

Simple interest is calculated using the following formula:

Simple interest [tex]=\frac{4000(4)(6)}{100} =960[/tex]

So,

Simple interest is equal to 960