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(a) The area of triangle PQR is 9.165 units².

(b) The formula for a plane given three points is: 10x - 7y - 2z = 0

(c) The volume of the parallelepiped with edges PO, PR, and PS is 148 units³.

(d)  A point on the line through P and Q which is two units away from P is (4/5, 6/5, 2/5).

(a) The area of triangle PQR is 9.165 units².

The formula for the area of a triangle given three points is:

Area = 1/2 | ((x2 − x1) × (y3 − y1)) − ((y2 − y1) × (x3 − x1)) |

The coordinates for P, Q, and R are: P (0, 0, -2)Q (2, 3, 4)R (4, 6, 5)

Substituting into the formula gives us:

Area = 1/2 | ((2 - 0) × (5 + 2)) − ((3 - 0) × (4 - 0)) |

Area = 9.165 units² (rounded to three decimal places)

(b) An equation of the form ax + by + cz = d for the plane containing points P, Q, and R is:

10x - 7y - 2z = 0

The formula for a plane given three points is: ax + by + cz = d

To find a, b, c, and d, we first need to find two vectors on the plane.

We can use PQ and PR.

PQ = Q - P = (2 - 0)i + (3 - 0)j + (4 + 2)k = 2i + 3j + 6k

PR = R - P = (4 - 0)i + (6 - 0)j + (5 + 2)k = 4i + 6j + 7k

Now we can find the normal vector by taking the cross product of PQ and PR:

PQ x PR = <3i - 26j - 12k>

So the equation of the plane is:3x - 26y - 12z = 0

We can simplify this by multiplying all terms by -2, which gives:10x - 7y - 2z = 0

(c) The volume of the parallelepiped with edges PO, PR, and PS is 148 units³.

The volume of a parallelepiped is given by the scalar triple product of three vectors.

We can use OP, PR, and PS.

OP = P - O = -i - j - 2k = < -1, -1, -2 >

PR = R - P = 4i + 6j + 7k = < 4, 6, 7 >

PS = S - P = 6i + 11j + 12k = < 6, 11, 12 >

The scalar triple product is:

OP ⋅ (PR x PS)OP ⋅ (PR x PS) = < -1, -1, -2 > ⋅ (< 54, -20, -10 >)OP ⋅ (PR x PS) = -148

The volume of the parallelepiped is 148 units³.

(d) A point on the line through P and Q which is two units away from P is (4/5, 6/5, 2/5).

The equation of the line through P and Q is:x = 2t, y = 3t, z = 4 + 6t

A point on the line that is two units away from P is given by:

t = 2/5

Substituting into the equations for x, y, and z gives:(4/5, 6/5, 2/5)

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The solution to the initial value problem is:

x(t) = [tex](1/4) * e^{(3t)} - (1/4) * e^{(4t)}[/tex] and y(t) = [tex]e^{(3t)} + (1/6) * e^{(4t)}[/tex]

To find the solution to the initial value problem Y' = AY, where A is the matrix with eigenvalues and eigenvectors given, we can use the eigenvalue-eigenvector method.

Let's denote the eigenvectors as v₁ and v₂:

v₁ = [2]

[8]

v₂ = [-3]

[2]

The general solution to the system of linear differential equations can be written as:

Y(t) = [tex]c_1 * e^{(X_1t)} * v_1 + c_2 * e^{(X_2t)} * v_2[/tex]

where c₁ and c₂ are constants.

Substituting the given eigenvalues and eigenvectors:

Y(t) = c₁ * [tex]e^{(3t)[/tex] * [2] + c₂ * [tex]e^(4t)[/tex] * [-3]

[8] [2]

Simplifying further:

Y(t) = [2c₁ * [tex]e^{(3t)[/tex] - 3c₂ * [tex]e^{(4t)[/tex]]

[8c₁ * [tex]e^{(3t)[/tex] + 2c₂ * [tex]e^{(4t)[/tex]]

To find the specific solution that satisfies the initial condition Y(0) = [0] and [8], we can substitute t = 0 into the general solution:

Y(0) = [2c₁ - 3c₂]

[8c₁ + 2c₂]

Equating this to the initial condition:

[2c₁ - 3c₂] = [0]

[8c₁ + 2c₂] [2]

Solving this system of equations will give us the values of c₁ and c₂:

2c₁ - 3c₂ = 0 ----(1)

8c₁ + 2c₂ = 2 ----(2)

Multiplying equation (1) by 4 and adding it to equation (2), we get:

16c₁ = 2

Solving for c₁, we find:

c₁ = 1/8

Substituting c₁ back into equation (1), we can solve for c₂:

2(1/8) - 3c₂ = 0

1/4 - 3c₂ = 0

3c₂ = 1/4

c₂ = 1/12

Therefore, the specific solution to the initial value problem is:

x(t) = [tex](1/8) * e^{(3t)} * 2 + (1/12) * e^{(4t) }* (-3)[/tex]

y(t) = [tex](1/8) * e^{(3t)} * 8 + (1/12) * e^{(4t)} * 2[/tex]

Simplifying further:

x(t) = [tex](1/4) * e^{(3t)} - (1/4) * e^{(4t)}[/tex]

y(t) = [tex]e^{(3t)} + (1/6) * e^{(4t)}[/tex]

Therefore, the solution to the initial value problem is x(t) = [tex](1/4) * e^{(3t)} - (1/4) * e^{(4t)}[/tex] and y(t) = [tex]e^{(3t)} + (1/6) * e^{(4t)}[/tex].

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Answer:

0.1666...

Step by step explanation:

By using long division (with 6 as the divisor) the number sentence would keep on going with 40-36.

0.166666666

1.000000000

− 0                  

 10                

−  6                

  40              

 −36              

   40            

   −36            

       40          

     − 36          

         40        

       − 36        

           40      

         − 36      

             40    

           − 36    

               40  

             − 36  

                 40

               − 36

Answer:

2(x plus 20)

Step-by-step explanation:

this is the highest common factor

Answer:

106

Step-by-step explanation:

reflection

Answer:

The answer is d

Step-by-step explanation:

Answer:

13.9% Approximately

Answer:

26

Step-by-step explanation:

Given

4x - a ← substitute a = - 2, x = 6 into the expression

= 4(6) - (- 2) [ note - (- ) is equivalent to + ]

= 24 + 2

= 26

Answer:

its 77 1/3

just do the math with a calculator

Answer: 48 1/3

Step-by-step explanation:

Answer:

           The slope-intercept form of the equation:  y = 0.5x + 5

           The slope:    m = 0.5

           The y-intercept:     b = 5

Step-by-step explanation:

Slope-intercept form is  y = mx + b, where m is the slope and b is y-intecept

4y = 2x + 20           {divide both sides by 4}

y = 0.5x + 5   ⇒   m = 0.5  and  b = 5

Answer:

The pythagorean theorem is a theorem which states that the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Pythagorean theorem

in the right angle triangles there is a relationship that governs the length of the three sides. if we knows the length of any two sides, the third side may be calculated by the use of the Pythagorean theorem.

This theorem states that the square on the hypotenuse of a right angled triangle is equal to the sum of the squares on the remaining two sides.

we only use Pythagorean theorem to find the length of the missing side of a right angled triangle only.

Answer:

yes.

Step-by-step explanation:

Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.

6/9 divided by 3/3= 2/3

proportional

Answer:

el numero 1

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

4 is choice C. THis is because the y intercept is 1 and when you go up 2 units, and go right once, you go to another point (rise over run)

Step-by-step explanation:

Answer:

Formula for circumference: 2 x pie(3.14 or 22/7) x radius(half of diameter or already given radius). Area of a circle: pie(3.14 or 22/7) x radius squared

Radius: 3, 6 is diameter and half of that is 3.

3 x 3.14 x 2 = 18.84 <------ circumference

3.14 x 3^2

3.14 x 9 = 28.26 <------ area of the circle

Answer:

5

Step-by-step explanation:

Distance Equation Solution:

[tex]d=\sqrt{(2-(-1)^2+(6-2)^2}\\d=\sqrt{(3)^2+(4)^2} \\d= \sqrt{9+6}\\d= \sqrt{25}\\d=5[/tex]

Answer:

118degrees

Step-by-step explanation:

Assuming we are given the following and m<k and ,<N lies on the same straight line, hence;

m<K = 62 degrees

n<N = ?

Since are on the same straight line, hence;

m<N + m<K = 180

m<N + 62 = 180

m<N = 180 - 62

m<N  = 118

Hence the measure of m<N is 118degrees

'

,

There is insufficient evidence of a significant difference in the proportion of males and females that have at least one tattoo.

Therefore, the correct answer is A.

To construct a confidence interval for the difference in proportions, we can use the following formula:

CI = (p1 - p2) ± Z ×√[(p1×(1 - p1) / n1) + (p2 × (1 - p2) / n2)]

Where:

p1 and p2 are the sample proportions for males and females, respectively.

n1 and n2 are the sample sizes for males and females, respectively.

Z is the critical value corresponding to the desired confidence level.

From the given information, we have:

p1 = 190/1233

n1 = 1233

p2 = 128/1033

n2 = 1033

Confidence level = 99% (which corresponds to a critical value of Z)

Calculating the confidence interval:

CI = (190/1233 - 128/1033) ± Z× √[(190/1233× (1 - 190/1233) / 1233) + (128/1033 ×(1 - 128/1033) / 1033)]

Now, let's find the critical value Z for a 99% confidence level. Since the sample sizes are large, we can use the standard normal distribution. The critical value for a 99% confidence level is approximately 2.576.

CI = (0.154 - 0.124) ± 2.576× √[(0.154× (1 - 0.154) / 1233) + (0.124 × (1 - 0.124) / 1033)]

CI = 0.030 ± 2.576×√[0.000118 + 0.000124]

CI = 0.030 ± 2.576×√(0.000242)

CI = 0.030 ± 2.576×0.015556

CI = 0.030 ± 0.040085

CI ≈ (-0.010, 0.070)

The lower bound of the 99% confidence interval is approximately -0.010, and the upper bound is approximately 0.070.

Interpreting the interval, we can say:

A. There is 99% confidence that the difference of the proportions is in the interval. Conclude that there is insufficient evidence of a significant difference in the proportion of males and females that have at least one tattoo.

Therefore, the correct answer is A.

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Answer:

8 students

Step-by-step explanation:

There are 20 boxes and there are a total of 40 students interviewed. So, each box is worth 2 students. Since blue has 4 boxes, 4*2 = 8 students chose blue as their favorite shoe color.

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There insufficient evidence to support the claim that the mean amount spent by a customer has significantly decreased since last year.

Step 1: State the hypotheses:

- Null hypothesis (H0): The mean amount spent by a customer is equal to or greater than last year's mean ($52).

- Alternative hypothesis (H1): The mean amount spent by a customer is significantly less than last year's mean ($52).

Step 2: Set the significance level:

The significance level (α) is given as 0.10. This represents a 10% chance of rejecting the null hypothesis when it is true.

Step 3: Formulate the decision rule:

Since the alternative hypothesis is stating a decrease in the mean amount spent, we will conduct a one-tailed t-test and reject the null hypothesis if the test statistic falls in the critical region corresponding to the left tail of the t-distribution.

Step 4: Calculate the test statistic:

We need to calculate the t-statistic using the formula:

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

Given data:

Population mean (μ) = $52

Sample mean (X) = $50

Sample standard deviation (s) = $11

Sample size (n) = 36

Plugging in the values:

t = ($50 - $52) / ($11 / √(36))

t = -2 / ($11 / 6)

t ≈ -1.0909

Step 5: Determine the critical value and make a decision:

Since the significance level is 0.10 and the test is one-tailed to the left, we need to find the critical t-value at a 0.10 significance level with degrees of freedom equal to (n - 1) = (36 - 1) = 35.

so, the critical t-value is -1.3104.

Since the calculated t-statistic (-1.0909) does not fall in the critical region (t < -1.3104), we do not have enough evidence to reject the null hypothesis.

Step 6: State the conclusion:

Based on the data and the hypothesis test, at the 0.10 significance level, there is insufficient evidence to support the claim that the mean amount spent by a customer has significantly decreased since last year.

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The markup would be 133.33%

30is 200% of 15

5 is 33.33333333% of 15

33.33333333%+100+=133.33333333%

The markup is 133.33% or 133.33333333%

Therefore, the total payment made today by the payee is $2,149.01

To total payment made today would place the payee in the same financial position as the scheduled payments if money can earn 6.25% we will use the  formula below.

PV = FV /(1 + Rr)^n

r =6.25%

FV = $1,260

PV = $ 1,260 / (1+ 0.0625) ^(7/12)

PV = $ 1,179.01

The value of the second payment is  $ 1,179.01.

Lets find the total payment. We can represent the  total payment by X.

X - $ 970 = $ 1,179.01.

To isolate X, we will add $ 970  to both sides.

X = $ 970 + $ 1,179.01.

X = $2,149.01

Therefore, the total payment made today by the payee is $2,149.01

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(a) If plurality voting is used, Plan E will be chosen.

b It has the most first-place votes, with 2 each from voters 1 and 5. No other plan has more than 1 first-place vote.

c If the Borda Count method is used, Plan C will be chosen.

a The best part of this project was learning about different voting methods and how they can be used to choose a winner. The worst part of the project was the difficulty of calculating the Borda Count.

b If Instant Runoff Voting is used, Plan C will be chosen. In the first round of counting, Plan E is eliminated, as it has the fewest first-place votes. In the second round, Plan C is eliminated, as it has the fewest second-place votes. In the third round, Plan B is eliminated, as it has the fewest third-place votes. In the fourth round, Plan D is eliminated, as it has the fewest fourth-place votes. This leaves Plan A as the winner, as it has the most votes remaining.

c If the Borda Count method is used, Plan C will be chosen. Each voter's ballot is assigned a number of points equal to the number of candidates ranked lower than that candidate. For example, voter 1's ballot gives Plan E 5 points, Plan C 4 points, Plan A 3 points, Plan B 2 points, and Plan D 1 point. The total number of points for each candidate is then calculated. Plan C has the most points, with 16, so it is the winner.

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Answer: n=-14

Step-by-step explanation:

CONCEPT:

SOLVE:

The expression in the questions is [tex](x^{3} )(x^{-17})[/tex] which is MULTIPLYING, which means we should add the exponents together

[tex](x^{3} )(x^{-17})[/tex]=[tex]x^n[/tex] ⇔ Given

[tex]x^{3+(-17)}[/tex]=[tex]x^n[/tex] ⇔ Adding Exponents Together

[tex]x^{3-17}[/tex]=[tex]x^n[/tex] ⇔ Simplify

[tex]x^{-14}[/tex]=[tex]x^n[/tex] ⇔ Simplify

[tex]n[/tex]=[tex]-14[/tex] ⇔ Correspondingly

Hope this helps!! :)

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Answer:

5%

Step-by-step explanation:

Answer:

5% increase

Step-by-step explanation:

30/600 equals .05 or 5%

Answer:

115.552 or 116 inches.

Step-by-step explanation:

Use the circumference of a circle formula which is C= 2piR. Where C is circumference and R is radius. So you get C=2(3.14×18.4) which gives you 115.552.

The mass flow rate is 0.56 kg/s

The formula for calculating the mass flow rate is expressed as;

m = W / (hf - hg)

Such that the parameters are expressed as;

Substitute the values, we get;

m = 90 MW / (2418 - 2257)

Subtract the values, we have;

m = 90/161

Divide the values, we get;

m=  0.56 kg/s

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Answer:

Supplementary Angles are 180 degrees. A triangle has 180 degrees. One angle is already 90 degrees, so 2 more angles with 180 degrees is impossible.

Step-by-step explanation:

If f(x) is reducible over Zp, then f(x) is reducible over Q.

If a polynomial f(x) with integer coefficients is reducible over Zp (the integers modulo p), where p is a prime number, then it is also reducible over Q (the rational numbers).

This result follows from the fact that if a polynomial is reducible over a smaller field (Zp), it must also be reducible over a larger field (Q).

Since Zp is a subset of Q, any factorization of the polynomial in Zp can also be used in Q. Therefore, if f(x) is reducible over Zp, it is also reducible over Q.

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