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Step-by-step explanation:

Given r = 12, s = 5,

[tex] {r}^{2} - {s}^{2} = {12}^{2} - {5}^{2} \\ = 144 - 25 \\ = 119[/tex]

Answer: 135/pi

Step-by-step explanation: Circumference is 16pi. So then 6/16pi is the fraction of the 360 arc measure of the entire circle that is the angle measure of the arc, so we multiply 6/16pi times 360 and yield 135/pi. Hope this helps!

Answer:

Given, x = 2 and z = 12

z + 5x³

12 + 5×2³

12 + 5×8

12 + 40

52

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Answer:

A

Step-by-step explanation:

Answer:

estimated price is $3167 and actual price is $3166.97

Answer:

C

Step-by-step explanation:

For a relationship to be proportional, x/y needs to be the same for all rows.

5/8 is not 12/15

5/3 is not 15/11

3/8 is not 5/12.

The table C checks out with a ratio of 3:5

Answer:

The answer is 0.28 lbs/ft or 0.3 lbs/ft, if rounded.

Step-by-step explanation:

In order to solve, divide the mass / length value by 14.882.

I hope this helps you.

Answer:

a. The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57

b. Yes

c. The power of the test is 0.03836

d. The sample size can be considered adequate

Step-by-step explanation:

a. The given data in the study

Catalyst 1: 57.9, 66.2, 65.4, 65.4, 65.2, 62.6, 67.6, 63.7, 67.2, 71.0

Catalyst 2: 66.4 , 71.7, 70.3, 69.3, 64.8, 69.6, 68.6, 69.4, 65.3, 68.8

Using the Average, Standard Deviation function from Microsoft Excel, we have;

The mean for Catalyst 1, [tex]\overline x_1[/tex] = 65.22

The standard deviation for catalyst 1, σ₁ = 3.444416

The mean for Catalyst 2, [tex]\overline x_2[/tex] = 68.42

The standard deviation for catalyst 2, σ₂ = 2.22401

The 95% confidence interval on the difference in mean is given as follows;

[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}[/tex]

The critical-z for a 95% confidence interval = 1.96

Therefore, we have;

[tex]\left (65.22-68.42 \right ) \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}}[/tex]

Therefore, we have;

The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57

The test statistics is given as follows;

[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]

Therefore we have;

[tex]z=\dfrac{(65.22-68.42)}{\sqrt{\dfrac{3^{2} }{10}+\dfrac{3^{2}}{10}}} = -2.385[/tex]

The p-value = P(Z<-2.39 or Z > 2.39) = 2P(Z<-2.39) = 2 × 0.00842 = 0.01684

b. From the confidence interval which range from approximately -5.83 to -0.57 and does not include 0, therefore, there is a difference in mean active concentration which depends on the choice of catalyst

c. The power of the test

 The sample mean difference is given as follows;

[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}[/tex]

Therefore, we have;

[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}} = \pm 2.6296[/tex]

The z-value is given as follows;

[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]

μ₁ - μ₂ = 5

When [tex]\bar{x}_1-\bar{x}_{2} = 2.6296[/tex]

[tex]z=\dfrac{2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -1.7667918[/tex]

When [tex]\bar{x}_1-\bar{x}_{2} = -2.6296[/tex]

[tex]z=\dfrac{-2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -5.686768[/tex]

The power of the test is given by P = P(Z<-5.69) + P(Z>-1.77) = 0 + 0.03836 = 0.03836

The power of the test = 0.03836

d. The sample size is statistically adequate because the confidence interval of -5.83 < μ₁ - μ₂ < -0.57 has a value of -5 as a possible population difference in mean

The assumption of normality seems adequate because the confidence interval obtained by using the sample standard deviation is given as follows;

(-5.74, -0.66) which also contains -5 which is the difference in the population mean

Answer:

Its D. 3cm

____________

Answer:

D=3

Step-by-step explanation:

Split this figure into 2 parts. Now you have 2 rectangles. One with sides 6 and 12. Other with sides (10 - 6) =4, and a.

Area of one rectangle is 12 × 6 = 72

Area of 2nd rectangle is 4 × a = 4a.

Since we know the total area of figure is 84

that means

72 + 4a = 84

4a = 84 - 72

4a = 12

a = 12 ÷ 4 = 3

a=3

Answer:

[tex]x<2[/tex]

Step-by-step explanation:

[tex]\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}[/tex]

[tex]4x+9-9<17-9[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]4x<8[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}4[/tex]

[tex]=x<2[/tex]

Answer:

4x+9=17

-9 -9 subtract 9 on both sides to cancel 9 on one side of equation and subtracted on the other side

4x=8

divide 4 on both sides to get x by itself

x=8/4

x=2 SOLUTION

Step-by-step explanation:

Answer:

I belive it would be 1/5. ;;;

Answer: 1.333

Step-by-step explanation:

Answer:

1.33

Step-by-step explanation:

nothing much to explain

Answer:

The probability is that the first marble is blue is 5/12 and the probability that the second marble is green is 4/11

Step-by-step explanation:

9514 1404 393

Answer:

  x = 12.75

  ∠C = 51.75°

Step-by-step explanation:

The two marked angles are complementary, so ...

  (5x -12) +(3x) = 90

  8x = 102

  x = 102/8

  x = 12.75

__

C = (5x -12)° = (5(12.75) -12)°

  ∠C = 51.75°

__

Check

E = 3x = 38.25, then C+E = 51.75 +38.25 = 90 . . . . as it should

Answer:

A. 1

Step-by-step explanation:

Answer:

The percentage score is 38.52%

Step-by-step explanation:

Conversion of a proportion to a percentage:

To convert from a proportion to a percentage, we multiply by 100%, that is, the decimal point is moved two positions to the right, and the percentage sign is placed in the number.

In this question:

Proportion .3852

0.3852*100% = 38.52%

The percentage score is 38.52%

Answer:

(x₁ ,  y₁) = (0,0)

(x₂ , y₂) = [tex]\frac{\sqrt[16]{3} }{19}[/tex] , [tex]\frac{12}{19}[/tex]

[tex]64*36=x^{2} \\2304=x^{2} \\x=48[/tex]

Answer:

10 minutes

Step-by-step explanation:

First, find how much higher the airplane has to travel:

35,000 - 30,000

= 5,000

To fine how long it will take, divide 5000 by 500

5000/500

= 10

So, it will take 10 minutes to get above 35,000 feet

Answer:

12:45

Step-by-step explanation:

Step One: An hour after 11:20 is 12:20, plus 15 minutes is 12: 35.

Step Two: Just add 10 minutes, because it doesn't matter when you add the ten minutes.

The radius is 10, so the diameter is 20. This means the parts of the diameter (the chord through the center P) to the left and right of the vertical chord have lengths 16 and 4, respectively.

Because the horizontal chord is a diameter, the vertical chord is cut in half, so its parts above and below the diameter both have length x.

Now, by the intersecting chord theorem,

16×4 = x × x

or

x ² = 64

so that

x = 8

9514 1404 393

Answer:

  π/4, 7π/4

Step-by-step explanation:

Adding √2 and dividing by 2 makes the equation ...

  cos(θ) = (√2)/2

The first-quadrant solution is ...

  θ = arccos((√2)/2) = π/4

The angle in the 4th quadrant with the same reference angle will have the same cosine value.

  θ = 2π -π/4 = 7π/4

The two solutions are θ = π/4, 7π/4.

Answer:

0

Step-by-step explanation:

am not sure, , have not studied

Answer:

50? or together will be 90?

Answer: the movie was 1 hour and 35 minutes and Amar got home at 6:15 P.M.

Step-by-step explanation:

to find out how long the movie was you have to find the distance between the time frames 3:55 and 5:30.

3:55+1 hour= 4:55

4:55+5 minutes= 5:00

5:00+30 minutes= 5:30

Add the times to find how long the movie was.

This is how I found how long the movie was.

To find out when Amar got home you have to do the same thing as well.

5:30+30 minutes= 6:00

6:00+15 minutes= 6:15

Hope this helps!

Answer:

Total volume of 80 balls = 2,263.2 inch³

Step-by-step explanation:

Given:

Diameter of lead ball = 6 inch

Number of ball need = 80

Find:

Total volume of 80 balls

Computation:

Radius of lead ball = Diameter / 2

Radius of lead ball = 6 / 2

Radius of lead ball = 3 inch

Volume of lead ball = πr²

Volume of lead ball = (22/7)(3)²

Volume of lead ball = (22/7)(9)

Volume of lead ball = 28.29 inch³ (Approx.)

Total volume of 80 balls = 80 x Volume of lead ball

Total volume of 80 balls = 80 x 28.29

Total volume of 80 balls = 2,263.2 inch³