Can you plz help with 16,17,18

Making handcrafted pottery generally takes two major steps: wheel throwing and firing. The time of wheel throwing and the time o

9966 [12]

Answer:

a) 8.23% probability that a piece of pottery will be finished within 95 minutes

b) 0.28% probability that it will take longer than 110 minutes.

Step-by-step explanation:

Normal distribution:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Two variables:

Means $\mu_{a}, \mu_{b}$

Standard deviations $\sigma_{a}, \sigma_{b}$

Sum:

$\mu = \mu_{a} + \mu_{b}$

$\sigma = \sqrt{\sigma_{a}^{2} + \sigma_{b}^{2}}$

In this question:

$\mu_{a} = 40, \mu_{b} = 60, \sigma_{a} = 2, \sigma_{b} = 3$

So

$\mu = \mu_{a} + \mu_{b} = 40 + 60 = 100$

$\sigma = \sqrt{\sigma_{a}^{2} + \sigma_{b}^{2}} = \sqrt{4 + 9} = 3.61$

A) What is the probability that a piece of pottery will befinished within 95 minutes?

This is the pvalue of Z when X = 95.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{95 - 100}{3.61}$

$Z = -1.39$

$Z = -1.39$ has a pvalue of 0.0823

8.23% probability that a piece of pottery will befinished within 95 minutes.

B) What is the probability that it will take longer than 110 minutes?

This is 1 subtracted by the pvalue of Z when X = 110.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{110 - 100}{3.61}$

$Z = 2.77$

$Z = 2.77$ has a pvalue of 0.9972

1 - 0.9972 = 0.0028

0.28% probability that it will take longer than 110 minutes.

5 0

3 years ago

What is container B that is full after the pumping is complete ?

scoray [572]

Answer

68.4%

Step-by-step explanation

The volume of a cylinder is calculated as follows:

$V=\pi r^2h$

where r is the radius and h is the height of the cylinder.

In the case of cylinder A, its radius is r = 5 ft (= 10/2) and its height is h = 14 ft. Then, its volume is:

$\begin{gathered} V_A=\pi\cdot5^2\cdot14 \\ V_A=350\pi\text{ ft}^3 \end{gathered}$

In the case of cylinder B, its radius is r = 8 ft (= 16/2) and its height is h = 8 ft. Then, its volume is:

$\begin{gathered} V_B=\pi\cdot8^2\cdot8 \\ V_B=512\pi\text{ ft}^3 \end{gathered}$

After the pumping is completed all the liquid in cylinder A, which was full, is placed in cylinder B. If the volume of cylinder B represents 100%, then we need to find what percent, x, represents the volume of cylinder A. We can do this with the help of the next proportion:

$\frac{512\pi\text{ ft}^3}{350\pi\text{ ft}^3}=\frac{100\text{ \%}}{x\text{ \%}}$

Solving for x:

$\begin{gathered} 512\pi\cdot x=100\cdot350\pi \\ x=\frac{100\cdot350\pi}{512\pi} \\ x\approx68.4\text{ \%} \end{gathered}$

6 0

1 year ago

There are 5 cards with a picture of a rose and 3 cards with a picture of a daisy. Alia keeps all the cards down on a table with

sasho [114]

The answer would be 4 over 7

this is because there were 8 cards in total to begin with but she removes one leaving only 7; that would result in the bottom number because it is the total

then the top number would be the amount of rose cards left so in this case 4

6 0

3 years ago

Completely factor the polynomial. 12x2 + 2x - 4

Vesna [10]

Happy holidays!!!!;)

3 0

3 years ago

PLEASE HELP!!

Illusion [34]

Answer:

8 and 10

Step-by-step explanation:

Our first step is to set x as the other side length, and y as the hypotenuse. We get that 6 + x + y = 24, and x + y = 18. The area gives us that 6x = 24(2) = 48. We then divide both sides by 6 and we get x = 8. We have x = 8 so we plug that into the equation x + y = 18 and we get that y = 10. So the other side lengths are 8 and 10.

5 0

2 years ago