The caffeine content (in mg) was examined for a random sample of 50 cups of black coffee dispensed by a new machine. The mean and the standard deviation were 110 mg and 7.1 mg respectively. Use the data to construct a 98% confidence interval for the mean caffeine content for cups dispensed by the machine. Interpret the interval!

Answers

Answer 1

Answer:

Answer:

We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 mg .

Step-by-step explanation:

Given -

The sample size is large then we can use central limit theorem

n = 50 ,

Standard deviation $(\sigma)$ = 7.1

Mean $\overline{(y)}$ = 110

$\alpha =$ 1 - confidence interval = 1 - .98 = .02

$z_{(\alpha)/(2)}$ = 2.33

98% confidence interval for the mean caffeine content for cups dispensed by the machine = $\overline{(y)}\pm z_{(\alpha)/(2)}\frac{\sigma}√(n)$

= $110\pm z_(.01)\frac{7.1}√(50)$

= $110\pm 2.33\frac{7.1}√(50)$

First we take + sign

$110 + 2.33\frac{7.1}√(50)$ = 112.34

now we take - sign

$110 - 2.33\frac{7.1}√(50)$ = 107.66

We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 .

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b. employers
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Answers

This answer would be B

Answer:

B) employers

Step-by-step explanation:

EDGE 2021

QuestionThe area of a triangular painting is 50 square inches. The base is 20 inches. What is the height?
Provide your answer below:
inches
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Content attribution
The area of a triangular painting is 50 in.² the base is 20 inches what is the height

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The height of the triangle is 5 inches.

Area of the triangle:

The region occupied by a triangle within its sides is known as the area of the triangle. The area of a triangle can be calculated by the calculating product of the base and height of the triangle with a half i.e 1/2. The formula for the area of the triangle is given by

Area of triangle = (1/2) × base × height

Here we have

Area of the triangle = 50 in²

The base of the triangle, b = 20 inches

As we know,

Area of the triangle = 1/2 (base × height)

From the given data,

=> 50 = 1/2 (20 × height)

Multiply by 2 on both sides

=> 100 = (20 × height)

Divided by 20 into both sides

=> 100/20 = (20 × height)/20

=> 5 = height

=> height = 5 in

Therefore,

The height of the triangle is 5 inches.

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The volume V of a growing spherical cell is V = 4 3 πr3, where the radius is measured in micrometers (1 µm = 10−6m). Find the average rate of change of V with respect to r when r changes from 6 to each of the following. (Round your answers to one decimal place.) (i) 6 to 9 µm
(ii) 5 to 6 µm
(iii) 5 to 5.1 µm

Answers

Final answer:

The average rate of volume change of a growing spherical cell for different changes in radius can be calculated using the formula for the volume of a sphere and the formula for average rate of change (ΔV/Δr).

Explanation:

To find the average rate of change of the volume V with respect to the radius r, you will need to subtract the initial volume from the final volume and then divide by the change in radius. This is represented by the formula ΔV/Δr, where Δ represents change in.

For r changing from 6 to 9 µm, ΔV = V(9) - V(6) = 4/3π(9^3) - 4/3π(6^3). Therefore, ΔV/Δr = (4/3π(9^3) - 4/3π(6^3)) / (9 - 6).
For r changing from 5 to 6 µm, ΔV = V(6) - V(5) = 4/3π(6^3) - 4/3π(5^3). Therefore, ΔV/Δr = (4/3π(6^3) - 4/3π(5^3)) / (6 - 5).
For r changing from 5 to 5.1 µm, ΔV = V(5.1) - V(5) = 4/3π(5.1^3) - 4/3π(5^3). Therefore, ΔV/Δr = (4/3π(5.1^3) - 4/3π(5^3)) / (5.1 - 5).

These calculations will give you the average rate of volume change for each of the radius changes indicated.

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A local department store sells carpet in 4 sizes . Each carpet comes in 3 different qualities. One of the size come in 5 colors . The other sizes come in 3 colors . How many choices of carpet are there?

Answers

The total number of choices is 42 if a local department store sells carpets in 4 sizes. Each carpet comes in 3 different qualities. One of the sizes comes in 5 colors.

What are permutation and combination?

A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.

It is given that:

A local department store sells carpets in 4 sizes.

Each carpet comes in 3 different qualities.

One of the sizes comes in 5 colors.

The other sizes come in 3 colors.

The number of choices can be found as follows:

= 1x3x5

= 15

= 3x3x3

= 27

Total number of choices = 15 +27

= 42

Thus, the total number of choices is 42 if a local department store sells carpets in 4 sizes. Each carpet comes in 3 different qualities. One of the sizes comes in 5 colors.

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there are 60 choices of carpet

reason:
4*3*5
12*5
=60
or
4*3*5
4*15
=60

Find the midpoint of the segment with these endpoint (4,6),(9,3)