Which expressions represent rational numbers? Check all that apply.

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.

1. 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).
2. 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).
3. 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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Answer:

• y = -2x + 7

Step-by-step explanation:

Solve for y:

• 2x + y = 7

Add - 2x to both sides

• 2x + y - 2x = 7 - 2x
• y = 7 - 2x

or

• y = -2x + 7

The design that every point on one side of the line coincides with a point on the other side of it is Line of symmetry

What is Symmetry?

Symmetry in mathematics means that when one shape is moved, rotated, or flipped, it looks exactly like the other shape.

A circle or band that divides a body's surface into two typically equal and symmetrical portions.

When a shape or item has a centralpoint, point symmetry occurs when all points on the opposing sides are at the same distance from the centre.

The term "line of symmetry" refers to the fictitious axis or line that can be used to fold a figure into symmetricalhalves.

It denotes that one half is the other half's mirror image.

Thus, the required design is Line of Symmetry.

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The Z-test of a population mean is used here because it is given that the population standard deviation is $75. The correct option is a).

Given :

• The current owner claims that over the past 5 years, the average daily revenue was $675 with a standard deviation of $75.
• A sample of 30 days reveals a daily average revenue of $625.

Let is the daily average revenue. So:

Null Hypothesis is,

The Alternate Hypothesis is,

Here, the Z-test of a population mean is used because it is given that the population standard deviation is $75.

where is the sampleaverage revenue, is the standard deviation and n is the sample size.

Therefore, the correct option is a).

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Answer:

We would use Z-test of a population mean.

Step-by-step explanation:

We are given that an entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 5 years, the average daily revenue was $675 with a standard deviation of $75. A sample of 30 days reveals a daily average revenue of $625.

And we have to test the hypothesis that the daily average revenue was $675.

Firstly, as we know that testing is always done on the population parameter.

So, let = daily average revenue over the pat 5 years

So, Null Hypothesis, : = $675

Alternate Hypothesis, : $675

Here, null hypothesis states that the owner's claim of average daily revenue was $675 over the past 5 years is correct.

And alternate hypothesis states that the owner's claim of average daily revenue was $675 over the past 5 years is not correct.

The test statistics that will be used here is Z-test of a population mean because here we have knowledge of population standard deviation of $75.

   Test statistics =  ~ N(0,1)

where, = sample average revenue = $625

            = population standard deviation = $75

             n = sample of days = 30

Therefore, to test the null hypothesis that the daily average revenue was $675, we should use Z-test of a population mean.

Answer:

5773185

Step-by-step explanation:

There are 110 seats

110 ways to choose the first empty seat

Now there are 109 seats

109 ways to choose the next empty seat

Now there are 108 seats

108 ways to choose the next empty seat

Now there are 107 seats

110*109*108*107=138556440

Now the order of the empty seats doesn't matter so we need to divide by 4!

138556440/ 4!

138556440/ 24

5773185

Final answer:

In this mathematics problem, we are asked to determine the number of ways that 4 seats can be left empty in a high school auditorium that seats 110 people. We can use the concept of combinations to solve this.

Explanation:

In this problem, we are asked to determine the number of ways that 4 seats can be left empty in a high school auditorium that seats 110 people. To solve this, we can use the concept of combinations. The total number of ways to choose 4 seats out of 110 is represented by the combination formula: C(110, 4). To calculate this, we can use the formula: C(n, r) = n! / (r!(n - r)!), where n is the total number of seats and r is the number of seats left empty. Plugging in the values, we have C(110, 4) = 110! / (4!(110 - 4)!).

Using a calculator, we can simplify this expression and calculate the answer.

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