Im giving all of my points. Please help me. A researcher has conducted a survey using a simple random sample of 225 elementary teachers to create a confidence interval to estimate the proportion of elementary teachers favoring the addition of a soda machine to the cafeteria. Assume that the sample proportion does not change. The researcher now decides to survey a random sample of 25 teachers instead of 225 elementary teachers. Which of the following statements best describes how the confidence interval is affected by this change?

The width of the new interval is about the same width as the original interval.
The width of the new interval is about twice the width of the original interval.
The width of the new interval is about one half the width of the original interval.
The width of the new interval is about one third the width of the original interval.
The width of the new interval is about three times the width of the original interval.

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step-by-step explanation:

x^(1/6) · x^(1/6) · x^(1/6)   ·x^(1/6) = x^(4/6)   since we add the exponents

4/6 can be simplified to 2/3

the simplified form is x^(2/3)

536

step-by-step explanation:

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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