In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1,014 adults aged 18 and

The diagonal measures 20.68 ft; the shorter base is 17.21 ft. To understand this, we recognize that with base angles summing to 140°, each angle is 70°, given the isosceles trapezoid's properties. We can apply the Law of Cosines to find the diagonal's length, denoted as d. The length of the diagonal determines to be d = 20.68 ft. Determining the shorter base is somewhat more complex. By drawing an altitude from the upper vertices to the base, which measures 22 ft, we create two similar smaller right triangles requiring us to find the height and base measures related to each of the 70-degree angles and the hypotenuse of 7. By working through the calculations for height and base from one triangle, we subsequently find that 22 minus twice the base measure gets us to the shorter base's measure, arriving at x = 17.21 ft.

the third graph

Response:

Regarding this scenario, we have the following details about the timeframe to organize a return

And we select a sample size =49>30, and we aim to find the standard deviation for the sample mean. Based on the central limit theorem, we understand that the sample mean distribution is represented by:

The standard deviation would then be:

Therefore, the most accurate response would be

b. 2 minutes

Step-by-step explanation:

Prior concepts

Normal distribution, defines a probability distribution that is symmetric around the mean, showing that occurrences near the mean are more frequent than those that are further away.

The central limit theorem states that "when we have a population with mean μ and standard deviation σ and draw sufficiently large random samples from the population with replacement, then the distribution of the sample means will resemble a normal distribution. This applies regardless of whether the original population is normal or skewed, given that the sample size is large enough".

Solution to the problem

For this case, we have the following information about the time to prepare a return

A sample size =49>30 also indicates that we are focused on determining the standard deviation for the sample mean. Based on the central limit theorem, we recognize that the sample mean distribution is described by:

And subsequently, the standard deviation will be:

Hence, the most accurate answer would be

b. 2 minutes

Answer:

We will mix 2.4 mL of water with 0.6 mL of the coloring solution.

The total solution volume amounts to 2.4 + 0.6, which equals 3 mL.

Therefore,

0.6 mL of coloring solution now contains 2.4 mL of water.

Alternatively,

1 mL of this coloring solution comprises 4 mL of water.

Thus,

We should prepare 3 mL of the coloring solution with the resultant water.

This 3 mL mixture will encapsulate 0.6 mL of the coloring solution.

Step-by-step explanation:

As stated:

The formula requires 0.6 mL of a coloring solution.

Using a 10-mL graduated cylinder that is divided from 2 to 10 mL in 1-mL increments:

We aim to apply the aliquot method to accurately measure 0.6 mL of the coloring solution.

Given that the graduated cylinder measures from 2mL to 10mL only, we'll blend 2.4 mL of water with 0.6 mL of coloring solution.

Thus, the total solution volume is 2.4 + 0.6, resulting in 3 mL.

Consequently,

This implies that 0.6 mL of coloring solution now carries 2.4 mL of water.

Additionally,

1 mL of coloring solution encapsulates 4 mL of water.

Hence,

We will quantify 3 mL of the final solution, which contains 0.6 mL of coloring solution.