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3 years ago

PLEASE HELP

Mathematics

1 answer:

Leto [7]3 years ago

3 0

Answer:

DA = 285.7 m

Step-by-step explanation:

First we need to find the side AB in the triangle ABC, and we can do this using Pythagoras' theorem:

AB^2 = BC^2 + AC^2

AB^2 = 300^2 + 400^2

AB^2 = 25000

AB = 500 m

We can find the angle ABC with the tangent relation:

tangent(ABC) = 400/300 = 4/3

ABC = 53.13°

From triangle ABC, we have:

ABC + BCA + CAB = 180°

53.13 + 90 + CAB = 180

CAB = 36.87°

From triangle DAC, we have:

DAC + ACD + CDA = 180

36.87 + 45 + CDA = 180

CDA = 98.13°

Now to find the side of DA, we can use law of sines in triangle DAC:

DA/sin(DCA) = AC/sin(CDA)

DA/sin(45) = 400/sin(98.13)

DA = 400 * 0.7071 / 0.9899 = 285.7258 m

Rounding to nearest tenth, we have DA = 285.7 m

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<h2>Explanation:</h2>

Hello! Recall you need to write complete questions in order to find exact answers. So in this problem I'll assume the question is:

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Answer:

<u>The correct answer is B. between 56.45% and 57.55% </u>

Complete statement and question:

The mean percentage of a population of people eating out at least once a week is 57% with a standard deviation of 3.50%. Assume that a sample size of 40 people was surveyed from the population a significant number of times. In which interval will 68% of the sample means occur?

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Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Mean percentage of a population of people eating out at least once a week = 57%

Standard deviation = 3.5%

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For answering this question, we should find out the standard deviation of the sample, using this formula:

Standard deviation of the sample = Standard deviation of the population/√Sample size

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Let's recall that a confidence level of 68% means that 68% of the sample data would have a value between the mean - 1 time the standard deviation of the sample and the mean + 1 time the standard deviation of the sample. Thus:

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