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2 years ago

In somalia, city b is 75 kilometers due north of city

Mathematics

1 answer:

nadya68 [22]2 years ago

4 0

We first approach this problem by forming a diagram. Refer to the attachment.

You might notice a right triangle forming when you connect cities A, B, and C. In this case, we'll just need the Pythagorean theorem when solving for the distance between city B and city A.

$AB^{2}=BC^{2} + AC^{2}= 75^{2} + 42^{2} =7389$
$AB=85.96$

ANSWER: The distance between city B and city A is 85.96 kilometers.

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Which of the following estimates at a 95% confidence level most likely comes from a small sample?

dusya [7]

The correct answer is:

A) 60% ± 18%.

Explanation:

In a confidence interval, the margin of error is given by z*(σ/√n), where σ is the standard deviation and n is the sample size.

First we find the value of z:

We want a 95% confidence level; 95% = 95/100 = 0.95.

To find the z-score, we first subtract this from 1:
1-0.95 = 0.05.

Divide by 2:
0.05/2 = 0.025.

Subtract from 1 again:
1-0.025 = 0.975.

Using a z-table, we find this value in the middle of the table. The z-score that is associated with this value is 1.96.

Back to our formula for margin of error, we have 1.96(σ/√n). The larger n, the sample size, is, the larger its square root is. When we divide by a larger number, our answer is smaller; this gives us a smaller margin of error.

This means that if we had a small sample size, we would divide by a smaller number, making our margin of error larger. The largest margin of error we have in this question is 18%, so this is our correct answer.

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2 years ago

PLSSS HELP PLS I WILL GIVE BRAINLIEST TO CORRECT PERSON!! 13 POINTS. Camille dilates a digital photograph by a factor of 1.25 to

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Answer:

the first one is A, the second one is D.

Step-by-step explanation:

For the perimeter you have to multiply by the original dilation number, and for the area, you have to dilate by 2.5

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2 years ago

Using V = lwh , find an expression in factored form for the volume of this prism. Explain the general steps you used to arrive a

Mademuasel [1]

The student made a mistake in Line 1: AC=2, DF=2 AC ≅ DF .

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2 years ago

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The heights of students at a college are normally distributed with a mean of 175 cm and a standard deviation of 6 cm. One might

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Answer:

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 175cm

Standard deviation = 6 cm

Percentage of students below 163 cm

163 = 175 - 2*6

So 163 is two standard deviations below the mean.

By the Empirical rule, 95% of the heights are within 2 standard deviations of the mean. The other 100-95 = 5% are more than 2 standard deviations of the mean. Since the normal distribution is symmetric, 2.5% of them are more than 2 standard deviations below the mean(so below 163cm) and 2.5% are more than two standard deviations above the mean.

2.5% of the students have heights less than 163cm.

Out of 1000

0.025*1000 = 25

25 is the answer

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2 years ago

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A environmental initiative has the goal of saving at least 25 2525 million hectares of rainforest through both planting trees an

Anestetic [448]

Answer:

The possible way for the initiative to accomplish its goal without exceeding its budget is use 12.5 hectares for planting trees and 12.5 hectares by purchasing land.

Step-by-step explanation:

Let the variable X represent the amount of land used for planting trees and Y represent the amount of land purchased.

The goal of the environmental initiative is to save at least 25 million hectares of rain forest.

That is:

X + Y = 25....(i)

Now it is provided that:

The cost of planting trees is $ 400 per hectare.
The cost of purchasing land is $ 260 per hectare.
The initiative has a budget of $8,250 million.

Using the above data it can be said that:

400X + 260Y = 8250....(ii)

Solve equations (i) and (ii) simultaneously.

$\ \ \ \ x+y=25]\times 260\\400x+260y=8250\\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\\\\\Rightarrow\\\\260x+260y=6500\\400x+260y=8250\\(-)\_\_\_\_\_\ (-)\_\_\_\_(-)\_\_\_\\\\\Rightarrow\\\\-140x=-1750\\\\x=\frac{1750}{140}\\\\x=12.5$

Then the value of y is:

$x+y=25\\y=25-x\\y=25-12.5\\y=12.5$

Thus, the possible way for the initiative to accomplish its goal without exceeding its budget is use 12.5 hectares for planting trees and 12.5 hectares for purchasing land.

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2 years ago