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2 years ago

Part 1: the following formula gives the area of a circle, A, dependent on its radius, r.

Mathematics

1 answer:

Dennis_Churaev [7]2 years ago

4 0

Answer:

3.43ft

Step-by-step explanation:

Step one:

given data

the expression for the area is

A = πr²

make r subject of the formula

divide both sides by π

A/π =r²

square root both sides

r=√A/π

step two:

given that A= 37 ft^2

r= √37/3.142

r=√11.77

r=3.43ft

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If IQ scores are normally distributed with a mean of 100 and a standard deviation of 5, what is the probability that a person se

notsponge [240]

Answer:

2.28% probability that a person selected at random will have an IQ of 110 or higher

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 100, \sigma = 5$

What is the probability that a person selected at random will have an IQ of 110 or higher?

This is 1 subtracted by the pvalue of Z when X = 110. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{110 - 100}{5}$

$Z = 2$

$Z = 2$ has a pvalue of 0.0228

2.28% probability that a person selected at random will have an IQ of 110 or higher

5 0

3 years ago

A city council consists of six Democrats and six Republicans. If a committee of seven people is selected, find the probability

Reika [66]

To 3 decimal places.

8 0

3 years ago

Maria needs to reach a window that is eight feet above the ground. When she placed a ladder so that it reached the bottom of the

mr_godi [17]

Answer:

10 feet

Step-by-step explanation:

Given that the distance to be reached is 8 feet above ground and she she placed a ladder so that it reached the bottom of the window, the base of the ladder was 6 feet from the house, the length of the ladder considered with the other lengths forms a right angled triangle.

The length of the ladder represents the hypotenuse side hence using pythagoras theorem

F^2 = 8^2 + 6^2

where F is the length of the ladder in feet

F^2 = 64 + 36

= 100

find the root of both sides

F = 10 feet

The ladder is 10 feet long

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3 years ago

Triangle WXY has coordinates W(1, 5), X(1, 1), and Y(5, 1). Which of the following sets of points represents a dilation of trian

timofeeve [1]

The correct answer for the question shown above is the second option, the option B, which is: B. <span>W'(2, 10), X'(2, 2), Y'(10, 2)
The explanation is shown below: As you can see, the original triangle has the following coordinates </span><span> W(1, 5), X(1, 1), and Y(5, 1); the triangle must be dilated by a common scale factor, so if you analize the option B, you can notice that the triangle was dilated by a scale factor of 2.</span>

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3 years ago

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aniked [119]

Answer:

Step-by-step explanation:

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3 years ago