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Svetach [21]
2 years ago
9

If the coordinates of a pre-image are (x, y), which motion rule represents a counterclockwise rotation of 90° about the origin?

Mathematics
1 answer:
soldier1979 [14.2K]2 years ago
5 0

Answer:

What is the angle of rotation for this counterclockwise rotation about the origin?

answer:

270°

Step-by-step explanation:

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A ski lift is designed with a total load limit of 20,000 pounds. It claims a capacity of 100 persons. An expert in ski lifts thi
Yanka [14]

Answer:

0.5 = 50% probability that a random sample of 100 independent persons will cause an overload

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sum of n values of a distribution, the mean is \mu \times n and the standard deviation is \sigma\sqrt{n}

An expert in ski lifts thinks that the weights of individuals using the lift have expected weight of 200 pounds and standard deviation of 30 pounds. 100 individuals.

This means that \mu = 200*100 = 20000, \sigma = 30\sqrt{100} = 300

If the expert is right, what is the probability that a random sample of 100 independent persons will cause an overload

Total load of more than 20,000 pounds, which is 1 subtracted by the pvalue of Z when X = 20000. So

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

Z = \frac{20000 - 20000}{300}

Z = 0

Z = 0 has a pvalue of 0.5

1 - 0.5 = 0.5

0.5 = 50% probability that a random sample of 100 independent persons will cause an overload

5 0
3 years ago
A circular quilt is made from 113.04 square feet of fabric. How much trim is needed to go around it’s edge?
erik [133]

Hey there!

We are looking for the circumference of the circle, which is the distance around it. We are given the area, which is the radius squared times pi.

First, we need to undo the area to find our radius.

113.04/3.14=36

We square root this to find the radius.

√36=6

Our radius is six. To find the circumference, we need to multiply the diameter by pi. The diameter is twice the radius.

6*2=12

12*3.14=37.68

Therefore, we will need 37.68 feet of trim to around the edge of the quilt.

I hope this helps!

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3 years ago
Nicholas has 8 pieces of rope that are 4 yards each. He uses 4 pieces that are each 4 feet long.
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What's the question nbnnbbb
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PLEASE HELPP Btw letter D. Says 80
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C
the explanation is in the photo

8 0
2 years ago
If log 3 = x and log 5 = y, express log 45 in terms of x and y.
Marysya12 [62]

Answer:

I believe that the answer is A

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