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inn [45]
3 years ago
13

Write an expression to model the perimeter of the rectangle. Length is x-9 and width is 3x-4. Part b The perimeter of the rectan

gle is 138. What is x. Plzz I will give you 100 points
Mathematics
2 answers:
koban [17]3 years ago
5 0

Step-by-step explanation:

To find the perimeter of something, we add all of the measurements of the sides together.

A rectangle has 4 sides, this means we must double the algebraic hints given to us.

If we add them all up together it will look like this:

x-9+x-9+3x-4+3x-4=138

If we simplify it by collecting the like terms:

8x-26=138

We add 26 onto 138

8x=164

To find out what x equals, we divide by 8:

164÷8= 20.5

Answer:

x=20.5cm

x-9 is 11.5

3x-4 is 57.5

I know that you will not give 100 points but just wanted to help.

Alexxx [7]3 years ago
3 0

Answer:

A: P = 8x - 26

B: x = 20.5

Step-by-step explanation:

Part A

Equation

P = 2*(L + W)

Givens

  • L = x - 9
  • W = 3x - 4

Solution

  • P = 2*(x - 9 + 3x - 4)
  • P = 2*(x + 3x - 9 - 4)
  • P = 2*(4x - 13)
  • P = 8x - 26

Part B

Given

P = 138

Equation

P = 8x - 26

Solution

  • 138 = 8x -26           Add 26 to both sides
  • 138 + 26 = 8x         Combine the left
  • 164 = 8x                  Divide by 8
  • x = 20.5                  Answer
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Answer:

a) 0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

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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 z-score 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 p-value, 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.

The mean of a population is 74 and the standard deviation is 15.

This means that \mu = 74, \sigma = 15

Question a:

Sample of 36 means that n = 36, s = \frac{15}{\sqrt{36}} = 2.5

This probability is 1 subtracted by the pvalue of Z when X = 78. So

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

By the Central Limit Theorem

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

Z = \frac{78 - 74}{2.5}

Z = 1.6

Z = 1.6 has a pvalue of 0.9452

1 - 0.9452 = 0.0548

0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

Question b:

Sample of 150 means that n = 150, s = \frac{15}{\sqrt{150}} = 1.2247

This probability is the pvalue of Z when X = 77 subtracted by the pvalue of Z when X = 71. So

X = 77

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

Z = \frac{77 - 74}{1.2274}

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Z = 2.45 has a pvalue of 0.9929

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

Z = \frac{71 - 74}{1.2274}

Z = -2.45

Z = -2.45 has a pvalue of 0.0071

0.9929 - 0.0071 = 0.9858

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Sample size of 219 means that n = 219, s = \frac{15}{\sqrt{219}} = 1.0136

This probability is the pvalue of Z when X = 74.2. So

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

Z = \frac{74.2 - 74}{1.0136}

Z = 0.2

Z = 0.2 has a pvalue of 0.5793

0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

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