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Sindrei [870]
3 years ago
12

2 questions! area of plane and composite figures

Mathematics
1 answer:
VikaD [51]3 years ago
4 0
Find the base and height of each side, subtract the triangle from the trapezoid then find the area of the parrellogram and add the subracted one and the obtuse square
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Based on historical data, your manager believes that 37% of the company's orders come from first-time customers. A random sample
fomenos

Answer:

0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38

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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

37% of the company's orders come from first-time customers.

This means that p = 0.37

A random sample of 225 orders will be used to estimate the proportion of first-time-customers.

This means that n = 225

Mean and standard deviation:

\mu = p = 0.37

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.37*0.63}{225}} = 0.0322

What is the probability that the sample proportion is between 0.26 and 0.38?

This is the pvalue of Z when X = 0.38 subtracted by the pvalue of Z when X = 0.26.

X = 0.38

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

By the Central Limit Theorem

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

Z = \frac{0.38 - 0.37}{0.0322}

Z = 0.31

Z = 0.31 has a pvalue of 0.6217

X = 0.26

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

Z = \frac{0.26 - 0.37}{0.0322}

Z = -3.42

Z = -3.42 has a pvalue of 0.0003

0.6217 - 0.0003 = 0.6214

0.6214 = 62.14% probability that the sample proportion is between 0.26 and 0.38

5 0
2 years ago
Terrell wants to Drive his car at a speed of 50 miles per hour for 2.75 hours. His car has a fuel efficiency of 25 miles per gal
Oduvanchick [21]
HI there! To find the number of gallons he needs for travel, the first step we need to do is find the number of miles he'll travel, by multiplying speed by time. 50 * 2.75 is 137.5. Terrell will travel 137.5 miles in 2.75 hours. There are 25 miles in a gallon. Now, let's divide the number by 25 to get the number of gallons. 137.5 / 25 = 5.5. There. Terrell will need 5.5 gallons of gas for his journey.
5 0
3 years ago
Read 2 more answers
Please help I'm really confused
inessss [21]

Answer:

your answer should look like this.

Step-by-step explanation:

The horizontal line goes through y-intercept -1/2

3 0
3 years ago
What is 1 2/3 - 2 1/3
zysi [14]

Answer:

-2/3

Step-by-step explanation:

I took the whole numbers and multiplied them by 3 and added them to the numerators, so I did 5/3 - 7/3, which would be -2/3

8 0
3 years ago
Read 2 more answers
What are the roots of the polynomial equation x^4+x^3=4x^2+4x? Use a graphing calculator and a system of equations.
Yuliya22 [10]
Desmos graphing calculator will draw this graph for you.

draw 2 curves

y = x^4 + x^3 
and
y = 4x^2 + 4x

The roots are the points where the 2 curves intersect.

You can see by simple substitution that one root is zero.

x^4 + x^3 - 4x^2 - 4x = 0

f(2)  = 16 + 8 - 4(4) - 4(2)  = 0   so 2 is another root

f(-2) = 16 - 8 - 16 + 8 = 0  so  -2 is another root

f(-1) = 1 - 1  - 4 + 4 = 0 so -1 is the other root

The answer is A
8 0
3 years ago
Read 2 more answers
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