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patriot [66]
3 years ago
14

A box has a volume of 135 feet3. The length is same as the height, and the width is 5 times the length. What are the dimensions

of the box?
Mathematics
1 answer:
snow_lady [41]3 years ago
7 0
Let the length be x ft, width=5x ft, height=x ft
thus the volume will be:
volume=length*width*height
thus
135=x×x×5x
135=5x³
solving for x we get:
27=x³
getting the cube root of both sides:
∛27=x³
x=3 ft
thus
length=3 ft, height=3ft, width=3×5=15 ft

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The amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.2 minutes and
masya89 [10]

Answer:

a) There is a 100% probability that the (sample) average time waiting in line for these customers is less than 10 minutes.

b) There is a 100% probability that the (sample) average time waiting in line for these customers is between 5 and 10 minutes.

c) There is a 0% probability that the (sample) average time waiting in line for these customers is less than 6 minutes.

d) Because there are less observations, it would be less accurate.

e) Because there are moreobservations, it would be more accurate.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}

Problems of normally distributed samples 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.

In this problem, we have that:

The amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.2 minutes and standard deviation 1.5 minutes. This means that \mu = 8.2, \sigma = 1.5.

Suppose that a random sample of n = 49 customers is observed

This means that s = \frac{1.5}{\sqrt{49}} = 0.21.

(a) Less than 10 minutes.

This probability is the pvalue of Z when X = 10. So:

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

Z = \frac{10 - 8.2}{0.21}

Z = 8.57

Z = 8.57 has a pvalue of 1.

This means that there is a 100% probability that the (sample) average time waiting in line for these customers is less than 10 minutes.

(b) Between 5 and 10 minutes.

This probability is the pvalue of Z when X = 10 subtracted by the pvalue of Z when X = 5.

From a), we have that the zscore of X = 10 has a pvalue of 1.

For X = 5.

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

Z = \frac{5 - 8.2}{0.21}

Z = -15.24

Z = -15.24 has a pvalue of 0.

Subtracting, we have that there is a 100% probability that the (sample) average time waiting in line for these customers is between 5 and 10 minutes.

(c) Less than 6 minutes.

This probability is the pvalue of Z when X = 6. So:

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

Z = \frac{6 - 8.2}{0.21}

Z = -10.48

Z = -10.48 has a pvalue of 0.

This means that there is a 0% probability that the (sample) average time waiting in line for these customers is less than 6 minutes.

(d) If you only had two observations instead of 49 observations, would you believe that your answers to parts (a), (b), and (c), are more accurate or less accurate? Why?

The less observations there are, the less acurrate our results are.

So, because there are less observations, it would be less accurate.

(e) If you had 1,000 observations instead of 49 observations, would you believe that your answers to parts (a), (b), and (c), are more accurate or less accurate? Why?

The more observations there are, the more acurrate our results are.

So, because there are moreobservations, it would be more accurate.

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3 years ago
StartFraction one-half left-parenthesis x plus 12 right-parenthesis equals 4 x minus 1.(x + 12) = 4x – 1
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Answer:

1/2.(x+12)=4x-1

x+12=2(4x-1)

x+12=8x-2

Group like terms

12+2=8x-x

14=7x

Divide both sides by 7

x=2

Step-by-step explanation:

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On Tuesday the value of a stock decreased by 1/2 point. On Wednesday, the value increased by 3/4 point. On Thursday the value de
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The change is -(1/2 + 3/4 + 3/8).
If you add the fractions, you get -(13/8).
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Pls help I need this asap​
Valentin [98]

Answer:

75%

Step-by-step explanation:

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I need help with Which table shows the correct methods used to justify the solution steps?
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Answer:

x = 8

Step-by-step explanation:

3 (x - 5) + 7x = 65

3x - 15 + 7x = 65

10x - 15 = 65

10x = 80

x = 8

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3 years ago
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