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vovangra [49]
3 years ago
14

1)The base of a triangular prism is a right triangle with a base of 20 feet and a height of 120 inches. The height of the prism

is 5 feet. What is the volume of the prism, in cubic feet? Enter your answer as a number, like this: 42 Do not enter any units.
2)Jake has a shipping box with the following dimensions.

length: 12 inches
width: 4 inches

height: 8 inches

Havana has a shipping box similar to Jake's box, but each dimension is half as long.

How many times larger is the volume of the Jake's box than Havana's box?
Mathematics
1 answer:
ivanzaharov [21]3 years ago
6 0

Answer:

(1)750 cubic feet

(2)8 Times

Step-by-step explanation:

<u>Question 1</u>

<u>Dimensions of the Right Triangular Base</u>

  • Base = 20 feet
  • Height= 120 inches = 10 feet

Base Area of the Prism

=\dfrac12 \times 20 \times 10\\=150$ square feet

  • Height of the Prism = 5 feet

Volume of the Prism = Base Area X Height

= 150 X 5

=750 cubic feet

<u>Question 2</u>

<u>Jake's Box</u>

  • Length: 12 inches
  • Width: 4 inches
  • Height: 8 inches

Volume = 12 X 4 X 8 =384 cubic inches

<u>Havana's box</u>

Havana has a shipping box similar to Jake's box, but each dimension is half as long.

Therefore:

  • Length: 12/2=6 inches
  • Width: 4/2=2 inches
  • Height: 8/2=4 inches

Volume = 6 X 2 X 4 =48 cubic inches

Now:

384/48=8

Therefore, the volume of Jake's box is 8 times larger than Havana's box.

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Step-by-step explanation:

53 : 42 = 106 : 84

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Two brands of AAA batteries are tested in order to compare their voltage. The data summary can be found below. Find the 93% conf
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Answer:

(\bar X_1 -\bar X_2) \pm z_{\alpha/2} \sqrt{\frac{s^2_1}{n_1}+\frac{s^2_}{n_2}}

And replacing we got:

(9.2 -8.8) - 1.811 \sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}= 0.2903

(9.2 -8.8) + 1.811 \sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}= 0.5097

And the confidence interval for the difference of means would be given by:

0.2903 \leq \mu_1 -\mu_2 \leq 0.5097

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

We have the following data given:

\bar X_1 = 9.2 , \bar X_2 = 8.8, \sigma_1= 0.3, n_1 = 27, \sigma_2 = 0.1, n_2 = 30

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 93% of confidence, our significance level would be given by \alpha=1-0.93=0.07 and \alpha/2 =0.035. And the critical value would be given by:  

z_{\alpha/2}=-1.811, z_{1-\alpha/2}=1.811  

The confidence interval is given by:

(\bar X_1 -\bar X_2) \pm z_{\alpha/2} \sqrt{\frac{s^2_1}{n_1}+\frac{s^2_}{n_2}}

And replacing we got:

(9.2 -8.8) - 1.811 \sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}= 0.2903

(9.2 -8.8) + 1.811 \sqrt{\frac{0.3^2}{27}+\frac{0.1^2}{30}}= 0.5097

And the confidence interval for the difference of means would be given by:

0.2903 \leq \mu_1 -\mu_2 \leq 0.5097

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The number equals -48
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A painter needs 5 gallons of paint to finish a house. He has 3 quarts and 1 pint. How much more paint does he need
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Answer:

Step-by-step explanation:

He needs 1 pint to get the 3 quarts to 4 quarts.

4 quarts = 1 gallon.

So if he buys 1 pint he will have 1 gallon.

He needs 5 gallons.

He has 1 gallon

He needs 5 - 1 = 4 gallons.

Answer: he needs 1 pint and 4 gallons.

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