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Anit [1.1K]
3 years ago
6

a rectangular prism has a volume of 810 cubic meters. it has a length of 10 meters and a width of 9 meters. What is the height o

f the prism
Mathematics
1 answer:
Ainat [17]3 years ago
6 0

Answer:

The height of the prism is 9 meters

Step-by-step explanation:

* Lets describe the rectangular prism

- The rectangular prism has six rectangular faces

- Two of them are bases and the other four are side faces

- The rectangular prism has three dimensions length, width , height

- The volume of any prism = Area of the base × its height

∵ The base of the rectangular prism is a rectangle

∵ Area any rectangle = length × width

∴ The volume of the rectangular prism V = length × width × height

* Lets solve the problem

∵ The volume of the prism is 810 meter³

∵ Its length is 10 meter

∵ Its width is 9 meters

∵ V = length × width × height

- Substitute the values of the volume , the length and the width in

 the equation of V

∴ 810 = 10 × 9 × h

∴ 810 = 90 × h

- Divide both sides by 90

∴ 9 = h

∴ The height of the prism is 9 meters

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The following prices, in dollars, of 7.5-cubic-foot refrigerators were recorded from a random sample. 314 305 344 283 285 310​ 3
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Answer:

t=\frac{310.9-300}{\frac{31.09}{\sqrt{10}}}=1.109      

The degrees of freedom are given by:

df=n-1=10-1=9  

And the p value would be given by:

p_v =P(t_{9}>1.109)=0.148  

Since the p value is higher than the significance level of 0.05 we don't have enough evidence to conclude that the true mean is significantly higher than $300 because we FAIL to reject the null hypothesis.

Step-by-step explanation:

Information given

314 305 344 283 285 310​ 383​ 285​ 300​ 300

We can calculate the sample mean and deviation with the following formula:

\bar X =\frac{\sum_{i=1}^n X_i}{n}

s =\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}

\bar X=310.9 represent the sample mean      

s=31.09 represent the standard deviation for the sample      

n=10 sample size      

\mu_o =300 represent the value to test

\alpha=0.05 represent the significance level

t would represent the statistic

p_v represent the p value

Hypothesis to test

We want to verify if the true mean is greater than 300, the system of hypothesis would be:      

Null hypothesis:\mu \leq 300      

Alternative hypothesis:\mu > 300      

The statistic is given by:

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)      

Replacing the info given we got:

t=\frac{310.9-300}{\frac{31.09}{\sqrt{10}}}=1.109      

The degrees of freedom are given by:

df=n-1=10-1=9  

And the p value would be given by:

p_v =P(t_{9}>1.109)=0.148  

Since the p value is higher than the significance level of 0.05 we don't have enough evidence to conclude that the true mean is significantly higher than $300 because we FAIL to reject the null hypothesis.

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3 years ago
Find the surface area of the triangular prism.<br><br> 15.6 cm<br> 10 cm<br> 11 cm<br> 12 cm
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Answer:

533.6cm²

Step-by-step explanation:

Hello!

I'm here to answer your question!

<u>Area of each triangular base:</u>

\frac{1}{2}(12)(10)=60

<u />

<u>Area of the rectangular faces:</u>

12\times 11 =132

15.6\times 11=171.6

10\times 11=110

<u>Add to find the surface area:</u>

60+60+132+171.6+110=533.6

Thus, the surface area of the triangular prism is = 533.6 yd²

Hope this helps you!

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