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andrezito [222]
3 years ago
11

Abdul is creating a cushion that is 1 foot by 2 feet by 3 feet. He wants to find the least amount of fabric he will need to cove

r the cushion. He starts by drawing the net shown here. A net is formed by 2 rectangles. 1 rectangle has a base of 4 feet and height of 3 feet. The other rectangle has a base of 5 feet and height of 2 feet. What is the least amount of fabric he will need to cover the cushion?
Mathematics
2 answers:
netineya [11]3 years ago
7 0

Answer:

The least amount of fabric are 22 square feet

Step-by-step explanation:

we know that

The surface area of a rectangular prism is given by the formula

SA=2B+PH

where

B is the area of the base

P is the perimeter of the base

H is the height of the prism

Let

L ---> the length pf the prism

W ---> the width of the prism

H ---> is the height of the prism

Let

L=2\ ft\\W=3\ ft\\H=1\ ft

Find the area of the base

B=LW=(2)(3)=6\ ft^2

Find the perimeter of the base

P=2(L+W)=2(2+3)=10\ ft

Find the surface area

SA=2(6)+10(1)=22\ ft^2

therefore

The least amount of fabric are 22 square feet

Novosadov [1.4K]3 years ago
4 0

Answer:

Abdul will need 22ft of fabric to cover the cushion

Step-by-step explanation:

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Answer:

a) t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{0.7 -0}{\frac{0.678}{\sqrt{5}}}=2.308  

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So the p values is lower than the significance level given 0.05, so then we can conclude that we reject the null hypothesis.

b) The p value is illustrated on the figure attached.

If we select \alpha=0.01 we see that p_v >\alpha so then we have enough evidence to FAIL to reject the null hypothesis.

Step-by-step explanation:

Part a

A paired t-test is used to compare two population means where you have two samples in  which observations in one sample can be paired with observations in the other sample. For example  if we have Before-and-after observations (This problem) we can use it.  

Let put some notation  

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1: 5.2 6.5 7.2 5.7 7.6

2: 6.4 7.8 6.8 6.5 8.2

The system of hypothesis for this case are:

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The 4 step is calculate the statistic given by :

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Now we can calculate the p value, since we have a right tailed test the p value is given by:

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Part b

The p value is illustrated on the figure attached.

If we select \alpha=0.01 we see that p_v >\alpha so then we have enough evidence to FAIL to reject the null hypothesis.

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