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muminat
3 years ago
15

Katalene wants to make a quilt in the shape of a golden rectangle. She only has enough binding material for a quilt with a perim

eter of 29 feet. What should the dimensions of the quilt be? a. 5.44 ft by 9.06 ft b. 5.54 ft by 8.96 ft c. 5.74 ft by 8.76 ft d. 5.64 ft by 8.86 ft
Mathematics
1 answer:
lara31 [8.8K]3 years ago
4 0
All of these choices would result in a 29-ft perimeter for the quilt.
But choice-b is significantly closer to the golden ratio than the others are.
Golden Ratio = (1/2) (1 + √5)  =  1.618... (rounded)
Choice a).  1.665
Choice b).  1.617 the answer is "B"
Choice c).  1.526
Choice d).  1.5709 
 
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Step-by-step explanation:

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Answer:

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and the critical value would be t_{\alpha/2}=1.669

And replacing we got

17.5-1.669\frac{4.2}{\sqrt{65}}=16.63    

17.5+1.669\frac{4.2}{\sqrt{65}}=18.37    

For the 95% confidence the critical value is t_{\alpha/2}=1.998

17.5-1.998\frac{4.2}{\sqrt{65}}=16.46    

17.5+1.998\frac{4.2}{\sqrt{65}}=18.54    

Step-by-step explanation:

Information given

\bar X¿ 17.5 represent the sample mean

\mu population mean (variable of interest)

s¿4.2 represent the sample standard deviation

n¿65 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

The degrees of freedom are given by:

df=n-1=65-1=64

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and the critical value would be t_{\alpha/2}=1.669

And replacing we got

17.5-1.669\frac{4.2}{\sqrt{65}}=16.63    

17.5+1.669\frac{4.2}{\sqrt{65}}=18.37    

For the 95% confidence the critical value is t_{\alpha/2}=1.998

17.5-1.998\frac{4.2}{\sqrt{65}}=16.46    

17.5+1.998\frac{4.2}{\sqrt{65}}=18.54    

8 0
3 years ago
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AveGali [126]
X+y=12
x-2y=6

hmm
multiply 2nd equation by -1 and add to first

-x+2y=-6
<u>x+y=12 +</u>
0x+3y=6

3y=6
y=2
sub back
x+y=12
x+2=12
x=10

x=10, y=2
7 0
3 years ago
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