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yawa3891 [41]
3 years ago
8

Sandy is working with a carpenter to frame a house. They are using 8-foot-long boards, but each board must be cut to be 7 feet i

nches long. How much is cut off each board? Note: 1 foot = 12 inches A. 1 1/4 inches B. 1 3/4 inches C. 7 inches D. 3/4 inch
Mathematics
1 answer:
Tju [1.3M]3 years ago
8 0

Answer:

5/4in

Step-by-step explanation:

The initial length:

1 ft = 12 in

8 ft = 8 * 12 in    

= 96 in

The final length:

7 ft 10 3/4 in = 7 ft + 10 in + 3/4 in

                     = 7 * 12 in + 10 in + 3/4 in                    

                     = 84 in + 10 in + 3/4 in        

                     = 94 in + 3/4 in

The final length:

96 in - 94 in - 3/4 in = 2 in - 3/4 in = 8/4 in - 3/4 in = 5/4 in

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Answer:

Accelerating to top speed, deaccelerating to finish line.

Step-by-step explanation:

If the runner kept a constant speed of 11 mph for the whole duration of his run (32 minutes), the distance he would have covered is:

d=11*\frac{32}{60}\\d= 5.87\ mi

This means that, in order to run the full 6.2 miles, the runner needs to reach a speed over 11 mph. Assume he starts from rest, while accelerating the runner reaches, and the surpasses, the 11 mph mark. Since his speed at the finish line is zero, the runner has to deaccelerate from his current running speed (which should be higher than 11 mph), passing through 11 mph and reaching zero at the finish line.

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3 years ago
B) Tyler swam 32 laps in the pool. Kevin swam 3 times as many laps as Tyler. Lets the number of
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If Tyler did 32 laps and Kevin did 3 times that amount; its quite simple, you would find three times the amount of Tylers laps which is 96.

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2 years ago
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PLEASE HELP<br><br> Graph the ordered pairs for y = 3x + 3 using r = {-2, 1, 2}.
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Answer:

  (-2, -3), (1, 6), (2, 9) are plotted in the attached graph

Step-by-step explanation:

For x = -2, y = 3(-2) +3 = -3. The ordered pair is (-2, -3).

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The graph is attached.

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Verify the identity. 4 csc 2x = 2 csc2x tan x
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Step-by-step explanation:

4csc(2x) = 2csc^2(x) tan(x)

We start with Left hand side

We know that csc(x) = 1/ sin(x)

So csc(2x) is replaced by 1/sin(2x)

4 \frac{1}{sin(2x)}

Also we use identity

sin(2x) = 2 sin(x) cos(x)

4 \frac{1}{2sin(x)cos(x)}

4 divide by 2 is 2

Now we multiply top and bottom by sin(x) because we need tan(x) in our answer

2\frac{1*sin(x)}{sin(x)cos(x)*sin(x)}

2\frac{sin(x)}{sin^2(x)cos(x)}

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3 years ago
In the book Essentials of Marketing Research, William R. Dillon, Thomas J. Madden, and Neil H. Firtle discuss a research proposa
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Answer:

Null hypothesis:p_{1} = p_{2}  

Alternative hypothesis:p_{1} \neq p_{2}  

z=\frac{0.179-0.15}{\sqrt{0.17(1-0.17)(\frac{1}{140}+\frac{1}{60})}}=0.500  

p_v =2*P(Z>0.500)=0.617  

So the p value is a very low value and using any significance level for example \alpha=0.05, 0,1,0.15 always p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the two proportions NOT differs significantly.  

Step-by-step explanation:

Data given and notation  

X_{1}=25 represent the number of homeowners who would buy the security system

X_{2}=9 represent the number of renters who would buy the security system

n_{1}=140 sample 1

n_{2}=60 sample 2

p_{1}=\frac{25}{140}=0.179 represent the proportion of homeowners who would buy the security system

p_{2}=\frac{9}{60}= 0.15 represent the proportion of renters who would buy the security system

z would represent the statistic (variable of interest)  

p_v represent the value for the test (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the two proportions differs , the system of hypothesis would be:  

Null hypothesis:p_{1} = p_{2}  

Alternative hypothesis:p_{1} \neq p_{2}  

We need to apply a z test to compare proportions, and the statistic is given by:  

z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}   (1)  

Where \hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{25+9}{140+60}=0.17  

Calculate the statistic  

Replacing in formula (1) the values obtained we got this:  

z=\frac{0.179-0.15}{\sqrt{0.17(1-0.17)(\frac{1}{140}+\frac{1}{60})}}=0.500  

Statistical decision

For this case we don't have a significance level provided \alpha, but we can calculate the p value for this test.    

Since is a two sided test the p value would be:  

p_v =2*P(Z>0.500)=0.617  

So the p value is a very low value and using any significance level for example \alpha=0.05, 0,1,0.15 always p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the two proportions NOT differs significantly.  

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