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torisob [31]
3 years ago
15

DeAngelo is training for a half marathon. Today he is running 13.25 miles. He jogs for the first half hour at a rate of 5.5 mile

s per hour, then increases his pace to p miles per hour for 1.5 hours. Write an equation representing this situation, and complete the statement that follows.
__+__ p = ___

DeAngelo's rate for the last 1.5 hours of his run is ___ miles per hour.
Mathematics
1 answer:
klemol [59]3 years ago
8 0
The first thing we must know is the following definition:
  d = v * t
  Where,
  d: distance
  v: speed
  t: time
  Therefore, the total distance traveled in this case is:
  (5.5) * (0.5) + (1.5) * p = 13.25
  Rewriting:
  2.75 + 1.5p = 13.25
   Clearing the value of p we have:
  p = (13.25-2.75) / (1.5)
  p = 7
   Answer:
  an equation representing this situation is: 
  2.75 + 1.5p = 13.25 
  DeAngelo's rate for the last 1.5 hours of his run is 7 miles per hour


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Viefleur [7K]

Answer:

Null hypothesis:p_{1} = p_{2}  

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

z=\frac{0.6-0.2}{\sqrt{0.4(1-0.4)(\frac{1}{50}+\frac{1}{50})}}=4.082    

p_v =2*P(Z>4.082)=4.46x10^{-5}  

So the p value is a very low value and using any significance level for example \alpha=0.05 always p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significantly different from proportion 2.

Step-by-step explanation:

1) Data given and notation  

X_{1}=30 represent the number of people with a characteristic in 1

X_{2}=10 represent the number of people with a characteristic in 2

n_{1}=50 sample of 1 selected  

n_{2}=50 sample of 2 selected  

p_{1}=\frac{30}{50}=0.6 represent the proportion of people with a characteristic in 1

p_{2}=\frac{10}{50}=0.2 represent the proportion of people with a characteristic in 2

z would represent the statistic (variable of interest)  

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

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the proportion 1 is different from proportion 2 , 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{30+10}{50+50}=0.4  

3) Calculate the statistic  

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

z=\frac{0.6-0.2}{\sqrt{0.4(1-0.4)(\frac{1}{50}+\frac{1}{50})}}=4.082    

4) 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>4.082)=4.46x10^{-5}  

So the p value is a very low value and using any significance level for example \alpha=0.05 always p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion 1 is significantly different from proportion 2.  

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A) -6a = 36

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a = -6

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So, a=-6

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Divide both sides by -9.

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Check work by plugging in 8 for d.

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So, d=8

~Hope I helped!~
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Answer:

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Step-by-step explanation:

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