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joja [24]
3 years ago
10

I need help! Can u help me?

Mathematics
1 answer:
liubo4ka [24]3 years ago
4 0

From clue 3, we know that the three numbers average to 15. This means we add up the three numbers x,y and z and divide by 3 to get 15. So one equation is (x+y+z)/3 = 15 which turns into x+y+z = 45 after multiplying both sides by 3.

Let's say that x < y < z. In other words x is the smallest number, y is the middle and z is the largest. Based on clue 2, this would tell us that z = 8*x (since largest is 8 times the smallest). We can replace the 'z' in the equation x+y+z = 45 with 8x like so

x+y+z = 45

x+y+8x = 45 ... replace z with 8x

9x+y = 45

Now onto clue #1. The smallest number x is a prime number and it is 1/6 times the size of the middle number y. Put another way, the middle number y is 6 times larger than the smallest number. We have this equation y = 6*x

9x+y = 45

9x+6x = 45 ... replace ywith 6x

15x = 45

x = 45/15

x = 3 which is a prime number

Now that we know x = 3, we can use it to find y

y = 6*x = 6*3 = 18

and then use x = 3 to find z

z = 8*x = 8*3 = 24

Therefore the three mystery numbers are 3, 18, and 24. Note how these three values add to 3+18+24 = 45 which you then divide over 3 to get 45/3 = 15. So the average of the values 3, 18, 24 is the number 15. This helps confirm the answer.

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company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 26
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Answer:

t=\frac{25.02-26}{\frac{4.83}{\sqrt{50}}}=-1.435    

p_v =P(t_{(49)}  

If we compare the p value and the significance level assumed \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant lower than 26 so then the specification is satisfied.

Step-by-step explanation:

Data given and notation  

\bar X=25.02 represent the sample mean

s=4.83 represent the sample standard deviation

n=50 sample size  

\mu_o =26 represent the value that we want to test

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

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

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is at least 26 mpg, the system of hypothesis would be:  

Null hypothesis:\mu \geq 26  

Alternative hypothesis:\mu < 26  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

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

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{25.02-26}{\frac{4.83}{\sqrt{50}}}=-1.435    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=50-1=49  

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

p_v =P(t_{(49)}  

Conclusion  

If we compare the p value and the significance level assumed \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant lower than 26 so then the specification is satisfied.

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