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3 years ago

Kalani has run 4 1/5 miles in 2/3 an hour. If he continues to run at this rate, how many miles will he run in one hour?

Mathematics

1 answer:

Blizzard [7]3 years ago

6 0

Answer:

Kalani will run 6.3 miles OR 6 3/10 miles.

Step-by-step explanation:

So first step that I would do is make it easier to understand by converting the fraction to a whole number. 2/3 hour= 40 minutes.

So Kalani runs 4 1/5 miles in 40 minutes.

Then, we convert 4 1/5 to 4.2. Next, I would divide 4.2 by 2 to get how long he ran in 20 minutes. 4.2/2=2.1.

The final step is to add 2.1 and 4.2 and we get 6.3.

Extra step:

But if we need to turn it back into a fraction, it would be 6 3/10

Hope this helps :)

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3 years ago

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In tests of a computer component, it is found that the mean time between failures is 937 hours. A modification is made which is

VladimirAG [237]

Answer:

Null hypothesis is $\mathbf {H_o: \mu > 937}$

Alternative hypothesis is $\mathbf {H_a: \mu < 937}$

Test Statistics z = 2.65

CONCLUSION:

Since test statistics is greater than critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.

P- value = 0.004025

Step-by-step explanation:

Given that:

Mean $\overline x$ = 960 hours

Sample size n = 36

Mean population $\mu =$ 937

Standard deviation $\sigma$ = 52

Given that the mean time between failures is 937 hours. The objective is to determine if the mean time between failures is greater than 937 hours

Null hypothesis is $\mathbf {H_o: \mu > 937}$

Alternative hypothesis is $\mathbf {H_a: \mu < 937}$

Degree of freedom = n-1

Degree of freedom = 36-1

Degree of freedom = 35

The level of significance ∝ = 0.01

SInce the degree of freedom is 35 and the level of significance ∝ = 0.01;

from t-table t(0.99,35), the critical value = 2.438

The test statistics is :

$Z = \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}}$

$Z = \dfrac{960-937 }{\dfrac{52}{\sqrt{36}}}$

$Z = \dfrac{23}{8.66}$

Z = 2.65

The decision rule is to reject null hypothesis if test statistics is greater than critical value.

CONCLUSION:

The P-value can be calculated as follows:

find P(z < - 2.65) from normal distribution tables

= 1 - P (z ≤ 2.65)

= 1 - 0.995975 (using the Excel Function: =NORMDIST(z))

= 0.004025

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3 years ago

the ratio of apples to oranges in a fruit basket is 12:4 if there are 7 oranges in the fruit basket then how many apples and ora

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Just simple proportions:

12(apples) x(apples)
-------------- = --------------
4(oranges) 7(oranges)

12*7 = 84
84/4 = 21

There are 21 apples + 7 oranges = 28 apples and oranges!

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The answer & explanation for this question is given in the attachment below.