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3 years ago

What value added to x2 − 8x would complete the square?

2 answers:

7 0

X^2 - 8x = (x - 4)^2 - 16

we add 16 to give x^2 - 8x + 16 which is a perfect square

x^2 - 8x + 16 = (x - 4)^2

answer is 16

andrey2020 [161]3 years ago

5 0

Answer:

16 is added to complete the square

Step-by-step explanation:

$x^2-8x$

We use completing the square method to complete the square.

In completing the square method, we take coefficient of x and then divide by 2 and square it

$\frac{-8}{2} =-4$

$(-4)^2=16$

We add 16 to complete the square

$x^2-8x+16$

$(x-4)(x-4)$

$(x-4)^2$

So, 16 is added to complete the square

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The local oil changing business is very busy on Saturday mornings and is considering expanding. A national study of similar busi

eimsori [14]

Answer:

$t=\frac{4.2-3.6}{\frac{1.4}{\sqrt{16}}}=1.714$

Reject the null hypothesis if the observed "t" value is less than -2.131 or higher than 2.131

Rejection Zone: $t_{calculated}$ or $t_{calculated}>2.131$

In our case since our calculated value is not on the rejection zone we don't have enough evidence to reject the null hypothesis at 5% of significance.

Step-by-step explanation:

Previous concepts and data given

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=4.2$ represent the sample mean

$s=1.4$ represent the sample standard deviation

n=16 represent the sample selected

$\alpha=0.05$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is different from 3.6, the system of hypothesis would be:

Null hypothesis: $\mu = 3.6$

Alternative hypothesis: $\mu \neq 3.6$

If we analyze the size for the sample is < 30 and we 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:

$t=\frac{4.2-3.6}{\frac{1.4}{\sqrt{16}}}=1.714$

Critical values

On this case since we have a bilateral test we need to critical values. We need to use the t distribution with $df=n-1=16-1=15$ degrees of freedom. The value for $\alpha=0.05$ and $\alpha/2=0.025$ so we need to find on the t distribution with 15 degrees of freedom two values that accumulates 0.025 of the ara on each tail. We can use the following excel codes:

"=T.INV(0.025,15)" "=T.INV(1-0.025,15)"

And we got $t_{crit}=\pm 2.131$

So the decision on this case would be:

Reject the null hypothesis if the observed "t" value is less than -2.131 or higher than 2.131

Rejection Zone: $t_{calculated}$ or $t_{calculated}>2.131$

Conclusion

In our case since our calculated value is not on the rejection zone we don't have enough evidence to reject the null hypothesis at 5% of significance.

3 0

3 years ago

Anna and joes father donated $3 for every lap they swam in a swim a thon Ann swam 21 laps and joe swam 15 laps is the distributi

vredina [299]

21 + 15 = 36

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Their father donated $108 to charity

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3 years ago

Read 2 more answers

joe and Eric have to ship 75 packages. Joe can do the job alone in 5 hours. if Eric helps, they get it done in 4 hours. How long

Umnica [9.8K]

Eric took 20 hours to do the job alone.

<u>Step-by-step explanation</u>:

<u>Given </u>:

Total work = 75 packages
Joe took 5 hours to complete the total work.

The amount of work Joe alone can do per hour = 75/5 = 15 packages.

The amount of work Joe and Eric together do per hour = 75/4 = 18.75

The amount of work Eric alone can do per hour = 18.75 - 15 = 3.75

The time Eric took to complete the entire work = 75 / 3.75 = 20 hours.

8 0

3 years ago

I need help with this?

Anastaziya [24]

Answer:

it is 7

Step-by-step explanation:

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3 years ago

The 10th grade is having a picnic this Friday. There will be 182 students and 274 adults. Each table seats 12 people. How many t

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Answer:

38 Tables

Step-by-step explanation:

182 + 274 = 456

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3 years ago