All categories

2 years ago

How do I write the sum of two numbers as the product of Their GCF and another sum with 32 and 20?

Mathematics

1 answer:

mina [271]2 years ago

4 0

$32+20=4(8+5)$

You might be interested in

Graph the circle (x+6)^2 + (y+5)^2 =9

Andrei [34K]

Answer:

This a circle centered at the point $(-6,-5)$ , and of radius "3" as it is shown in the attached image.

Step-by-step explanation:

Recall that the standard formula for a circle of radius "R", and centered at the point $(x_0,y_0)$ is given by:

$(x-x_0)^2+(y-y_0)^2=R^2$

Therefore, in our case, by looking at the standard equation they give us, we extract the following info:

1) $R^2 = 9\,\,\,then\,\,\,R=3$ since the radius must be a positive number and ( $R=-3$ ) is not a viable answer.

2) $x_0=-6$ for ( $x-x_0$ ) to equal $(x+6)$

3) $y_0=-5$ for ( $y-y_0$ ) to equal $(y+5)$

Therefore, we are in the presence of a circle centered at the point $(-6,-5)$ , and of radius "3". That is what we draw as seen in the attached image.

5 0

2 years ago

Given 3X - Y = -13 solve for y

Yanka [14]

Maybe u should do inverse operation on both sides idk but just try it

4 0

2 years ago

An examination of the records for a random sample of 16 motor vehicles in a large fleet resulted in the sample mean operating co

levacccp [35]

Answer:

1. The 95% confidence interval would be given by (24.8190;27.8010)

2. $4.7048 \leq \sigma^2 \leq 16.1961$

3. $t=\frac{26.31-25}{\frac{2.8}{\sqrt{16}}}=1.871$

$t_{crit}=1.753$

Since our calculated value it's higher than the critical value we have enough evidence at 5% of significance to reject th null hypothesis and conclude that the true mean is higher than 25 cents per mile.

4. $t=(16-1) [\frac{2.8}{2.3}]^2 =22.2306$

$\chi^2 =24.9958$

Since our calculated value is less than the critical value we don't hav enough evidence to reject the null hypothesis at the significance level provided.

Step-by-step explanation:

Previous concepts

$\bar X=26.31$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=2.8 represent the sample standard deviation

n=16 represent the sample size

Part 1

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=16-1=15$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-T.INV(0.025,15)".And we see that $t_{\alpha/2}=2.13$

Now we have everything in order to replace into formula (1):

$26.31-2.13\frac{2.8}{\sqrt{16}}=24.819$

$26.31+2.13\frac{2.8}{\sqrt{16}}=27.801$

So on this case the 95% confidence interval would be given by (24.8190;27.8010)

Part 2

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=16-1=15$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical values.

The excel commands would be: "=CHISQ.INV(0.05,15)" "=CHISQ.INV(0.95,15)". so for this case the critical values are:

$\chi^2_{\alpha/2}=24.996$

$\chi^2_{1- \alpha/2}=7.261$

And replacing into the formula for the interval we got:

$\frac{(15)(2.8)^2}{24.996} \leq \sigma^2 \leq \frac{(15)(2.8)^2}{7.261}$

$4.7048 \leq \sigma^2 \leq 16.1961$

Part 3

We need to conduct a hypothesis in order to determine if actual mean operating cost is at most 25 cents per mile , the system of hypothesis would be:

Null hypothesis: $\mu \leq 25$

Alternative hypothesis: $\mu > 25$

We don't know the population deviation, so for this case 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)

Calculate the statistic

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

$t=\frac{26.31-25}{\frac{2.8}{\sqrt{16}}}=1.871$

Critical value

On this case we need a critical value on th t distribution with 15 degrees of freedom that accumulates 0.05 of th area on the right and 0.95 of the area on the left. We can calculate this value with the following excel code:"=T.INV(0.95,15)" and we got $t_{crit}=1.753$

Conclusion

Since our calculated valu it's higher than the critical value we have enough evidence at 5% of significance to reject th null hypothesis and conclude that the true mean is higher than 25 cents per mile.

Part 4

State the null and alternative hypothesis

On this case we want to check if the population standard deviation is more than 2.3, so the system of hypothesis are:

H0: $\sigma \leq 2.3$

H1: $\sigma >2.3$

In order to check the hypothesis we need to calculate the statistic given by the following formula:

$t=(n-1) [\frac{s}{\sigma_o}]^2$

This statistic have a Chi Square distribution distribution with n-1 degrees of freedom.

What is the value of your test statistic?

Now we have everything to replace into the formula for the statistic and we got:

$t=(16-1) [\frac{2.8}{2.3}]^2 =22.2306$

What is the critical value for the test statistic at an α = 0.05 significance level?

Since is a right tailed test the critical zone it's on the right tail of the distribution. On this case we need a quantile on the chi square distribution with 15 degrees of freedom that accumulates 0.05 of the area on the right tail and 0.95 on the left tail.

We can calculate the critical value in excel with the following code: "=CHISQ.INV(0.95,15)". And our critical value would be $\chi^2 =24.9958$

Since our calculated value is less than the critical value we FAIL to reject the null hypothesis.

7 0

3 years ago

Answer what you can please!

Fed [463]

Answer:

Something's Fishy:

Domain = Time

Range = Gallons of water remaining.

Smart Phone, but is it a Smart Deal?

Domain = Weeks passing

Range = Interest ($)!!!!

Step-by-step explanation:

Something's Fishy:

First and foremost, Candice, very gently, removes the fish from the tank and places them into a clean, healthy, temporary environment.

AKA Candice glances to check if the coast is clear before chucking the fish into the nearest toilet as fast as possible. (Stop laughing, Fish deserve equal rights too [no, but really]).

Candice then begins to empty the tank, draining 10 gallons per minute.

Again, if you know anything of physics or mathmatical graph placement, the TIME variable will 9.99999999/10x be the independent variable, this won't change. Make it a rule of thumb, get the sharpie-tat, do whatever you need to do to remember it.

From a literal perspective, we can see that the water is draining at a constant rate. The rate isn't changing, but something IS. That "something" is the water remaining IN the tank per periodic interval.

Time is independent.

Puny water is dependent and inferior.

The fish are depending upon the hope that the one gassy guy from IT doesn't get to the toilet before Candice comes back.

The fate of the fish are dependent upon hoping the guy from IT doesn't have beans and cheese for lunch. (Remember Pompeii?! Anyone? Imagine Pompeii in a 2x2 ceramic & plastic can now :). You're welcome!)

End of story.

Smart Phone, but is it a smart deal?

Your cousin is ripping you off. He knows it, his momma knows it, and the dog knows that it's hungry, and it will definitely eat the phone. Yeah, the dog knows it too.

Every week that passes, cuzzo gets double the cash from you to pocket. It's all fun and games until 30 weeks have passed and you're two-feet in the grave of debt, because you always chose McDonalds over settling debts.

Because CUZZO (that conniving worm) knew that your INTEREST was dependent upon the number of weeks it'd take you to pay cuzzo his cash back.

Hope this helps!!

(No fish were harmed in the making of this post)

8 0

3 years ago

Help me plz..........

vekshin1

Answer:

The answer to your question is the third option

6 0

2 years ago

Read 2 more answers