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3 years ago

Prove 151^3-25^3 is divisible by 126

Mathematics

1 answer:

stiks02 [169]3 years ago

4 0

9514 1404 393

Answer:

151 -25 = 126 is a factor of the difference of those cubes

Step-by-step explanation:

The expression can be factored as ...

a^3 -b^3 = (a -b)(a^2 +ab +b^2)

151^3 -25^3 = (151 -25)(151^2 +151·25 +25^2)

= 126(151^2 +151·25 +25^2)

That is, 126 is a factor of the difference of the given cubes. The difference is divisible by 126.

Your calculator tells you 151^3 -25^3 = 126 · 27201.

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Ludwig borrowed $700,000 for a period of 2 years. His interest rate is 10%. How much interest will Ludwig pay in all?

harkovskaia [24]

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3 years ago

We wish to give a 90% confidence interval for the mean value of a normally distributed random variable. We obtain a simple rando

coldgirl [10]

Answer: $(9.27025,\ 11.12975)$

Step-by-step explanation:

Given : Sample size : n= 9

Degree of freedom = df =n-1 =8

Sample mean : $\overline{x}=10.2$

sample standard deviation : $s= 1.5$

Significance level ; $\alpha= 1-0.90=0.10$

Since population standard deviation is not given , so we use t- test.

Using t-distribution table , we have

Critical value = $t_{\alpha/2, df}=t_{0.05 , 8}=1.8595$

Confidence interval for the population mean :

$\overline{x}\pm t_{\alpha/2, df}\dfrac{s}{\sqrt{n}}$

90% confidence interval for the mean value will be :

$10.2\pm (1.8595)\dfrac{1.5}{\sqrt{9}}$

$10.2\pm (1.8595)\dfrac{1.5}{3}$

$10.2\pm (1.8595)(0.5)$

$10.2\pm (0.92975)$

$(10.2-0.92975,\ 10.2+0.92975)$

$(9.27025,\ 11.12975)$

Hence, the 90% confidence interval for the mean value= $(9.27025,\ 11.12975)$

6 0

3 years ago

1/4 divided by 2 = ??

Iteru [2.4K]

Answer:

1/8

Step-by-step explanation:

Hi there!

To divided fractions, you must flip the second fraction and multiply instead.

For example,

1/4 divided by 2 is the same thing as 1/4 x 1/2.

You then multiple straight across to get 1/8.

Really hope this helps!

8 0

3 years ago

Read 2 more answers

Write an equation in slop-intercept form the line with slope 1/4 and y-intercept -7

Licemer1 [7]

When you write an equation in the slope-intercept form

$y=mx+b$

the two coefficients m and b represent, respectively, the slope and the intercept.

So, in your case, m=1/4 and b= -7, which leads to the equation

$y=\dfrac{1}{4}x-7$

7 0

4 years ago

Find the surface area of the part of the sphere x2+y2+z2=81 that lies above the cone z=x2+y2−−−−−−√

TiliK225 [7]

Parameterize the part of the sphere by

$\mathbf s(u,v)=(9\cos u\sin v,9\sin u\sin v,9\cos v)$

with $0\le u\le2\pi$ and $0\le v\le\dfrac\pi4$ . Then

$\mathrm dS=\|\mathbf s_u\times\mathbf s_v\|=81\sin v\,\mathrm du\,\mathrm dv$

So the area of $S$ (the part of the sphere above the cone) is given by

$\displaystyle\iint_S\mathrm dS=81\int_{v=0}^{v=\pi/4}\int_{u=0}^{u=2\pi}\sin v\,\mathrm du\,\mathrm dv=81(2\pi)\left(1-\dfrac1{\sqrt2}\right)=(162-81\sqrt2)\pi$

4 0

4 years ago