All categories

4 years ago

Factor this problem ? 125 +27y^3

Mathematics

1 answer:

koban [17]4 years ago

6 0

Answer:

(5 + 3y)(25 - 15y + 9y²)

Step-by-step explanation:

This is a sum of cubes and factors in general as

a³ + b³ = (a + b)(a² - ab + b²), thus

125 + 27y³

= 5³ + (3y)³ with a = 5 and b = 3y

= (5 + 3y)(5² - 5(3y) + (3y)² )

= (5 + 3y)(25 - 15y + 9y²)

You might be interested in

A survey of 85 families showed that 36 owned at least one DVD player. Find the 99% confidence interval estimate of the true prop

Katyanochek1 [597]

Answer: $(0.367,\ 0.473)$

Step-by-step explanation:

The confidence interval for population mean is given by :-

$\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

, where $\hat{p}$ is the sample proportion, n is the sample size , $z_{\alpha/2}$ is the critical z-value.

Given : Significance level : $\alpha:1-0.99=0.01$

Sample size : n= 85

Critical value : $z_{\alpha/2}=2.576$

Sample proportion: $\hat{p}=\dfrac{36}{85}\approx0.42$

Now, the 99% confidence level will be :

$\hat{p}\pmz_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.42\pm(2.576)\sqrt{\dfrac{0.42(1-0.42)}{85}}\\\\\approx0.42\pm0.053\\\\=(0.42-0.053,\ 0.42+0.053)=(0.367,\ 0.473)$

Hence, the 99% confidence interval estimate of the true proportion of families who own at least one DVD player is $(0.367,\ 0.473)$

3 0

3 years ago

9–5(x+4)=3(2–x) help!!!!!1

netineya [11]

Answer:

-17/2 =x

Step-by-step explanation:

9–5(x+4)=3(2–x)

Distribute

9 - 5x - 20 = 6 -3x

Combine like terms

-5x-11 = 6-3x

Add 5x to each side

-5x-11 +5x = 6-3x+5x

-11 = 6+2x

Subtract 6 from each side

-11-6 = 6+2x-6

-17 = 2x

Divide by 2

-17/2 = 2x/2

-17/2 =x

3 0

4 years ago

Read 2 more answers

0.25k+1.5-k-3.50.25k+1.5−k−3.5. please I need help who ever answers it first will become brainliest

Vilka [71]

Answer:

0.25k+1.5−k−3.5

Subtract k from 0.25k.

−0.75k+1.5−3.5

Subtract

3.5 from 1.5.

−0.75k−2

Step-by-step explanation:

5 0

3 years ago

P + 46 = 94, what is p?

Natalka [10]

<h2>P is equal to:</h2>

48.

Because 46+48 equals 94.

You can easily find out equations to this by subtracting the 46 from 94 to see what p is equal to.

4 0

2 years ago

The length of the diagonal of a wooden cube is 24 cm. The cube is cut into the cylinder of the

jek_recluse [69]

The biggest possible volume of the cylinder will be $2089.497\hspace{1mm}\text{cm}^3$ .

<h3>What will be the diameter and height of the cylinder obtained from a cube and what are the formulas for the diagonal of a cube and the volume of a cylinder?</h3>

If a cylinder with the biggest possible volume is cut inside the cube, the height of the cylinder and the diameter of the cylinder will be equal to the side length of the cube.
For example, consider the following figure in which the cylinder is cut inside of the cube and since the side length of the cube is $x$ , the diameter and the height of the cylinder are also $x$
If the side length of a cube is $x$ unit, then its diagonal will be $x\sqrt{3}$ unit.
The formula for the volume of a cylinder is $V=\pi r^2h$ , where $r$ is the radius and $h$ is the height of the cylinder. If $d$ is the diameter, then $r=\frac{d}{2}$ .

Now, given that the diagonal of the cube is $24$ cm. So, if the side length of the cube is $x$ cm, then we must have

$x\sqrt{3}=24\\\Longrightarrow x=\frac{24}{\sqrt{3}}\\\Longrightarrow x=8\sqrt{3}$

Thus, the side length of the cube is $8\sqrt{3}$ cm.

So, the height of the cylinder with maximum volume will be $h=8\sqrt{3}$ cm and the diameter will be $d=8\sqrt{3}$ cm i.e. the radius will be $r=\frac{d}{2}=\frac{8\sqrt{3}}{2}=4\sqrt{3}$ cm.

So, using the above formula for the volume of a cylinder, we get

$V=\pi r^{2}h=\pi\times (4\sqrt{3})^2\times 8\sqrt{3}=2089.497\hspace{1mm}\text{cm}^3$ .

Therefore, the biggest possible volume of the cylinder will be $2089.497\hspace{1mm}\text{cm}^3$ .

To know more about volume, refer: brainly.com/question/1972490

#SPJ9

4 0

2 years ago

Read 2 more answers