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2 years ago

Write the expression as a sum of a difference of cubes and factor it: 1/64m^3+1000

Mathematics

1 answer:

yarga [219]2 years ago

3 0

Answer:

(1\64m + 20) (1\4096m^2 - 5\322m + 100)

Step-by-step explanation:

use a^3 + b^3 = (a+b)(a^2 - ab + b^2) to factor the expression = (1\64m+10)(1\4096m^2 - 10\64m + 100)

reduce the fractions with 2 = (1\64m + 10)(1\4096m^2 - 5\32m + 100)

= (1\64m + 20) (1\4096m^2 - 5\322m + 100)

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The promising alternative energy sources currently under development are fuel cell technology and large-scale solar energy power

Mumz [18]

Answer:

Step-by-step explanation:

a) Denote the event of commercially availability of f_uel cell technology as F_, commercial availability of solar power technology as S

Write the probability of energy supplied by these energy sources in the next 10 years

P(energy supplied) = P(S ∪ F) -----(1)

Rewrite eqn (1)

P(energy supplied) = P(S) + P(F) - P(F) P(S) ----(2)

substitute 0.85 for P(S) and 0,7 for P(F) in eqn (2) to find the probability of energy supplied by these energy sources

P(energy supplied) = 0.85 + 0.7 - (0.7 * 0.85)

= 0.85 + 0.7 - (0.595)

= 1.55 - 0.595

= 0.955

Therefore, the probability that there will be energy supplied by these two alternative sources in the next 10 years is 0.955

B) write the probability of only one source of energy available

P(only one source of energy available) = $P(\bar F S)$ ∪ $P( \bar S F)$ ---(3)

Rewrite the equation (3)

P(only one source of energy available) =

$=P(\bar F S)+P(\bar S F)\\\\=\{[1-P(F)]P(S)+[1-P(S)]P(F)\}---(4)$

$=\{[1-0.7]0.85+[1-0.85]0.7\}\\\\=0.255+0.105\\\\=0.36$

Therefore,The probability that only one of the two alternative energy sources will be commercially viable in the next 10 years is 0.36

4 0

2 years ago

Jeri drew the following model to represent the fraction. What's wrong with her model?

Shtirlitz [24]

Answer: were is the model

6 0

3 years ago

PLS PLS HELP FIND THE VOLUME!!! PLS PLS I GIVE U ALL MY POINTS

ICE Princess25 [194]

Answer:

1232

Step-by-step explanation:

Step 1: 8x14 to find the base

Step 2: Base times Height

Good Luck! And have a great day!

5 0

2 years ago

Read 2 more answers

Statements that are true for a cylinder with radius r and height h.

vampirchik [111]

Answer:

Only the second and third statements are correct:

Doubling r quadruples the volume.

Doubling h doubles the volume.

Step-by-step explanation:

The volume of a cylinder is given by:

$\displaystyle V=\pi r^2h$

We can go through each statement and examine its validity.

Statement 1)

If the radius is doubled, our new radius is now 2r. Hence, our volume is:

$\displaystyle V=\pi (2r)^2h=4\pi r^2h$

So, compared to the old volume, the new volume is quadrupled the original volume.

Statement 1 is not correct.

Statement 2)

Using the previous reasonsing, Statement 2 is correct.

Statement 3)

If the height is doubled, our new height is now 2h. Hence, our volume is:

$V=\pi r^2(2h)=2\pi r^2h$

So, compared to the old volume, the new volume has been doubled.

Statement 3 is correct.

Statement 4)

Statement 4 is not correct using the previous reasonsing.

Statement 5)

Doubling the radius results in 2r and doubling the height results in 2h. Hence, the new volume is:

$V=\pi (2r)^2(2h)=\pi (4r^2)(2h)=8\pi r^2h$

So, compared to the old volume, the new volume is increased by eight-fold.

Statement 5 is not correct.

7 0

2 years ago

The burning time of a very large candle is normally distributed with mean of 2500 hours and standard deviation of 20 hours. Find

dezoksy [38]

Answer: C.-1.5

Step-by-step explanation:

Given: The burning time of a very large candle is normally distributed with mean $(\mu)$ of 2500 hours and standard deviation $(\sigma)$ of 20 hours.

Let X be a random variable that represent the burning time of a very large candle.

Formula: $Z=\dfrac{X-\mu}{\sigma}$

For X = 2470

$Z=\dfrac{2470-2500}{20}\\\\\Rightarrow\ Z=\dfrac{-30}{20}\\\\\Rightarrow\ Z=\dfrac{-3}{2}\\\\\Rightarrow\ Z=-1.5$

So, the z-score they corresponds to a lifespan of 2470 hours. =-1.5

Hence, the correct option is C.-1.5.

7 0

2 years ago