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3 years ago

Plz help me i am stuck

Mathematics

1 answer:

Minchanka [31]3 years ago

8 0

Given:

The two statements.

To find:

The probability of an impossible event.

The probability of a certain event.

Solution:

Formula for probability is:

$P=\dfrac{\text{Possible favorable outcomes}}{\text{Total number of outcomes}}$

For an impossible event, the possible favorable outcomes is 0. So,

$P=\dfrac{0}{\text{Total number of outcomes}}$

$P=0$

For a certain event (sure event), the possible favorable outcomes is equal to total number of outcomes. So,

$P=\dfrac{\text{Total number of outcomes}}{\text{Total number of outcomes}}$

$P=1$

Therefore, an event that is impossible has probability 0 and an event that is certain has probability 1.

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Evaluate the definite integral. <br> 1 x4(1 + 2x5)5 dx.

Nata [24]

Answer:

Step-by-step explanation:

Given the definite integral $\int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx$ , we to evaluate it. Using integration by substitution method.

Let u = 1-2x⁵ ...1

du/dx = -10x⁴

dx = du/-10x⁴.... 2

Substitute equation 1 and 2 into the integral function and evaluate the resulting integral as shown;

$= \int\limits {\dfrac{x^4}{u^5} } \, \dfrac{du}{-10x^4}$

$= \dfrac{-1}{10} \int\limits {\dfrac{du}{u^5} } \\\\= \dfrac{-1}{10} \int\limits {{u^{-5}du } \\= \dfrac{-1}{10} [{\frac{u^{-5+1}}{-5+1}] \\\\= \dfrac{-1}{10} ({\frac{u^{-4}}{-4})\\\\$

$= \dfrac{u^{-4}}{40} \\\\\\= \dfrac{1}{40u^4} +C$

substitute u = 1-2x⁵ into the result

$= \dfrac{1}{40(1-2x^5)^4} +C$

Hence $\int\limits {\dfrac{x^4}{(1-2x^5)^5} } \, dx$ $= \dfrac{1}{40(1-2x^5)^4} +C$

5 0

3 years ago

Christopher is going to install wallpaper on the four walls of his room. Two of the walls are 14 feet long by 9 feet high. The o

Aliun [14]

Given:
2 walls - 14ft by 9ft
2 walls - 20ft by 9ft

Wall 1 & 2 = 14ft * 9ft = 126 ft² x 2 = 252 ft²
Wall 3 & 4 = 20ft * 9ft = 180 ft² x 2 = 360 ft²

Total area = 252 ft² + 360 ft² = 612 ft²

Cost of 1 single roll: $20
612 ft² ÷ 18 ft² = 34 rolls * $20 = $680

Cost of double roll: $40
612 ft² ÷ 54 ft² = 11.33 rolls ⇒ 12 double rolls
12 * $40 = $480

If Christopher opts for 1 single roll of wallpaper, he'll spend $680.
If he opts for double roll of wallpaper, he'll spend $480.

Double roll of wallpaper is the cheaper option. He'll save $200 if he'll buy the double roll of wallpaper.

4 0

3 years ago

Read 2 more answers

What is the vertex form of this equation x^2-20x+91=7

lakkis [162]

Here’s the answers have a good one