What is the value of x?<br> O 40<br> 409<br> 0 70<br> 140<br> O 160

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LiRa [457]

The radius of the cylinder's base is 8, so the volume of the cylinder is $\pi8^218\approx3617.28$ (using the approximation of $\pi\approx3.14$ ).

The sphere has radius 6, so the volume of the sphere is $\dfrac43\pi6^3\approx904.32$ .

The volume of the shaded region is the difference between the two: 3617.28 - 904.32 = 2712.96. Rounded to the nearest integer gives an answer of 2713.

3 0

3 years ago

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1: Ken earned $176 from his part-time job this summer. He spent 25% of his money on games. He is going to donate 14 of the rema

tatiyna

The charity will receive $ 11

<h3><u>Solution:</u></h3>

Ken earned $176 from his part-time job this summer

Amount earned = $ 176

He spent 25% of his money on games

Therefore,

Money spent on games = 176 - 25 % of 176

$\text{Money spent on games } = 176 - \frac{25}{100} \times 176\\\\\text{Money spent on games } = 176 - 0.25 \times 176\\\\\text{Money spent on games } = 176 - 44\\\\\text{Money spent on games } = 132$

He is going to donate 1/4 of the remaining money to charity

Reamining amount = 176 - 132 = 44

Therefore,

$Money\ given\ to\ charity = \frac{1}{4} \times 44 = 11$

Thus he gave $ 11 to charity

8 0

3 years ago

Given that z is a standard normal random variable, find z for each situation. The area between 0 and z is .4750. Answer The area

algol13

Answer:

$P(0$

And solving for z we have

$P(Z$

And we can find the value for z with the following excel code:

"=NORM.INV(0.975,0,1)"

And we got z =1.96

$P(Z>z)= 0.1314$

And we can use the complement rule and we got:

$P(Z>z) = 1-P(Z$

$P(Z$

And we can find the value for z with the following excel code:

"=NORM.INV(0.8686,0,1)"

And we got z =1.120

$P(Z$

And we can find the value for z with the following excel code:

"=NORM.INV(0.67,0,1)"

And we got z =0.440

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

We want this probability:

$P(0$

And solving for z we have

$P(Z$

And we can find the value for z with the following excel code:

"=NORM.INV(0.975,0,1)"

And we got z =1.96

For the next part we want to calculate:

$P(Z>z)= 0.1314$

And we can use the complement rule and we got:

$P(Z>z) = 1-P(Z$