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3 years ago

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Container A is cylinder with a radius of 10 units and a height of 10 units. A right cone has been carved from its base and has a

height of 10 units. Container B has the same radius as container A. Which statement derives the formula to find the volume of container B? π(102)(10) − π (102)(10) 2[π(102)(10) − π(102)(10)] π(102)(10) − π(102)(10) 2[π(102)(10) − π(102)(10)]

1 answer:

jekas [21]3 years ago

7 0

Complete Question

The complete question is shown on the first uploaded image

Answer:

The correct option is C

Step-by-step explanation:

From the question we are told that

The radius of the cylinder is $r = 10 \ units$

The height of the right cone is $h = 10 \ units$

From the diagram we see that container B is a semi -sphere and the volume of a semi-sphere is mathematically represented as

$V = \frac{2}{3} \pi r^3$

The question tells us that both container has the same radius so

$V = \frac{2 \pi }{3} 10^3$

This equivalent to

$V = \pi (10^2) (10) - \frac{1}{3} (10^2) (10)$

Solving the equation will produce the same formula as

$V = \frac{2 \pi }{3} 10^3$

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Approximately 5% of calculators coming out of the production lines have a defect. Fifty calculators are randomly selected from t

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Answer:

0.2611 = 26.11% probability that exactly 2 calculators are defective.

Step-by-step explanation:

For each calculator, there are only two possible outcomes. Either it is defective, or it is not. The probability of a calculator being defective is independent of any other calculator, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

5% of calculators coming out of the production lines have a defect.

This means that $p = 0.05$

Fifty calculators are randomly selected from the production line and tested for defects.

This means that $n = 50$

What is the probability that exactly 2 calculators are defective?

This is P(X = 2). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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Answer:

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4 years ago

Write y=x^2+16x−7 in vertex form. Then identify the vertex.

WARRIOR [948]

The vertex form of the function is y = (x + 8)² - 71

The vertex is (-8 , -71)

Step-by-step explanation:

The vertex form of the quadratic equation y = ax² + bx + c is

y = a(x - h)² + k, where

(h , k) are the coordinates of the vertex point
a, b, c are constant where a is the leading coefficient of the function (coefficient of x²) , b is the coefficient of x and c is the y-intercept
$h=\frac{-b}{2a}$
k is the value of y when x = h

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∵ y = ax² + bx + c

∴ a = 1 , b = 16 , c = -7

∵ $h=\frac{-b}{2a}$

∴ $h=\frac{-16}{2(1)}$

∴ h = -8

To find k substitute y by k and x by -8 in the equation above

∵ k is the value of y when x = h

∵ h = -8

∴ k = (-8)² + 16(-8) - 7 = -71

∵ The vertex form of the quadratic equation is y = a(x - h)² + k

∵ a = 1 , h = -8 , k = -71

∴ y = (1)(x - (-8))² + (-71)

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∵ (h , k) are the coordinates of the vertex point

∵ h = -8 and k = -71

∴ The vertex is (-8 , -71)

The vertex form of the function is y = (x + 8)² - 71

The vertex is (-8 , -71)

Learn more:

You can learn more about quadratic equation in brainly.com/question/9390381

#LearnwithBrainly

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3 years ago

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