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2 years ago

9

A cylinder has a surface area of 150π inches2 . What is its height if the radius is 5 inches?

2 answers:

Masteriza [31]2 years ago

8 0

15inches
Double the radius is 10 which is the diameter and 150π divide by 10<span>π equal to 15 inches</span>

Aloiza [94]2 years ago

8 0

Using the formula

h=(A/2πr)﹣r
Plug in the values in the equation
h = (150π/2π5)-5
(π would cancel π and 2×5=10. Therefore 150÷10=15)
h= 15-5
h = 10

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Which two expressions is equivalent to 8(5+x)

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40 + 8x

Step-by-step explanation:

Distribute the 8 by multiplying by each value inside the parentheses.

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2 years ago

The co-ordinate of the point whose abscissa is -3 and ordinate is 0 is (0,-3)

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2 years ago

The prior probabilities for events A1 and A2 are P(A1) = 0.35 and P(A2) = 0.50. It is also known that P(A1 ∩ A2) = 0. Suppose P(

forsale [732]

Answer:

Step-by-step explanation:

Hello!

Given the probabilities:

P(A₁)= 0.35

P(A₂)= 0.50

P(A₁∩A₂)= 0

P(BIA₁)= 0.20

P(BIA₂)= 0.05

a)

Two events are mutually exclusive when the occurrence of one of them prevents the occurrence of the other in one repetition of the trial, this means that both events cannot occur at the same time and therefore they'll intersection is void (and its probability zero)

Considering that P(A₁∩A₂)= 0, we can assume that both events are mutually exclusive.

b)

Considering that $P(BIA)= \frac{P(AnB)}{P(A)}$ you can clear the intersection from the formula $P(AnB)= P(B/A)*P(A)$ and apply it for the given events:

$P(A_1nB)= P(B/A_1) * P(A_1)= 0.20*0.35= 0.07$

$P(A_2nB)= P(B/A_2)*P(A_2)= 0.05*0.50= 0.025$

c)

The probability of "B" is marginal, to calculate it you have to add all intersections where it occurs:

P(B)= (A₁∩B) + P(A₂∩B)= 0.07 + 0.025= 0.095

d)

The Bayes' theorem states that:

$P(Ai/B)= \frac{P(B/Ai)*P(A)}{P(B)}$

Then:

$P(A_1/B)= \frac{P(B/A_1)*P(A_1)}{P(B)}= \frac{0.20*0.35}{0.095}= 0.737 = 0.74$

$P(A_2/B)= \frac{P(B/A_2)*P(A_2)}{P(B)} = \frac{0.05*0.50}{0.095} = 0.26$

I hope it helps!

5 0

2 years ago

What is f–1(8)??<br><br> Please select the best answer

notka56 [123]

Answer:

$f^{-1}(8)=\frac{3}{2}$

Step-by-step explanation:

Given f(x)= $2x+5$

We have to find $f^{-1}(8)$

In order to find $f^{-1}(x)$ we have to make x as the subject of the formula

Let us assume f(x)=y

⇒ $2x+5=y$

Subtracting both sides by 5

$2x+5-5=y-5$

$2x=y-5$

Dividing both sides by 2

$\frac{2x}{2}=\frac{y-5}{2}$

⇒ $x=\frac{y-5}{2}$

Now substituting y with x

we have $f^{-1}(x)=\frac{x-5}{2}$

Now $f^{-1}(8)=\frac{8-5}{2}$

= $\frac{3}{2}$

So option (ii) is correct

5 0

2 years ago

Read 2 more answers

What is the solution set for 2x+5y>-1 and 4x-3<-3?

bekas [8.4K]

PROBLEM ONE

•

Solving for x in 2x + 5y > -1.

•

Step 1 ) Subtract 5y from both sides.

2x + 5y > -1

2x + 5y - 5y > -1 - 5y

2x > -1 - 5y

Step 2 ) Divide both sides by 2.

2x > -1 - 5y

$\displaystyle\frac{2x}{2} > \displaystyle\frac{-1 - 5y}{2}$

$\displaystyle\ x > \frac{-1 - 5y}{2}$

So, the solution for x in 2x + 5y > -1 is...

$\displaystyle\ x > \frac{-1 - 5y}{2}$

•

Solving for y in 2x + 5y > -1.

•

Step 1 ) Subtract 2x from both sides.

2x + 5y > -1

2x - 2x + 5y > -1 - 2x

5y > -1 - 1x

Step 2 ) Divide both sides by 5.

5y > -1 - 1x

$\displaystyle\frac{5x}{5} > \frac{-1 -1x}{5}$

$\displaystyle\ x > \frac{-1 -1x}{5}$

So, the solution for y in 2x + 5y > -1 is...

$\displaystyle\ x > \frac{-1 -1x}{5}$

•

PROBLEM TWO

•

Solving for x in 4x - 3 < -3.

•

Step 1 ) Subtract 3 from both sides.

4x - 3 < -3

4x -3 - 3 < -3 - 3

4x < 0

Step 2 ) Divide both sides by x.

4x < 0

$\displaystyle\frac{4x}{4}$

x < 0

So, the solution for x in 4x - 3 < -3 is...

x < 0

•

•

- <em>Marlon Nunez</em>

7 0

2 years ago