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Arte-miy333 [17]
3 years ago
5

Grace hit 12 balls in the batting cage out of 20 pitches. Tomorrow she is going to go to the same batting cage and get 30 pitche

s.
Use experimental probability to predict how many of the 30 pitches she will hit.
Mathematics
1 answer:
bearhunter [10]3 years ago
6 0

Answer:

she is expected to hit 18 out of the 30 pitches

Step-by-step explanation:

In this question, we are required to use experimental probability to make a prediction.

From the hits she has today, we can estimate the number of hits she might be getting tomorrow.

Since she made 12 hits out of 20 today, the probability that she has a hit will be 12/20 = 3/5

Now if she is having 30 pitches tomorrow, the expected number of hits would be the probability of getting a hit multiplied by the total number of pitches.

That would be 3/5 * 30 = 18 pitches

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Step-by-step explanation:

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Suppose that you randomly draw one card from a standard deck of 52 cards. After writing down which card was drawn, you replace t
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Answer:

0.139

Step-by-step explanation:

We are given that

Total number of cards=52

n=18

We have to find the probability of drawing at least 7 spades

Total number of spaded in deck of 52 cards=13

Probability  of getting spade=p=\frac{13}{52}=\frac{1}{4}

Probability,P(E)=\frac{favorable\;cases}{total\;number\;of\;cases}

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By binomial theorem of probability

P(X=x)=\binom{n}r}p^rq^{n-r}

P(x\geq 7)=1-P(x\leq 6)

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The probability of drawing at least 7 spades=0.139

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3 years ago
if a bag contains 2 red marbles, 3 blue marbles, 5 yellow marbles and 2 green marbles, if a marble is randomly selected what is
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The values of h and r to maximize the volume are r = 4 and h = 2

<h3>The formula for h in terms of r</h3>

From the question, we have the following equation

2r + 2h = 12

Divide through by 2

r + h = 6

Subtract r from both sides of the equation

h = 6 - r

Hence, the formula for h in terms of r is h = 6 - r

<h3>Formulate a function V(r)</h3>

The volume of a cylinder is

V = πr²h

Substitute h = 6 - r in the above equation

V = πr²(6 - r)

Hence, the function V(r) is V = πr²(6 - r)

<h3>The single critical point</h3>

V = πr²(6 - r)

Expand

V = 6πr² - πr³

Integrate

V' = 12πr - 3πr²

Set to 0

12πr - 3πr² = 0

Divide through by 3π

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Factor out r

r(4 - r) = 0

Divide through by 4

4 - r = 0

Solve for r

r = 4

Hence, the single critical point on the interval [0. 6] is r = 4

<h3>Prove that the critical point is a global maximum</h3>

We have:

V = πr²(6 - r)

and

V' = 12πr - 3πr²

Determine the second derivative

V'' = 12π - 6πr

Set r = 4

V'' = 12π - 6π* 4

Evaluate the product

V'' = 12π - 24π

Evaluate the difference

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Because V'' is negative, then the single critical point is a global maximum

<h3>The values of h and r to maximize the volume</h3>

We have

r = 4  and h = 6 - r

Substitute r = 4  in h = 6 - r

h = 6 - 4

Evaluate

h = 2

Hence, the values of h and r to maximize the volume are r = 4 and h = 2

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