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1 year ago

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Your friend has locked themselves out of the house, and they need your help to get back in. They have a 15 foot long ladder, and

there is an open window 12 feet above the ground. How far from the of should you hold the ladder while they climb back in

1 answer:

Darina [25.2K]1 year ago

3 0

w = 9 feet far you should hold the ladder while they climb back in

Let the length be $l$ = 15 feet and open window feet above the ground be k= 12 feet

The value of w will be given by the Pythagoras theorem,

Pythagoras theorem: In a right-angled triangle, the square of the long side is equal to the sum of the squares of the other two sides.

It is stated in this formula:

$w^{2} =l^{2}- k^{2} \\\\w^{2}= 15^{2}- 12^{2} \\\\w^{2} = 225-144\\\\w^{2} = 81\\\\w=9$

Hence, w = 9 feet far you should hold the ladder while they climb back in.

Learn more about Pythagoras' theorem here https://brainly.in/question/2829237

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The Slow Ball Challenge or The Fast Ball Challenge.

cupoosta [38]

Answer:

Fast ball challenge

Step-by-step explanation:

Given

Slow Ball Challenge

$Pitches = 7$

$P(Hit) = 80\%$

$Win = \$60$

$Lost = \$10$

Fast Ball Challenge

$Pitches = 3$

$P(Hit) = 70\%$

$Win = \$60$

$Lost = \$10$

Required

Which should he choose?

To do this, we simply calculate the expected earnings of both.

Considering the slow ball challenge

First, we calculate the binomial probability that he hits all 7 pitches

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

Where

$n = 7$ --- pitches

$x = 7$ --- all hits

$p = 80\% = 0.80$ --- probability of hit

So, we have:

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

$P(7) =^7C_7 * 0.80^7 * (1 - 0.80)^{7 - 7}$

$P(7) =1 * 0.80^7 * (1 - 0.80)^0$

$P(7) =1 * 0.80^7 * 0.20^0$

Using a calculator:

$P(7) =0.2097152$ --- This is the probability that he wins

i.e.

$P(Win) =0.2097152$

The probability that he lose is:

$P(Lose) = 1 - P(Win)$ ---- Complement rule

$P(Lose) = 1 -0.2097152$

$P(Lose) = 0.7902848$

The expected value is then calculated as:

$Expected = P(Win) * Win + P(Lose) * Lose$

$Expected = 0.2097152 * \$60 + 0.7902848 * \$10$

Using a calculator, we have:

$Expected = \$20.48576$

Considering the fast ball challenge

First, we calculate the binomial probability that he hits all 3 pitches

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

Where

$n = 3$ --- pitches

$x = 3$ --- all hits

$p = 70\% = 0.70$ --- probability of hit

So, we have:

$P(3) =^3C_3 * 0.70^3 * (1 - 0.70)^{3 - 3}$

$P(3) =1 * 0.70^3 * (1 - 0.70)^0$

$P(3) =1 * 0.70^3 * 0.30^0$

Using a calculator:

$P(3) =0.343$ --- This is the probability that he wins

i.e.

$P(Win) =0.343$

The probability that he lose is:

$P(Lose) = 1 - P(Win)$ ---- Complement rule

$P(Lose) = 1 - 0.343$

$P(Lose) = 0.657$

The expected value is then calculated as:

$Expected = P(Win) * Win + P(Lose) * Lose$

$Expected = 0.343 * \$60 + 0.657 * \$10$

Using a calculator, we have:

$Expected = \$27.15$

So, we have:

$Expected = \$20.48576$ -- Slow ball

$Expected = \$27.15$ --- Fast ball

<em>The expected earnings of the fast ball challenge is greater than that of the slow ball. Hence, he should choose the fast ball challenge.</em>

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2 years ago

Jenn equally shares 40 jellybeans with some friends. Is the number that each friends gets greater than 40 or less than 40? Expla

blagie [28]

I would say that it would be less than. The question says Jenn shared a total of 40 jellybeans equally and to share with others, Jenn would have to divide the jellybeans among her friends. Since she is dividing the jellybeans, the amount each friend gets would be less than the total. Therefore it would be less than 40.

6 0

2 years ago

Probability, The correct answer gets brainliest.

Ostrovityanka [42]

I think it’s 1/4 Buh I’m not sure

8 0

2 years ago

Hey guys! Can u help me with these three questions?

Margaret [11]

Hey guys it equals 12 alight

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2 years ago

What is m∠4 if m∠8 = 40°? A. 50°<br> B. 180° C. 70° D. 40°

Rudik [331]

Answer:

if it right angled

m<4+m<8=90

m<4=90-40=50 is your answer.

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2 years ago