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3 years ago

9

A person who is 5 feet tall is standing 108 feet from the base of a tree, and the tree casts a 120 foot shadow. The persons shad

ow is 12 feet in length. What is the height of the tree?

1 answer:

slega [8]3 years ago

4 0

Answer:

50ft

Step-by-step explanation:

let x=height of tree.

AB/DE = BC/EC

The ratio is == x/5 =120/12

x/5 = 10

x = 50

Height of tree is 50 ft.

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Jane babysits for $8 per hour. She earned $240 last week. This equation represents the number of hours, h, Jane babysat last wee

Tatiana [17]

Answer:

30 Hours

Step-by-step explanation:

8h=240

240÷8=30

8 0

3 years ago

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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3 years ago

On this map, Oxford Street is perpendicular to_______ , and Rosewood Street is perpendicular to ________. Assume that the street

melamori03 [73]

Hi there!

We are looking for perpendicular angles, which means the angle between the streets is 90 degrees. So, each time we need to find the street that intersects the given street with a 90 degree angle.

On this map, Oxford Street is perpendicular to Waterloo St., and Rosewood Street is perpendicular to Oak St..

The answers are (in correct order): Waterloo St. and Oak St..
~ Hope this helps you!

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3 years ago

Leokris [45]

<em>Independent variables are variables of a quantity that are not affected by any conditions. </em>

<em>Dependent variables are variables of a quantity that change if conditions relative to that variable changes.</em>

For example, we generally we take x as independent variable by x variable and dependent variable by y variable.

To find the rate of change we get two values of independent variable (x's) and two values of dependent variables (y's) to get two coordinates in form of

(x,1,y1) and (x2,y2).

<h3>And we can find the rate of change by applying slope formula</h3>

$m= \frac{y_2-y_1}{x_2-x_1}$ .

3 0

3 years ago

Please solve whatever this is, I’ll mark whoever gives me the right answer as brainliest!

Reptile [31]

Answer:

y= -a/bx +c/b

m= -a/b

b= c/b

Step-by-step explanation:

Hope this helps

8 0

3 years ago