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3 years ago

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A player pays $15 to play a game in which a chip is randomly selected from a bag of chips. The bag contains 10 red chips, 4 blue

chips, and 6 yellow chips. The player wins $5 if a red chip is
selected, $10 if a blue chip is selected, and $20 if a yellow chip is selected. Let the random variable X represent the amount won from the selection of the chip, and let the random variable W
represent the total amount won, where W= X - 15. What is the mean of W?
$10.50
B
$4.50
-$4.50
D
- $6.50
E
-$10.50

2 answers:

adelina 88 [10]3 years ago

4 0

Answer:b. 4.50

Step-by-step explanation:

muminat3 years ago

4 0

Answer:

C. -$4.50

Step-by-step explanation:

To find the mean of W we must first find the mean of X. So, 10/20*5+4/20*10+6/20*20=10.5

Then because mean is impacted by transformations, the mean of W=the mean of X-15=10.5-15=-$4.50

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see the attached figure to better understand the problem

Step-by-step explanation:

we have

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we Know that

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step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

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L(-3, 6) and P(1, -8)

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Find the slope of the segment NM

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N(3, 2) and M(-1,-1)

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Convert to slope intercept form

Isolate the variable y

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$y=\frac{3}{4}x-\frac{9}{4}+2$

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Part B) Find the equation of the right bisector of LP

we Know that

The right bisector is perpendicular to LP and passes through midpoint segment LP

step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

L(-3, 6) and P(1, -8)

substitute the values

$M(\frac{-3+1}{2},\frac{6-8}{2})$

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step 2

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

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we have

L(-3, 6) and P(1, -8)

substitute the values

$m=\frac{-8-6}{1+3}$

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$m=-\frac{14}{4}$

$m=-\frac{7}{2}$

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Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=-\frac{7}{2}$

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step 4

Find the equation of the line in point slope form

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we have

$m=\frac{2}{7}$

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Convert to slope intercept form

Isolate the variable y

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Part C) Find the equation of the altitude from N

we Know that

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step 1

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

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step 2

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

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we have

$m_1=-\frac{7}{2}$

so

$m_2=\frac{2}{7}$

step 3

Find the equation of the line in point slope form

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we have

$m=\frac{2}{7}$

$point\ N(3,2)$

substitute

$y-2=\frac{2}{7}(x-3)$

step 4

Convert to slope intercept form

Isolate the variable y

$y-2=\frac{2}{7}x-\frac{6}{7}$

$y=\frac{2}{7}x-\frac{6}{7}+2$

$y=\frac{2}{7}x+\frac{8}{7}$

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