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forsale [732]
3 years ago
8

Suppose that you and a friend are playing cards and decide to make a bet. If you draw three face cards, where a face card is a J

ack, a Queen, or a King, in succession from a standard deck of 52 cards without replacement, you win $40. Otherwise, you pay your friend $10. What is the expected value of your bet? Round your answer to the nearest cent, if necessary.
Mathematics
1 answer:
Nataly_w [17]3 years ago
3 0

Answer:

Step-by-step explanation:

Expected value of the bet =

<h3>P(you make the correct draw) * 40 + P(you do not make the correct draw) * (-10) = </h3>

(4/52)(4/51)(4/50) * 40 + (1 - (4/52)(4/51)(4/50)) * (-10) =

(64/132600) * 40 + (1 - 64/132600) *(-10) =

64/3315 + (132536/132600) * (-10) =

64/3315 - (132536/13260) =

64/3315 - 33134/3315 =

-33070/3315 =

-9.97586726998 =

-$9.98, rounded to the nearest cent  

(i.e., the expected value of the bet is a loss of $9.98)

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Both sets of values have an average of 13. Is Set A's standard deviation smaller, larger, or about the same as Set B's? (Note: T
Softa [21]

Answer:

  Set A's standard deviation is larger than Set B's

Step-by-step explanation:

Standard deviation is a measure of variation. One way to judge the value of standard deviation is by looking at the range of the data. In general, a dataset with a smaller range will have a smaller standard deviation.

The range of data Set A is 25-1 = 24.

The range of data Set B is 18-8 = 10.

Set A's range is larger, so we expect its standard deviation to be larger.

__

The standard deviation is the root of the mean of the squares of the differences from the mean. In Set A, the differences are ±12, ±11, ±10. In Set B, the differences are ±5, ±3, ±1. We don't actually need to compute the RMS difference to see that it is larger for Set A.

Set A's standard deviation is larger than Set B's.

5 0
3 years ago
The student-to-faculty ratio at a small college is 17 to 3. The total number of students and faculty is 740. How many faculty me
ryzh [129]

17+3=20

740/20=37 Classes

37 classes x 3 faculty members=111

3 0
3 years ago
Can someone help me find the midpoint?
ioda

Answer:

(6,-2.5)

Step-by-step explanation:

The formula for the midpoint between two points is:

(\frac{x_{1} + x_{2}}{2},\frac{y_{1}+y_{2}}{2})

Now we substitute

We have than (9, -1) is (x_{1}, y_{1}) and (3, - 4) is (x_{2}, y_{2})

So:

(\frac{(9) + (3)}{2},\frac{(-1)+(-4)}{2})\\\\(-1) + (-4) = -5\\9 + 3 = 12\\

So, we have:

(\frac{12}{2}, \frac{-5}{2})\\\\12 / 2 = 6\\-5 / 2 = -2.5\\\\(6, -2.5)

<h2>(6,-2.5)</h2><h2 />

I can do a graphic explanation if you want.

6 0
3 years ago
What is the first step needed to solve 2 over 5 multiplied by x minus 6 equals negative 16 ? (1 point) Subtract 16 from both sid
AfilCa [17]

Answer:

The first step is Add 6 to both sides

Step-by-step explanation:

we have

\frac{2}{5}x-6=-16

Solve for x

That means ----> isolate the variable x

step 1

Adds 6 both sides

\frac{2}{5}x-6+6=-16+6

\frac{2}{5}x=-10

step 2

Multiply by 5/2 both sides

\frac{2}{5}x(\frac{5}{2})=-10(\frac{5}{2})

x=-25

therefore

The first step is Add 6 to both sides

8 0
3 years ago
Read 2 more answers
1/2 (4x -2) - 2/3 (6x + 9) ≤ 4
KatRina [158]
Answer: x ≤ -5.5

reason:

first, multiply 4x and -2 by 1/2 and 6x and 9 by -2/3.
this makes the equation 2x-1-4x-6 ≤ 4
combine like terms to make it -2x-7 ≤ 4
add 7 to both sides to get -2x ≤ 11
divide both sides by -2 and get x ≤ -5.5
3 0
4 years ago
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