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3 years ago

14

If a $2 bet is placed for a chance to win $500 for drawing a 10 of any suit from a standard deck of cards, what is the value of

expectation?
A. $2
B. $250
C. $125
D. $500

1 answer:

OverLord2011 [107]3 years ago

6 0

P(winning) = 4/52 = 1/13 P(losing) = 48/52 = 12/13 Expected value = 1/13 ($498) + 12/13 (−$2) = $498/13 − $24/13 = $474/13 = $36.46

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X = -2y + 300 3y = 800 - 4x

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Answer:

Please check the explanation.

Step-by-step explanation:

Given the inequality

-2x < 10

-6 < -2x

<u>Part a) Is x = 0 a solution to both inequalities</u>

FOR -2x < 10

substituting x = 0 in -2x < 10

-2x < 10

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0 < 10

TRUE!

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<u>Part b) Is x = 4 a solution to both inequalities</u>

FOR -2x < 10

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FOR -6 < -2x

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FALSE!

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x = 4 is NOT a solution to both inequalites.

Part c) Find another value of x that is a solution to both inequalities.

<u>solving -2x < 10</u>

$-2x\:$

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$\left(-2x\right)\left(-1\right)>10\left(-1\right)$

Simplify

$2x>-10$

Divide both sides by 2

$\frac{2x}{2}>\frac{-10}{2}$

$x>-5$

$-2x-5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-5,\:\infty \:\right)\end{bmatrix}$

<u>solving -6 < -2x</u>

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switch sides

$-2x>-6$

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$\left(-2x\right)\left(-1\right)$

Simplify

$2x$

Divide both sides by 2

$\frac{2x}{2}$

$x$

$-6$

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$\left(-\infty \:,\:3\right)$

$\left(-5,\:\infty \:\right)$

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$\left(-\infty \:,\:3\right)$ and $\left(-5,\:\infty \:\right)$

As x = 1 is included in both intervals.

so x = 1 would be another solution common to both inequalities.

<h3>SUBSTITUTING x = 1</h3>

FOR -2x < 10

substituting x = 1 in -2x < 10

-2x < 10

-3(1) < 10

-3 < 10

TRUE!

Thus, x = 1 satisfies the inequality -2x < 10.

∴ x = 1 is the solution to the inequality -2x < 10.

FOR -6 < -2x

substituting x = 1 in -6 < -2x

-6 < -2x

-6 < -2(1)

-6 < -2

TRUE!

Thus, x = 1 satisfies the inequality -6 < -2x

∴ x = 1 is the solution to the inequality -6 < -2x.

Conclusion:

x = 1 is a solution common to both inequalites.

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3 years ago