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vredina [299]
3 years ago
9

In the New York State Numbers Lottery, you pay $1 and can bet that the sum of the numbers that come up is 13. The probability of

winning is 0.075, and if you win, you win $6.50, which is a profit of $5.50. If you lose, you lose $1. What is the expected value of your profit? Is it an expected gain or an expected loss?
Mathematics
1 answer:
Harman [31]3 years ago
7 0

Answer:

The expected value of profit is -0.5125. This is expected loss as value is negative.        

Step-by-step explanation:

We are given the following in the question:

P(winning) = 0.075

Thus,

P(Loosing) =

1 - 0.075 = 0.925

If we win we gain a profit of $5.50 and if we loose the lottery, we loose $1.

Thus, we can form the probability distribution in the following manner:

  Event:      Winning       Loosing

Profit(x):      +5.50               -1

     P(x):       0.075             0.925

We have to calculate the expected value of the profit.

E(X) = \displaystyle\sum x_i(P(x_i))\\E(x) = +5.50(0.075) + (-1)(0.925)\\E(x) = -0.5125

Thus, the expected value of profit is -0.5125. This is expected loss as value is negative.

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The hypotenuse of a right triangle is 10cm long. The longer leg is 2cm longer than the shorter leg. Find the side lengths of the
Crazy boy [7]
We need Pythagoras theorem here
a^2+b^2 = c^2
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c = length of hypotenuse

Let S=shorter leg, in cm, then longer leg=S+2 cm
use Pythagoras theorem
S^2+(S+2)^2 = (10 cm)^2
expand (S+2)^2
S^2 +   S^2+4S+4  = 100 cm^2   [collect terms and isolate]
2S^2+4S =  100-4 = 96 cm^2
simplify and form standard form of quadratic
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Solve by factoring
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or                                   (S-6)=0, S=6
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5 0
3 years ago
Consider the following system of equations: 10 + y = 5x + x2 5x + y = 1 The first equation is an equation of a . The second equa
aleksley [76]

Answer: The first equation is an equation of a parabola. The second equation is an equation of a line.

Explanation:

The first equation is,

10+y=5x+x^2

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The second equation is,

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In this equation the degree of x is 1 and the degree of y is 1. The degree of both variables are same. Since both variables have same degree which is 1, therefore it is linear equation and it forms a line.

Therefore, the first equation is an equation of a parabola. The second equation is an equation of a line.

5 0
3 years ago
Read 2 more answers
m∠WYX=(2x−1)° and m∠WYZ=(4x+1)°. If ∠WYX and ∠WYZ are complementary, what is the measure of each angle?
Neko [114]

We are given : m∠WYX=(2x−1)° and m∠WYZ=(4x+1)°.

∠WYX and ∠WYZ are complementary.

We know, sum of complementary angles is = 90°.

So, we need to add ∠WYX and ∠WYZ and set it equal to 90°.

m∠WYX + m∠WYZ = 90°.

Plugging values of ∠WYX and ∠WYZ in the above equation, we get

(2x−1)° + (4x+1)° = 90°.

Removing parentheses from both sides,

2x-1 + 4x+1 =90.

Combining like terms,

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6x +0 =90.

6x=90.

Dividing both sides by 6.

6x/6 =90/6

x= 15.

Plugging value of x=15.

m∠WYX=(2x−1)° = 2*15 -1 = 30 -1 =29

m∠WYZ=(4x+1)° = 4*15 +1 = 60+1 = 61.

Therefore, ∠WYX=29° and ∠WYZ=61°.



5 0
3 years ago
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