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Elena L [17]
2 years ago
8

Sophia and Scott each open a bank account with an initial deposit of $50 each. Scott planned to save 30% of his earnings from hi

s after-school job. The job pays $8 per hour, and he works 25 hours each week. For four weeks, Sophia saved $45 per week. After that, she saved an additional $30 per week. During which WEEK will they have the same amount of money in their bank accounts?
Mathematics
1 answer:
scoray [572]2 years ago
6 0

Answer:

During the 9th week

Step-by-step explanation:

Scott: 50 + (0.3)(8×25)t

= 50 + 60t

Sophia: 50 + 45t + 30(t-4)

= -70 + 75t

60t + 50 = 75t - 70

15t = 120

t = 8

After 8 weeks they will have the same amount,

Which is during the 9th week

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Suppose you roll a pair of honest dice. If you roll a total of 7 you win $22, if you roll a total of 11 you win $66, if you roll
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Answer:

The expected payoff for this game is -$1.22.

Step-by-step explanation:

It is given that a pair of honest dice is rolled.

Possible outcomes for a dice = 1,2,3,4,5,6

Two dices are rolled then the total number of outcomes = 6 × 6 = 36.

\{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),\\(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),\\(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}

The possible ways of getting a total of 7,

{ (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) }

Number of favorable outcomes = 7

Formula for probability:

Probability=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}

So, the possibility of getting a total of 7 = \frac{6}{36}=\frac{1}{6}

The possible ways of getting a total of 11,

{(5,6), (6,5)}

So, the probability of getting a total of 11 = \frac{2}{36} = \frac{1}{18}

Now, other possible rolls = 36 - 6 - 2 = 36 - 8 = 28,

So, the probability of getting the sum of numbers other than 7 or 11 = \frac{28}{36} = \frac{7}{9}

Since, for the sum of 7, $ 22 will earn, for the sum of 11, $ 66 will earn while for any other total loss is $11,

Hence, the expected value for this game is

\frac{1}{6}\times 22+\frac{1}{18}\times 66-\frac{7}{9}\times 11

\frac{11}{3}+\frac{11}{3}-\frac{77}{9}

\frac{22}{3}-\frac{77}{9}

\frac{66-77}{9}

-\frac{11}{9}

-1.22

Therefore the expected payoff for this game is -$1.22.

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CORRECTED QUESTION

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