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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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Problem 5 (4+4+4=12) We roll two fair 6-sided dice. Each one of the 36 possible outcomes is assumed to be equally likely. 1) Fin
tekilochka [14]

Answer:

1

p(b) =  \frac{1}{6}

2

p(k) =  \frac{1}{3}

3

P(a) =  \frac{1}{3}

Step-by-step explanation:

Generally when two fair 6-sided dice is rolled the doubles are

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

The total outcome of doubles is N = 6

The total outcome of the rolling the two fair 6-sided dice is

n = 36

Generally the probability that doubles (i.e., having an equal number on the two dice) were rolled is mathematically evaluated as

p(b) =  \frac{N}{n}

p(b) =  \frac{6}{36}

p(b) =  \frac{1}{6}

Generally when two fair 6-sided dice is rolled the outcome whose sum is 4 or less is

(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1)

Looking at this outcome we see that there are two doubles present

So

The conditional probability that doubles were rolled is mathematically represented as

p(k) =  \frac{2}{6}

p(k) =  \frac{1}{3}

Generally when two fair 6-sided dice is rolled the number of outcomes that would land on different numbers is L = 30

And the number of outcomes that at least one die is a 1 is W = 10

So

The conditional probability that at least one die is a 1 is mathematically represented as

P(a) =  \frac{W}{L}

=> P(a) =  \frac{10}{30}

=> P(a) =  \frac{1}{3}

3 0
2 years ago
suppose the commute times for employees of a large company follow a normal distribution. if the mean time is 18 minutes and the
stepladder [879]

Answer:I think A

Step-by-step explanation:

Hopefully I am right

4 0
2 years ago
Read 2 more answers
A baseball costs $4.00.If the sales tax is 5%,what is the total prics?
Liula [17]
In order to get the total price, we can multiply the 4 dollars by .05 to find 5 percent of the object's cost and add it to the sales tax. So, .05 times 4 is 0.2, meaning there is a sales tax of 0.2 dollars. We add that to the four, so the total price is 4.20 dollars. Hope this helps.
7 0
2 years ago
Read 2 more answers
Suppose 1000 people enter a chess tournament. Use a rooted tree model of the tournament to determine how many games must be play
Vlada [557]

Answer: 999 games

Step-by-step explanation:

There are many ways to illustrate the rooted tree model to calculate the number of games that must be played until only one player is left who has not lost.

We could go about this manually. Though this would be somewhat tedious, I have done it and attached it to this answer. Note that when the number of players is odd, an extra game has to be played to ensure that all entrants at that round of the tournament have played at least one game at that round. Note that there is no limit on the number of games a player can play; the only condition is that a player is eliminated once the player loses.

The sum of the figures in the third column is 999.

We could also use the formula for rooted trees to calculate the number of games that would be played.

i=\frac{l - 1}{m - 1}

where i is the number of "internal nodes," which represents the number of games played for an "<em>m</em>-ary" tree, which is the number of players involved in each game and l is known as "the number of leaves," in this case, the number of players.

The number of players is 1000 and each game involves 2 players. Therefore, the number of games played, i, is given by

i=\frac{l - 1}{m - 1} = i=\frac{1000 - 1}{2 - 1} = \frac{999}{1} =999

7 0
2 years ago
When 27x^2z/-3x^2z^6 is completely simplified, the exponent on the variable z is _____.
Savatey [412]
<span>The expression given (27x^2)z/(-3x^2)(z^6), can be simplify as below:

 By properties of powers, if you have the same base, you can substract the exponents. Then:

 =(</span>27x^2)z/(-3x^2)(z^6)
 =-9z/z^6  (As you can see: x^2-2= x^0=1)
 =-9/z^5    (Then, z^6-1=z^5)
<span>
 Therefore, the answer is: The exponent on the variable z is 5.</span> 
7 0
2 years ago
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