Factor the expression. Use the fundamental identities to simplify, if necessary.
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- The contribution of the friend's company is of: $60.
- The account's balance after 20 years will be of: $130,694.36.
- The total deposits after 20 years are given as follows: $28,800 by the friend and $14,400 by the company.
- The interest earned during this entire period was of: $87,494.36.
The balance is obtained using the future value formula, which is presented as follows:
The meaning of each parameter is explained as follows:
- P is the total month deposit.
- r is the interest rate.
- n is the number of coupoundings per period, that is, compoundings per year.
- t is the number of years.
The deposits will be of:
- Friend: $120.
- Company: $60, as it is half of the friend.
Then the parameter P is of:
P = 120 + 60 = 180.
The remaining parameters to obtain the balance after 20 years are given as follows:
r = 0.03, n = 12, t = 20.
Then the balance after 20 years is obtained as follows:
B = $130,694.36.
The total deposits will be of:
- Friend: 120 x 20 x 12 = $28,800.
- Company: half of friend -> $14,400.
The interest accrued is the balance subtracted by the total deposits, hence:
130694.36 - (28800 + 14400) = $87,494.36.
A similar problem, also featuring the future value formula, is presented at brainly.com/question/24703884
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The two temperatures could be removed so that the average of the remaining numbers is the same as the average of the original set of numbers are -1 and -9
Step-by-step explanation:
The formula of the average of a set of data is , where
- S is the sum of the data in the set
- N is the number of the data in the set
∵ The low temperatures in Anchorage, Alaska, for a week were
− 6, − 3, − 1, 1, − 3, − 9, and − 14 degrees Celsius
∴ The set of the data is { -6 , -3 , -1 , 1 , -3 , -9 , -14}
- Add the data in the set
∵ S = -6 + -3 + -1 + 1 + -3 + -9 + -14
∴ S = -35
∵ The set has 7 data
∴ N = 7
- Use the formula of the average above to find it
∴
∴ A = -5
∴ The average of the original set of numbers is -5
To keep the average the same after removing two numbers multiply the average by the new number of data to find the new sum
∵ The number of data after removing two numbers is 5
∴ N = 5
∵ A = -5
- By using the rule of average
∴
- Multiply both sides by 5
∴ -25 = S
∴ The new sum is -25
- Lets find which two numbers of have a sum of -10 because
the difference between -35 and -25 is -10
∵ -1 + -9 = -10
∵ -6 + -3 + 1 + -3 + -14 = -25
∴ We could removed -1 and -9
The two temperatures could be removed so that the average of the remaining numbers is the same as the average of the original set of numbers are -1 and -9
Learn more:
You can learn more about the average in brainly.com/question/10764770
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