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spin [16.1K]
3 years ago
7

An account had an initial deposit made and then interest was applied once a year at a fixed rate. The amount of money, in dollar

s, in the account after t years, was 103(1.02) t . What was the annual interest rate?
Mathematics
2 answers:
Nat2105 [25]3 years ago
8 0
Amount in compound interest = p(1 + r/t)^nt where p is the initial deposit, r = rate, t = number of compunding in a period and n = period.

Here, Amount after t years = 103(1.02)^t
i.e. 1 + r = 1.02
r = 1.02 - 1 = 0.02
Therefore, annual interest rate = 0.02 x 100 = 2%
Natali5045456 [20]3 years ago
4 0

Answer:

The annual interest rate is 20%.

Step-by-step explanation:

Since, we know that,

If an sum of money P is increasing yearly at a fixed rate,

Then the amount after t years,

A=P(1+r)^t

Where, r is the annual rate,

t is the number of years,

Here, the given amount after t years,

A'=103(1.02)^t

By comparing,

1 + r = 1.02

⇒ r = 0.02   ( Subtracting 1 on both sides )

⇒ r = 20 %

Hence, the annual interest rate is 20%.

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What is the factored form of -1/2(32x - 40) - (20x - 4)? ​
inna [77]

Answer:

12(-3x + 2)

Step-by-step explanation:

-1/2 ( 32x - 40) - (20x - 4) = -16x + 20 - 20x + 4 = -36x + 24 = 6(-6x + 4) = 12(-3x + 2)

8 0
2 years ago
Read 2 more answers
Given the equation 5x − 4 = –2(3x + 2), solve for the variable. Explain each step and justify your process.
blagie [28]
A.
5x-4=-2(3x+2) \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\
5x-4=-2 \times 3x-2 \times 2 \\
5x-4=-6x-4 \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 6x to both sides} \\
11x-4=-4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 4 to both sides} \\
11x=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{divide both sides by 11} \\
x=0

B.
3(2x-4)=5x-1 \\
6x-12=5x-1 \\
\boxed{11x-12=-1} \Leftarrow \hbox{the first mistake} \\
11x=11 \\
\boxed{x=11} \Leftarrow \hbox{the second mistake}

Megan's solution isn't correct.
The first mistake: she subtracted 5x from the right-hand side of the equation, but added 5x to the left-hand side.
The second mistake: she divided the right-hand side of the equation by 11, but didn't divide the left-hand side.

The correct solution:
3(2x-4)=5x-1 \ \ \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\
3 \times 2x+3 \times (-4)=5x-1 \\ 6x-12=5x-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{subtract 5x from both sides} \\
x-12=-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  |\hbox{add 12 to both sides} \\
x=11
3 0
3 years ago
Martha earned a gross pay of $1,215,60 last week. Using the fact that Social Security tax is 6.7% of gross pay, determine the
scoray [572]

Answer:

c) $ 75.37

Step-by-step explanation:

The correct question is:

Martha earned a gross pay of $1,215.60 last week. Using the fact that Social Security tax is 6.2% of gross pay, determine the

amount of Social security tax deducted from Martha's gross pay

a $7.54

b. $65.37

c. $75.37

d. $75.40

<u>ANSWER: </u>

<em>Martha's gross pay </em>= $ 1,215.60

<em>Social Security Tax </em>= 6.2%

<em><u>Calculate Social Security tax:</u></em>

6.2% of 1,215.60

6.2/100 x 1,215.60 = $ 75.37

Therefore, the correct answer is option c: $ 75.37

!!

6 0
3 years ago
5x-8=2x+25 help help
Maurinko [17]
The answer would be x=11
7 0
2 years ago
A statistics professor drew a random sample of 81 observations and found that x with bar on top equals 62 s equals 15. Estimate
ratelena [41]

Answer:

LCL = 59.26 to two decimal places

Step-by-step explanation:

Here, we want to estimate the LCL of the population mean with 90% confidence

We proceed as follows;

Given alpha = 0.1, then Z(0.05)=1.645 (from standard normal table), s = 15

Mathematically;

LCL =x_bar -Z*s/√( n)= 62 - (1.645 * 15)/√81

LCL = 62- (24.675)/9 = 59.2583

LCL = 59.26 to two decimal places

3 0
2 years ago
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