Question

in a data set of numbers, the number that repeats the most is called the median. true false edwardo wants to invest a certain amount of money into an account at 3 1/4 % wher interest is compounded annually. how much does he need to invest to get a return o $16,000 in 10 years? interest compounded annually formula: a = a₁(1 + r)ᵗ

Explanation:

First Question (True/False)

The mode is the number that appears most frequently in a data set. The median is the middle value when data is ordered. So the statement confuses mode and median, making it false.

Step1: Identify given values

We know \( A = 16000 \), \( r = 3\frac{1}{4}\%=\frac{13}{4}\% = 0.0325 \), \( t = 10 \). The formula is \( A=a_1(1 + r)^t \), so we solve for \( a_1 \): \( a_1=\frac{A}{(1 + r)^t} \).

Step2: Substitute values

Substitute \( A = 16000 \), \( r = 0.0325 \), \( t = 10 \) into the formula: \( a_1=\frac{16000}{(1 + 0.0325)^{10}} \).

Step3: Calculate \( (1 + 0.0325)^{10} \)

\( (1.0325)^{10}\approx1.376894 \) (using a calculator for exponentiation).

Step4: Solve for \( a_1 \)

\( a_1=\frac{16000}{1.376894}\approx11620.57 \) (rounded to two decimal places).

Answer:

False

Second Question (Investment Calculation)