1. Astronomers measure large distances in light-years. One light year is the distance that light can travel in one year, or approximately 5.88 x 10^12 miles. Suppose a star is 9.8 x 10^1 light years from Earth. In scientific notation, approximately how many miles is it?

A. 5.88 x 10^13 miles

B. 5.76 x 10^14 miles

C. 5.88 x 10^12 miles

D. 9.8 x 10^12 miles

2. A 1,600.00 principal earns 7% annual interest, compounded semiannually (twice per year). After 33 years, what is the balance in the account?

A. $4,979.11

B. $14,920.54

C. $112,992.00

D. $15,494.70

Question

Mathematics

Sarai Mcneil

1 August, 21:30

1. Astronomers measure large distances in light-years. One light year is the distance that light can travel in one year, or approximately 5.88 x 10^12 miles. Suppose a star is 9.8 x 10^1 light years from Earth. In scientific notation, approximately how many miles is it?

A. 5.88 x 10^13 miles

B. 5.76 x 10^14 miles

C. 5.88 x 10^12 miles

D. 9.8 x 10^12 miles

2. A 1,600.00 principal earns 7% annual interest, compounded semiannually (twice per year). After 33 years, what is the balance in the account?

A. $4,979.11

B. $14,920.54

C. $112,992.00

D. $15,494.70

+3

Answers (1)

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Fleming · Answer 1

1. Distance: d=9.8x10^1 light years

d=9.8x10^1x5.88x10^12 miles

d=57.6x10^13 miles

d=5.76x10^14 miles

Answer: Option B. 5.76x10^14 miles

2. Principal: P=1,600

Annual interest: i=7%=7/100→i=0.07

Number of years: t=33

Balance: B=?

Compounded semiannually (twice per year) → n=2

B=P (1+i/n) ^ (nt)

Replacing the values:

B=$1,600 (1+0.07/2) ^ (2x33)

B=$1,600 (1+0.035) ^66

B=$1,600 (1.035) ^66

B=$1,600 (9.684185201)

B=$15,494.69632

B=$15,494.70

Answer: Option D. $15,494.70