A gas station sells m gallons of gasoline fuel at $3.80 per gallon and n gallons of diesel fuel

Ahmad just put some money into a cd that pays 11.3% interest compounded semiannually according to the rule of 72 in approximatel

lilavasa [31]

The "rule of 72" says that the doubling time in years is approximately 72 divided by the interest rate in percent. To make the money grow by a factor of 4 requires that it double twice, so will take twice as long as the period to double once.
2×72/11.3 ≈ 12.7 . . . . years

_____
The "rule of 72" is an approximation. The actual quadrupling time for this interest rate and compounding is about 12.6 years. (The actual product of doubling time and nominal interest rate is about 71.25.)

5 0

2 years ago

A feather blew out of a bird nest 10 feet in the air. It drifted to the ground at a constant rate of 2 feet per second. Write an

bonufazy [111]

The answer would be 10/2=5

6 0

1 year ago

What is the true solution to the equation below?

jarptica [38.1K]

Answer:

Step-by-step explanation:

some rules of logarithmic function

$ln(a) - ln(b)=ln(\frac{a}{b})$

$e^{ln(a)}=a$

$ln(a)^{n}=nln(a)$ vice-versa $nln(a)=ln(a)^{n}$

If ㏑(a) = ㏑(b), then a = b

∴ $2ln(e^{ln(2x)})-ln(e^{ln(10x)})=ln(30)$

Use the 2nd rule to simplify it

$e^{ln(2x)}=2x\\e^{ln(10x)}=10x\\$

2㏑(2x) - ㏑(10x) = ㏑(30)

Use the 3rd rule in the 1st term

∵ 2㏑(2x) = ㏑(2x)² = ㏑(4x²)

∴ ㏑(4x²) - ㏑(10x) = ㏑(30)

- Use the 1st rule with the left hand side

$ln(4x^{2})-ln(10x)=ln(\frac{4x^{2}}{10x})\\\\ln(\frac{4x^{2}}{10x})=ln(30)\\\\ \frac{4x^{2}}{10x}=\frac{2x}{5}=\frac{2}{5}x\\\\ ln(\frac{2}{5}x)=ln(30)$

Use the 4th rule

$\frac{2}{5} x = 30$

Multiply both sides by 5

∴ 2 x = 150

- Divide both sides by 2

∴ x = 75

The value of x = 75

3 0

2 years ago

Chayton read a report that said the probability that a randomly selected American is left-handed is 14\%14%14, percent. He was c

denpristay [2]

Answer:

0.36 or 9/25

9 students of the 25 twenty-student classes were left handed. Answer can be written as a fraction 9/25 or a decimal, 0.36

4 0

2 years ago

This line plot shows something about trails in a state park. What is true about the data in this line plot?

Zepler [3.9K]

Answer:

The total length of the Dogwood Trail is 24 kilometers

The difference between the lengths of the trails is 6 kilometers

Step-by-step explanation:

The complete and correct question is

The diagram shows two different nature trails in a state park. The solid line shows the Dogwood Trail. The dashed line shows the Elm Trail.

Which of the following statements are true about the lengths of the trails? Check all that apply.

1.The total length of the Dogwood Trail is 16 kilometers.

2.The total length of the Dogwood Trail is 24 kilometers.

3.The Elm Trail is longer than the Dogwood Trail.

4.The difference between the lengths of the trails is 2 kilometers.

5.The difference between the lengths of the trails is 6 kilometers.

The picture in the attached figure

step 1

Find the value of a

Applying the Pythagorean Theorem in the right triangle ABC

$13^2=a^2+5^2\\a^2=169-25\\a^2=144\\a=12\ km$

step 2

Find the value of b

Applying the Pythagorean Theorem in the right triangle CDE

$5^2=b^2+3^2\\b^2=25-9\\b^2=16\\b=4\ km$

step 3

Find the total length of the Dogwood Trail (solid blue line)

The total length is equal to

$AD=AB+BC+CE+ED$ ---> by segment addition postulate

substitute the given values

$AD=a+5+b+3=(a+b+8)\ km$

substitute the value of a and b

$AD=(12+4+8)=24\ km$

step 4

Find the total length of the Elm Trail (dashed red line)

The total length is equal to

$AD=AC+CD$ ---> by segment addition postulate

substitute the given values

$AD=13+5=18\ km$

Verify the following statements

Part 1) The total length of the Dogwood Trail is 16 kilometers

The statement is false

Because

The total length of the Dogwood Trail is 24 kilometers (see the explanation)

Part 2) The total length of the Dogwood Trail is 24 kilometers

The statement is true (see the explanation)

Part 3) The Elm Trail is longer than the Dogwood Trail

The statement is false

Because

The Elm Trail is smaller than the Dogwood Trail

$18\ km < 24\ km$

Part 4) The difference between the lengths of the trails is 2 kilometers

The statement is false

Because

The difference is equal to

$24-18=6\ km$

Part 5) The difference between the lengths of the trails is 6 kilometers

The statement is true

Because

The difference is equal to

$24-18=6\ km$

4 0

2 years ago

Read 2 more answers