QuestionHow much should Mary Ellen invest at $5\%$ to earn \$1185 in interest in one year?

Studdy Solution

STEP 1

Assumptions1. The interest rate is5% . The total interest to be gained in one year is $11853. The interest is calculated annually, not compounded monthly or daily4. Mary Ellen wants to find out how much she should invest to gain this interest

STEP 2

We can find the amount Mary Ellen needs to invest by rearranging the formula for simple interest.
The formula for simple interest is $=RT$ where = Interest = Principal (the initial amount of money) R = Rate of interest = Time in yearsSince we want to find the principal, we can rearrange the formula to $= \frac{}{RT}$

STEP 3

Now, plug in the given values for the interest, rate of interest, and time to calculate the principal.
$= \frac{\$1185}{5\% \times1}$

STEP 4

Convert the percentage to a decimal value.
$\% =0.05$ $= \frac{\$118}{0.05 \times1}$

STEP 5

Calculate the principal amount.
$= \frac{\$1185}{0.05} = \$23,700$ Mary Ellen needs to invest $23,700 to gain$ 1185 in interest in one year.

STEP 6

Assumptions for the second problem1. The airplane climbs at a slope of3/82. The airplane needs to reach an altitude of12,000 ft3. We want to find out how far the airplane will fly in the horizontal direction to reach this altitude

STEP 7

The slope of a line is defined as the change in the vertical direction (rise) divided by the change in the horizontal direction (run). In this case, the slope (m) is the ratio of the vertical distance (altitude) to the horizontal distance (distance flown).
We can rearrange the formula for the slope to find the horizontal distance $m = \frac{rise}{run}$ Rearranging for run gives $run = \frac{rise}{m}$

STEP 8

Now, plug in the given values for the rise (altitude) and slope to calculate the run (horizontal distance).
$run = \frac{12,000\, ft}{3/8}$

STEP 9

Calculate the horizontal distance.
$run = \frac{12,000\, ft}{3/8} =32,000\, ft$ The airplane will fly32,000 ft in the horizontal direction to reach an altitude of12,000 ft.

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QuestionHow much should Mary Ellen invest at $5\%$ to earn \$1185 in interest in one year?

Studdy Solution

STEP 1

Assumptions1. The interest rate is5% . The total interest to be gained in one year is $11853. The interest is calculated annually, not compounded monthly or daily4. Mary Ellen wants to find out how much she should invest to gain this interest

STEP 2

STEP 3

Now, plug in the given values for the interest, rate of interest, and time to calculate the principal.
$= \frac{\$1185}{5\% \times1}$

STEP 4

Convert the percentage to a decimal value.
$\% =0.05$ $= \frac{\$118}{0.05 \times1}$

STEP 5

Calculate the principal amount.
$= \frac{\$1185}{0.05} = \$23,700$ Mary Ellen needs to invest $23,700 to gain$ 1185 in interest in one year.

STEP 6

Assumptions for the second problem1. The airplane climbs at a slope of3/82. The airplane needs to reach an altitude of12,000 ft3. We want to find out how far the airplane will fly in the horizontal direction to reach this altitude

STEP 7

STEP 8

Now, plug in the given values for the rise (altitude) and slope to calculate the run (horizontal distance).
$run = \frac{12,000\, ft}{3/8}$

STEP 9

Calculate the horizontal distance.
$run = \frac{12,000\, ft}{3/8} =32,000\, ft$ The airplane will fly32,000 ft in the horizontal direction to reach an altitude of12,000 ft.

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QuestionHow much should Mary Ellen invest at 5%5\%5% to earn \$1185 in interest in one year?

Studdy Solution

STEP 1

Assumptions1. The interest rate is5% . The total interest to be gained in one year is $11853. The interest is calculated annually, not compounded monthly or daily4. Mary Ellen wants to find out how much she should invest to gain this interest

STEP 2

STEP 3

Now, plug in the given values for the interest, rate of interest, and time to calculate the principal.=$11855%×1 = \frac{\$1185}{5\% \times1}=5%×1$1185​

STEP 4

Convert the percentage to a decimal value.%=0.05\% =0.05%=0.05=$1180.05×1 = \frac{\$118}{0.05 \times1}=0.05×1$118​

STEP 5

Calculate the principal amount.=$11850.05=$23,700 = \frac{\$1185}{0.05} = \$23,700=0.05$1185​=$23,700Mary Ellen needs to invest 23,700togain23,700 to gain 23,700togain1185 in interest in one year.

STEP 6

Assumptions for the second problem1. The airplane climbs at a slope of3/82. The airplane needs to reach an altitude of12,000 ft3. We want to find out how far the airplane will fly in the horizontal direction to reach this altitude

STEP 7

STEP 8

Now, plug in the given values for the rise (altitude) and slope to calculate the run (horizontal distance).run=12,000 ft3/8run = \frac{12,000\, ft}{3/8}run=3/812,000ft​

STEP 9

Calculate the horizontal distance.run=12,000 ft3/8=32,000 ftrun = \frac{12,000\, ft}{3/8} =32,000\, ftrun=3/812,000ft​=32,000ftThe airplane will fly32,000 ft in the horizontal direction to reach an altitude of12,000 ft.

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QuestionHow much should Mary Ellen invest at $5\%$ to earn \$1185 in interest in one year?

Now, plug in the given values for the interest, rate of interest, and time to calculate the principal.
$= \frac{\$1185}{5\% \times1}$

Convert the percentage to a decimal value.
$\% =0.05$ $= \frac{\$118}{0.05 \times1}$

Calculate the principal amount.
$= \frac{\$1185}{0.05} = \$23,700$ Mary Ellen needs to invest $23,700 to gain$ 1185 in interest in one year.

Now, plug in the given values for the rise (altitude) and slope to calculate the run (horizontal distance).
$run = \frac{12,000\, ft}{3/8}$

Calculate the horizontal distance.
$run = \frac{12,000\, ft}{3/8} =32,000\, ft$ The airplane will fly32,000 ft in the horizontal direction to reach an altitude of12,000 ft.