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Oliga [24]
2 years ago
11

Melody can cycle for 30 miles against the wind in the same amount of time that it takes to cycle 56 miles with the wind. If the

speed of the wind is 3mph, what is Melody's speed when she cycles with the wind?
Answer with Solution:​
Mathematics
1 answer:
erma4kov [3.2K]2 years ago
3 0

Answer:

  • 12.92 mph

Step-by-step explanation:

<u>Given:</u>

  • Speed of the wind = 3 mph
  • Speed in calm weather = x
  • Speed with the wind = x + 3
  • Speed against the wind = x - 3

<u>We know that:</u>

  • distance = time*speed or
  • time = distance / speed

<u>We have equal time in both cases so comparing d/s ratios:</u>

  • 30/(x - 3) = 56/(x + 3)

<u>Solve for x:</u>

  • 56(x - 3) = 30(x + 3)
  • 56x - 168 = 30x + 90
  • 56x - 30x = 90 + 168
  • 26x = 258
  • x = 258/26
  • x ≈ 9.92

<u>The speed with the wind is:</u>

  • 9.92 + 3 = 12.92 mph
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Answer:

95%

Step-by-step explanation:

\frac{19}{20} x 5 = \frac{95}{100}

\frac{95}{100} = 0.95

0.95 = 95%

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3 years ago
When a 757 passenger jet begins its descent to the Ronald Reagan National Airport in Washington, D.C., it is 3900 feet from the
Svetradugi [14.3K]

Answer:

Option A. 37106 ft.

Step-by-step explanation:

Given: An 757 passenger jet at the height of 3900 feet from the ground means vertical height = 3900 feet.

Angle of descent to the airport in Washington,D.C. is 6 degrees.

To find: Horizontal distance the plane will cover to reach the run way.

Solution: As we know tan ∅  = \frac{Height}{Base}

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3 years ago
Read 2 more answers
On April 1, the price of gas at Bob's Corner Station was $3.35 per gallon. On May 1, the price was $3.85 per gallon. On June 1,
Zina [86]
<h2>Answer:</h2>

1. Between April 1 and May 1, Bob's price incrdased by <u>$0.50 or 15%</u>.

2. Between May 1 and June 1, Bob's price decreased by <u>$0.50 or 13%</u>.

3. Suppose that atgas station across the street, prices are always 20% higher than Bob's. In absolute dollar terms, the difference between Bob's prices and the prices across the street is <u>$0.1 more expensive</u> when gas costs $3.85 than when gas costs $3.35.

4. Suppose the Fed raises the target for the federal fundsb rate from 2% to 2.25%. This change of percentage points means that the Fed raised its target by approximately <u>0.25%</u>.

<h2>Step-by-step explanation:</h2>

<h3>1. Between April 1 and May 1, Bob's price incrdased by...</h3>

<em>Take the difference of the prices to find an absolute value:</em>

$3.85 - $3.35= $0.50.

<em>Use the following formula to find the relative value:</em>

C= |Original value - New value|/ Original value

C=\frac{|OV-NV|}{OV}=\frac{|3.35-3.85|}{3.35}  =0.15=15%.

<h3>2. Between May 1 and June 1, Bob's price decreased by...</h3>

<em>Take the difference of the prices to find an absolute value:</em>

$3.85 - $3.35= $0.50.

<em>Use the following formula to find the relative value:</em>

C= |Original value - New value|/ Original value

C=\frac{|OV-NV|}{OV}=\frac{|3.35-3.85|}{3.85}  =0.13=13%.

<h3>3. Suppose that atgas station across the street, prices are always 20% higher than Bob's. In absolute dollar terms, the difference between Bob's prices and the prices across the street is (blank) when gas costs $3.85 than when gas costs $3.35.</h3>

<em>In this question we are looking for the difference of a difference. </em>

<em>If the proces across the street are always 20% higher, to find how much the gallon costs just multiply the price by 1.20, to increase 0.2 or 20%:</em>

$3.85 * 1.20= $4.62.

<em>Now, to see how much expensive this price is compared to Bob's, take de difference between the prices:</em>

$4.62 - $3.85= $0.77.

<em>Do the same to find the difference between the gas prices when the price is $3.35.</em>

$3.35 * 1.20= $4.02.

$4.02 - $3.35= $0.67.

Now, find the difference of those differences:

$0.77 - $0.67= $0.1.

<h3>4. Suppose the Fed raises the target for the federal funds rate from 2% to 2.25%. This change of percentage points means that the Fed raised its target by approximately (blank).</h3>

<em>Find the difference between percentages:</em>

2.25% - 2%= 0.0225 - 0.02= 0.0025= 0.25%.

<em>Simpler method:</em>

2.25% - 2%= 0.25%.

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