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brilliants [131]
1 year ago
11

A cyclist rides her bike at a rate of 15 miles per hour. What is this rate in kilometers per hour? How many kilometers will the

cyclist travel in 2 hours? In your computations, assume that I mile is equal to 1.6 kilometers. Do not round your answers.
Mathematics
1 answer:
Trava [24]1 year ago
3 0

Answer:

1. 24 km/hour

2. 48 km

Step-by-step explanation:

1 mile = 1.6 km

cyclist = 15 miles/ hour

we want to multiply speed by something that will cancel miles out and leave km. to do this, we want to multiply it by something with miles on the bottom and km on the top.

this is because

miles * km / miles = km as the miles cancel out and km is left in the numerator

thus,

1 mile = 1.6 km

divide both sides by 1.6 km to get 1 on a side

1 mile / 1.6 km = 1

alternatively, divide both sides by 1 mile to get 1 on a side

1.6 km / 1 mile = 1

since we want miles on the bottom, we choose the second option

cyclist = 15 miles / hour = 15 miles/hour * 1 = 15 miles/hour * 1.6km / 1 mile = 24 km /hour

24 km/hr for 2 hours = 24 km/hr * 2 hours = 24 * 2 km = 48 km

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Answer:

"To the nearest year, it would be about 9 years"

Step-by-step explanation:

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This is compound growth problem. It goes by the formula:

F=P(1+r)^t

Where

F is the future amount

P is the present (initial) amount

r is the rate of growth, in decimal

t is the time in years

Given,

P = 20,000

r = 8% = 8/100 = 0.08

F = double of initial amount = 2 * 20,000 = 40,000

We need to find t:

F=P(1+r)^t\\40,000=20,000(1+0.08)^t\\2=(1.08)^t

To solve exponentials, we can take Natural Log (Ln) of both sides:

2=(1.08)^t\\Ln(2)=Ln((1.08)^t)

Using the rule shown below we can simplify and solve:

Ln(a^b)=bLn(a)

We can write:

Ln(2)=Ln((1.08)^t)\\Ln(2)=tLn(1.08)\\t=\frac{Ln(2)}{Ln(1.08)}\\t=9.0064

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3 years ago
Describe and correct the error in finding the solution of the equation 2x=6x
kipiarov [429]
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3 years ago
Solve (x – 3)2 = 49. Select the values of x.
PIT_PIT [208]

Answer:

<h3>x = 27.5</h3>

Step-by-step explanation:

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2 years ago
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sergij07 [2.7K]

Answer:

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2x+12=24

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The 12-12 should cancel itself, the rest of the equation you bring down to get

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Now you have 2x=12.
you then divide 2x by both sides.

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The 2x/2x cancels itself out so you then solve for 12/2x.

For this you just divide 12/2 which is 6!

x= 6 is your final answer.
to check this equation you can plug your number back into x to see if it is true! 2(6)+12=24.
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hope this helps! :D

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I don’t understand you second question but this is the work for the first one.

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