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vagabundo [1.1K]
3 years ago
12

Susan and her family took a trip during their vacation. They travelled a total of 3982 miles. They averaged 24 miles per gallon

of gasoline. How much did the gasoline cost is the price per gallon was $2.48?
Mathematics
1 answer:
ExtremeBDS [4]3 years ago
7 0

Answer:

The gasoline cost $411.47.

Step-by-step explanation:

This problem can be solved using rules of three.

The first step is finding how many gallons were used.

They travelled a total of 3982 miles. They averaged 24 miles per gallon of gasoline.

So

1 gallon = 24 miles

x gallons - 3982 miles

24x = 3982

x = \frac{3982}{24}

x = 195.9

195.9 gallons were used.

How much did the gasoline cost is the price per gallon was $2.48?

Each gallon costs $2.48. 195.9 gallons were used. So

$2.48*195.9 = $411.47

The gasoline cost $411.47.

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Answer:

The linear relationship is represented by y = 2x + 3.

Step-by-step explanation:

We are given a y-intercept of an equation as well as a slope:

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We can use this information and substitute it into the slope-intercept form equation to get our linear relationship:

  • y = mx + b

In this formula, m is our slope and b is our y-intercept.

Therefore:

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Finally, let us substitute these into the equation:

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This is our final equation.

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Step-by-step explanation:

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9. Determine how long it takes for 80% of the material to decay.
Vilka [71]

Using an exponential function, it is found that it takes 18.6 days for 80% of the material to decay.

The amount of a substance after t days is modeled by:

A(t) = A(0)e^{-kt}

In which:

  • k is the decay rate, as a decimal.
  • A(0) is the initial amount.

The half-life is of 8 days, hence A(8) = 0.5A(0), and this is used to find k.

A(t) = A(0)e^{-kt}

0.5A(0) = A(0)e^{-8k}

e^{-8k} = 0.5

\ln{e^{-8k}} = \ln{0.5}

-8k = \ln{0.5}

k = -\frac{\ln{0.5}}{8}

k = 0.08664339757

Hence:

A(t) = A(0)e^{-0.08664339757t}

The time it takes for 80% of the material to decay it t for which A(t) = 0.2A(0), hence:

0.2A(0) = A(0)e^{-0.08664339757t}

e^{-0.08664339757t} = 0.2

\ln{e^{-0.08664339757t}} = \ln{0.2}

-0.08664339757t = \ln{0.2}

t = -\frac{\ln{0.2}}{0.08664339757}

t = 18.6

It takes 18.6 days for 80% of the material to decay.

To learn more about exponential functions, you can take a look at brainly.com/question/24906920

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