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1 year ago

Solve: 55) A pool is filling at 3 pts per min. How many gallons per hour is that?

1 answer:

6 0

Conversion factors:
2 pints = 1 quart
4 quarts = 1 gallon
60 minutes = 1 hour

15 pints/minute x 60 minutes/hour x 1 quart/2 pints x 1 gallon/4 quarts = 112.5 gallons/hour

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The linear equation y=-2x+3 has a positive slope of 2, true or false ?

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Step-by-step explanation:

the slope is -2/1 AKA -2 so it is negative

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2 years ago

In 2016 the United States had a population of about 323 million people and was growing at 0.7 %. Use an explicit exponential mod

ElenaW [278]

Answer:

2047

Step-by-step explanation:

We are given that

Growing rate=0.7%

$\frac{dp}{dt}=\frac{0.7}{100}P$

$\int \frac{dP}{P}=0.007\int dt$

$lnP=0.007t+C$

Using the formula

$\int \frac{dx}{x}=ln x+C$

$P=e^{0.007t+C}=e^{0.007t}\cdot e^C=Ae^{0.007t}$

$e^C=A$

Initially when t=0,P=323 million

Substitute the values

$323 million=A$

$P=323e^{0.007t}$

Now, substitute P=400 million

$400=323e^{0.007t}$

$ln\frac{400}{323}=0.007t$

$ln(1.2384)=0.007t$

$t=\frac{ln(1.2384}{0.007}$

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Year=2016+31=2047

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2 years ago

The diagram represents a reduction of a triangle by using a scale factor of 0.8.

Alekssandra [29.7K]

Answer:

4.8 inches

Step-by-step explanation:

<em>See comment for complete question</em>

Represent the larger triangle with 1 and the smaller with 2.

So, we have:

$H_1 =6\ in$ -- height of 1

Required

Determine H2 --- Height of 2

To do this we apply dilation formula.

$Original * Scale\ Factor = New$

In this case:

$H_1 * Scale\ Factor = H_2$

Substitute 6 for H1 and 0.8 for Scale Factor

$6* 0.8 = H_2$

$4.8= H_2$

Hence, the height of the smaller triangle is 4.8 inches

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2 years ago