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Roman55 [17]
3 years ago
10

this is due today help please!!!!!! A study involving middle-aged adults was designed to determine the relationship between the

amount of caffeine consumed during the day and the time required to fall asleep at night. What are the independent and dependent variables for this study? A. The independent variable is the amount of caffeine consumed, and the dependent variable is the time required to fall asleep. B. The independent variable is the amount of caffeine consumed, and the dependent variable is the age of the people. C. The independent variable is the time required to fall asleep, and the dependent variable is the amount of caffeine consumed.. D. The independent variable is the age of the people, and the dependent variable is the time required to fall asleep.
Mathematics
1 answer:
IceJOKER [234]3 years ago
4 0
The answer should be c because the independent variable should not be manipluated. 
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Farmer bob's square plot ofland is slowly eroding away. Worried about the future of his farm. Farmer Bob measures the rate of er
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Answer:

Option A.

Step-by-step explanation:

Area of a square is

A=x^2               .... (1)

where, x is side length.

The length of each side of his square plot is decreasing at the constant rate of 2 feet/year.

\dfrac{dx}{dt}=2

It is given that bob currently owns 250,000 square feet of land.

Fist find the length of each side.

A=250000

x^2=250000

Taking square root on both sides.

x=500

Differentiate with respect to t.

\dfrac{dA}{dt}=2x\dfrac{dx}{dt}

Substitute x=500 and \frac{dx}{dt}=2 in the above equation.

\dfrac{dA}{dt}=2(500)(2)

\dfrac{dA}{dt}=2000

Farmer bob is losing 2,000 square feet of land per year.

Therefore, the correct option is A.

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3 years ago
Consider the system of equations: Equation 1: -2x + 3y=9 Equation 2 : -8.1 – 7y = 10 Before adding the equations together, which
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The first option :

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5 0
3 years ago
Triangle ABC is similar to triangle DEF. The length of
zavuch27 [327]

Answer: EF=15cm

Step-by-step explanation:

You know that the triangle ABC and the triangle DEF are similar.

Therefore, if the lenght of AC is 12 centimeters and the lenght of DF is 10 centimeters, then you can find the ratio as following:

ratio=\frac{DF}{AC}\\\\ratio=\frac{10cm}{12cm}\\\\ratio=0.8333

Then, the calculte the length of EF, you must multiply the lenght BC of the triangle ABC by the ratio obtained above.

Therefore, the lenght EF is the following:

EF=0.8333(18cm)\\EF=15cm

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3 years ago
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The ratio of the dimensions of a rectangular patio are 4:7. if the shorter
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If the ratio of the dimensions is 4:7 and the shorter dimension is 10ft, we know that the 10ft corresponds to the 4 in this scenario. We can set up the equation as follows:

\frac{4}{7} =\frac{10}{x}

You have to multiply by 2.5 to get from 4 to 10. And since we want to make sure we are maintaining the ratio, we have to multiply the denominator, 7, by 2.5 as well.

\frac{4}{7}*\frac{2.5}{2.5}=\frac{10}{17.5}

This means your shorter side has a length of 10ft and your longer side has a length of 17.5ft.

AREA

The formula for the area of a rectangle is: w*l

So we can plug our dimensions into the formula: 10*17.5=175

So 175 is our area. But we can't forget about units! Since this is area and we multiplied our units together, our units would be squared. That means our answer is <u>175 square feet</u>.

PERIMETER

The formula for the perimeter of a rectangle is: 2(w+l)

We can plug our dimensions into the formula: 2(10+17.5)=55

So 55 is our perimeter. Of course, we can't forget about our units. Because this is perimeter, we only added our units together, so they don't change. That means our answer is <u>55 feet</u>.

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50 cents beacuse in 1970 it cost 50 cents in 1980 it cost 1.00

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