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Semmy [17]
3 years ago
15

information about two homes in a city is given below. Home A has a value of $110,000, which is expected to increase exponentiall

y by 4% each year. Home B has a value of $100,000, which is expected to increase exponentially by 6% each year. Which equation can be used to determine t, the number of years in which the expected value of home B would be twice the expected value of home A? A 110,000(1.04)t=2(100,000)(1.06)t B 100,000(1.06)t=2(110,000)(1.04)t C 110,000(0.04)t=2(100,000)(0.06)t D 100,000(0.06)t=2(110,000)(0.04)t
Mathematics
1 answer:
SOVA2 [1]3 years ago
6 0

Answer:

100000(1.04)^t=2[110000(1.04)^t

Step-by-step explanation:

B=2A

100000(1.04)^t=2[110000(1.04)^t

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Find the least squares regression equation using the school year (in number of years after 2000) for the input variable and the
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<u>Answer-</u>

<em>The least squares regression equation using the school year (in number of years after 2000) for the input variable and the average cost (in thousands of dollars) for the output variable is "y=0.937x+12.765" .</em>

<u>Solution-</u>

The independent variable / input variable= x = Number of years after 2000 ( = year-2000)

The dependent variable / output variable = y = Average cost in thousands of dollars

(The table has been attached herewith.)

To find the regression equation for a group of (x,y) points,

We have to calculate the slope and y-intercept, then we can put those values in the equation y = mx + c ( Slope - Intercept formula)

We know that,

Slope=m=\frac{N\sum xy -\sum x\sum y}{N\sum x^{2}- (\sum x)^{2}}

Putting the values from the table,

m=\frac{(8 \times 1020.206)-(52 \times 150.894)}{(8 \times 3810)-(52^2)}

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\Rightarrow m =\frac{8161.648-7846.488}{3040-2704} =\frac{315.16}{336}=0.937

Now, for the y-intercept,

c =\frac{\sum y -m(\sum x)}{N}

Putting the values,

c=\frac{150.894-(52 \times 0.937)}{8}=\frac{102.125}{8}=12.765

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y=0.937x+12.765


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