Answer:
g=-4
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
Answer:

Step-by-step explanation:
The equation of the line through the point
&
can be represented by:

Making m the subject;

∴
we need to carry out the equation of the line through (0,1) and (1,2)
i.e
y - 1 = m(x - 0)
y - 1 = mx
where;

m = 1
Thus;
y - 1 = (1)x
y - 1 = x ---- (1)
The equation of the line through (1,2) & (4,1) is:
y -2 = m (x - 1)
where;


∴

-3(y-2) = x - 1
-3y + 6 = x - 1
x = -3y + 7
Thus: for equation of two lines
x = y - 1
x = -3y + 7
i.e.
y - 1 = -3y + 7
y + 3y = 1 + 7
4y = 8
y = 2
Now, y ranges from 1 → 2 & x ranges from y - 1 to -3y + 7
∴



![\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( [xy^2]^{-3y+7}_{y-1} \bigg ) \ dy](https://tex.z-dn.net/?f=%5Ciint_D%208y%5E2%20%5C%20dA%20%3D8%20%5Cint%5E2_1%20%20%5Cbigg%20%28%20%5Bxy%5E2%5D%5E%7B-3y%2B7%7D_%7By-1%7D%20%5Cbigg%20%29%20%5C%20dy)
![\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ( [y^2(-3y+7-y+1)]\bigg ) \ dy](https://tex.z-dn.net/?f=%5Ciint_D%208y%5E2%20%5C%20dA%20%3D8%20%5Cint%5E2_1%20%20%5Cbigg%20%28%20%5By%5E2%28-3y%2B7-y%2B1%29%5D%5Cbigg%20%29%20%5C%20dy)
![\iint_D 8y^2 \ dA =8 \int^2_1 \bigg ([y^2(-4y+8)] \bigg ) \ dy](https://tex.z-dn.net/?f=%5Ciint_D%208y%5E2%20%5C%20dA%20%3D8%20%5Cint%5E2_1%20%20%5Cbigg%20%28%5By%5E2%28-4y%2B8%29%5D%20%5Cbigg%20%29%20%5C%20dy)

![\iint_D 8y^2 \ dA =8 \bigg [\dfrac{ -4y^4}{4}+\dfrac{8y^3}{3} \bigg ]^2_1](https://tex.z-dn.net/?f=%5Ciint_D%208y%5E2%20%5C%20dA%20%3D8%20%5Cbigg%20%5B%5Cdfrac%7B%20-4y%5E4%7D%7B4%7D%2B%5Cdfrac%7B8y%5E3%7D%7B3%7D%20%5Cbigg%20%5D%5E2_1)
![\iint_D 8y^2 \ dA =8 \bigg [ -y^4+\dfrac{8y^3}{3} \bigg ]^2_1](https://tex.z-dn.net/?f=%5Ciint_D%208y%5E2%20%5C%20dA%20%3D8%20%5Cbigg%20%5B%20-y%5E4%2B%5Cdfrac%7B8y%5E3%7D%7B3%7D%20%5Cbigg%20%5D%5E2_1)
![\iint_D 8y^2 \ dA =8 \bigg [ -2^4+\dfrac{8(2)^3}{3} + 1^4- \dfrac{8\times (1)^3}{3}\bigg]](https://tex.z-dn.net/?f=%5Ciint_D%208y%5E2%20%5C%20dA%20%3D8%20%5Cbigg%20%5B%20-2%5E4%2B%5Cdfrac%7B8%282%29%5E3%7D%7B3%7D%20%2B%201%5E4-%20%5Cdfrac%7B8%5Ctimes%20%281%29%5E3%7D%7B3%7D%5Cbigg%5D)
![\iint_D 8y^2 \ dA =8 \bigg [ -16+\dfrac{64}{3} + 1- \dfrac{8}{3}\bigg]](https://tex.z-dn.net/?f=%5Ciint_D%208y%5E2%20%5C%20dA%20%3D8%20%5Cbigg%20%5B%20-16%2B%5Cdfrac%7B64%7D%7B3%7D%20%2B%201-%20%5Cdfrac%7B8%7D%7B3%7D%5Cbigg%5D)
![\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{64-8}{3}\bigg]](https://tex.z-dn.net/?f=%5Ciint_D%208y%5E2%20%5C%20dA%20%3D8%20%5Cbigg%20%5B%20-15%2B%20%5Cdfrac%7B64-8%7D%7B3%7D%5Cbigg%5D)
![\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{56}{3}\bigg]](https://tex.z-dn.net/?f=%5Ciint_D%208y%5E2%20%5C%20dA%20%3D8%20%5Cbigg%20%5B%20-15%2B%20%5Cdfrac%7B56%7D%7B3%7D%5Cbigg%5D)
![\iint_D 8y^2 \ dA =8 \bigg [ \dfrac{-45+56}{3}\bigg]](https://tex.z-dn.net/?f=%5Ciint_D%208y%5E2%20%5C%20dA%20%3D8%20%5Cbigg%20%5B%20%20%5Cdfrac%7B-45%2B56%7D%7B3%7D%5Cbigg%5D)
![\iint_D 8y^2 \ dA =8 \bigg [ \dfrac{11}{3}\bigg]](https://tex.z-dn.net/?f=%5Ciint_D%208y%5E2%20%5C%20dA%20%3D8%20%5Cbigg%20%5B%20%20%5Cdfrac%7B11%7D%7B3%7D%5Cbigg%5D)

Answer:
($2.123 ; $2.149)
Step-by-step explanation:
The prediction interval is expressed as :
Predicted value ± standard Error
Predicted value = $2.136
Standard Error = $0.013
Prediction interval :
Lower boundary = $2.136 - $0.013 = $2.123
Upper boundary = $2.136 + $0.013 = $2.149
($2.123 ; $2.149)
B.) The prediction interval provides a range for which the predicted value or price should fall Given a certain degree of probability. If the true value falls within this interval, then, our prediction would be deemed to have occurred not by chance.
Since the actual price within the predicted price interval, then I agree with the judge's Decison that the price was not artificially depressed.
Question:
Which of the following options have the same value as 65% of 20?
Choose 2 answers:
(A) 0.65⋅20
(B) 65/100 divided by 20
(C) 65/20 * 100
(D) 65 * 20
Answer:
Option A has the same value as 65% of 20
Step-by-step explanation:
Let x be the value of 65% of 20




Thus 65% of 20 is 13
Now ,
<u>Solving Option A</u>
=> 
=> 13
<u>Solving Option B</u>
=> 65/100 divided by 20
=>
=>
=>0.0325
<u>Solving Option C</u>
=>65/20 * 100
=>
=>
=>325
<u>Solving Option D</u>
=> 65 * 20
=>
=> 1300