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Irina-Kira [14]

3 years ago

6

Solve the inequality. Write the inequality in interval notation. 9(t-2)>3(t-7)

1 answer:

Vitek1552 [10]3 years ago

3 0

Answer:

$\large\boxed{t>\dfrac{1}{2}\to t\in\left(\dfrac{1}{2},\ \infty\right)}$

Step-by-step explanation:

$9(t-2)>3(t-7)\qquad\text{use distributive property}\\\\(9)(t)+(9)(-2)>(3)(t)+(3)(-7)\\\\9t-18>3t-21\qquad\text{add 18 to both sides}\\\\9t>3t-3\qquad\text{subtract 3t from both sides}\\\\6t>3\qquad\text{divide both sides by 6}\\\\t>\dfrac{3}{6}\\\\t>\dfrac{1}{2}$

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Given the following data: X 1 4 6 7 Y 9 7 8 1 a) Find the coefficient of correlation. b) Find the equation of the regression lin

Viktor [21]

Answer:

a) r=-0.719

b) y=10.642-0.976x

c)Predicted y=7.714

Step-by-step explanation:

a)

sumx=1+4+6+7=18

sumy=9+7+8+1=25

sumxy=1*9+4*7+6*8+7*1=92

sumx²=1²+4²+6²+7²=102

sumy²=9²+7²+8²+1²=195

n=number of observation=4

The correlation coefficient is computed by following formula

$r=\frac{nsumxy-(sumx)(sumy)}{\sqrt{[nsumx^{2} -(sumx)^2][nsumy^2-(sumy)^2]}}$

$r=\frac{4(92)-(18)(25)}{\sqrt{[4(102) -(18)^2][4(195)-(25)^2]}}$

$r=\frac{368-450}{\sqrt{[408 -324][780-625]}}$

$r=\frac{-82}{\sqrt{[84][155]}}$

$r=\frac{-82}{\sqrt{13020}}\\r=\frac{-82}{114.1052}\\r=-0.7186$

By rounding r to 3 decimal places we get r=-0.719.

b)

The regression equation can be written as y=a+bx

We have to find "a" and "b" for regression equation

$b=\frac{nsumxy-(sumx)(sumy)}{{nsumx^{2} -(sumx)^2}}$

$a=ybar-b(xbar)$

$b=\frac{4(92)-(18)(25)}{{4(102) -(18)^2}}$

$b=\frac{-82}{{84}}$

b=-0.976

xbar=sumx/n

xbar=18/4=4.5

ybar=sumy/n

ybar=25/4=6.25

a=ybar-b(xbar)

a=6.25-(-0.976)4.5

a=6.25+4.392

a=10.642

Thus, the regression equation is

y=a+bx

y=10.642-0.976x

c)

The predicted value of y for x=3 can be computed by putting the value of x in regression equation

y=10.642-0.976(3)

y=10.642-2.928

y=7.714

Hence, the predicted y-value for x=3 is 7.714.

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