Jill earned 40$ from a carpool plus 9$ per hour (h) babysitting this week. turn into an Expression

write an equation in slope intercept form for the line that passes through (4, -4) and is parallel to 3x+4x=2y-9

photoshop1234 [79]

Answer:

$\large\boxed{y=\dfrac{7}{2}x-18}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

Convert the equation of a line 3x + 4x = 2y - 9 to the slope-intercept form:

$3x+4x=2y-9$

$7x=2y-9$ add 9 to both sides

$7x+9=2y$ divide both sides by 2

$\dfrac{7}{2}x+\dfrac{9}{2}=y\to y=\dfrac{7}{2}x+\dfrac{9}{2}$

Parallel lines have the same slope. Therefore we have the equation:

$y=\dfrac{7}{2}x+b$

Put the coordinates of the point (4, -4) to the equation:

$-4=\dfrac{7}{2}(4)+b$

$-4=7(2)+b$

$-4=14+b$ subtract 14 from both sides

$-18=b\to b=-18$

Finally we have the equation:

$y=\dfrac{7}{2}x-18$

8 0

3 years ago

Integrate x+1/sqrt(x). I know that the answer is 2/3 • sqrt(x) • (x+3) + C, but I don't know how it is simplified from 2/3 • x^3

Andreas93 [3]

$\displaystyle\int\frac{x+1}{\sqrt x}\,\mathrm dx=\int\frac x{x^{1/2}}+\frac1{x^{1/2}}\,\mathrm dx$

$=\displaystyle\int x^{1/2}+x^{-1/2}\,\mathrm dx$

By the power rule,

$=\dfrac{x^{3/2}}{\frac32}+\dfrac{x^{1/2}}{\frac12}+C$

(this seems to be the step you're not getting?)

$=\dfrac23x^{3/2}+2x^{1/2}+C$

The next step is to pull out a common factor of $x^{1/2}$ from the antiderivative:

$x^{3/2}=x^{1/2+1}=x^{1/2}\cdot x^1$

so that the final result is

$\dfrac23x^{3/2}+2x^{1/2}+C=\dfrac23x^{1/2}(x+3)+C$

3 0

3 years ago

Costs are rising for all kinds of medical care. The mean monthly rent at assisted-living facilities was reported to have increas

polet [3.4K]

Answer:

a) The 90% confidence interval estimate of the population mean monthly rent is ($3387.63, $3584.37).

b) The 95% confidence interval estimate of the population mean monthly rent is ($3368.5, $3603.5).

c) The 99% confidence interval estimate of the population mean monthly rent is ($3330.66, $3641.34).

d) The confidence level is how sure we are that the interval contains the mean. So, the higher the confidence level, more sure we are that the interval contains the mean. So, as the confidence level is increased, the width of the interval increases, which is reasonable.

Step-by-step explanation:

a) Develop a 90% confidence interval estimate of the population mean monthly rent.

Our sample size is 120.

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

$df = 120-1 = 119$

Then, we need to subtract one by the confidence level $\alpha$ and divide by 2. So:

$\frac{1-0.90}{2} = \frac{0.10}{2} = 0.05$

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 119 and 0.05 in the t-distribution table, we have $T = 1.6578$ .

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

$s = \frac{650}{\sqrt{120}} = 59.34$

Now, we multiply T and s

$M = T*s = 59.34*1.6578 = 98.37$

The lower end of the interval is the mean subtracted by M. So it is 3486 - 98.37 = $3387.63.

The upper end of the interval is the mean added to M. So it is 3486 + 98.37 = $3584.37.

The 90% confidence interval estimate of the population mean monthly rent is ($3387.63, $3584.37).

b) Develop a 95% confidence interval estimate of the population mean monthly rent.

Now we have that $\alpha = 0.95$

So

$\frac{1-0.95}{2} = \frac{0.05}{2} = 0.025$

With 119 and 0.025 in the t-distribution table, we have $T = 1.9801$ .

$M = T*s = 59.34*1.9801 = 117.50$

The lower end of the interval is the mean subtracted by M. So it is 3486 - 117.50 = $3368.5.

The upper end of the interval is the mean added to M. So it is 3486 + 117.50 = $3603.5.

The 95% confidence interval estimate of the population mean monthly rent is ($3368.5, $3603.5).

c) Develop a 99% confidence interval estimate of the population mean monthly rent.

Now we have that $\alpha = 0.99$

So

$\frac{1-0.95}{2} = \frac{0.05}{2} = 0.005$

With 119 and 0.025 in the t-distribution table, we have $T = 2.6178$ .

$M = T*s = 59.34*2.6178 = 155.34$

The lower end of the interval is the mean subtracted by M. So it is 3486 - 155.34 = $3330.66.

The upper end of the interval is the mean added to M. So it is 3486 + 155.34 = $3641.34.

The 99% confidence interval estimate of the population mean monthly rent is ($3330.66, $3641.34).

d) What happens to the width of the confidence interval as the confidence level is increased? Does this seem reasonable? Explain.

The confidence level is how sure we are that the interval contains the mean. So, the higher the confidence level, more sure we are that the interval contains the mean. So, as the confidence level is increased, the width of the interval increases, which is reasonable.

4 0

3 years ago

7x+3y =-4 X-5y=-6 substitution please explain

inysia [295]

First you have to isolate one of the equations for y=mx+b.
Then substitute the equation is made into the first equation

4 0

3 years ago

A triangle has two sides that are perpendicular could the triangle be isosceles, equilateral or scalene explain

oksano4ka [1.4K]

The triangle can be isosceles or scalene but not equilateral

7 0

3 years ago