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2 years ago

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Which inequality can be used to represent this problem? A company spent $15,000 developing a new graffiti repelling paint. The c

ompany makes $10 on the sale of each gallon of paint after subtracting manufacturing costs. How many gallons, x, will they need to sell to have a profit of at least $50,000?
A 10x — 15000 ≥ 50000

B 10x — 15000 > 50000

C 10x + 50000 > 15000

D 10x + 50000 ≥ 15000

1 answer:

AleksandrR [38]2 years ago

7 0

Answer:

The correct answer is:

Option A: A 10x — 15000 ≥ 50000

Step-by-step explanation:

Given that the total cost of manufacturing by the company is $15000.

Let x be the number of gallons the company sells.

It is also mentioned that the company earns $10 on each gallon.

So the total profit will be the the difference of the selling cost of gallons and manufacturing cost

Mathematically,

$10x-15000$

Now it is mentioned that the profit should be at least 50000 dollars which means the profit can be minimally 50000 and also can be greater than it so

$10x-15000 \geq 50000$

The number of gallons can be found by solving the obtained inequality.

Hence,

The correct answer is:

Option A: A 10x — 15000 ≥ 50000

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Answer:

height = 2.5 ft , base = 8 ft

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = $\frac{1}{2}$ bh ( b is the base and h the height )

height = h then base = 2h + 3 and A = 10 , then

$\frac{1}{2}$ h(h + 3) = 10 ( multiply both sides by 2 to clear the fraction )

h(h + 3) = 20 , that is

h² + 3h = 20 ( subtract 20 from both sides )

h² + 3h - 20 = 0 ← in standard form

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equate each factor to zero and solve for h

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ludmilkaskok [199]

Answer:

a) $y=-0.317 x +46.02$

b) Figure attached

c) $S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03$

Step-by-step explanation:

We assume that th data is this one:

x: 30, 30, 30, 50, 50, 50, 70,70, 70,90,90,90

y: 38, 43, 29, 32, 26, 33, 19, 27, 23, 14, 19, 21.

a) Find the least-squares line appropriate for this data.

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i = 30+30+30+50+50+50+70+70+70+90+90+90=720$

$\sum_{i=1}^n y_i =38+43+29+32+26+33+19+27+23+14+19+21=324$

$\sum_{i=1}^n x^2_i =30^2+30^2+30^2+50^2+50^2+50^2+70^2+70^2+70^2+90^2+90^2+90^2=49200$

$\sum_{i=1}^n y^2_i =38^2+43^2+29^2+32^2+26^2+33^2+19^2+27^2+23^2+14^2+19^2+21^2=9540$

$\sum_{i=1}^n x_i y_i =30*38+30*43+30*29+50*32+50*26+50*33+70*19+70*27+70*23+90*14+90*19+90*21=17540$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=49200-\frac{720^2}{12}=6000$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}=17540-\frac{720*324}{12}{12}=-1900$

And the slope would be:

$m=-\frac{1900}{6000}=-0.317$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{720}{12}=60$

$\bar y= \frac{\sum y_i}{n}=\frac{324}{12}=27$

And we can find the intercept using this:

$b=\bar y -m \bar x=27-(-0.317*60)=46.02$

So the line would be given by:

$y=-0.317 x +46.02$

b) Plot the points and graph the line as a check on your calculations.

For this case we can use excel and we got the figure attached as the result.

c) Calculate S^2

In oder to calculate S^2 we need to calculate the MSE, or the mean square error. And is given by this formula:

$MSE=\frac{SSE}{df_{E}}$

The degred of freedom for the error are given by:

$df_{E}=n-2=12-2=10$

We can calculate:

$S_{y}=\sum_{i=1}^n y^2_i -\frac{(\sum_{i=1}^n y_i)^2}{n}=9540-\frac{324^2}{12}=792$

And now we can calculate the sum of squares for the regression given by:

$SSR=\frac{S^2_{xy}}{S_{xx}}=\frac{(-1900)^2}{6000}=601.67$

We have that SST= SSR+SSE, and then SSE=SST-SSR= 792-601.67=190.33[/tex]

So then :

$S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03$

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