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mojhsa [17]
3 years ago
11

A box office sold reserved seat tickets for $10

Mathematics
1 answer:
Anastasy [175]3 years ago
8 0
Please elaborate on the question so that I may help you.
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Determine the mean, median, and more for the given data in each graph.
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An experiment was conducted to observe the effect of an increase in temperature on the potency of an antibiotic. Three 1-ounce p
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

5 0
3 years ago
ariana grande is coming to north gulfport middle school for a fundraising benefit concert!Nevaeh is selling tickets.This week,sh
ArbitrLikvidat [17]

Answer:

Adult = $7

Kids = $4

Step-by-step explanation:

Before we can find the price of the tickets, we first need to create expressions that can be used to explain the prices.

Let x = Price of kids tickets

Let y = Price of adults tickets

For this week the expression is:

3x + 9y = 75

For the last week the expression is:

8x + 5y = 67

Now to be able to find the value of x or y, we can use the Solving Linear Equations by Multiplying First Method.

3x + 9y = 75

8x + 5y = 67

Now we need to remove either the x or y by multiplying the whole expressions by a certain number.

8(3x + 9y = 75)

24x + 72y = 600

3(8x + 5y = 67)

24x + 15y = 201

Now that we have our equations and we can eliminate the x by subtracting both expressions.

24x + 72y = 600

<u>- 24x + 15y = 201</u>

         57y = 399

To find the value of y, we divide both sides by 57.

\dfrac{57y}{57}=\dfrac{399}{57}

y = 7

Now that we have the value for y, we simply substitute the value in any of our expressions.

3x + 9y = 75

3x + 9(7) = 75

3x + 63 = 75

3x = 75 - 63

3x = 12

Now we divide both sides by 3 to find the value of x.

\dfrac{3x}{3}=\dfrac{12}{3}

x = 4

So the ticket prices are:

Adult = $7

Kids = $4

3 0
3 years ago
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