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Brums [2.3K]
3 years ago
11

Write a system of equations to describe the situation below, solve using substitution, and fill

Mathematics
1 answer:
BlackZzzverrR [31]3 years ago
5 0

Answer:

Revenue and Expense = $230

No. of attendees: 10

Step-by-step explanation:

Let n be the no. of attendees

Expense = 50 + 18n

Revenue = 23n

Break even when:

50 + 18n = 23n

50 = 5n

n = 10

23n = 230

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If EF = 5w + 20, FG = 7w + 28, and EG = 72, find the value of w. Find EF and FG
IrinaK [193]

Answer:

 w = 2, EF = 30 , FG = 42

Explanation:

We have EF = 5w + 20  and FG = 7w + 28

 Since these points E, F and G are col-linear points we have.

    EG = EF + FG

  And given that EG = 72

So, EF+EG = 72

     5w + 20 + 7w + 28 = 72

     12w + 48 = 72

      12 w = 24

       w = 2

So EF = 5w + 20 = 5x2 + 20 = 30

     FG = 7w + 28 = 7x2 + 28 = 42

7 0
3 years ago
Please help me!!! I need help bad and my parents don't know this stuff.....
galben [10]

Answer:

Option A

Step-by-step explanation:

To be considered skew lines, both must not intersect or be parallel.

4 0
2 years ago
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Prove that cos(2????) = 2cos2(????) − 1 for any real number ????.
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Answer:

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Step-by-step explanation:

6 0
3 years ago
Assume you have noted the following prices for books and the number of pages that each book contains. Book Pages (x) Price (y) A
belka [17]

Answer:

a) y=0.00991 x +1.042  

b) r^2 = 0.7503^2 = 0.563

c) r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503  

Step-by-step explanation:

Data given

x: 500, 700, 750, 590 , 540, 650, 480

y: 7.00, 7.50 , 9.00, 6.5, 7.50 , 7.0, 4.50

Part a

We want to create a linear model like this :

y = mx +b

Wehre

m=\frac{S_{xy}}{S_{xx}}  

And:  

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}  

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}=2595100-\frac{4210^2}{7}=63085.714  

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=30095-\frac{4210*49}{7}=625  

And the slope would be:  

m=\frac{625}{63085.714}=0.00991  

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

\bar x= \frac{\sum x_i}{n}=\frac{4210}{7}=601.429  

\bar y= \frac{\sum y_i}{n}=\frac{49}{7}=7  

And we can find the intercept using this:  

b=\bar y -m \bar x=7-(0.00991*601.429)=1.042  

And the line would be:

y=0.00991 x +1.042  

Part b

The correlation coefficient is given by:

r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}  

For our case we have this:

n=7 \sum x = 4210, \sum y = 49, \sum xy = 30095, \sum x^2 =2595100, \sum y^2 =354  

r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503  

The determination coefficient is given by:

r^2 = 0.7503^2 = 0.563

Part c

r=\frac{7(30095)-(4210)(49)}{\sqrt{[7(2595100) -(4210)^2][7(354) -(49)^2]}}=0.7503  

4 0
3 years ago
Given the following definition, compute Q(5). Q(n) = 0 if n = 0 2 if n = 1 4 if n = 2 Q(n − 1) + Q(n − 2) + Q(n − 3) if n > 2
aalyn [17]
We have 
Q(0)=0\\
Q(1)=2\\
Q(2)=4
and Q(n)=Q(n-1)+Q(n-2)+Q(n-3)\mbox{ when } n\ \textgreater \ 2.
So 
Q(3)=Q(2)+Q(1)+Q(0)=4+2+0=6\\
Q(4)=Q(3)+Q(2)+Q(1)=6+4+2=12\\
Q(5)=Q(4)+Q(3)+Q(2)=12+6+4=22.

3 0
2 years ago
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