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soldi70 [24.7K]
3 years ago
10

1: Explain Why (4,1) is not a solution to the equation y=3x+1

Mathematics
2 answers:
guapka [62]3 years ago
8 0
1. (4,1) is not a solution because when u sub it into the equation, it does not come out correct. It would be correct if it was (1,4).

2. C = 2.50d.....where C is the cost and d is the number of drinks bought. And if u pick any number for d, then u can solve for the cost (C).
Amiraneli [1.4K]3 years ago
8 0

Answer:

1. The point (4,1) is not a solution for the equation.

2. y=2.50x

Step-by-step explanation:

1. We are asked to explain why (4,1) is not a solution to the equation y=3x+1.

We can see that right side of equation would be greater than left side, when we will substitute coordinates of point (4,1).

Let us substitute coordinates of point (4,1) in our given equation as:

1=3(4)+1

1=12+1

1=13

Therefore, the point (4,1) is not a solution for the equation.

2. We have been given that drinks at the fair cost $2.50.

Let x represent number of drinks, so cost of x drinks would be 2.50x.

The total cost (y) of x drinks would be y=2.50x.

Therefore, the equation 2.50x represents the given equation.

Table:

Number of drinks                       Total cost

1                                                       $2.50

2                                                      $5.00

3                                                       $7.50

4                                                      $10.00

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Step-by-step explanation:

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2x=length of pool

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the area of this rectangle minus the area of the pool is 196 square feet

(2x+4)(x+4)-(x)(2x)=196

2x^2+4x+8x+16-2x^2=196

combine similar terms

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3 years ago
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Step-by-step explanation:

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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  

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= 157 in²

The semicircle is cut out of the rectangle

Find the area of the paper board that remains after the semicircle is cut out of it by subtracting the area of a semi circle from the area of a rectangle

Area of the paper board that remains = Area of a rectangle - Area of a semi circle

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