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kakasveta [241]
3 years ago
13

What is the solution to the system that is created by the equation y=-x+6 and the graph shown below?

Mathematics
2 answers:
34kurt3 years ago
6 0
1st let/s find the equation of the graph shown. It has te form of y₁ =mx since it oases by the origin. Moreover we notice that the slope m = rise/run = 1/2. hence the equation IS y₁ = (1/2)x.
To find the solution of y₁ = 1/2 x and y= -x + 6, let's y=y₁

-x + 6 = 1/2 x ↔ -2x +12 = x ↔ -3x= -12  and x = 4. For x = 4 , y =2.

And the solution is the intersection point between y and y₁ which is nothing but the solution or te coordinate of this point that is (4,2)
mina [271]3 years ago
3 0
The graph graphed is y=1/2x

so
y=1/2x and y=-x+6
y=y so
1/2x=-x+6
times 2 both sides
x=-2x+12
add 2x both sides
3x=12
x=4

sub back
y=1/2x
y=1/2(4)
y=2

(4,2) is the solution
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At a recent county fair, you observed that at one stand people's weight was forecasted, and were surprised by the accuracy (with
MatroZZZ [7]

Answer:

a)Slope: \hat \beta_1 =\frac{7625.9}{1248.9}=6.106

Intercept: \hat \beta_o = 157.955 -6.106 (69.686)=-267.548

b) r=\frac{7625.9}{\sqrt{[1248.9][94228.8]}}=0.657  

And the determination coeffecient is r^2 = 0.657^2 =0.432  

Step-by-step explanation:

Data given and definitions

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"    

When we conduct a multiple regression we want to know about the relationship between several independent or predictor variables and a dependent or criterion variable.  

n=110, \sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9 , sum y^2_i=\sum(y-\bar y)^2 =94228.8  

\sum Y_i =17375 , \sum X_i = 7665.5

Part a

The slope is given by this formula:

\hat \beta_1 =\frac{\sum (x-\bar x) (y-\bar y)}{\sum (x-\bar x )^2}

If we replace we got:

\hat \beta_1 =\frac{7625.9}{1248.9}=6.106

We can find the intercept with the following formula

\hat \beta_o = \bar y -\hat \beta_1 \bar x

We can find the average for x and y like this:

\bar X=7665.5/110 =69.686, \bar y= 17375/110=157.955

And replacing we got:

\hat \beta_o = 157.955 -6.106 (69.686)=-267.548

Part b

In order to calculate the correlation coefficient we can use this formula:  

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

For our case we have this:  

n=110, \sum x_i y_i = \sum (X-\bar X)(Y-\bar Y) =7625.9,\sum x^2_i=\sum (x-\bar x)^2 =1248.9 , sum y^2_i=\sum(y-\bar y)^2 =94228.8  

So we can find the correlation coefficient replacing like this:

r=\frac{7625.9}{\sqrt{[1248.9][94228.8]}}=0.657  

And the determination coeffecient is r^2 = 0.657^2 =0.432  

6 0
3 years ago
Solve the following equation. 6x−15=4x+55 6 x − 15 = 4 x + 55
algol [13]

Answer:

x = 35

Step-by-step explanation:

Solve for x:

6 x - 15 = 4 x + 55

Hint: | Move terms with x to the left hand side.

Subtract 4 x from both sides:

(6 x - 4 x) - 15 = (4 x - 4 x) + 55

Hint: | Combine like terms in 6 x - 4 x.

6 x - 4 x = 2 x:

2 x - 15 = (4 x - 4 x) + 55

Hint: | Look for the difference of two identical terms.

4 x - 4 x = 0:

2 x - 15 = 55

Hint: | Isolate terms with x to the left hand side.

Add 15 to both sides:

2 x + (15 - 15) = 15 + 55

Hint: | Look for the difference of two identical terms.

15 - 15 = 0:

2 x = 55 + 15

Hint: | Evaluate 55 + 15.

55 + 15 = 70:

2 x = 70

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 2 x = 70 by 2:

(2 x)/2 = 70/2

Hint: | Any nonzero number divided by itself is one.

2/2 = 1:

x = 70/2

Hint: | Reduce 70/2 to lowest terms. Start by finding the GCD of 70 and 2.

The gcd of 70 and 2 is 2, so 70/2 = (2×35)/(2×1) = 2/2×35 = 35:

Answer: x = 35

3 0
3 years ago
Write an expression to represent the product of 6 and the square of a number plus 15.
inn [45]

Answer:

6x² + 15

6

Step-by-step explanation:

Let the number be x.

"the square of a number"

x²

"the product of 6 and the square of a number"

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"the product of 6 and the square of a number plus 15"

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The coefficient is the number that multiplies the variable, so it is 6.

8 0
2 years ago
V = Bh for h. <br> A. h = BV<br> B. h=B/V<br> C. h=V/B<br> D. h = V – B
Darina [25.2K]
C. h=V/B to solve for this you need to get the variable h by itself and since h is being multiplied to B you use the opposite operation of division by divide both sides by B. Then you have h solved for h=V/B
5 0
3 years ago
In a recent awards​ ceremony, the age of the winner for best actor was 35 and the age of the winner for best actress was 54. For
Arada [10]

Answer:

The actress has the more extreme age because

Step-by-step explanation:

Given

Male Athletes:

x = 35

\=x = 42.1

SD = 6.6

Female Athletes

x = 54

\=x = 34.3

SD = 10.1

Required

Determine which athlete had more extreme age

To do this, we simply calculate the standard z score using

z = \frac{x - \=x}{SD}

For the actor:

z = \frac{35 - 42.1}{6.6}

z = \frac{-7.1}{6.6}

z = 1.0758

For the actress:

z = \frac{54 - 34.3}{10.1}

z = \frac{19.7}{10.1}

z = 1.950

Comparing both z values;

The actress has the more extreme age because

  • <em>It has a positive z value</em>
  • <em>Its z value is greater than that of the actor</em>

<em></em>

6 0
3 years ago
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