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2 years ago

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Use the data in the table to answer the question. Citations are "speeding tickets." You may fill in the table to help you answer

the question. Original data Line of "best guess" Line of best fit Mph greater than speed limit Number of citations Outputs Residuals Outputs Residuals 5 3 7.5 6 10 10 15 5 20 6 Find the linear approximation of the data that passes through the points (5, 3) and (20, 6).

1 answer:

Vikentia [17]2 years ago

8 0

Answer:

Linear approximation is given by: $y = \frac{x}{5}+2$

Step-by-step explanation:

We are given the following information in the question:

Number of citations: 5 7.5 10 15 20

Outputs Residuals: 3 6 10 5 6

We have to find the linear approximation of the data that passes through the points (5, 3) and (20, 6).

Linear approximation is given by:

The equation of line is given by:

$(y-y_1) = \displaystyle\frac{y_2-y_2}{x_2-x_1}(x-x_1)$

where, $(x_1,y_1), (x_2.y_2)$ is the point through which the line passes.

The equation of line is:

$(y-3) = \displaystyle\frac{6-3}{20-5}(x-5)\\\\15(y-3)= 3(x-5)\\15y = 3x-15+45\\15y = 3x + 30\\y = \frac{x}{5}+2$

The above equation is the required linear approximation.

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It takes Evan 6 3/4 hours to mow 3 lawns. it takes him 2 1/3 hours to mow Mr. Smiths yard and 1 3/4 hours to mow Ms. Lee's yard.

Ratling [72]

Answer: $2\frac{2}{3}\ hours$

Step-by-step explanation:

Given: The total time taken by Evan to mow the 3 lawns = $6\frac{3}{4}=\frac{27}{4}\ \text{hours}$

Time taken by Evan to mow the first lawn = $2\frac{1}{3}=\frac{7}{3}\ \text{hours}$

Time taken by Evan to mow the second lawn = $1\frac{3}{4}=\frac{7}{4}\ \text{hours}$

Now,Time taken by Evan to mow the third lawn = $\frac{27}{4}-\frac{7}{3}-\frac{7}{4}$

⇒Time taken by Evan to mow the third lawn = $\frac{81-28-21}{12}$

⇒Time taken by Evan to mow the third lawn = $\frac{32}{12}=\frac{8}{3}=2\frac{2}{3}\ hours$

Hence, the time taken by Evan to mow the third lawn = $2\frac{2}{3}\ hours$

7 0

2 years ago

Sanjay consulted three electricians about upgrading the wiring in his home. Each electrician uses a linear formula that incorpor

Reptile [31]

<u><em>Answer:</em></u>
b.Each electrician charges a different base fee:

<u><em>Explanation:</em></u>
<u>Each of the equations has two parts:</u>
1- base fee that is independent of any variable (this would be the number that has no variable next to it)
2- an hourly rate depending on the number of hours x (this would be the number that has an x next to it)

<u>For the first electrician:</u>
y = 25x + 30
base fee = $30
hourly rate = $25

<u>For the second electrician:</u>
y = 30x + 25
base fee = $25
hourly rate = $30

<u>For the third electrician:</u>
y = 25x + 20
base fee = $20
hourly rate = $25

<u>Now, let's check the choices:</u>
<span><u>a.Each electrician charges a different hourly rate:</u>
</span>This is incorrect as electricians 1 and 3 charge the same hourly rate ($25)

<span><u>b.Each electrician charges a different base fee:</u>
This is correct as all three base fees are different ($30, $20 and $25)

</span><span><u>c.All three electricians charge the same hourly rate:</u>
This is incorrect as electrician 2 has a different hourly rate

</span><span><u>d. All three electricians charge the same base fee:</u>
This is incorrect as the base fees for the three electricians are different ($30, $25 and $20)

Hope this helps :)</span>

4 0

2 years ago

Read 2 more answers

Which expression is an equivalent expression of 12x + 10 + 4y?

Nutka1998 [239]

-3x-2.5=y would be an equivalent to that equation

6 0

2 years ago

What is the equation of a line that is parallel to the line 2x + 5y = 10 and passes through the point (–5, 1)? Check all that ap

Bond [772]

So the right options are:

$y=-\frac{2}{5}x-1$

$2x+5y = -5$

$y-1=-\frac{2}{5}(x+5)$

Further explanation:

Given equation of line is:

2x+5y=10

We have to convert it into point-slope form

$2x+5y=10\\5y=-2x+10\\Dividing\ both\ sides\ by\ 5\\y=-\frac{2}{5}x+\frac{10}{5}\\y=-\frac{2}{5}x+2$

The co-efficient of x is the slope of the line

So,

$m= -\frac{2}{5}$

As the required line is parallel to given line, it will also have same slope.

Let m1 be the slope of required line

Then the line will be:

$y=m_1x+b$

Putting the value of slope

$y=\frac{2}{5}x+b$

Putting (-5,1) in the equation to find the value of b

$1=-\frac{2}{5}(-5)+b\\1=2+b\\b=1-2\\b=-1$

Putting the values of slope and b in equation

$y=-\frac{2}{5}x-1$

Multiplying the whole equation by 5 will give us:

5y = -2x-5

2x+5y = -5

Another form of equation of line is Point-slope form

$y-y_1=m(x-x_1)$

Putting the values of slope and point in the equation, we get

$y-1=-\frac{2}{5}(x+5)$

So the right options are:

$y=-\frac{2}{5}x-1$

$2x+5y = -5$

$y-1=-\frac{2}{5}(x+5)$

Keywords: Point-Slope form, Parallel lines

Learn more about point slope form at:

#LearnwithBrainly

4 0

2 years ago

Read 2 more answers

According to an informal poll in Glenview 1/3

Talja [164]

Answer:

Percent form: 41.65%

Fraction form: $\frac{833}{2000}$

Step-by-step explanation:

33% of men support John Smith.

67% of women support John Smith.

Lets say, for instance, that there are 20 polled individuals -- 10 women and 10 men.

However, since 1.5 times as many men voted as women, we have to apply our poll to 15 men and 5 women.

33% of the 15 men makes 5 men who voted for Smith and 10 who did not.

67% of the 5 women makes 3.33 women who voted for Smith and 1.67 who did not.

Add these numbers together.

8.33 total voters were cast for John Smith, while 11.67 were not.

Now, divide 8.33 by 20 and multiply by 100 to obtain a percentage.

$\frac{8.33}{20} \\.4165\\41.65$

41.65% of voters voted for John Smith according to the results of the poll.

7 0

2 years ago