I need help please! Thank you!

use a graphing calculator or other technology to answer the question which quadratic regression equation best fits the data set

Greeley [361]

Answer:

Option C is the correct option.

In other words, the quadratic regression $y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\:$ best fits the data set, as it gets very much close to the data values given in the data table.

The graph of the equation $y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\:$ is also attached.

Step-by-step explanation:

x y

3 470

4 416

5 403

Analyzing Option A:

Considering the equation

$y=32.86\:\left(x\right)^2+379.14\left(x\right)-1369.14\:$

From (3, 470), putting x = 3

$y=32.86\:\left(3\right)^2+379.14\left(3\right)-1369.14\:$

$y=64.02$

From (4, 470), putting x = 4

$y=32.86\:\left(4\right)^2+379.14\left(4\right)-1369.14\:\:$

$y=673.18$

From (5, 403), putting x = 5

$y=32.86\:\left(5\right)^2+379.14\left(5\right)-1369.14\:$

$y=1348.06$

Analyzing Option B:

$y=32.86\:\left(x\right)^2-379.14\left(x\right)$

From (3, 470), putting x = 3

$y=32.86\:\left(3\right)^2-379.14\left(3\right)$

$y=-841.68$

From (4, 470), putting x = 4

$y=32.86\:\left(4\right)^2-379.14\left(4\right)$

$\:y=-990.8$

From (5, 403), putting x = 5

$y=32.86\:\left(5\right)^2-379.14\left(5\right)$

$\:y=-1074.2$

Analyzing Option C:

Considering the equation

$y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\:$

From (3, 470), putting x = 3

$y=32.86\:\left(3\right)^2-379.14\left(3\right)+1369.14\:$

$y=527.46$

So, the approximately result is (3, 527)

From (4, 470), putting x = 4

$y=32.86\:\left(4\right)^2-379.14\left(4\right)+1369.14\:$

$y=378.34$

So, the approximately result is (4, 378)

From (5, 403), putting x = 5

$y=32.86\:\left(5\right)^2-379.14\left(5\right)+1369.14\:\:\:$

$y=294.94$

So, the approximately result is (5, 295)

Analyzing Option D:

Considering the equation

$y=-1369.14\:\left(x\right)^2-379.14\left(x\right)+32.86$

From (3, 470), putting x = 3

$y=-1369.14\:\left(3\right)^2-379.14\left(3\right)+32.86\:\:$

$y=-13426.82$

From (4, 470), putting x = 4

$y=-1369.14\:\left(4\right)^2-379.14\left(4\right)+32.86$

$y=-23389.94$

From (5, 403), putting x = 5

$y=-1369.14\:\left(5\right)^2-379.14\left(5\right)+32.86\:\:$

$y=-36091.34$

Therefore, from the above calculations and analysis, we conclude that Option C is the correct option.

In other words, the quadratic regression $y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\:$ best fits the data set, as it gets very much close to the data values given in the data table.

The graph of the equation $y=32.86\:\left(x\right)^2-379.14\left(x\right)+1369.14\:$ is also attached.

3 0

3 years ago

If three pears and four oranges cost $4.85 and three pears and ten oranges cost $8.75 what is the cost of a pear and an orange

marishachu [46]

Answer:

1 pear = $0.75; 1 orange = $0.65

Step-by-step explanation:

(1) 3P + 4O = 4.85

(2) 3P + 10O = 8.75 Eqn (2) - Eqn (1)

3P + 10O – 3P – 4O = 8.75 – 4.85 Combine like terms

6O = 3.90 Divide each side by 6

O = $0.65 Substitute into Eqn (1)

3P + 4×0.65 = 4.85

3P + 2.60 = 4.85 Subtract 2.60 from each side

3P = 2.25 Divide each side by 3

P = $0.75

Oranges cost $0.65 each and pears are $0.75 each

4 0

3 years ago

Ifn || m, find the value of x and the value of y.

Marat540 [252]

Answer: Option C

$y=5$ , $x=10$

Step-by-step explanation:

If the lines m and n are parallel then the large triangle and the small triangle are similar triangles, because they have equal angles.

By definition for similar triangles it is satisfied that if they have sides of length a, b, c and a', b', c' then:

$\frac{a}{a'}=\frac{b}{b'} =\frac{c}{c'}$

In this case

$a = 12\\a' = 4\\c = 15\\c' = y$

So:

$\frac{12}{4}=\frac{15}{y}$

Now solve the equation for the variable y

$3=\frac{15}{y}$

$y=\frac{15}{3}$

$y=5$

We know that

$x+y=15$ and $y=5$

Then

$x+5=15$

$x=10$

Finally the answer is:

$y=5$ , $x=10$

5 0

3 years ago

A school fair ticket costs $8 per adult and $1 per child. On a certain day, the total number of adults (a) and children (c) who

gtnhenbr [62]

Let a be the number of adults which bought a ticket and c the number of children who bought a ticket. We can use the information given to assemble a system of equations.

Tickets cost 8 dollars for a, 1 dollar for c, and the total amount made is 100

8a + c = 100

The total of a and c is 30

a + c = 30

We can now subtract one equation from the other to use the elimination method to solve the system.

8a + c = 100

-(a + c = 30)

7a + 0 = 70

We can now solve for a.

7a = 70

a = 10

There were 10 adults who bought tickets. We can use this value as a known, plugging it into an equation to solve for the number of children.

a + c = 30

10 + c = 30

c = 20

So, the final answer is "20 children and 10 adults Equation 1: a + c = 30 Equation 2: 8a + c = 100".

6 0

3 years ago

Simplify the following fraction by putting it in lowest terms or by performing the indicated operation.

netineya [11]

(2x-1)(2x-1)
(4x^2+2x+1)(2x-1)

(2x-1) cancels out so

2x-1
4^2+2x+1

8 0

3 years ago