There are 4 juice cartons and 7 milk cartons in the school refrigerator. What is the ratio of juice cartons to total cartons?

(A) 3 to 4
(B)3 to 11
(C)4 to 7
(D) 4 to 11

Answer-

Quadratic regression equation  [tex]y=0.392x^2 - 5.583x + 21.167}[/tex]

Solution-

Quadratic Regression  Equation,

[tex]ax^2+bx+c[/tex]

[tex]a=\frac{(\sum x^2y\sum xx)-(\sum xy\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex]

[tex]b=\frac{(\sum xy\sum x^2x^2)-(\sum x^2y\sum xx^2)}{(\sum xx\sum x^2x^2)-({\sum xx^2)}^2}[/tex]

[tex]c=\frac{\sum y}{n}-b\frac{\sum x}{n}-a\frac{\sum x^2}{n}[/tex]

Where,

[tex]\sum xx=\sum x^2-\frac{(\sum x)^2}{n}[/tex]

[tex]\sum xy=\sum xy-\frac{\sum x\sum y}{n}[/tex]

[tex]\sum xx^2=\sum x^3-\frac{\sum x\sum x^2}{n}[/tex]

[tex]\sum x^2y=\sum x^2y-\frac{\sum x^2\sum y}{n}[/tex]

[tex]\sum x^2x^2=\sum x^4-\frac{(\sum x^2)^2}{n}[/tex]

Calculating the values from the table,

a= 0.392

b= -5.583

c= 21.167

∴ Quadratic regression equation,

[tex]y=0.392x^2 - 5.583x + 21.167[/tex]

An integer is close to zero if it is "small".

By small, we mean that it is small in absolute value. In fact, for any given distance [tex] d [/tex], there are two integers that are [tex] d [/tex] units away from zero: [tex]d [/tex] and [tex] -d [/tex].

So, for example, -6 is close to zero than 8, because -6 is six units away from zero, while 8 is eight units away from zero.

So, the answer is B, -8, because it is 8 units away from zero. The other options A, C and D are, respectively, 12, 10 and 14 units away from zero.

Answer:

[tex]x=+-2i\sqrt{6}[/tex]

Step-by-step explanation:

[tex]x^2+24=0[/tex]

To solve for x we need to get x alone

Subtract 24 from both sides

[tex]x^2+24=0[/tex]

[tex]x^2=-24[/tex]

Now take square root on both sides to remove the square

[tex]x^2=-24[/tex]

[tex]\sqrt{x^2} =\sqrt{-24}[/tex]

[tex]x=+-2\sqrt{-6}[/tex]

square root of -1 is 'i'

[tex]x=+-2i\sqrt{6}[/tex]

Answer:

Step-by-step explanation:

2i√6 and -2i√6 :))

x > 4 is your answer

slope = - 2, midpoint = (2, - 2 )

the slope m is calculated using the ' gradient formula '

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (4, - 6 ) and (x₂, y₂ ) = (0, 2 )

m = [tex]\frac{2+6}{0-4}[/tex] = [tex]\frac{8}{-4}[/tex] = - 2

calculate midpoint using midpoint formula

{[tex]\frac{1}{2}[/tex] (4 + 0 ), [tex]\frac{1}{2}[/tex] (- 6 + 2 )] = (2, - 2 )

gradient of perpendicular bisector = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]

equation in slope-intercept form is

y = mx + c ( m is slope and c the y-intercept )

partial equation is y = [tex]\frac{1}{2}[/tex] x + c

to find c substitute ( 2, - 2) into the partial equation

- 2 = 1 + c ⇒ c = - 3

y = [tex]\frac{1}{2}[/tex] x - 3 in slope-intercept form

Answer:

-2

(2,-2)

1/2

y=(1/2)x-3

Step-by-step explanation:

It’s correct on edge.

To prime factorization would be A: 2 X 3 X 5 X 7

Because if your do 2 X 3 it would be 6

Then you do 5 X 7 it would be 35

And 6 X 35 would be 210

AND THAT IS FACTORING THE PROBLEM

[tex]210:2=105\\\\105:5=21\\\\21:3=7\\\\7:7=1\\\\210=2\cdot3\cdot5\cdot7[/tex]

Answer:

The value [fog](3) is 29.

Step-by-step explanation:

The given functions are

[tex]f(x)=2x+7[/tex]

[tex]g(x)=x^2+2[/tex]

We have to find [fog](3).

[tex](f\circ g)(x)=f(g(x))[/tex]

[tex](f\circ g)(3)=f(g(3))[/tex]

[tex](f\circ g)(3)=f(3^2+2)[/tex]              [tex][\because g(x)=x^2+2][/tex]

[tex](f\circ g)(3)=f(11)[/tex]

[tex](f\circ g)(3)=2(11)+7[/tex]              [tex][\because f(x)=2x+7][/tex]

[tex](f\circ g)(3)=22+7[/tex]

[tex](f\circ g)(3)=29[/tex]

Therefore the value [fog](3) is 29.

The polynomial degree relates to the number of "zeros" or points of intersection of the polynomial function (curve in the (x,y) plane) with the x axis (that is, points where y=0). These zeros can sometimes be coinciding but that phenomenon aside, you will see N such intercepts with the x axis for a polynomial expression of N-th degree.

Example of a polynomial of 3rd degree is: x^3 + 2 x^2 - x - 2

You can factor it to (x-1)(x+1)(x+2) to see that the zeros are +1, -1, and -2. The plot is attached as an image - note the intercepts. Lmk if you have questions.

A degree in a polynomial function is the greatest exponent of that equation, which determines the most number of solutions that a function could have and the most number of times a function will cross the x-axis when graphed or we can  also say that degree of polynomial determines the number of  zeroes of that polynomial  function.

Let us take an example of polynomial expression of degree three,

For e.g.  [tex]x^{3}+2x^{2} -x-2=0[/tex]              ...(1)

By hit  and trial method we have to solve it .

Firstly, we put [tex]x = +1[/tex] in above equation ,

We get , [tex]1+2-1-2=0[/tex]

Thus, x = +1 is  first zero of the equation.

Now ,we put [tex]x = -1[/tex] in equation...(1) ,

We get,

[tex]-1+2-(-1)-2=0[/tex]

i.e. x = -1 is also  second zero of the equation.

Then, we put [tex]x = -2[/tex] in equation...(1) ,

We get ,

[tex]-8+8-(-2)-2=0[/tex]

Thus, the third zero of the equation is x = -2.

Therefore there are three zeroes of the polynomial function  are x = -1, +1 and -2.

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Answer:

About [tex]20cm^2[/tex]

Step-by-step explanation:

In the given image each of the square has side 1 cm by 1 cm.

If we could count the whole squares in the image we can see that there are about 14 whole squares, then there are 6 squares which are nearly half occupied so that makes about 3 whole squares. And then there are almost 12 squares whose quarter area is enclosed by the lines so that makes about 3 whole squares.

So the total area of the given figure is about [tex]20 cm^2[/tex].

Answer:

Option "C" would be the correct answer

Answer:

Admission to the fair = $ 18

[tex]y = 2.50x +18[/tex].

Where the coefficient of x represents the cost of each ticket and the constant represents the cost of admission to the fair.

Step-by-step explanation:

The total money Henry spent was $ 55.50

If Henry only spent the money on the tickets for the rides and at the entrance to the fair, then we know that:

Bought 15 tickets at 2.5 $

Therefore the price of the admission to the fair is the total expense ($ 55.50) minus the expense in the tickets for the rides ($ 2.50 * 15)

55.50 - 15 * 2.50 = 18

So:

Admission to the fair = $ 18

Ticket for the rides = $ 2.50

So if we call y at the total cost and x the number of tickets for the rides:

[tex]y = 2.50x +18[/tex].

This is a linear equation that represents the total cost.  

Where the coefficient of x represents the cost of each ticket and the constant represents the cost of admission to the fair.

To find the cost of admission to the fair, set up a linear equation using the given information: 2.5x + y = 55.50. The coefficient of x (2.5) represents the cost of each ride ticket, while the constant (55.50) represents the total expenditure that includes both the ride tickets and the admission fee.

To find the cost of admission to the fair, we can set up a linear equation based on the given information. Let's denote the cost of the admission as y and the number of ride tickets as x. We are given that the county fair charges $2.50 per ticket, so the cost of the ride tickets would be 2.5x. Additionally, we know that Henry bought 15 ride tickets and spent a total of $55.50, so we have the equation 2.5x + y = 55.50.

The linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission is 2.5x + y = 55.50.

In this equation, the coefficient of x (2.5) represents the cost of each ride ticket, while the constant (55.50) represents the total expenditure that includes both the ride tickets and the admission fee.

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Answer:

123123131231231312312

Step-by-step exp13123123123lanation:

jkbbhivbyuiiyu1312312

3 * 4 + 3 = 12 + 3 = 15

Answer: He had 15 apples.

Answer:

y = -8/7x - 3

Step-by-step explanation:

A line represents a linear relationship between x and y with constant slope and defined for all values of x and y.

Any line equation in slope intercept form would be of the form

y =mx+c where

m = slope of line

and c = y intercept

In our quesion we are given that slope of line = -8/7

and intercept = negative 3 = -3

Hence equation is

y =-8x/7-3

ANSWER

The solution is [tex](-1,9)[/tex]

EXPLANATION

We want to solve the simultaneous equations

[tex]y=-3x+6---(1)[/tex]

and

[tex]y=9--(2)[/tex].

We substitute equation (2) in to equation (1), to obtain

[tex]9=-3x+6[/tex]

This has now become a linear equation in a single variable [tex]x[/tex].

We solve for x  by grouping like terms.

[tex]9-6=-3x[/tex]

[tex]3=-3x[/tex]

We divide through by negative 3 to get;

[tex]-1=x[/tex].

Hence, the solution is [tex](-1,9)[/tex]

Answer:

At 11:00 am the both trains will be at same distance away from Roseville

Step-by-step explanation:

The first train was 40 miles away from Roseville at 7:00 am

After some time t the both trains will be at the same distance away from Roseville.

We will make equation for that situation

d- distance      v1= 40mph and v2= 50mph -  velocity

d =  v1*t + 40 = v2*t  => v2*t - v1*t = 40 => t (v2-v1) = 40 -> t = 40/ (v2-v1)

t = 40/(50-40) = 40/10= 4h      t = 4h

7:00 am * 4h = 11:00 am

Good luck!!!

Explanation of how to find the remainder using long division with a polynomial expression.

Long Division Example:

We are given (x² + 3x – 9) ÷ (x – 2). To find the remainder using long division, we need to divide x² + 3x - 9 by x - 2 step by step.

Start by dividing x² by x, which gives x. Multiply x by (x - 2) to get x² - 2x.

Subtract x² - 2x from x² + 3x to get 5x. Bring down the -9.

Repeat the process: divide 5x by x to get 5. Multiply 5 by (x - 2) to get 5x - 10.

Subtract 5x - 10 from 5x - 9. The remainder is 1, which is the value over the divisor x - 2.

JKLM is a parallelogram. - Given

JM is a parallel to KL. - Definition of bisect

Given - LN bisects <KLP.

<2 ~= <3 - Definition of bisect

<1 ~= <3 - Transitive Property of Congruence

Answer:

31.5 minutes only

Inverse proportion

Step-by-step explanation:

It takes 45 minutes for Laura to mow the lawn.

For Kelly it takes 1 hour 45 minutes or 60+45 = 105 minutes

In one minute Laura can mow 1/45 of the lawn.

Similarly in one minute Kelly can mow 1/105 of the lawn

Together in one minute they can mow the sum

= [tex]\frac{1}{45} +\frac{1}{105}[/tex]

Take lcd for 45 and 105 and make them equivalent fractions with same denominator

LCD of 45 and 105 is 15(3) (7) = 315

[tex]\frac{1}{45} +\frac{1}{105}=\frac{7+3}{315}=\frac{10}{315}\\=\frac{2}{63}[/tex]

In other words it would take 63/2 = 31.5 minutes only to lawn if they work together.

The situation here is the problem on inverse proportion.  If no of people increase, work time would decrease.

Final answer:

To calculate the growth of a coral reef over 5 weeks at a rate of 0.12 meters per week, you multiply the weekly growth by 5, resulting in a total growth of 0.6 meters.

Explanation:

If a coral reef grows 0.12 meters every week, we can calculate its growth over 5 weeks by multiplying the weekly growth rate by the number of weeks.

Perform the calculation: 0.12 m/week × 5 weeks = 0.6 meters.

Therefore, a coral reef grows 0.6 meters in 5 weeks.

f(x) = x2 ÷ 3 + x

f(6)

Replace X with 6 then follow order of operations.

6^2 / 3 + 6

6^2 = 36:

36 / 3 + 6

36 /3 = 12:

Add:

12 + 6 = 18

The answer is 18

Answer:

C(6.25 , 0)

Step-by-step explanation:

Draw the diagram

A is at (0,0)

B is at (6,8)

Draw a line from A to B.

Put a large dot where (0,6) is. Call this D

Draw BD

Draw another line from (0,0) to just beyond (6,0) Call this C. Draw in BC

What You Have Drawn

The height of the triangle is BD and it is 8. That comes from B which is (6,8)

Solve

Formula

Area = 1/2 * B * H

Area = 25

H = 8

Area = 1/2 B * H

25 = 1/2 * B * 8             Switch sides

1/2  * B * 8 = 25            Combine factors on the left.

4 B = 25                       Divide both sides by 4

4B/4  = 25/4        

B = 6.25

What that means is that AC is 6.25 units long and is on the x axis

C is C(6.25,0)

2 - 3(2x + 1) < 6x(2 - 4)

2 - 6x - 3 < 12x - 24x

-1 - 6x < -12x

-1 < -6x

Dividing by -6 both sides gives you;

1/6 < x or;

Final answer is x > 1/6

Answer:

A) x ≥ 1 6

: )

Answer:

I inch = 25.4mm

Step-by-step explanation:

i inch =25.4mm

       = 2.54×10^1

25.4 millimeters in scientific notation can be written as [tex]2.54 \times 10^1 \text {milimeters}[/tex]

The value "25.4 millimeters" must be expressed as a decimal number between 1 and 10, multiplied by a power of 10, in order to be written in scientific notation.

We may write the given number, 25, as follows:

[tex]2.54 \times 10^1[/tex]

In scientific notation, the decimal point is placed after the first non-zero digit, and in this case it is 2. The exponent 1 indicates that we move the decimal point one place to the right to get the original value.

Therefore, 25.4 millimeters in scientific notation is [tex]2.54 \times 10^1\text{millimeters }[/tex]

Learn more about scientific notations here:

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Use the formula (n - 2) * 180 to find the sum of the interior measures of a polygon.

n stands for the number of sides that the polygon has, so substitute 10 for n since a decagon has 10 sides.

(10 - 2) * 180, start by solving inside the parentheses and subtracting 10 and 2.

(8) * 180, multiply.

B. 1,440 is your answer.

Final answer:

The trinomial factorization -1(x - 6)(x + 8) corresponds to the trinomial -x² - 2x + 48.

Explanation:

The trinomial factorization you are asking about is -1(x - 6)(x + 8). To find out the trinomial it factors from, you need to multiply the two binomials together and then multiply by -1. Let's do this step by step:

Multiply the binomials using the FOIL method, which stands for First, Outer, Inner, Last. This gives us the following intermediate step: (x - 6)(x + 8) = x(x) + x(8) - 6(x) - 6(8)

Simplify the intermediate step: x² + 8x - 6x - 48

Combine like terms: x² + 2x - 48

Finally, multiply the entire expression by -1 to give the final trinomial: -x² - 2x + 48.

Thus, the trinomial factorization -1(x - 6)(x + 8) corresponds to the trinomial -x² - 2x + 48.