Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.(The pair of variables have a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below.
(a) x=3 hours
(b) x=4.5 hours
(c) x=13 hours
(d) x=1.5 hours

Use quadratic regression  a model for the following data set is [tex]y=1.96 x^2-5.2 x+5.33[/tex].

What is quadratic regression?

A statistical method called quadratic regression is used to identify the parabola equation that best fits a given collection of data. Finding the equation of the straight line that most closely fits a collection of data is the goal of this sort of regression, which is an extension of simple linear regression.

The equation of the parabola that best fits a collection of data is the process of a quadratic regression. As a consequence, we arrive at the equation y=ax2+bx+c where a≠0. The least squares approach is the most effective way to manually locate this equation.

[tex]$$\begin{aligned}& x=1, f(x)=2.1 \\& x=3 \quad f(x)=7.4 \\& x=5 \quad f(x)=20 \cdot 4 \\& y=a x^2+b x+c \\& \text { Print (1) } \\& 2 \cdot 1=a(1)^2+b \times 1+c \\& 2.1=a+b+c \\& \text { Point(2) } \\& 7.4=a(3)^2+b \times 3+c \\& 7.4=9 a+3 b+c \\& \text { Poin (3) } \\& 28.4=a(5)^2+b \times 5+c \\& 28 \cdot 4=25 a+5 b+c \\& \text { by solving (4) (5) (6) } \\& a=1.96 \\& b=-5.2 \\& c=5.33 \\&\end{aligned}$$[/tex]

so, quadratic equation -

[tex]y=1.96 x^2-5.2 x+5.33[/tex]

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The equation of the required parabola is  y = [tex]6x^2+6x+ 8[/tex]

What is a parabola?

Parabola is a curve where all the point on the curve maintains a fixed distance from a point called the focus and a line called the directrix.

Let the equation of the parabola be y = [tex]ax^2+bx+c[/tex]

Here, a = 6

So equation of parabola is y = [tex]6x^2+bx+c[/tex]

The parabola passes through (0, 8) and (-1, 8)

Putting x = 0 and y = 8 in the equation

c = 8

y = [tex]6x^2+bx+8[/tex]

Putting x = -1 and y = 8

[tex]8 = 6(-1)^2 + b(-1) + 8\\ b = 6[/tex]

So equation of the parabola is y = [tex]6x^2+6x+ 8[/tex]

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The value of A is -28 according to arithmetic

What is BODMAS?

BODMAS is associate descriptor and it stands for Bracket, Order, Division, Multiplication, Addition, and Subtraction. In sure regions, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) is employed, that is that the word of BODMAS.

Main body:

According to question:

2-[(8×2)+(8×2)]+2=A ​

to find:    value of A

firstly we need to remove brackets according to rule

⇒2-[(8×2)+(8×2)]+2

⇒2-[16+16]+2

⇒2- 32 +2

⇒-28

hence value of A is -28

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the correct answer is a=(2,3)

The sum of the next three consecutive even integers greater than 2n, where n is an integer, is: Sum = 6n + 12

We know that n is an integer number, we want to find the sum of the next three consecutive even integers greater than 2n2n is already an even integer, and consecutive even integers are given by adding 2 to the smaller one.

Then the 3 consecutive integers larger than 2n are:2n + 22n + 42n + 6

The sum of these 3 gives:(2n + 2) + (2n + 4) + (2n + 6)3*(2n) + 2 + 4 + 66n + 12

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The amount that was invested in each account is:

Maricopa Success invested $47,858 in stocks.

Maricopa Success invested $63,571 in bonds.

Maricopa Success invested $47,571 in CDs.

Let c represent Cds

Let b represent bonds

Let s represent stocks

Equations:

b = c + 15000

s = 160000 - b - c = 160000 - c - 15000 - c = -2c + 145,000

0.08(-2c + 145000) + 0.036(c + 15000) + 0.04c = 7520

-0.16c + 11600 + 0.036c + 540 + 0.04c = 7520

-0.084c = -4,080

Divide both side by -0.084

c = -4,080 / 0.084

c= $48,571 (CDs)

b = 48,571+ 15000

b=$63,571 (bonds)

s = 160,000 - $63,571- 48,571

s= $47,858 (stock)

Therefore Maricopa Success invested $47,858  in stocks,Maricopa Success invested $63,571 in bonds and Maricopa Success invested $47,571 in CDs.

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The quadratic equation 3 / x - [x / x + 6] = 18 / (x² + 6) have roots at 0 and 3

Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is given as ax² + bx + c = 0

In the given equation, we are to solve for the value of x

3 / x - [x / x + 6] = 18 / (x² + 6)

On the left hand side of the equation, we can find the LCM and simplify

3(x + 6) - x² = 18

3x + 18 - x² = 18

x = 3 or x = 0

The solutions to the equation are 0 and 3

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Answer:

Step-by-step explanation:

To determine the total cost of the DVD, you need to calculate the amount of sales tax and add it to the cost of the DVD.

The sales tax is equal to the cost of the DVD multiplied by the sales tax rate:

Sales tax = $18.99 * 6.5% = $1.23

To determine the total cost, you need to add the cost of the DVD to the sales tax:

Total cost = $18.99 + $1.23 = $20.22

So the total cost of the DVD is $20.22.

Fun fact-

Washington Sales Tax. State Sales Tax: 6.5%

The solution to the first and the second equation are 28.648 and 183.5 respectively.

A radical expression is an expression consisting of a square root or nth root.

(1) The given equation is [tex]-5\sqrt[4]{x-1}=12[/tex].

Solve the equation as follows:

[tex]-5\sqrt[4]{x-1}=12\\\\\sqrt[4]{x-1}= -\frac{12}{5}\\\\(x-1) = (-\frac{12}{5})^4\\x-1 = 27.648\\x = 28.648[/tex]

(2) The given equation is [tex]-2\sqrt[6]{4x-5}+9 =3[/tex].

Solve the equation as follows:

[tex]-2\sqrt[6]{4x-5}+9 =3\\ \\2\sqrt[6]{4x-5}= 9-3\\\\\sqrt[6]{4x-5}=3\\\\4x-5=3^6\\\\4x=729+5\\\\x=734/4\\\\x=183.5[/tex]

The third equation is the same as the first equation.

Hence, the solution to the first and the second equation are 28.648 and 183.5 respectively.

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1. To convert 0.00526 into scientific notation, follow these steps:

Move the decimal 3 times to right in the number so that the resulting number, m = 5.26, is greater than or equal to 1 but less than 10

Since we moved the decimal to the right the exponent n is negative

n = -3

Write in the scientific notation form, m × 10n

= 5.26 × 10-3

Therefore, the decimal number 0.00526 written in scientific notation is 5.26 × 10-3 and it has 3 significant figures.

2. To convert 0.00639 into scientific notation also known as standard form, follow these steps:

Move the decimal 3 times to right in the number so that the resulting number, m = 6.39, is greater than or equal to 1 but less than 10

Since we moved the decimal to the right the exponent n is negative

n = -3

Write in the scientific notation form, m × 10n

= 6.39 × 10-3

Therefore, 0.00639 in scientific notation is 6.39 × 10-3 and It has 3 significant figures. In scientific e-notation it is written as 6.39e-3.

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Check the picture below, so the hyperbola looks more or less like so.

the center of the hyperbola is half-way between the foci, so namely at (-2 , -1) as you see there, since we know the covertices, half that distance is the "b" component, so all we're really missing is the "a" component, but we know what "c", since it's just the distance from a foci to the center, so

[tex]\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-2\\ k=-1\\ b=15 \end{cases}\implies \cfrac{( ~~ x- (-2) ~~ )^2}{ a^2}-\cfrac{( ~~ y- (-1) ~~ )^2}{ 15^2}=1[/tex]

[tex]\stackrel{\textit{we know that}}{c=17}\qquad 17=\sqrt{a^2+15^2}\implies 17^2=a^2+15^2\implies 17^2-15^2=a^2 \\\\\\ \sqrt{17^2-15^2}=a\implies \sqrt{64}=a\implies 8=a \\\\[-0.35em] ~\dotfill\\\\ \cfrac{( ~~ x- (-2) ~~ )^2}{ 8^2}-\cfrac{( ~~ y- (-1) ~~ )^2}{ 15^2}=1\implies {\Large \begin{array}{llll} \cfrac{(x+2)^2}{64}-\cfrac{(y+1)^2}{225}=1 \end{array}}[/tex]

Answer: (b-8)(b-5)

Step-by-step explanation:

Find the multiple of 40 that adds up to -13 while being mutiplied by multiples of b^2

1*-5=-5

1*-8=-8

-8-5=13

-8*-5=40

(b-8)(b-5)

Value of the expression 4n - 5r when n = -2 and r = 3 is -23.

The surface area in square feet rectangular prism when s=4 feet and h=6feet is 128 square feet.

What do you mean by algebraic expression?

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Given expression:

4n - 5r

When n = -2 and r = 3

The value of the expression become,

4(-2) - 5(3)

= -8 - 15

= -23

Hence, option D is correct.

Now, it is given that the surface area for a rectangular prism with a square base is given by the expression 2s²+4sh, where s is the side length of the square h is the height of the prism.

The surface area in square feet rectangular prism when s=4 feet and h=6feet is

2[tex](4)^{2}[/tex] + 4(4)(6)

= 2(16) + 96

= 32 + 96

= 128 square feet

therefore, the surface area in square feet rectangular prism when s=4 feet and h=6feet is 128 square feet.

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on the number line, 2.0 is to the right of 2, and multiplying 2.0 by 10 moves it 10 times as far to the right as 2.0 is from 2. This is why 2 is 10 times the value of 2.0.

What is the number line?

The number line is a visual representation of the set of all real numbers, which are the numbers that can represent any value on the continuous number scale, including fractions and decimals. On the number line, each point corresponds to a specific real number.

The number 2 is represented by a point on the number line, as is the number 2.0. These two numbers are different because 2.0 is a decimal number, while 2 is a whole number.

2 is 10 times the value of 2.0 if you multiply 2.0 by 10. This is because multiplying a number by 10 shifts its decimal point one place to the left, which increases its value by a factor of 10. For example, if you multiply 2.0 by 10, you get 20.0, which is 10 times the value of 2.0.

Hence, on the number line, 2.0 is to the right of 2, and multiplying 2.0 by 10 moves it 10 times as far to the right as 2.0 is from 2. This is why 2 is 10 times the value of 2.0.

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Answer:

264 kg.

Step-by-step explanation:

To convert from pounds to kilograms, divide the number of pounds by 2.20462. In this case, we have:

580 lb / 2.20462 = 263.74 kg

So, rounded to the nearest hundredth, the answer is 264 kg.

I'm sorry i don't know :(

He spend 0.48 per pounds

What is division ?

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

A group is divided into equal portions. Division can be used to divide a class into equal groups for a game or activity, or even to divide a pizza among a group of friends in equal quantities. Partitive division and quotative division are the two types of division.

As it is $5.76 for 12 pounds

∴ for one pound

5.76 / 12

= 0.48 pounds

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Services provided by public service companies are also known as utilities.

What are public utilities, housing expenses, cost of living and bills?

The term "public utilities" describes a group of particular services offered by entities and organisations that are both public and private and make up the public services sector.

The sum of a homeowner's monthly mortgage principal and interest payments and any additional costs related to their home constitutes their total housing expense.

The cost of living is the sum of money required in a certain location and time frame to meet necessities including housing, food, taxes, and medical care.

A declaration of money owed for products or services provided is referred to as a bill.

Based on the above definition,

Hence, services provided by public service companies are also known as utilities.

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Answer:

Step-by-step explanation:

let Rajani be carrying r = 9.725kg

let Mamata be carrying m = 8.500kg

difference = r - m = 9.725 - 8.500 = 1.225kg

hence Rajani is carrying 1.225kg more than Mamata

====================================================

Reason:

The leading coefficient is 6, which is the coefficient of the leading term (aka the first term). The constant is 5, which is the last term.

Here are some examples of what f(x) could be.

[tex]f(\text{x}) = 6\text{x}^2+\text{x}+5\\\\f(\text{x}) = 6\text{x}^3+2\text{x}^2-7\text{x}+5\\\\f(\text{x}) = 6\text{x}^5+4\text{x}^3-81\text{x}^2+5[/tex]

The middle terms don't matter and neither does the exponent on the leading term.

So this is what the general template would look like

[tex]f(\text{x}) = 6\text{x}^{n}+\ldots+5\\\\[/tex]

where n is a positive integer.

If we were to plug in x = 0, then all of the terms involving x go to zero. They cancel out. The only thing left standing would be the "5" at the very end.

So,

[tex]f(\text{x}) = 6\text{x}^{n}+\ldots+5\\\\f(0) = 6*0^{n}+\ldots+5\\\\f(0) = 0+0+\ldots+0+0+5\\\\f(0) = 5\\\\[/tex]

In short, the constant value is the y intercept of the polynomial curve. It allows us to quickly spot it without having to do much (or any) math.

This is why choice B is a false statement.

The other answer choices cannot be proven true or false since we don't have enough information about this particular function.

The answer to your problem is $26

The required probability for the 2 men's names are selected is 0.358.

Given that,
A doctor has 2 doses of flu protection vaccine left. He has 5 women and 8 men who want the medication.
The names of 2 of these people are selected at random, determining the probability that 2 men's names are selected is to be determined,

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
The number of ways to select 2 men = 8C2 = 28
The number of ways to select 2 people from 13 = 13C2 = 78
The probability of the 2 men's names being selected = 28 / 78 = 0.358

Thus, the required probability for the 2 men's names are selected is 0.358.

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Answer:

Step-by-step explanation:

B

The inverse of y=-x²+9 is [tex]x=\sqrt{9-y}[/tex]

What is Inverse of a Function ?

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.

The output of a function is returned by the inverse function, which also returns the initial value.

If f and g are inverse functions, then f(g(x)) = g(f(x)) = x. The initial value is fetched via a function that is its inverse.

For instance, f(x) = 2x + 5 = y

Therefore, the inverse of f is g(y) = (y-5)/2 = x. (x).

The relationship that results from swapping out an independent variable with a variable that depends on a given equation; the inverse may or may not be a function.

A function is said to be an inverse function if its own inverse is represented by the symbol f-1.

[tex]x^2=9-y\\\\\x=(9-y)^\frac{1}{2}\\\\ x=\sqrt{9-y}[/tex]  is the inverse of y=-x²+9

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Answer:

3_0

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

Isolate the variable by dividing each side b factors that don't contain the variable.

The area of the rectangle is 4 (7-2) unit².

A rectangle is a quadrilateral with four equal vertices and parallel sides of equal length.

Given, the sides of the rectangle are 4 and 7.

And in the diagram,

The rectangle overshadowed by the rectangle having the sides 4 and 2.

So, the sides of the shaded rectangle are 4 and (7-2).

So, the area of the rectangle

= length x width

= 4 x (7-2)

= 4 (7-2)

Therefore, the area is 4 (7-2) unit².

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Answer:

350 enrolled

Step-by-step explanation:

.7 x 20000 = 1400

.25 x 1400 = 350

Answer:

3500

Step-by-step explanation:

20000 * 0.70 = 14000

14000 * 0.25 = 3500

Answer:

6,63,9 and 90

Step-by-step explanation:

The slope of the table is 9.

36/4 is equal to 9.

54/9 = 6

7*9=63

81/9=9

10*9=90

the only criteria, really, to be a function is to assign exactly 1 y-value to every valid x-value. not 2 or 0 y-values.

we see here, x = 2 has one assigned y-value : y = 3.

x = 4 has y = 9.

x = 6 has y = 10.

x = 9 has y = 5.

there is no indication that there are more valid x-values.

each x-value used has exactly 1 y-value.

so, the criteria is fulfilled. it is a function.