A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 80.



Regression Equation:

Final Answer:

The graph of the function g(x) is added as an attachment

From the question, we have the following parameters that can be used in our computation:

f(x) equals log2 x

Express the equation properly

So, we have

f(x) = log₂(x)

Also, we have

g(x) = -log₂(x - 3)

The transformation from f(x) to g(x) is that:

This means that

g(x) = -f(x - 3)

So, we apply the above transformations on the graph of f(x) to form g(x)

See attachment for graph of g(x)

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The next operation that should be done when evaluating this expression 9-12+-2+3(-3) is A. 3(-3)=-9

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

In this case, it should be noted that the expression given is written as 9-12+-2+3(-3). In PEDMAS, the first operation is parentheses. Therefore, the number on parentheses will be solved first.

In this case, the number in parentheses will be 3(-3). Therefore, the correct option is A.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

here we go~

[tex]\qquad \sf  \dashrightarrow \: 4x {}^{2} - 25y {}^{2} [/tex]

[ identity : a² - b² = (a + b)(a - b) ]

[tex]\qquad \sf  \dashrightarrow \: (2x) {}^{2} - (5y) {}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: (2x + 5y)(2x - 5y)[/tex]

The degree of the polynomial [tex]5x^{3} + 4x^{2} + 7x[/tex]  is 3 , that means it is a third degree polynomial called as cubic polynomial  .

What is Degree Of Polynomial ?

The degree of the polynomial is defined as  the highest power of the polynomial expression. But, if the polynomial has multiple variables, the degree of polynomial can be found by adding the powers of the different variables  in the polynomial expression.

For Example : the degree of polynomial ⇒  [tex]9x^{2} + 7x + 2[/tex] is  2 .

The polynomial is given as : [tex]5x^{3} + 4x^{2} + 7x[/tex] , we have to find the degree ,

So , we can see that the the term having the highest power of the given polynomial is [tex]5x^{3}[/tex] , and the degree is 3 .

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The equation that models the height of the tent, h, in feet, with respect to the horizontal distance in feet from the left edge, d, is h = 1.5 d + h0.

The height of the tent is 22. 5 feet at a horizontal distance of 15 feet.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The height of the tent varies at a rate of 1. 5 feet with the horizontal distance from the left edge.

This can be written as -

h = 1.5 d, where d is the distance.

So, the equations that models the situation is -

h = 1.5 d + h0

The peak of the tent is at 30 feet and is at a horizontal distance of 20 feet from the left edge.

So, when d =20, then h =30.

Plugging the values in the equation -

30 = 1.5 (20) + h0

30 = 30 + h0

h0 = 0

The height of the tent is 22. 5 feet.

So, now h = 1.5 d and h = 22.5.

Equating these two -

22.5 = 1.5 d

d = 22.5/1.5

d = 15

Therefore, the distance value is obtained as 15 feet.

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The probability of Greg being late again, along with the type of probability, is given as follows:

1/7, experimental probability.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

In the context of this problem, the outcomes are given as follows:

The probability of Greg being late is then calculated as follows:

3/21 = 1/7.

Which is an experimental probability, as the number of outcomes are taken from previous "experiments".

The other type of probability is theoretical, for example, a fair coin has a 50% chance of falling heads and 50% change of falling tails.

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Leo's balance after 8 months is $1725.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

Example:

2, 4, 8, 16 is a geometric sequence.

We have,

1500, 1530, and 1560 is a geometric sequence.

First term.

a = 1500

Common ratio.

r = 1.02

The nth term of a geometric sequence is a[tex]r^{n-1}[/tex].

Now,

For n = 8,

8th term.

= 1500 x [tex]1.02^7[/tex]

= 1500 x 1.15

= 1725

Thus,

The balance after 8 months is $1725.

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To rewrite the inequalities in slope-intercept form, the student would first need to solve for y.

2x + 3y > 6 can be rewritten as 3y > -2x + 6 and then solving for y by dividing both sides by 3, the student can have y > (-2/3)x + 2

x-4y > 8 can be rewritten as -4y > -x + 8, and then solving for y by dividing both sides by -4 , the student can have y < (1/4)x - 2

To graph the inequalities, the student would plot the y-intercepts of the equations, which are (0,2) and (0,-2) and then use the slope to find a second point to plot, and then graph the line. Then, based on the inequality symbol the student should shade the appropriate side of the line. If the inequality is greater than > or less than < then they shade one side, otherwise if the inequality is less than or equal to >= or greater than or equal to <= they shade both sides.

It's also important to remember that the slope intercept form is y=mx+b where m is the slope, and b is the y-intercept, if the student already has the equation in this form, they only need to plot the y-intercept point and use the slope to get a second point.

Step-by-step explanation:

what do you not understand ? please let me know where you need more instructions.

the basic rule : every term of one side has to be multiplied with every term of the other side, and the results are added (by using the correct signs of the products).

remember :

+ × + = +

- × - = +

+ × - = -

- × + = -

(3x - 3)(5x - 4) = 3x × 5x + 3x × -4 + -3 × 5x + -3 × -4 =

= 15x² - 12x - 15x + 12 = 15x² - 27x + 12

The solution of the function f(x) = 2(x - 3)² is at x = 3 as shown in the graph.

An equation is used to show the relationship between numbers and variables.

Polynomial can be classified based on degree as linear, quadratic, cubic.

Given the function:

f(x) = 2(x - 3)²

The graph of f(x) is plotted. The solution of the graph can be gotten from its x intercept. Hence the solution is at x = 3

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Answer:

Step-by-step explanation:Select any two random points on the graph of the line (preferably with integer coordinates).

Label them as A and B (in any order).

Calculate the "rise" from A to B. While going vertically from A to B, if we have to go

"up", then the rise is positive;

"down", then the rise is negative.

Calculate the "run" from A to B. While going horizontally from A to B, if we have to go

"right", then the run is positive;

"left", then the run is negative.

Now, use the formula: slope = rise/run.

Answer: 70-20x = 60-15x, where x is the number of pizzas purchased.

Step-by-step explanation:

(TLDR, the solution to the given equation is that the cards will have the same amount of money left on them if both jim and clara buy two pizzas each. feel free read my explanation on how to write equations like this in the future, should you need it.)

so, we know that since jim and clara received $70 and $60 gift cards (respectively), these numbers are called constants, because their original values do not depend on anything (they are given). while these numbers may decrease with the amount of pizzas bought, their original values are fixed.

now, the price for one pizza at jim's pizza restaurant is $20, right? so if you buy 2 pizzas, it'll be $40, 3 pizzas are $60, and so on. but we can actually represent the price of the pizzas as 20x (where x is the number of purchased pizzas, and 20 is the price of one pizza), and this expression works for any number of pizzas you buy. you can also apply this to clara's restaurant, as the total price of the number of pizzas she buys is represented by 15x.

the words charges and left in this problem tells you that you're going to need to subtract from the total amount of money on the gift cards. using the expressions above, the amount of money jim has left on his card can be expressed as 70 (amount of money on the card) MINUS 20x (number of money spent on however many pizzas were bought (x)). likewise, the amount of money left on clara's card after she buys however many pizzas can be represented as 60-15x. you can then set the equations equal to each other and solve for x, which tells you how many pizzas they each need to buy to have the same number of $$ left on their cards.

70-20x = 60-15x

10=5x

2=x. hope this helped :3

Answer:

James used 5 yards of fabric to make 7 identical bags, so he used 5/7 yards of fabric per bag.

Step-by-step explanation:

Answer:

=3/11 of (1×3+5/9)÷9/15

=3/11 of (8/9)÷9/15

=3/11 of 8/9÷9/15

=8/33÷9/15

=8/33×15/9

=40/99

*mark me brainliest

:)

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The values of p that satisfy the inequality for all[tex]$q > 0$[/tex] are

[tex]$p > \frac{3+\sqrt{21}}{2}$[/tex]and [tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex]

Given:[tex]$$\frac{3(pq^2 p^2q 3q^2 3pq)}{p q} > 2p^2q^2$$[/tex]

Step 1: Multiply both sides by [tex]$\frac{pq}{3}$[/tex] to get: [tex]$$pq^3 p^2q 3q^2 3pq > 2p^2q^3$$[/tex]

Step 2: Simplify the left side to get: [tex]$$3p^2q^3+3pq^3+3q^2 > 2p^2q^3$$[/tex]

Step 3: Divide both sides by [tex]$q^2$[/tex] to get: [tex]$$3p^2q+3pq+3 > 2p^2$$[/tex]

Step 4: This is a quadratic inequality in[tex]$p$[/tex]with solution[tex]$p > \frac{3+\sqrt{21}}{2}$[/tex] and [tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex]. Therefore, the values of p that satisfy the inequality for all  [tex]$p > \frac{3+\sqrt{21}}{2}$[/tex] and [tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex]

the given inequality can be simplified to a quadratic inequality in p by multiplying both sides by[tex]$\frac{pq}{3}$[/tex], simplifying the left side, and dividing both sides by[tex]$q^2$[/tex] The solution of the quadratic inequality is

[tex]$p > \frac{3+\sqrt{21}}{2}$[/tex] and

[tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex]. Therefore, the values of p that satisfy the inequality for all [tex]$q > 0$[/tex] are

[tex]$p > \frac{3+\sqrt{21}}{2}$[/tex]and

[tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex], which means that any value of p that is greater than[tex]$\frac{3+\sqrt{21}}{2}$[/tex] or less than

[tex]$-\frac{3+\sqrt{21}}{2}$[/tex]will satisfy the inequality for all [tex]$q > 0$[/tex]

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To convert the log base 2 to log base 10, we can use the change of base formula for logarithms. The change of base formula for logarithms is as written:

log b(x)=logc(x) logc(b)

By Using this formula, we can convert or find log base 2 to log base 10, where log base 10 is called the common logarithm, and we denote log10 (x) as log(x). The change of base formula gives the following:

log2(x)=log10(x)log10(2)=log(x)log(2)

This gives us the formula we can use to convert a logarithm with base 2 to a common logarithm with base 10.

The log function of e to the base 10 is denoted as “log 10 e”. Where the value of e is 2.7182818. The natural log function of e is denoted as “log e e”.

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Answer:

v=πr²h

divide both sides by πh

v/πh=r²

r²=v/πh

square root both sides

r=√v/√πh

I hope this helps

The 3 parts of a quadratic equation are standard form, factored form and vertex form.

A quadratic equation is a polynomial equation of degree two in one variable of type f(x) = ax² + bx + c where a, b, c, ∈ R and a ≠ 0.

There are three forms of quadratic equations

Standard form of quadratic equation y = ax² + bx + c

factored form of quadratic equation y = a(x − r₁)(x − r₂​)

Vertex form of quadratic equation y = a(x − h)² + k

Each of the above quadratic forms looks unique, allowing the different problems to be more easily solved in one form than another.

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Answer:D. 1 and 2

Step-by-step explanation:

Domain cannot repeat

To solve this equation for y, you can follow these steps:

First, get all the terms with y on one side of the equation and all the other terms on the other side. To do this, you can add 2/5 to both sides to get rid of the 2/5 on the left side:

0.5y - 2 2/5 + 2/5 = 1/2y + 2.4 + 2/5

Simplify the left side of the equation:

0.5y - 2 + 2/5 = 1/2y + 2.4 + 2/5

0.5y - 2 + 2/5 + 2/5 = 1/2y + 2.4 + 2/5 + 2/5

0.5y - 2 + 4/5 = 1/2y + 2.4 + 4/5

Combine like terms on each side:

(0.5y + 4/5) - 2 = (1/2y + 2.4) + 4/5

Simplify:

0.5y + 4/5 - 2 = 1/2y + 2.4 + 4/5

0.5y - 2 + 4/5 = 1/2y + 2.4 + 4/5

Combine like terms on each side:

(0.5y + 4/5) = (1/2y + 2.4) + 4/5

Simplify:

0.5y + 4/5 = 1/2y + 2.4 + 4/5

Combine like terms on each side:

0.5y = 1/2y + 2.4

Subtract 1/2y from both sides:

0.5y - 1/2y = 1/2y - 1/2y + 2.4

0 = 2.4

Solve for y:

0 = 2.4

This equation has no solution, so there is no value of y that satisfies the given equation.

Answer:

Step-by-step explanation:nosoulution

The expression is t = 0.3 + 3.2p, where t is the box's overall weight and p is the number of plaques it contains.

Let's review the data given to us to properly respond to the question:

Weight of a box by itself = 0.3 kg

Weight of a plaque = 3.2 kg

The expression can be used to determine the total weight of the box :

We shall use the following phrase to respond to the query:

Total weight of the box in kg = t

Number of plaques inside the box = p

Hence, the expression t = 0.3 + 3.2p

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The correct relation which shows the function is,

⇒ (-6, 2), (-2, 3), (2, 7), (6, 2)

Option B is true.

A relation between a set of inputs having one output each is called a function.

Now, We know that;

Function is a relation between a set of inputs having one output each.

So, By given options;

A. (-2, -2), (-6, -5), (2, 8), (2, 2)

Here, Two value of outputs 8, 2 have same input 2.

So, This is not a function.

B. (-6, 2), (-2, 3), (2, 7), (6, 2)

Here, A set of inputs having one output each.

So, This is function.

C. (6, -10), (-6, 7), (6, 6), (-6, 12)

Here, Two value of outputs - 10, 6 have same input 6.

So, This is not a function.

D. (-6, 0), (-2, 5), (-6, -3), (2, 9)

Here, Two value of outputs 0, -3 have same input -6.

So, This is not a function.

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The annual income of a certain household that has a z-score of 1.5, is 80,000.

The relationship between a value and a group of values' mean is described statistically by the Z-score. Standard deviations from the mean serve as the unit of measurement for Z-score. The score for a data point is equal to the mean score if the Z-score is 0. A value that deviates by one standard deviation from the mean is indicated by a Z-score of 1.0.

Z-scores can either be positive or negative, with a positive value indicating that the score is above the mean and a negative value indicating that the score is below the mean. Z-scores are measurements of an instrument's variability used in investing and trading that traders can use to estimate volatility.

Let the annual income be x.

x has μ = 50000, σ = 20000

We know that for given x, z = (x−μ)/σ

Given that z - score = 1.5

Substituting the values we get

⇒ 1.5 = (x−50000)/20000

​⇒ 1.5 × 20000 = x−50000

​⇒ 30000 = x − 50000

⇒ x = 30000 + 50000

⇒ x = 80,000

Thus, The annual income of a certain household that has a z-score of 1.5, is 80,000.

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The smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4 is 11.

To compute this, first convert 5 to binary and base-4:

5 in binary: 101

5 in base-4: 11

Since 11 is the same in both bases, the next number that would be a palindrome in both bases is 11.

To find the base 10 number of this palindrome, we convert 11 from binary and base-4 to base 10:

11 in binary: 1011

11 in base-4: 111

Therefore, the smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4 is 11.

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Answer:

The answer to this question is x= 51/4

Using trigonometric ratios, the value of x is as follows:

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the angle of a right angle triangle can be found using trigonometric ratios as follows:

Hence, let's find angle x

Therefore,

sin x = opposite / hypotenuse

opposite side = 7 ft

hypotenuse side = 18 ft

Hence,

sin x = 7 / 18

x = sin⁻¹ 7 / 18

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The diameter of the circle C/13

The formula provides the circumference of a circle.

The circumference of any shape in mathematics designates the path or limit that surrounds the shape. In other words, the circumference, sometimes referred to as the perimeter, aids in figuring out how long the contour of a shape is. The size and perimeter of a circle are, as we all know, its two most important properties.

C = pi * d, where d is the diameter and c is the circumference.

C = pi * 13 gives the diameter as 13.

Subtract 13 from each side, C/13 = d.

Dimensions are C/13.

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Answer:

56a+40b

Step-by-step explanation:

43a plus 13a is 56a, -12b + 52b is 40b, together it's 56a+40b

The domain and scope of the identity function are the same. Equation for the identity function is  f(x) = x, or y = x.

An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.

identity function are the same.

Equation for the identity function is

f(x) = x, or y = x.

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On solving the provided question, we can say that by unitary method Irene spend on gas =  $ 33.82

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

by unitary method

Irene must pay back the money she used for gas.

Irene filled up her tank with gas for $33.82.

One gallon of gasoline costs $3.80.

There are 6.1 gallons of the petrol Irene purchased in the tank.

amount required = 15 -6.1 = 8.9 gallons

1 gallon = 3.8 dollars

8.9 gallons = $ 33.82

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