Hector plays a video game that awards gems based on how long he plays. He made this graph to study how his playing time relates to number of gems:
A graph plots t=playing time in hours on the horizontal axis, from 0 to 7, in increments of 1, versus g=total gems on the vertical axis, from 0 to 48, in increments of 8, on a coordinate plane. Points are plotted as follows: (2, 16), (4, 32), and (6, 48).
A graph plots t=playing time in hours on the horizontal axis, from 0 to 7, in increments of 1, versus g=total gems on the vertical axis, from 0 to 48, in increments of 8, on a coordinate plane. Points are plotted as follows: (2, 16), (4, 32), and (6, 48).
How many total gems will Hector get if he plays for
10.5
10.510, point, 5 hours?
gems

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]\stackrel{h(x)}{y}~~ = ~~2x^3+3\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~2y^3 + 3} \\\\\\ x-3=2y^3\implies \cfrac{x-3}{2}=y^3\implies \sqrt[3]{\cfrac{x-3}{2}}=y=f^{-1}(x)[/tex]

Check the picture below.

Answer: A.

Step-by-step explanation:

Sarah made 6 dozen cupcakes which is (12 x 6)

Then if her co-workers or c ate 3 cupcakes EACH, it will be (c x 3)
and since they ate them it's subtraction with a left over of 45 cupcakes

The property illustrated for the given expression is substitution method.

The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.

Given that the two expressions are:

x=y+4 and y+4=-22

Here, the value of y + 4 is substituted in the value of x for the first expression.

Hence, the property illustrated for the given expression is substitution method.

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Plan B: Choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

A sample is only a small portion of the population.

Let's imagine you were interested in determining the average income for all Americans in your population.

Instead of knocking on every door in America because of time and money constraints, you decide to ask 1,000 random people. Your sample consists of these a thousand persons.

Given, A gardener wants to determine which of two brands of fertilizer is best for the plants.

And the gardener decides to conduct an experiment using 28 individual plants.

Plan A will be a biased sampling and the experiment would not yield

desired results.

Therefore, The gardener should choose 14 of the 28 plants at random. Apply Brand X fertilizer to those 14 plants and Brand Y fertilizer to the remaining 14 plants.

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The weighted average of the Coen's test scores is calculated to be 73.75

Each data point is multiplied by its weight before being added together to determine the weighted average. After that, add the weights for each data point. Last but not least, divide the weight*value products by the total weights.

The weighted average is calculated as below

Weighted average = (80 * 1 + 90 * 2 + 70 * 5 + 90 * 8) / (1 + 2 + 5 + 8)

Weighted average = 73.75

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Answer:

2 right, 4 down

Step-by-step explanation:

By subtracting 2 inside the function, the graph is shifted 2 to the right and by subtracting 4, it is shifted 4 down.

To think of this more intuitively, in the original function, inputting 0 would  yield the same output as plugging in a function with (x - 2) inside:

[tex]x^3=0^3=0\\(x-2)^3=(2-2)^3=0^3=0[/tex]

In addition, by subtracting -4, the value would always go down 4 from the original value of x^3:

[tex]x^3 = 0^3 = 0[/tex]  

[tex]x^3-4 = 0^3-4=0-4=-4[/tex]

By putting these together we get the answer above.

Answer:

x = 28

Step-by-step explanation:

Consider the two triangles ΔAPR and ΔCDR

We see that AP ║ CD

Therefore m∠PAR = m∠CR, m∠APR= m∠CDR
Angle ∠R is common to both triangles

So the triangles are similar

Therefore the ratios of the sides must be the same ratio

[tex]\dfrac{AR}{CR} = \dfrac{PR}{DR}\\\\[/tex]

AR = x + 10

CR = x

PR = 42 + 15 = 57

DR = 42

PR = 42 + 15 = 57

Plugging in the values for these sides:

[tex]\dfrac{x + 10}{x} = \dfrac{57}{42}\\[/tex]

Cross-multiplying we get

[tex]42(x + 10) = 57x\\\\42x + 420 = 57x\\\\420 = 57x - 42x = 15x\\\\15x = 420\\\\x = 420/15\\\\= 28[/tex]

Answer:

0.9, 0.6 7/10, 11/100, 0.21, 0.35

Step-by-step explanation:

Answer:

3 rd choice

Step-by-step explanation:

If you flip ΔABC over and lay it over ΔXYZ, you'll see how the sides correspond:

AB≅XZ

BC≅ZY

CA≅YX

just a quick addition to "MelRUZ" great reply above.  Check the picture below.

There are a total of 2285 people in the given town.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, fourteen percent of the town's population is above the age of 65.

Since there are 320 residents who are above the age of 65,

Thus,

14% of the population = 320

So,

1 % of the population = 320 /14

Thus,

Total population = 320/14 * 100

Total population of the town = 2285.71

Therefore, there are a total of 2285 people in the given town.

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The wrap has an area of  1.12π square inches.

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

Given, The net of a cylinder with a diameter of both circles labeled 1.6 inches.

So, The complete circle or the circumference of the circle will be the length of the wrap which is,

= 2π×0.8.

= 1.6π and the height of the wrap is 0.7 inches.

Therefore, the area of the wrap is 1.6π×0.7 square inches.

= 1.12π square inches.

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Answer: The real answer is 2.4π square inches (B)

Step-by-step explanation:

(Get ready for a long explanation)

So, we are trying to find the Surface Area of the cylinder.

We need to use the formula (SA = 2πr^2 + 2πrh)

Looks like a very long formula, but let do it in parts.

So the first part is just finding the area of the circle and multiplying by 2 because there are two bases. The area formula for circles is (πr^2)

But this time put a 2 in there. (2πr^2)

Okay lets get started. The diameter is 1.6. The radius is half the diameter, so divide 1.6 by 2 and you will get 0.8 which is the radius.

Now times the radius by itself (0.8 * 0.8 = 0.64) Now times that by 2 (0.64 * 2 = 1.28) The answer should be in terms of pi so just put the pi symbol next to 1.28  (1.28π)

On to the next part, (2πrh) you are basically taking the circumference of either circle base, and multiplying that by the height, which is (0.7)

The formula for Circumference is (2πr)

We already have the diameter so we don't need times the radius by 2.

So take the diameter of the circle base (1.6) and multiply that by the height, which is (0.7)
(1.6 * 0.7 = 1.12π)

Now for the last part, we need to add the two values together to find the surface area.

The first value we found is (1.28π ) and the second is (1.12π)

Now add (1.28π  + 1.12π = 2.4π)

Answer: 2.4π square inches

Sorry for the really long explanation. I took the same test and I got it right so here is proof that it is correct. Have a great day y'all.

Jada stacked 23 boxes inside the container.

Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.

Given that, Jada put some cube-shaped boxes having lengths 20 in, in a cubed container has side lengths of 60 inches in.

After, Jada stacks the boxes inside the container, there are still 32,000 in³ of empty space remaining in the container.

We need to find the number of the boxes in the container.

Volume of cube = (side)³

Volume of container = 60³ = 216000 in³

Volume of the container covered by stacking the boxes =

216000 - 32000

= 184000 in³

Volume of each box = 20³

= 8000 in³

Number of boxes in the container = volume of the container covered by stacking / volume of each box

Number of boxes = 184000 / 8000

= 23

Hence, Jada stacked 23 boxes inside the container.

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Answer:

He includes foreshadowing to indicate events

to come

The missing step of the solution is : Simplify by combining like terms: Option A

You should understand that these are the terms that contain the same variable which has the same power.

The  given question,

In step 2, the left side of the equation is  3/2 - 2x

We get 3/2  by adding 1/2 and 1 on the left side of the equation  1/2-2x+1=-13/2

As  1/2 and 1 are constants and all constant terms are like terms.

The second step would be simplify by combining like terms.

Therefore, the missing step of the solution is : Simplify by combining like terms.

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Inga is solving 2x² + 12x – 3 = 0 therefore the steps which she could use to solve the quadratic equation include the following below:

This is referred to as an algebraic equation of the second degree in x and its standard form is ax² + bx + c = 0

Solution to the quadratic equation

2x² + 12x - 3 = 0

2x² + 12x = 3

Divide by 2

x² + 6x = ³/₂

(x + 3)² = ³/₂ + 3²

x² + 6x + 9 = 9 + ³/₂

2(x² + 6x + 9) = 18 + 3

Thus, the steps that she could use to solve the quadratic equation is determined as option 1, 3 and 4.

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The dimensions of the playing field are a length is 99 ft, and a width is 55 ft.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The perimeter of a rectangle = 2(L+W)

Where W is the width of the rectangle and L is the length of the rectangle

Given that the length is 44ft longer than the width.

This means L = W + 44  ....(i)

Since the perimeter of a playing field is 308 ft

So 2(L+W) = 308

Substitute the value of the equation (i), and we get

2(W + 44 + W) = 308

2(2W + 44) = 308

4W + 88 = 308

4W = 220

W = 55

Substitute the value of W = 55 in equation (i), and we get

L = 55 + 44 = 99

Thus, the length is 99 ft, and the width is 55 ft.

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Therefore , the solution of the given problem of linear equation comes out to be  it is true for some n=k, where k represents one of the values for which we want to prove the proposition.

The equation y=mx+b serves as the basis for a regression model curve. The slope is B, and the y-intercept is m. Even if y or y were separate components, the foregoing sentence is occasionally referred to as a "mathematical formula combining two variables." Bivariate linear equations only have two variables. Application problems involving linear equations have no known solutions. The formula for a simple set of equations is Y=mx+b.

Here,

given :

=> n = k+2

In such situation, you can still use induction to demonstrate this claim for any numbers n2. (If you want to give it a try, it's a nice workout.) In the base situation, n=2 rather than n=1 would exist.

In order to be clear, I'd want to point out that the logical step does not consist of 'proving the assertion for n=k+1 given it is true for n=k.

The inductive step is to demonstrate that the assertion is true for n=k+1 after assuming that it is true for some n=k, where k represents one of the values for which we want to prove the proposition.

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Answer:

Assume the formula is true for some other value.

Step-by-step explanation:

It's the second step

n=k+2 isn't a thing

n=k "This is not part of a proof by mathematical induction."

Assume that the formula is true for the (k + 1) term. "This is not part of a proof by mathematical induction.

The total length on each side of the 5 foot painting is given by the equation A = 5 feet each

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total length on each side of the 5 foot painting be A

Now , the equation will be

The length of the painting = 5 feet

The length of the wall = 15 feet

So , when 5 foot wide painting is centered on a 15 foot wide wall , the remaining space will be

2A = length of the wall - length of the painting

Substituting the values in the equation , we get

2A = 15 - 5

2A = 10 feet

Now , total length on each side of the 5 foot painting A = 10 / 2

On simplifying the equation , we get

The total length on each side of the 5 foot painting A = 5 feet

Hence , the equation is A = 5 feet

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Answer: what the hell the happened

Step-by-step explanation:

The monthly mortgage payment for a $204,000 home with a 10% down payment and a 30 year loan at an interest rate of 3.5% would be approximately $808.44.

To calculate the monthly mortgage payment for a $204,000 home with a 10% down payment and a 30 year loan.

We'll need to first calculate the amount of the loan and then use the following formula to calculate the monthly payment:

M = P * r * (1 + r)^n / ((1 + r)^n - 1)

First, we'll calculate the down payment:

Down payment = 204,000 * 0.10 = $20,400

Next, we'll calculate the loan amount:

Loan amount = 204,000 - 20,400 = $183,600

Now, we'll need to convert the 30 year loan term into the number of payments (n) and the interest rate into the monthly interest rate (r):

n = 30 years * 12 months/year = 360 payments

r = (Annual interest rate) / 12 months/year

Assuming an annual interest rate of 3.5%, the monthly interest rate would be:

r = 0.035 / 12 = 0.002917

Finally, we can plug the values into the formula to calculate the monthly mortgage payment:

M = 183,600 * 0.002917 * (1 + 0.002917)^360 / ((1 + 0.002917)^360 - 1) = $808.44

Therefore, the monthly mortgage payment for a $204,000 home with a 10% down payment and a 30 year loan at an interest rate of 3.5% would be approximately $808.44.

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Answer:

six hindered twenty seven thousand three hundred ninety one

Step-by-step explanation:

please follow me

The solution to the inequality is x≥-1 or x ≥ 17. Option A

Inequalities are simply described as non-equal comparison between numbers, variables, expressions, etc.

They are used to organize numbers based on their sizes in the number line.

From the information given, we have that;

1/4|x + 1| ≥ 4

It is important to note that the symbol. "| |" modulus states that a number cannot be negative irrespective of its direction in the number line

Now, let's solve the inequality

cross multiply

|x + 1| ≥ 4 ×4

Multiply the values

|x + 1| ≥ 16

collect like terms

x ≥ 16 + 1

x ≥ 17

x ≥ - 1

Hence, the values are 17 and -1

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Answer:

y = 4x-5.

Step-by-step explanation:

So with the form y = mx+b, you already have y = 4x+b.

Plugging in (2,3) (x=2, y=3), we have 3 = 4*2+b, giving b = -5.

The graph of the cubic function [tex]f(x)=x^3[/tex] is plotted.

The correct answer is Option C.

Given data:

The graph of a cubic function is a type of polynomial graph that has the form  [tex]f(x) = ax^3 + bx^2 + cx + d[/tex] , where 'a', 'b', 'c', and 'd' are constants.

The graph of the cubic function  [tex]f(x) = x^3[/tex]  is a smooth curve that passes through the origin (0,0) and extends into the four quadrants of the Cartesian coordinate system.

Y-Intercept:

The cubic function passes through the origin (0,0), so it has a y-intercept of (0,0).

X-Intercept:

The x-intercept occurs when f(x) = 0.

On solving for x:

[tex]x^3 = 0[/tex]

x = 0

So, the cubic function has an x-intercept of (0,0).

Hence, the cubic function is [tex]f(x)=x^3[/tex] and is plotted below.

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The solution of the linear equations −7x + 3y = −48 and 3x + 5y = −36 will be (3, −9)

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equations are given below.

−7x + 3y = −48           ...1

3x + 5y = −36            ...2

Multiply equation 1 by 5 and equation 2 by - 3, then we have

−35x + 15y = −240

−9x − 15y = 108

Add both equations, then we have

−44x = −132

x = 132 / 44

x = 3

Then the value of 'y' is given as,

3(3) + 5y = −36

9 + 5y = −36

5y = −45

y = −9

The solution of the linear equations −7x + 3y = −48 and 3x + 5y = −36 will be (3, −9)

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f(x)=x is the parent function of the given function  f(x) = -2x + 2

A relation is a function if it has only One y-value for each x-value.

The given function is f(x)=-2x+2

We have to find the parent function of the given function.

A parent function is the simplest function of a family of functions that preserves the definition of the entire family.

f(x)=x is the parent function because from this function we can make transformations that allow us to obtain the function f(x) = -2x + 2

Hence, f(x)=x is the parent function of the given function  f(x) = -2x + 2

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We have compared the given expression using inequalities

[tex]1/4+2/5 > 1/4+1/5[/tex]

[tex]\frac{16}{20} > \frac{9}{20}[/tex].

What is the comparison of factor?

When evaluating a job, factor comparison is a systematic, scientific process that evaluates candidates according to a number of characteristics rather than grading the job as a whole.

Given:

[tex]1/4+2/5 \\ 1/4+1/5[/tex]

Cross multplying the  fractions:

[tex]\frac{1}{4}+\frac{2}{5}[/tex]  = [tex]\frac{4}{20}+ \frac{8}{20}[/tex]

         = [tex]\frac{12}{20}[/tex]

         =[tex]\frac{4}{5}[/tex]

Similarly ,

[tex]\frac{1}{4}+ \frac{1}{5}[/tex]=[tex]\frac{5}{20} +\frac{4}{20}[/tex]

        =[tex]\frac{9}{20}[/tex]

Compare 4/5 and 9/20.

Find the LCD:

The multiples of 5 are 5, 10, 15, 20, 25, etc. The multiples of20 are 20, 40, 60, 80, etc. The lowest common multiple is 20 so we use that as the lowest common denominator.

Convert each fraction to its equivalent fraction using the LCD.

For 4/5, multiply numerator and denominator by 4 to have LCD = 20 in the denominator.

=[tex]\frac{4}{5} *\frac{4}{4}[/tex]=[tex]\frac{16}{20}[/tex]

For 9/20,  20 is the denominator.

Compare the fractions. Because there are like denominators you can compare the numerators.16 is larger and 9 is smaller so,

[tex]\frac{16}{20} > \frac{9}{20}[/tex]

so,

[tex]1/4+2/5 > 1/4+1/5[/tex]

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