Identify which year’s population will hit zero

(F - G)(x) is equal to -2x - 3 when we subtract G(x) from F(x). Option B

To find (F - G)(x), we subtract G(x) from F(x). Let's substitute the given functions into the expression:

(F - G)(x) = F(x) - G(x)

F(x) = x + 2

G(x) = 3x + 5

Substituting these values, we have:

(F - G)(x) = (x + 2) - (3x + 5)

Now, let's simplify the expression:

(F - G)(x) = x + 2 - 3x - 5

Combining like terms, we get:

(F - G)(x) = -2x - 3

Therefore, the correct answer is -2x - 3.

Option B (-2x - 3) is the correct answer.

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Answer:

f(x)=5x

g(x)=1/x-5

f(g)=5(1/x-5)

f(x)=5/x- 25

therefore domain is x=0

the answer is D

The figure can be divided into a rectangle and 2 triangles

The area of the parallelogram is  189 square units

First, we have the determine the length of the base and height.

The distance between the lines x = 9 and f(x) = 9 + 2x is the height

We have that the line parallel to f(x) passes through (4, 11)

The equation in point-slope form is;

y - 11 = 2(x - 4

y = 2x + 3

Substitute x = 9 in the equation,  y = 2x + 3.

y = 2(9) + 3 = 21

The  points are then (9, 21) and (9, 0).

The distance between the y-axis and the line x = 9 is the base.

Base = 9 units.

The formula for calculating area of a parallelogram is given by ;

= base × height

= 9 × 21

= 189 square units.

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The lengths of the three sides of the pie-shaped lake-front lot are:

Shortest side: 100 feet

Second side: 400 feet

Third side: 600 feet

Let's denote the lengths of the three sides of the triangular lake-front lot as x, x + 300, and x + 500.

The perimeter of a triangle is the sum of its three sides, so we can set up an equation to represent the given information:

x+ (x + 300) + (x + 500) = 1,100

Simplifying the equation:

3x + 800 = 1,100

Subtracting 800 from both sides:

3x = 300

Dividing both sides by 3:

x = 100

Now that we have found the length of the shortest side, we can substitute this value back into the expressions for the other two sides:

Shortest side (x) = 100 feet

Second side (x + 300) = 100 + 300 = 400 feet

Third side (x + 500) = 100 + 500 = 600 feet

Therefore, the lengths of the three sides of the pie-shaped lake-front lot are:

Shortest side: 100 feet

Second side: 400 feet

Third side: 600 feet

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Answer:

w(25) = 96

There are 96 wolves in the year 2020

Step-by-step explanation:

Given:

[tex]w(x)=14\cdot 1.08^{x}[/tex]

w(25) =

[tex]w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96[/tex]

Number of years : 1995 + 25 = 2020

In 2020, there are 96 wolves

a) The fruit vendor sold 3/10 of the grapefruits on Saturday, b) The vendor had 100 grapefruits at first, and c) 40 grapefruits were sold on Friday.

a) On Saturday, the fruit vendor sold 1/2 of the remaining grapefruits. Since 2/5 of the grapefruits were sold on Friday, there are 3/5 of the original amount left. Therefore, on Saturday, the vendor sold (1/2) x (3/5) = 3/10 of the grapefruits.

b) To find the original number of grapefruits, we need to calculate the total amount remaining after Friday's sales. Since there were 60 grapefruits left after Saturday's sales and 3/5 of the original amount remained, we can set up the equation (3/5) [tex]\times[/tex]x = 60, where x represents the original number of grapefruits.

Solving for x, we have x = (60 x 5) / 3 = 100 grapefruits. Therefore, the fruit vendor had 100 grapefruits at first.

c) To find the number of grapefruits sold on Friday, we subtract the amount remaining after Friday's sales from the original number. 2/5 of the grapefruits were sold on Friday, so the number sold is (2/5) x 100 = 40 grapefruits.

In summary, a) the fruit vendor sold 3/10 of the grapefruits on Saturday, b) the vendor had 100 grapefruits at first, and c) 40 grapefruits were sold on Friday.

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Answer:

the possible length and width b:

1 and 20

10 and 2

5 and 4

120 = 1*20*6

120 = 10*2*6

120 = 5*4*6

The possible length and width for Derek's rectangular prism with a volume of 120 cubic inches and a height of 6 inches is 6 inches and 20 inches, respectively.

To find the possible length and width of Derek's rectangular prism, we can use the formula for the volume of a rectangular prism:

Volume = Length x Width x Height

Given that the volume is 120 cubic inches and the height is 6 inches, we can substitute these values into the formula:

120 = Length x Width x 6

To find the possible values for length and width, we need to factorize 120 and check the combinations that satisfy the equation. Let's find the factors of 120:

1 x 120

2 x 60

3 x 40

4 x 30

5 x 24

6 x 20

8 x 15

10 x 12

Now let's substitute these factors into the equation and solve for the missing dimension:

For the combination 1 x 120:

120 = 1 x 120 x 6

This does not work because the width would be 120 inches, which is not feasible.

For the combination 2 x 60:

120 = 2 x 60 x 6

This does not work because the width would be 60 inches, which is not feasible.

For the combination 3 x 40:

120 = 3 x 40 x 6

This does not work because the width would be 40 inches, which is not feasible.

For the combination 4 x 30:

120 = 4 x 30 x 6

This does not work because the width would be 30 inches, which is not feasible.

For the combination 5 x 24:

120 = 5 x 24 x 6

This does not work because the width would be 24 inches, which is not feasible.

For the combination 6 x 20:

120 = 6 x 20 x 6

This works because the width would be 20 inches:

120 = 6 x 20 x 6

120 = 720

This combination satisfies the equation.

For the combination 8 x 15:

120 = 8 x 15 x 6

This does not work because the width would be 15 inches, which is not feasible.

For the combination 10 x 12:

120 = 10 x 12 x 6

This does not work because the width would be 12 inches, which is not feasible.

Therefore, the possible length and width for Derek's rectangular prism with a volume of 120 cubic inches and a height of 6 inches is 6 inches and 20 inches, respectively.

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The canoe's actual speed is approximately 9.66 mph at a bearing of 12° south of east.

To determine the canoe's actual speed and direction, we need to consider the vector addition of the canoe's velocity and the current.

Let's start by drawing a diagram to visualize the problem.

We'll use a scale where 1 cm represents 10 mph.

Draw a line segment representing the canoe's velocity of 10 mph at a bearing of 25° south of east.

From the endpoint of the canoe's velocity vector, draw another line segment representing the current's velocity of 2 mph at a bearing of 80° west of south.

Connect the starting point of the canoe's velocity vector with the endpoint of the current's velocity vector to form a triangle.

Next, we can find the resultant velocity (actual speed and direction) of the canoe by calculating the vector sum of the canoe's velocity and the current's velocity.

Using the law of cosines, we can find the magnitude of the resultant velocity:

c² = a² + b² - 2ab [tex]\times[/tex] cos(C)

Where:

a = 10 mph (canoe's velocity)

b = 2 mph (current's velocity)

C = 80° (angle between the velocities)

Substituting the values:

c² = 10² + 2² - 2 [tex]\times[/tex] 10 [tex]\times[/tex] 2 [tex]\times[/tex] cos(80°)

c² = 100 + 4 - 40 [tex]\times[/tex] cos(80°)

Solving for c, the magnitude of the resultant velocity:

c ≈ √(100 + 4 - 40 [tex]\times[/tex] cos(80°))

c ≈ √(104 - 40 [tex]\times[/tex] cos(80°))

To find the direction, we can use the law of sines:

sin(A) / a = sin(C) / c

Where:

A = 25° (angle of the canoe's velocity)

a = 10 mph (magnitude of the canoe's velocity)

C = 80° (angle between the velocities)

c ≈ √(104 - 40 [tex]\times[/tex] cos(80°)) (magnitude of the resultant velocity)

Substituting the values:

sin(25°) / 10 = sin(80°) / √(104 - 40 [tex]\times[/tex] cos(80°))

Solving for sin(80°):

sin(80°) ≈ (sin(25°) [tex]\times[/tex] √(104 - 40 [tex]\times[/tex] cos(80°))) / 10

Finally, we can use the inverse sine function to find the direction:

Direction ≈ arcsin((sin(25°) [tex]\times[/tex]√(104 - 40 [tex]\times[/tex] cos(80°))) / 10)

Calculating the numerical values using a calculator will give us the actual speed and direction of the canoe.

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The volume of concrete required is

The volume of concrete required is solved by area * thickness

Area of the figure

First section = 20 * 8 = 160

second section = π(R² - r²)/4 = π(16² - 8²)/4 ≈ 151

Third section = 12 * 8 = 96

sum of areas = 160 + 151 + 96 = 407 ft

Volume of concrete required = volume of the shape

= sum of areas * thickness

thickness = 6'' = 0.5

= 407 * 0.5

= 203.5 cubic ft

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True, the surface area of the cylinder is 100units²

The surface area of a three-dimensional object is the sum of the area of all the outer surfaces, it is also measured in square units.

The surface area of a cylinder is expressed as;

SA = 2πrh + 2πr²

where 2πr² is the area of the bases

2πrh = lateral area

75 = 2 × 3.14 × 6 × r

r = 75/37.68

r = 1.99 unit

base area = 2 × 3.14 × 1.99²

= 25 units ( nearest whole number)

The surface area = 75+25

= 100units²

Therefore the surface area of the cylinder to nearest whole number is 100units².

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Answer:

(8,5)(0,-3)

Step-by-step explanation:

-y=-x+3

y=x-3

Substitute for y:

(x-3)^2-2x=9

x^2-6x+9-2x=9

x^2-8x=0

x(x-8)=0

x=0,8

if x=0,

0-y=3

y=-3

if x=8

8-y=3

-y=-5

y=5

Answer :

x - y = 3

x = 3 + y

y^2 - 2x = 9

y^2 - 2(3+y) = 9

y^2 - 2y -6 -9 = 0

y^2 - 2y -15 = 0

Factorize

y = -3 y = 5

when y = -3

x -(-3) = 3

x = 0

when y = 5

x - 5 = 3

x = 8

Answer:

Step-by-step explanation:

65x2-26x

Using the future value formula and an equation, we can see that Larry must deposit $263.48 each month.

To determine how much Larry should deposit each month into his account so that both men will have the same amount of money at age 65, we need to calculate the monthly deposit amount for Larry.

Let's break down the problem into steps:

Step 1: Calculate the number of months each person will be making deposits.

Both Ben and Larry will make monthly deposits for (65 - 21) * 12 = 528 months.

Step 2: Calculate the future value of Ben's account at age 65.

Using the formula for the future value of an ordinary annuity:

[tex]FV = P * [(1 + r)^n - 1] / r[/tex]

where:

Since Ben has been depositing $200 at the end of each month for 528 months, we can substitute the values into the formula:

[tex]FV_Ben = 200 * [(1 + 0.035/12)^{528} - 1] / (0.035/12)[/tex]

Step 3: Calculate the future value of Larry's account at age 65.

Larry started depositing 5 years after Ben, so he will only be making deposits for (65 - 21 - 5) * 12 = 456 months.

Using the same formula, we can calculate the future value for Larry:

[tex]FV_Larry = P * [(1 + 0.035/12)^{456} - 1] / (0.035/12)[/tex]

Step 4: Set up an equation to find the monthly deposit amount for Larry.

Since both Ben and Larry will have the same amount at age 65, we equate the future values:

FV_Ben = FV_Larry

[tex]200 * [(1 + 0.035/12)^{528} - 1] / (0.035/12) = P * [(1 + 0.035/12)^{456} - 1] / (0.035/12)[/tex]

Step 5: Solve the equation for P (the monthly deposit amount for Larry).

[tex]P = [200 * [(1 + 0.035/12)^{528} - 1] / [(1 + 0.035/12)^{456} - 1]\\\\P = 263.48[/tex]

That is how much he must deposit per month.

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The calculated percentage error with the assumed answer of 10%

To find the percentage error in actual weights, we can use the formula:

Percentage Error = [(|Measured Value - Expected Value|) / Expected Value] * 100%

In this case, the expected weight is 4 ounces. Let's assume the measured value is 10% off from the expected value. So the measured value would be:

Measured Value = Expected Value + (10% of Expected Value)

              = 4 ounces + (10/100) * 4 ounces

              = 4 ounces + 0.4 ounces

              = 4.4 ounces

Now we can calculate the percentage error:

Percentage Error = [(|4.4 ounces - 4 ounces|) / 4 ounces] * 100%

               = [(0.4 ounces) / 4 ounces] * 100%

               = (0.4/4) * 100%

               = 0.1 * 100%

               = 10%

Comparing the calculated percentage error with the assumed answer of 10%, we can see that they are the same.

The percentage error represents the deviation from the expected value as a percentage of the expected value itself. In this case, it indicates that the actual weights deviate by 10% from the expected weight of 4 ounces. The calculated percentage error with the assumed answer of 10%

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The point on the number line that is 5/7 of the way from A = -4 to B = 17 is approximately -1.8571.

To find the location of a point on the number line that is a certain fraction of the way from one point to another, we can use the concept of linear interpolation.

In this case, we want to find the point that is 5/7 of the way from A = -4 to B = 17.

To calculate this point, we can use the formula:

Point = A + (Fraction × Distance)

where A is the starting point, Fraction is the desired fraction, and Distance is the total distance between the two points.

In this case, A = -4, B = 17, and the desired fraction is 5/7. The distance between A and B can be calculated as:

Distance = B - A = 17 - (-4) = 21

Plugging in these values, we have:

Point = -4 + (5/7 × 21)

Simplifying the expression, we get:

Point = -4 + (15/7) = -4 + 2.1429 ≈ -1.8571

Therefore, the point on the number line that is 5/7 of the way from A = -4 to B = 17 is approximately -1.8571.

Among the given options, none of them match the calculated value. However, the closest option is C. 9.

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Answer:

Intersecting (fourth answer choice)

Step-by-step explanation:

First, let's convert both lines to slope-intercept form, whose general equation is y = mx + b, where

Converting y - 3x = 4x to slope-intercept form:

(y - 3x = 4x) + 3x

y = 7x

Thus, the slope of this line is 7 and the y-intercept is 0.

Converting 6 - 2y = 8x to slope-intercept form:

(6 - 2y = 8x) - 6

(-2y = 8x - 6) / -2

y = -4x + 3

Thus, the slope of this line is -4 and the y-intercept is 3.

Checking if y = 7x and y = -4x + 3 are perpendicular lines:

We can show this in the following formula:

m2 = -1 / m1, where

Thus, we only have to plug in one of the slopes for m1.  Let's do -4.  

m2 = -1 / -4

m2 = 1/4

Thus, the slopes 7 and -4 are not negative reciprocals of each other so the two lines are not perpendicular.

 Checking if y = 7x and y = -4x + 3 are parallel lines:

The slopes of parallel lines are equal to each other.

Because 7 and -4 are not equal, the two lines are not parallel.

Checking if the lines intersect:

Method to solve the system:  Elimination:

We can multiply the first equation by -1 and keep the second equation the same, which will allow us to:

-1 (y = 7x)

-y = -7x

----------------------------------------------------------------------------------------------------------

    -y = -7x

+

    y = -4x + 3

----------------------------------------------------------------------------------------------------------

(0 = -11x + 3) - 3

(-3 = -11x) / 11

3/11 = x

Now we can plug in 3/11 for x in y = 7x to find y:

y = 7(3/11)

y = 21/11

Thus, x = 3/11 and y = 21/11

We can check our answers by plugging in 3/11 for x 21/11 for y in both y = 7x and y = -4x + 3.  If we get the same answer on both sides of the equation for both equations, the lines intersect:

Checking solutions (x = 3/11 and y = 21/11) for y = 7x:

21/11 = 7(3/11)

21/11 = 21/11

Checking solutions (x = 3/11 and y = 21/11) for y = -4x + 3:

21/11 = -4(3/11) + 3

21/11 = -12/11 + (3 * 11/11)

21/11 = -12/11 + 33/11

21/11 = 21/11

Thus, the lines y = 3x = 4x and 6 - 2y = 8x are intersecting lines (the first answer choice).

This also means that lines are not skew since lines had to be neither perpendicular nor parallel nor intersecting to be skew.

The quotient of the division is x² - 6x + 43 and the remainder is 0

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

P(x) = x³ + 4x² - 17x + 430

d(x)= x + 10

Using the long division method of quotient, we have

x + 10 | x³ + 4x² - 17x + 430

The division steps are as follows

           x² - 6x + 43

x + 10 | x³ + 4x² - 17x + 430

           x³ + 10x²

--------------------------------------------------------------

                     -6x² - 17x + 430

                     -6x² - 60x

--------------------------------------------------------------

                                 43x + 430

                                 43x + 430

--------------------------------------------------------------

                                         0

Hence, the quotient is x² - 6x + 43 and the remainder is 0

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Answer:

x = 10

Step-by-step explanation:

the figure inscribed in the circle is a cyclic quadrilateral , all 4 vertices lie on the circumference.

the opposite angles in a cyclic quadrilateral sum to 180° , that is

6x + 1 + 10x + 19 = 180

16x + 20 = 180 ( subtract 20 from both sides )

16x = 160 ( divide both sides by 16 )

x = 10

Answer:

Por lo tanto, el capital final después de 8 años sería de aproximadamente $2061.68.

Step-by-step explanation:

Para calcular el capital final, utilizaremos la fórmula del interés compuesto:

Capital Final = Capital Inicial * (1 + Tasa de Interés)^Tiempo

Donde:

Capital Inicial = $1200

Tasa de Interés = 8% = 0.08 (expresada como decimal)

Tiempo = 8 años

Sustituyendo los valores en la fórmula:

Capital Final = $1200 * (1 + 0.08)^8

Calculando el resultado:

Capital Final = $1200 * (1.08)^8 ≈ $2061.68

Por lo tanto, el capital final después de 8 años sería de aproximadamente $2061.68.

The average slope of the climb is approximately 0.404.

To find the average slope of the climb, we need to calculate the change in elevation divided by the horizontal distance covered.

Change in elevation = Final elevation - Initial elevation = 1943 ft - 875 ft = 1068 ft

Horizontal distance covered = 2645 ft

Average slope = Change in elevation / Horizontal distance covered = 1068 ft / 2645 ft

Using a calculator or dividing these values, we find that the average slope is approximately 0.404 to the nearest hundredth.

The average slope of the climb is approximately 0.404. This means that for every 1 foot of horizontal distance covered, the hiker ascends approximately 0.404 feet in elevation.

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The polynomial with real coefficients from the zeros is P(x) = 2x³ - 18x² + 2x + 58

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

zeros =  5+2i, 5-2i, -1

One such polynomial P(x) can be defined as

P(x) = x³ - 9x² + x + 29.

When this polynomial is multiplied by a costant, the roots and zeros remain the same

Let the constant be 2

So, we have

New P(x) = 2(x³ - 9x² + x + 29)

Evaluate

New P(x) = 2x³ - 18x² + 2x + 58

Hence, the function is P(x) = 2x³ - 18x² + 2x + 58

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The second pair of points representing the solution set of the system of equations is (-6, 29).

To find the second pair of points representing the solution set of the system of equations, we need to substitute the x-coordinate of the second point into one of the equations and solve for y.

Given the system of equations:

y = x^2 - 2x - 19

y + 4x = 5

Substituting the x-coordinate of the second point (-6) into equation 2:

y + 4(-6) = 5

y - 24 = 5

y = 5 + 24

y = 29

Therefore, the second pair of points representing the solution set of the system of equations is (-6, 29).

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Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

y = x2 − 2x − 19

y + 4x = 5

The pair of points representing the solution set of this system of equations is (-6, 29) and

_________.

The cost to ship 1,800 lbs of goods from Atlanta to Louisville using overnight shipping is $7,200.

To calculate the cost of shipping 1,800 lbs of goods from Atlanta to Louisville using overnight shipping, we need to determine the price per 100 lbs and apply the 100% premium for overnight shipping.

From the information, we can see that the price per 100 lbs for the distance range of 401-600 miles is $200.

Since the distance from Atlanta to Louisville is 390 miles, which falls within the 401-600 miles range, we can use the corresponding price per 100 lbs of $200.

To calculate the cost, we need to divide the total weight of 1,800 lbs by 100 to get the number of 100 lb units: 1,800 lbs / 100 = 18 units.

Then, we multiply the number of units by the price per 100 lbs, taking into account the 100% premium for overnight shipping:

18 units * $200 * 2 = $7,200.

Therefore, the cost is $7,200.

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a. The distribution of X is X ~ N(68, 14).

b. The corresponding area to the right of 0.9286, which is approximately 0.1772.

c. The longest amount of time a patron can spend and still receive the discount is approximately 48.5654 minutes.

d. The Inter Quartile Range (IQR) for time spent at the hot springs is approximately 21.373 minutes.

a. The distribution of X is X ~ N(68, 14), where X represents the amount of time a person spends at Grover Hot Springs, 68 is the mean, and 14 is the standard deviation.

b. To find the probability that a randomly selected person stays longer than 81 minutes, we need to calculate the area under the normal curve to the right of 81.

Using the z-score formula: z = (x - μ) / σ, where x is the value (81), μ is the mean (68), and σ is the standard deviation (14).

Plugging in the values, we have z = (81 - 68) / 14 = 0.9286.

Using a standard normal distribution table or a calculator, we can find the corresponding area to the right of 0.9286, which is approximately 0.1772.

c. To find the longest amount of time a patron can spend at the hot springs and still receive the discount, we need to find the value that corresponds to the lowest 8% of the distribution.

Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to the 8th percentile, which is approximately -1.4051.

Using the z-score formula, we can calculate the longest amount of time: x = μ + z [tex]\times[/tex] σ = 68 + (-1.4051) [tex]\times[/tex] 14 = 48.5654 minutes.

Therefore, the longest amount of time a patron can spend and still receive the discount is approximately 48.5654 minutes.

d. The Inter Quartile Range (IQR) is a measure of the spread of the data and represents the range between the first quartile (Q1) and the third quartile (Q3).

To find Q1 and Q3, we can use the z-score formula and the standard normal distribution table.

For Q1, we find the z-score corresponding to the 25th percentile, which is approximately -0.6745.

Using the formula Q1 = μ + z [tex]\times[/tex] σ, we have Q1 = 68 + (-0.6745) [tex]\times[/tex] 14 = 57.053.

Therefore, Q1 is approximately 57.053 minutes.

For Q3, we find the z-score corresponding to the 75th percentile, which is approximately 0.6745.

Using the formula Q3 = μ + z [tex]\times[/tex] σ, we have Q3 = 68 + (0.6745) [tex]\times[/tex] 14 = 78.426.

Therefore, Q3 is approximately 78.426 minutes.

Finally, we can calculate the IQR by subtracting Q1 from Q3: IQR = Q3 - Q1 = 78.426 - 57.053 = 21.373 minutes.

Therefore, the Inter Quartile Range (IQR) for time spent at the hot springs is approximately 21.373 minutes.

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The hourly wage, the number of hours and the number of days Jaxon works indicates that the amount Jaxon gets paid is $192

The formula for hourly wage can be presented as follows;

Hourly wage  = Total earnings/Total hours worked

The question in the link is presented as follows;

Jaxon gets paid $6 an hour. He works for 8 hours each day for four days. How much will Jaxon get paid

The amount Jaxon gets paid per hour (his hourly wage) = $6

The number of hours he works each day = 8 hours

The number of days Jaxon works = Four days

The amount Jaxin gets paid = Hourly wage × Hours per day × Number of days

Therefore we get;

Amount he gets paid = $6 per hour × 8 hours/day × 4 days = $192

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