Austin makes a
commission of 20% on
his sales each week.
Last week, his sales
were $520. How much
was Austin’s
commission?

Answer:

HERE YOU GO HOPE IT HELPS

The system of equations is:

To solve the system of equations by graphing, we need to make a graph of each equation. For that, we solve for y in both equations:

We have two equations to graph:

Comparing with the slope-intercept equation:

Where m is the slope and b is the y-intercept.

We can see that the slope of the two equations is m=-2, this means that the lines will have the same rate of change of -2 in y for every 1 in x. And one graph will cross the y-axis at 4 and the other at +6.

The graph of the two equations is shown in the following image:

Where the green line is the first equation, and the red line is the second equation.

There is no solution to this system of equations because the lines do not intersect each other.

The lengths of PA and PB are 3.1622 units if the point is P (0, 5).

The distance between two points is defined as the length of the line segment between two places representing their distance. Most significantly, segments that have the same length are referred to as congruent segments and the distance between two places is always positive.

The formula of the distance between two points exists P(x₁, y₁) and Q(x₂, y₂) is given by:

d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².

The given points exists A(1, 2) and B(–3, 4).

The perpendicular bisector of AB will pass through the midpoint of AB.

Now the perpendicular bisector of AB will meet the Y-axis at P(0, y).

∴ AP = BP

Applying the distance formula, we get4

⇒ PA² = PB²

⇒ (x₁ – 0)² + (y₁ – y)² =  (x₂ – 0)² + (y₂ – y)²

⇒ (1 – 0)² + (2 – y)² =  (–3 – 0)² + (4 – y)²

After solving, we get y = 5

Therefore, the point is P (0, 5).

Now calculating the lengths of PA and PB

PA = √(1 – 0)² + (2 – 5)² = 3.1622

PB = √(-3 – 0)² + (4 – 5)² = 3.1622

Therefore, the lengths of PA and PB are 3.1622 units.

To learn more about the distance between two points refer to:

brainly.com/question/15958176

#SPJ13

Answer:

16°F

Step-by-step explanation:

The temperature is −4°F. What will the temperature be if the temperature rises 20°F?

-4 + 20 = 16

so:

16°F

Two or more expressions with an Equal sign is called as Equation. x=-3 for function f(x)=−13.

Two or more expressions with an Equal sign is called as Equation.

We know that f(x) = -13. This means that:

f(x)= -13 = 2x-7

-13= 2x-7

Now we all need to do is solve this equation. First add 7 to both sides

-13 + 7= 2x

-6=2x

Divide by 2 on both sides.

-6 ÷ 2= x

x= -3

Hence x=-3 for function f(x)=−13.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

Answer:8r+7-6r-5Combine the like terms=8r-6r+7-5Thenafter, simplify=2r+2

good luck

Step-by-step explanation:

The amount of money that Emilio will pay back in two years is $1392.00.

The accrued amount includes principal plus interest.

Simple interest formula can be expressed as;

A = P( 1 + rt )

Where A is accrued amount, P is principal, r is rate and t is time elapsed.

Given the data in the question;

First, converting percent to decimal.

Rate r = 8% = 8/100 = 0.08

Now, plug the given values into the above formula and solve for the accrued amount.

A = P( 1 + rt )

A = $1200( 1 + 0.08 × 2 )

A = $1200( 1 + 0.16 )

A = $1200( 1.16 )

A = $1392.00

Therefore, the accrued amount is $1392.00.

Learn more about simple interest here: https://brainly.com/question/25845758

#SPJ1

a) 10 men are selected at random, the probability their average height is above 72 inches is 0.0122.

b) Exactly one man is selected at random, the probability his average height is above 72 inches is 0.0122.

c) The 80th percentile for the average height of 10 men is 0.0097%.

d) The probability the average height of 10 men is between 70 and 71 inches is 0.13607.

Mean = 69.7 inches

Standard Deviation = 2.8 inches

a) Using normal distribution,

P(Y > 72) = P(Y - mean > 72 - mean)

P(Y > 72) = P((Y - mean ÷ SD) > (72 - mean ÷ SD))

P(Y > 72) = P(Z > (72 - mean ÷ SD))

P(Y > 72) = P(Z > (72 - 69.7 ÷ 2.8))

P(Y > 72) = P(Z > 2.25)

P(Y > 72) = 1 - P(Z  ≤ 2.25)

P(Y > 72) = 0.0122

b) P(man's height is above 72 inches) = 0.0122

c) (80 × 0.0122) ÷ 100

= 0.0097%

d) P( 70 > Y > 71) = P(70 - mean > Y - mean > 71 - mean)

P( 70 > Y > 71) = P((70 - mean ÷ SD) > (Y - mean ÷ SD) > (71 - mean ÷ SD))

P( 70 > Y > 71) = P((70 - mean ÷ SD) > Z > (71 - mean ÷ SD))

P( 70 > Y > 71) = P((70 - 69.7 ÷ 2.8) > Z > (71 - 69.7 ÷ 2.8))

P( 70 > Y > 71) = P(0.107 > Z > 0.464)

P( 70 > Y > 71) = 0.13607

Learn more about normal distribution at

https://brainly.com/question/19087804?referrer=searchResults

#SPJ4

The equation of each line in slope-intercept form are:

1. y = -2x + 3

2. y = -3/5x - 6

3. y = 1/4x + 8

If we are given a point (a, b) and the slope of a line (m), we can write the linear equation in slope-intercept form by first plugging in the given values into y - b = m(x - a), then rewrite it in the slope-intercept form as y = mx + b.

1. Slope (m) = -2

Point (a, b) = (0, 3)

Plug in the values into y - b = m(x - a):

y - 3 = -2(x - 0)

y - 3 = -2x + 0

y = -2x + 0 + 3

y = -2x + 3 [slope-intercept form]

2. Slope (m) = -3/5

Point (a, b) = (-5, -3)

Plug in the values into y - b = m(x - a):

y - (-3) = -3/5(x - (-5))

y + 3 = -3/5x - 3

y + 3 - 3 = -3/5x - 3 - 3

y = -3/5x - 6 [slope-intercept form]

3. Slope (m) = 1/4

Point (a, b) = (-8, 6)

Plug in the values into y - b = m(x - a):

y - 6 = 1/4(x - (-8))

y - 6 = 1/4(x + 8)

y - 6 = 1/4x + 2

y - 6 + 6 = 1/4x + 2 + 6

y = 1/4x + 8 [slope-intercept form]

Learn more about the slope-intercept form on:

https://brainly.com/question/1884491

#SPJ1

Based on your earnings from each of the part-time jobs, your fortnightly earnings would be $1,520

First, find out how much you earn in the first part-time job per week:
= (Number of days per week x Number of hours per day x Pay per hour)

= (3 x 6 x 20)

The find out how much you earn in the second part-time job:

= (Number of days per week x Number of hours per day x Pay per hour)

= (2 x 8 x 25)

In a fortnight (two weeks), your earnings would be:

= (2 weeks x (3 x 6 x 20)) + (2 weeks x (2 x 8 x 25))

= (2 x 360) + (2 x 400)

= 720 + 800

= $1,520

Find out more on fortnightly earnings at https://brainly.com/question/28442068

#SPJ1

Fortnightly earnings would be $1,520 based on previous earnings.

Two or more expressions with an Equal sign is called as Equation.

Given that there are two part time jobs.

For first part time

3 days per week I work for 6 hours each day and I earn $20.00 per hour

(3 x 6 x 20)

=360

Second part time

2 days per week, I earn $25.00 per hour, working an 8-hour day.

=2×25×8

=400

Now we need to calculate, the total fortnightly earnings.

= (2 weeks x360) + (2 weeks x 400)

= (2 x 360) + (2 x 400)

= 720 + 800

= $1,520

Hence $1520 is the fortnightly earnings.

To learn more on fortnightly earnings click:

https://brainly.com/question/24235157

#SPJ1

Answer:x=

−1/4y+ −3/4

Step-by-step explanation

A problem that consists of the multiplication of two fractions, and in which the simplified product is 4/5 is presented as follows;

[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} = \frac{4}{5} }[/tex]

A fraction consists of a number that is expressed as a quotient, such that the numerator is being divided by the value in the denominator.

The multiplication problem with two fractions that ha a simplified product of 4/5 is found as follows;

let the fractions be [tex] \displaystyle \frac{a}{b} [/tex] and [tex] \displaystyle \frac{c}{d} [/tex]

The multiplication product is therefore;

[tex] \displaystyle \frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b\cdot d} = \frac{4}{5}[/tex]

The lowest common multiple of a and c is 4, while the lowest common multiple of b and d is 5

Taking b as 15, and a as 14 and c as 6, while d is taken as 7, such that we have;

[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} =\frac{2 \times 7}{5 \times 3} \times \frac{2 \times 3}{7} = \frac{2 \times 2}{5 \times 1} =\frac{4}{5} }[/tex]

The multiplication problem is therefore;

[tex] \displaystyle {\frac{14}{15} \times \frac{6}{7} = \frac{4}{5} }[/tex]

Learn more about lowest common multiples of numbers shere:

https://brainly.com/question/28109219

#SPJ1

If the equation y = -x, then the equation of the line that is parallel to the given line and passes through the point (-8,2) is y = -x-6

The equation is

y = -x

The slope intercept form

y = mx+b

Where m is the slope of the line

Comparing the slope intercept form and the given equation

Slope of the line m = -1

The line is passing through the points (-8,2)

The point slope form of the line

[tex](y-y_1)=m(x-x_1)[/tex]

Substitute the values in the equation

y-2 = -1(x-(-8))

y-2 = -1(x+8)

y-2 = -x-8

y = -x-8+2

y = -x-6

Hence, if the equation y = -x, then the equation of the line that is parallel to the given line and passes through the point (-8,2) is y = -x-6

Learn more about slope intercept form here

brainly.com/question/9682526

#SPJ1

Answer:

1/4

Step-by-step explanation:

The points (-4, 5) and (0, 6) lie on the line. Substituting into the slope formula,

[tex]\frac{6-5}{0-(-4)}=\frac{1}{4}[/tex]

P(B) such that a and b are mutually exclusive is 0.23

A group of potential results from a specific experiment is an event. Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot obtain both outcomes. Since they do not occur at the same time, such occurrences are also known as disjunct events.

Given: P(A) =0.28

P(AUB) = 0.51

We know,

P(AUB) = P(A) + P(B) - P(A∩B)

Since A and B are mutually exclusive events, they cannot happen together.

So, P(A∩B) = 0

Then,

P(AUB) = P(A) + P(B)

0.51 = 0.28+ P(B)

P(B) = 0.51 - 0.28 = 0.23.

Hence, P(B) = 0.23

To read more about mutually exclusive events, visit https://brainly.com/question/28565577

#SPJ4

A parameter that represents the amount of spread of individuals in the entire population of interest, which is typically unknown is the population mean.

The population mean can be determined by dividing the total number of values in the given data/population by the sum of all values in the data/population. The whole sum of the numbers is referred to as summation. The μ sign stands for the population mean.

The average calculated from the entire group, distribution, or population is known as the population mean. It is calculated by dividing the sum of all population variables by the total population of variables. Here, μ exists the population mean. ∑X exists the sum of all the observations in the population.

The population mean is a quantity that expresses the population's overall degree of individual variation, which is often unknown.

Therefore, the correct answer is option c) the population mean.

The complete question is:

a parameter that represents the amount of spread of individuals in the entire population of interest, which is typically unknown is group of answer choices the (true) standard error.

a) the sample standard deviation.

b) the estimated standard error.

c) the population mean.

d) the population standard deviation.

To learn more about population mean refer to:

https://brainly.com/question/28103278

#SPJ4

SOLUTION

The total amout of solution given is

From thequestion, 1/2 of the solution is used, then the amount of solution used for the experiment will be

Hence

The amount of solution the scientist use is 1/3 litres

Horizontal leg = 6 units

Vertical leg is 4 units

Lets Represent the diagonal as line AB where A and B are the endpoints of the line segment

The coordinates of point A is ( 12,4)

The coordinates of point B is ( 6,0)

Slope = ( Y2 - Y1 ) / (X2 -X1) = (0 - 4) / ( 6 - 12) = -4 / -6 = 2/3

or simply.

slope = rise / run = vertical leg/ horizontal leg = 4/6 = 2/3

ANSWER

Horizontal leg = 6 units

Vertical leg is 4 units

Slope = 2/3

The length, [tex]x[/tex], of the other base, in meters is 10.

The area of trapezoid = 24 square meters

The altitude = 4 meters

The length of one base = 2 meters

We have to find the length [tex]x[/tex] of the other base in meters.

To find the value of the length [tex]x[/tex] we use formula of area of trapezoid.

We use the area of trapezoid to find the value of length [tex]x[/tex] because we know the value of area of trapezoid, length of one base and altitude.

As we know the formula of area of the trapezoid

[tex]A=\frac{a+b}{2}\times H[/tex]

In the formula,

[tex]A=[/tex] area of trapezoid

[tex]a[/tex] and [tex]b[/tex] are the two length of two different base of the trapezoid

[tex]H=[/tex] height or altitude of the trapezoid

From the given question, [tex]A[/tex] = 24 square meters, [tex]a=x[/tex] meter, [tex]b[/tex] = 2 meters and [tex]h[/tex] = 4 meters.

Now putting the values in the formula.

[tex]24=\frac{x+2}{2}\times 4[/tex]

[tex]24=(x+2)\times 2[/tex]

Divide by [tex]2[/tex] on both side

[tex]\frac{24}{2} =\frac{(x+2)\times 2}{2}[/tex]

[tex]12=x+2[/tex]

Subtract [tex]2[/tex] on both side

[tex]12-2=x+2-2[/tex]

[tex]10=x[/tex]

[tex]x=10[/tex]

Hence, the length, [tex]x[/tex], of the other base, in meters is 10.

To learn more about trapezoid link is here

https://brainly.com/question/21025771

#SPJ1

The null hypothesis is [tex]H_{0} : x=0.60[/tex] and alternative hypothesis is [tex]H_{1} :x\neq 0.60[/tex].

What is null and alternative hypothesis?

The null hypothesis is that the statement that researchers usually aim to disprove by performing tests of significance on the dataset. the most purpose of the null hypothesis is to help disprove a hypothesis or nullify it in favor of the alternate hypothesis that the researchers want to prove.

Let the percentage of readers who own a laptop be [tex]x.[/tex]

As newsletter publisher believes that [tex]60[/tex]`% of their readers own a laptop.

Therefore the null hypothesis is [tex]H_{0} : x=0.60[/tex] and alternative hypothesis is [tex]H_{1} :x\neq 0.60[/tex].

To know more about null hypothesis and alternative hypothesis from given link,

https://brainly.com/question/25263462

#SPJ4

Answer:

8.1

Step-by-step explanation:

just calculate 45 of 18%

The new coordinates when we rotate the triangle counterclockwise is  (3, -1), (-2, -4),  (-5, 3).

Given,

The triangle with vertices;

(-3, 1) (2, 4) and (5, -3).

We have to find the new coordinates, when the triangle rotated 180 degrees counter clockwise;

Here,

The vertices;

(-3, 1) (2, 4) and (5, -3).

When we rotate 180 degree counter clockwise, the plane changes not the point.

That is,

(-3, 1) becomes (3, -1)

(2, 4) becomes (-2, -4)

(5, -3) becomes (-5, 3)

That is,

The new coordinates when we rotate the triangle counterclockwise is  (3, -1), (-2, -4),  (-5, 3).

Learn more about vertices of triangle here;

https://brainly.com/question/14619124

#SPJ1

The new coordinates when we rotate the triangle counterclockwise is  (3, -1), (-2, -4),  (-5, 3).

Given,

The triangle with vertices;

(-3, 1) (2, 4) and (5, -3).

We have to find the new coordinates, when the triangle rotated 180 degrees counter clockwise;

Here,

The vertices;

(-3, 1) (2, 4) and (5, -3).

When we rotate 180 degree counter clockwise, the plane changes not the point.

That is,

(-3, 1) becomes (3, -1)

(2, 4) becomes (-2, -4)

(5, -3) becomes (-5, 3)

That is,

The new coordinates when we rotate the triangle counterclockwise is  (3, -1), (-2, -4),  (-5, 3).

Learn more about vertices of triangle here;

https://brainly.com/question/14619124

#SPJ1

We need to make h the subject of formula:

The given calculation, -3+1-7- (-4)+10, can be rewritten as (1+4) so that it only involves addition and the result is 5.

According to the question,

We have the following expression:

-3+1-7- (-4)+10

Now, we have to remove all the negative signs from this expression.

So, we will first solve this expression to the step where we have only addition.

Now, we know that the multiplication of two negative integers is always positive.

-3+1-7+4+10

Adding the numbers with the negative sign:

-10+10+1+4

1+4

5

Hence, -3+1-7- (-4)+10 can be rewritten as (1+4) so that it only involves addition and the result is 5.

To know more about addition here

https://brainly.com/question/14092461

#SPJ1

The ratio of the number of blue marbles to the number of marbles that are orange or green is 1 : 3.

Ratio is defined as the relationship between two quantities. It can be expressed as a to b, a/b, or a : b.

Let a = total number of blue marbles

b = total number of orange and green marbles

If the total number of blue marbles is 5 and the total number of orange and green marbles are 9 and 6, respectively, then the ratio is 5 to (9 + 6).

Simplify the ratio.

5 : (9 + 6) = 5 : 15 = 1 : 3

Hence, the ratio is 1:3.

Learn more about ratio here: brainly.com/question/2328454

#SPJ4

Given

Let's represent movies with M

Let's represent video with V

Solution

Using substitution method

I will solve your system by substitution.

Substitute for m in Equation 2

To clear the fraction multiply all through by 4

Separate the similar term

Substitute for v =5 in equation 3

The rental cost for each movie

The rental cost for each video game.

Answer:

V = 243 - 0.2s

Step-by-step explanation:

See attached document for questions 1 - 3.

5. Write a function rule to represent the situation:

The volume, V, remaining in a 243 ft3 pile of gravel

decreases by .2 ft3 with each shovelful, s, of gravel

spread in a walkway.

Volume Remaining (V) = Initial - Used

Volume Remaining (V) = 243 ft^3 - (0.2 ft^3/shovel)(s shovels)

V = 243 - 0.2s

6.  Tell whether the relation is a function. Explain your

reasoning.

{(-1, 7), (9, 4), (3, -2), (5, 3) , (9, 1)

This is not a function.  When x = 8, it results in more than one output.

7.  Pattern:

-2

-5

-8

-11

Each step decreases by 3

-14

-17

8.  

Given:

There are given the equation:

Explanation:

According to the question:

we need to find the factor of the given equation:

So,

From the equation:

Final answer:

Hence, the factor of the given equation is shown below:

We can solve this by means of the change of base formula:

By replacing x for y, 3 for a, and 27.3 for x into the above formula, we get:

Then, x = 3.0101