Mathematics Middle School

Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weekly salary is $900.
The weekly paycheck amount for each salesman, p, is a function of the number of sales, s, they had in that week.

What is the slope of the function representing the weekly paycheck amount for Salesman A? Use complete sentences to explain your reasoning, or show your calculations.
What is the slope of the function representing the weekly paycheck amount for Salesman B? Use complete sentences to explain your reasoning, or show your calculations.
What is the slope of the function representing the weekly paycheck amount for Salesman C? Use complete sentences to explain your reasoning, or show your calculations.

Answers

Answer 1
1) Salesman A:

He earns $65 per sale, with a maximum weekly commission of $1,300.

=> p(s) = 65s / p ≤ $1,300. This is the paycheck (p) equal 65 times the number of sales s, with an upper bound of $1,300.

The slope of the function is the coefficient of the the indepent variable s, this is 65.

The slope is the rate of change on the paycheck per unit of sales done (s).

Answer: slope 65.

2) Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale.

p(s) = $300 + 40s

The slope is 40 (the coefficient of the independent variable).

Again, the slope is the increase in the paycheck per unit of sale (s) performed.

Answer: slope = 40

3) Salesman C does not earn any commission. His weekly salary is $900.

p(s) = $900

It turns out that really the paycheck of this salesman is not a function of the number of sales. His/her paycheck is constant. That means that the paycheck does not change with the number of sales, and so the slope is 0.

The function is a horizontal line (slope 0).

 Answer: slope 0
Answer 2

Final answer:

Slope of function for Salesman A: 65

Slope of function for Salesman B: 40

Slope of function for Salesman C: 0

Explanation:

Slope of function for Salesman A: The slope of the function representing Salesman A's weekly paycheck is $65 per sale, as he earns $65 per sale. Since the commission is a constant rate per sale, the slope remains constant.

Slope of function for Salesman B: The slope of the function representing Salesman B's weekly paycheck is $40 per sale. This is because he earns $40 per sale, which makes the slope $40.

Slope of function for Salesman C: The slope of the function representing Salesman C's weekly paycheck is 0. Salesman C does not earn any commission, so his weekly salary remains constant at $900, regardless of the number of sales made.

Related Questions

what is the tangent of 33.0?

Answers

Tan(33) = 0.6494
This is just a problem for your calculator. Most put the number in as
Tan(
3
3
=

What is the greatest common factor of 15 and 45? Explain your answer.

Answers

Factors of 15: 1, 3, 5, 15

Factors of 45: 1, 3, 5, 9, 15, 45

The Greatest common factor is 15.

if a line is tangent to a circle at how many points does it interest the circle?

Answers

The intersection of a tangent to a circle and the circle is at exactly one point. Don't let a drawing fool you. In a drawing, it looks like there are several points of intersection, but keep in mind that a point has no dimensions, no length, width, or height, and a line has only length but no width. A drawing is just a representation of a point and a line, so we can see them.
If a line is tangent with a circle, it has one point in common with it.

rewrite using scientific notation 0.058

Answers

[tex]5.8 \times {10}^{ - 2} [/tex]

~~

I hope that helps you out !!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey
0.058 is written in scientific notation 
5.8*10^-2
hope this helps

Light travels at a speed of about 186,000 miles per second. How far does light travel in 5 seconds? Use repeated addition to solve.

Answers

186,000+186,000+186,000+186,000+186,000=186,000*5=

930,000 miles in 5 seconds. Good luck my friend!

Final answer:

Light travels at a speed of 186,000 miles per second. Using repeated addition, we find that in 5 seconds, light travels a total of 930,000 miles.

Explanation:

To calculate how far light travels in 5 seconds, we can use repeated addition. Light travels at a speed of about 186,000 miles per second. If we add this number for each second, five times, we can find the total distance light travels in 5 seconds.

Let's perform the repeated addition:

After 1 second, light has traveled 186,000 miles.

After 2 seconds, light has traveled 186,000 miles + 186,000 miles = 372,000 miles.

After 3 seconds, light has traveled 372,000 miles + 186,000 miles = 558,000 miles.

After 4 seconds, light has traveled 558,000 miles + 186,000 miles = 744,000 miles.

After 5 seconds, light has traveled 744,000 miles + 186,000 miles = 930,000 miles.

Therefore, light travels 930,000 miles in 5 seconds.

Please help with these I need to pass

Answers

3-
[tex]((11 + 19) \times 10) \div 2 \\ = (30 \times 10) \div 2 = 300 \div 2 = 150[/tex]the answer is 150 units^2

4- the area of the rectangle:
[tex]14 \times 21 = 294[/tex]
the area of the triangle :
[tex](16 \times(21 - 12)) \div 2 = \\ (16 \times 9) \div 2 = 144 \div 2 = 72[/tex]
the area of the whole shape:
[tex]294+ 72 = 366[/tex]
the answer is 366 units^2
hope this helps

Last year, there were 80 students in the orchestra. This year there are 100 students in the orchestra. Determine the percent of increase in the number of students taking orchestra from last year to this year.
A 25%, because 100-80/80= 25%
B 20%, because 100-80/100= 20%
C 80%, because 80/100= 80%
D 125%, because 100/80= 125%

Answers

Hi there!

The answer is A. 

To find the percent increase, you need to 1. Find the difference between the two numbers, and 2. Divide it by the original number. 

100-80/80 = 25%

Hope this helps!

The celski's wants to drive the 288 miles to a campground in 6 hours. what should their average speed be in miles per hour

Answers

To find the average speed in miles per hour, we need to divide 288 by 6.

288 ÷ 6 = 48

The average speed should be 48 mph.

In which quadrant of the coordinate graph does point F lie? Quadrant I Quadrant II Quadrant III Quadrant IV

Answers

Please provide the graph that shows point F.
But, Quadrant 1 is the top right corner, Quadrant 2 is the top left, and it continues like that in a counterclockwise way. 

The quadrant of the coordinate graph does point F lie in quadrant IV.

What is Quadrant in Graph?

The coordinate system's two axes, the x-axis and the y-axis, constitute a region called a quadrant.

The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle. These areas include coordinates, or positive and negative values of the x- and y-axes.

The sign notations for four Quadrants is as follows:

Quadrant I :

both x and y positive.

Quadrant II :

x negative and y positive

Quadrant III:

x and y both negative.

Quadrant IV:

x positive and y negative.

As, the point F has coordinates (1,-5) which shows x is positive and y is negative.

So, point F is in quadrant IV.

Learn more about Quadrant here:

https://brainly.com/question/9182164

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Solve the equation and show all work please show steps!!
2n-3=9

Answers

2n - 3 = 9

If you are solving for n:

Isolate it by doing the opposite of PEMDAS; Also, what you do to one side you do to the other (because of the equal sign)


2n - 3 = 9

2n - 3 (+3) = 9 (+3)

2n = 12

2n/2 = 12/2

n = 6

n = 6 is your answer

hope this helps
2n-3=9
------------
Add 3 to each side
2n−3+3=9+3
2n = 12
------------------
Divide each side by 2
2n ÷ 2 = 12 ÷ 2
n = 6

What situation could this diagram represent?

Answers

Answer: B- Flipping two coins once


Step-by-step explanation:


B. Tossing Two Coins Once

I Got it Right i Promise

Assessment items On a piece of paper, use a protractor and a ruler to construct △ABC with AB=6 cm , m∠A=80° , and m∠B=50° . What is AC ?

A) 3 cm

B) 6 cm

C) 9 cm

D) 12 cm

Answers

We know that the summation of angles of a triangle is 180°. Then we find angle of C by,m∠A + m∠B + m∠C=180° 80° + 50° + m∠C=180°m∠C=180°- 80°+ 50° m∠C=50°Since we now angle of C, we can use Sine Law in solving for ACsinC/AB=sinB/ACsin50°/6 =sin50°/ACAC=6cmTherefore, AC is equal to 6cm.
Read more on Brainly.com - https://brainly.com/question/2951163#readmore
Hello!
Out of the following options the correct answer is:
6 cm

Hope i helped!
-Cupcakegurl

A cake recipe requires 1 2/3 cups of milk how many cups altogether are necessary to make 4 cakes

Answers

For four cakes you would need to multiply 4 times 1 2/3 which equals 
6 and 2/3
1 2/3*4=

5/3*4=

20/3=

6 2/3.

Hope this helped☺☺

A cathedral has a large,circular stained glass window. A visitor measures the window and calculates that it has a circumference of 12.56 yards. What is the windows area

Answers

First, we find the diameter.
12.56 divided by 3.14 = 4.
Next, find the radius.
4 divided by 2 = 2.
Then, use the formula to calculate the area.
2 times 2 times 3.14 = 12.56 is your area. 
In this case, the area and the circumference are the same. Sometimes that is not that case though. Hope it helps! :)
Final answer:

The area of the stained glass window is approximately 12.56 square yards. We obtained this by first calculating the radius (2 yards) using the given circumference, then substituting the radius into the formula for the area (πr²).

Explanation:

The area of a circle can be found using the formula A = πr². where A represents the area, r is the radius, and π is a mathematical constant approximately equal to 3.14. First, we should find the radius of the window. The circumference of a circle is given by the formula C = 2πr. If the circumference is known to be 12.56 yards, we can solve for the radius as follows:

Setting the two formulas equal to each other, we get 12.56 = 2πrDividing both sides by 2π, we get r = 12.56/2π = 2 yards.

Next, we substitute the radius into the area formula: A = π(2)² = 4π = 12.56 square yards.

Learn more about Area here:

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The equivalent of 6/11 is a repeating decimal.How many digits are in the repeating decimal?

Answers

Hi there!

There are infinite digits in a repeating decimaI. 

Usually, repeating decimals go on forever. They rarely stop ;)

Hope this helps!
I think its 15 counting the whole thing;
0.54545454545455

Jason has two bags with 6 tiles each. The tiles in each bag are shown below: Make 6 squares. The squares are numbered sequentially from 1 to 6. Without looking, Jason draws a tile from the first bag and then a tile from the second bag. What is the probability of Jason drawing the tile numbered 2 from the first bag and the tile numbered 3 from the second bag?

Answers

The answer would be 1/12 or 2/12 im not sure.

The correct answer is [tex]\frac{1}{36}[/tex]

To solve this problem, we need to find the probability of drawing the tile numbered 2 from the first bag and the tile numbered 3 from the second bag.

Given:

- Bag 1 contains tiles numbered 1, 2, 3, 4, 5, 6.

- Bag 2 contains tiles numbered 1, 2, 3, 4, 5, 6.

- The desired outcome is drawing tile 2 from Bag 1 and tile 3 from Bag

Step 1: Find the total number of possible outcomes.

Total number of outcomes = Number of tiles in Bag 1 × Number of tiles in Bag 2

Total number of outcomes = 6 × 6 = 36

Step 2: Find the number of favorable outcomes.

Number of favorable outcomes = 1 (drawing tile 2 from Bag 1 and tile 3 from Bag 2)

Step 3: Calculate the probability of the desired outcome.

Probability = Number of favorable outcomes / Total number of outcomes

Probability =[tex]\frac{1}{36}[/tex]

v(j+y)=61y+82
please solve!!!!
need help

Answers

Get y by itself...

y= -(jV-82)/(V-61)


if a cone-shaped hole is 3 feet deep and the circumference of the base of the hole is 44 ft, what is the volume of the hole? use 22/7 for pi

Answers

To find the volume of the whole, you will use the formula for finding the volume of a cone. V = 1/3 x r^2 x h.

You will first need to find the radius by using the information given about the circumference and the circumference formula.

C = pi x d
44 = 22/7 d
d = 14 feet.

Then use the diameter to find the radius of 7 feet.

V = 1/3 x r^2 x h
1/3 x 7^2 x 3
V = 49 cubic feet

Final answer:

To find the volume of a cone-shaped hole with a depth of 3 feet and a base circumference of 44 ft, calculate the radius using the circumference formula, then plug the radius and height into the volume formula to get 154 cubic feet.

Explanation:

The volume of a cone-shaped hole can be calculated using the formula V = (1/3) × π × r² × h, where r is the radius of the base and h is the height of the cone. In this case, the circumference of the base, 44 ft, can be used to find the radius. Given that the radius is 14 ft, and the height is 3 ft, you can substitute these values into the formula to find the volume of the hole.

Calculate the radius: Circumference = 2πr, so r = Circumference / 2π = 44 / 2π = 7 ft.

Calculate the volume: V = (1/3) × 22/7 × 7² × 3 = 154 ft³.

Find point B on the graph. In which quadrant does the point lie

Answers

I will give you a general explanation to locate a point in a graph and to determine the quadrant in which it is.

Any point is associated with an ordered pair. In general form it will be point A = (x,y).

That ordered pair is located is a cartesian coordinate plane: a drawing with two perpendicular lines, one veritcal and one horizontal, named axis.

The y-axis is vertical. The x-axis is horizontal.

The first value of the ordered pair tell the x-coordinate, and the second value of the ordered pair tells the y-coordinate.

For example: the ordered pair (3,5) has x-coordinate 3 and y-coordinate 5.

The location of the point (3,5) in the plane is in the intersection of the line that goes parallel to the y-axis and passes through the mark 3 on the x-axis, and the line parallel to the x-axis and passes through the mark 4 on the y-axis.

To tell the quadrant you can use this table:

Quandrat                    x-coordinate        y-coordinate     example

First                            positive                 positive            (3,5)
Second                       negative               positive            (-3,5)
Third                           negative               negative           (-3,-5)
Fourth                         positive                negative           (-3,5)

A point that is in an axis does not belong to any quadrant. That is (x,0) or (0,y) are points on the axis and do not belong to any quadrant. For example, (3,0) is on the x-axis and not any quadrant. (0,5) is on the y-axis.

What is the approximate volume of a basketball with the circumference of 42ft ?

Answers

we know that

[volume of a sphere]=(4/3)*pi*r³

length of a circumference=42 ft
[length of a circumference]=2*pi*r-------> r=[length of a circumference]/(2*pi)
r=[42]/(2*pi)---------> r=6.6845 ft

[volume of a sphere]=(4/3)*pi*6.6845³-----------> 1251.11 ft³

the answer is 1251.11 ft³

five criterion team bikes cost $ 11,300. How much would the club have to pay for a dozen criterion team bikes?

Answers

First of all divide 11,300 by 5 and get 2,260 which then multiply it by 12 which will get you 27,120 as the answer.

So it would cost $27,120 to get a dozen criterion team bikes.

The cost for one Criterion team bike is $2,260, calculated by dividing $11,300 by 5. Therefore, for a dozen bikes, which amounts to 12, the club would have to pay a total of $27,120.

The question involves a simple ratio or unit price problem and can be solved using basic multiplication. If five Criterion team bikes cost $11,300, to find the cost of one bike, divide the total cost by the number of bikes: $11,300 / 5 = $2,260 per bike. Then, to find the cost for a dozen (12) bikes, multiply the cost of one bike by 12: $2,260 x 12 = $27,120. Therefore, the club would have to pay $27,120 for a dozen Criterion team bikes.

9/3 write the fraction as a whole number

Answers

The answer is 3 because 9 divided by 3 is 3
Hey, Name's Jessy. I hope, I answer your question.

48/5 = 9 3/5

It converting mixed numbers into Improper Fractions. To convert a mixed number into an improper fraction, multiply the whole number by the denominator and add it to the numerator.

It is given that y varies directly as x. If y = 5 when x = 4 determine the constant of variation.

A) -4/5
B) 4
C) 5
D) 5/4

Answers

D) 5/4, I had this question on a quiz.
When one thing varies to another there is always a constant of variation. direct variation it is; y = kx

use the x,y values to find k
5 = 4k
5/4 = k

answer is D

A bicycle manufacturer is reducing the number of spokes on each bicycle wheel by 4. A wheel on one of the company's new cross-country bikes has 32 spokes. Which equations could be used to determine the number of spokes s that a wheel on a cross-country bike used to have? A. S + 32 = 4 B. S + 4 = 32 C. S - 32 = 4 D. S - 4 = 32

Answers

The answer is letter a

A basketball has a circumference of 29.5 inches. Using 3.14 what is the basketballs volume to the nearest cubic inch?

Answers

It is about 434 cubic inches


Solve each equation. Factor and use the zero product property to solve. Show all work algebraically.

Answers

23.

5n^2 = 4n^2 - 4n

n^2 + 4n = 0

n(n + 4) = 0

n = 0   or   n + 4 = 0

n = 0   or   n = -4

24.

d^2 - 4d = 3d

d^2 - 7d = 0

d(d - 7) = 0

d = 0   or   d - 7 = 0

d = 0   or d = 7

25.

3 - 13h = 3 - 8h + h^2

Subtract 3 from both sides.

-13h = -8h + h^2

Add 13h to both sides.

0 = 5h + h^2

0 = h(5 + h)

h = 0   or   5 + h = 0

h = 0   or   h = -5

PLEASE NEED HELP WITH A-D

Answers

a.
4(d+3c)

b.
6(3x+5y)

c.
7(3a+4y)

d.
8(3f + 7g)
Hello there! I can help you! For this question, we write this in distributive property by finding the GCF of both terms. As far as we see for all 4 of them, there are no like variables, and we find the GCF, just like we would for constants. When you find the GCF, be sure to divide each terms by the GCF, and then place the GCF outside the parenthesis. If you solve this correctly, here are your answers:

a. 4(a + 3e)

b. 6(3x + 5y)

c. 7(3a + 4y)

d. 8(3f + 7g)

Two sides of a triangle measure 20 cm and 30cm. What is the third side?

Answers

Hi there!

It depends on what angles there are, and how many degrees are in each angle. In order to figure this problem out, you need to know at least one angle ;)

Hope this helps!
I think the measure of the third side is 11 cm.

Hope this helped☺☺

Please answer! Show your work or give an explanation! Thank you!

Answers

B , C and E are functions because all the x's have exactly one y values

Please answer all
WILL GIVE BRAINLIEST!

Answers

A and C are obvious. Not sure about B though.
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