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. Is the function representing the weekly paycheck amount of Salesman A a proportional relationship? Use complete sentences to explain your reasoning. Is the function representing the weekly paycheck amount of Salesman B a proportional relationship? Use complete sentences to explain your reasoning. Is the function representing the weekly paycheck amount of Salesman C a proportional relationship? Use complete sentences to explain your reasoning.

Answers

Answer 1
Q1)
is the function representing the weekly paycheck of salesman A a proportional relationship? 
p - function
s - number of sales
Salesman A earns £65 per sale. Therefore if he earns s number of sales, the total amount he earns is 65*s = 65s
Lets assume for s number of sales he receives his maximum weekly commission, therefore the equation for A's weekly payment is; 
p = 65s +1300 
to determine if p and s are proportional to each other, it should take the form of equation p=ks
where k is a constant. If we graph p=ks, then k is the slope that is a constant and the line should pass through the origin, which means that y intercept is 0. 
however in this equation there is an intercept of +1300, therefore p and s are not proportional values.

Q2)
For salesman B he has a weekly base salary of £300 and commission of £40 per sale. Then the salary is fixed however for s number of sales, the commission he will receive is 40*s = 40s
the function for B's payment is as follows;
p = 40s + 300
This equation if we take it as a graph equation with p and s as y and x coordinates respectively, the equation we get is of one with an intercept of +300
 therefore if we graph it, the line will not pass through the origin which means that the p and s values are not proportional to each other. 

Q3)
Salesman C receives a weekly salary of £900. This is a fixed amount and does not vary depending on the sales. Therefore this is anyway not proportional as p function is not affected by s value. 
therefore p and s are not related, hence they aren't proportional. 
p = 900
Answer 2

Final answer:

The paychecks of Salesman A, B, and C are not proportional relationships. Salesman A has a commission cap, Salesman B has a base salary plus commission, and Salesman C has a fixed salary with no commission.

Explanation:

Proportionality of Salesmen's Paychecks

A proportional relationship exists between two variables if one variable is always a constant multiple of the other, meaning the ratio between the two variables is constant. When it comes to the paycheck structure of sales employees, the addition of a base salary or a cap on commission can impact the proportionality.

For Salesman A, the paycheck function is not a proportional relationship because there is a maximum weekly commission of $1,300. Even if he makes more sales beyond a certain point, his paycheck will not increase, breaking the constant ratio.For Salesman B, the paycheck function is also not a proportional relationship. Although there is no cap on the commission, the addition of a base salary means that the total paycheck isn't just a constant multiple of the number of sales. The base salary adds a constant amount regardless of the number of sales, therefore altering the ratio as sales increase.Lastly, for Salesman C, the paycheck function is not a proportional relationship as he receives a fixed weekly salary with no commission. Regardless of the number of sales, his paycheck remains the same, indicating no relation to the number of sales.

Properly designed sales incentives, consisting of a blend of straight salary and commissions, are crucial for motivating sales employees while aligning with company objectives, including achieving optimal sales volume, profitability, and customer satisfaction.

Related Questions

If 5a=-4b+5 and 3a=-2b+3, what is 6b?

Answers

There are two equations and two variables. You can solve for each variable using either the elimination method or the substitution method. Here, I believe the elimination method would be best:
5a = -4b + 5
3a = -2b + 3
You can multiply the second equation by two, so the 4b and -4b in both equations will cancel each other out when you add them. So:
5a = -4b +5
6a = 4b +6
Add both equations together.
11a = 11
a = 1
Plug in the a value into any of the previous equations:
5(1) = -4b + 5
-4b = 0
b = 0
So, since we know that b = 0, 6b is also 0.

can someone please help me i don’t know this and i’m really stuck so please

Answers

Joaquin can send between at most 250 text messages per month. Since he has already sent 141, we must have
.. 141 +t ≤ 250

The solution to this model of the situation can be found by subtracting 141.
.. t ≤ 109

We graph the lower limit as zero because we know Joaquin cannot send a negative number of text messages.

Interpretation:
Joaquin can send between 0 and 109 additional text messages this month.

Me and my mate Dave order pizzas.I eat six eights of mine, Dave only manages two sevenths of his. If we put the remains together,can we make one whole pizza?

Answers

No, because 6/8 + 2/7 > 1

a train traveled 1/5 of the distance between two cities in 3/4 hour. at this rate, how many hours will it take the train to travel the entire distance between these two cities

Answers

Im not sure but it might be six

sarita use 54 ounces of apples to make an apple pie how many pounds and ounces of apples did sarita use

Answers

one pound is 16oz. So you take 54 and minus it by 16 until you get something less that 16. Then you take how many times you subtracted it, and that is how many pounds. Then you take the "leftover" number and they you have your answer. 
so Sarita used 3 pounds and 8 oz. 
Hello,

Here is your answer:

The proper answer to this question is "3".

Here is how:

54 ounces= 3.375 pounds (rounded to 3)

1 pound=16 ounces

Your answer is 3.

If you need anymore help feel free to ask me!

Hope this helps!

Sandy's orchard has only apple trees and pear trees and she is wanting to add some avocado trees. Currently, there are 4 apple trees for every 3 pear trees. She is wanting to plant enough avocado trees so that she has 2 avocado trees for every 5 pear trees in the orchard.
Sandy is planting 18 avocado trees, making the ratio of avocado trees to apple trees be to .

Answers

For every 3 pears there are 4 apples; therefore 1 pear = 1.33 apple.And in every 5 pears, there are 2 avocados; therefore 1 avocado = 2.5 pears.Since there are 18 avocado trees, the number of pears would be 45 pear trees. And since there are 45 pear trees, there will be 59.85 apple trees, rounding it off to 60 apple trees. So the ratio of avocado trees to apple trees would be 18 to 60 or 18: 60.

Hope this helped☺☺

(I think this is the answer)

Answer:

3 to 10 OR 3:10

Step-by-step explanation:

graph the quadratic function f(x)=(x−4)(x+2).

Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

GRAPH FOR BRAINLIEST

Answers

see attached picture:
 vertex (1,-9)

Answer:

(1,-9) and (0,-8)

Step-by-step explanation:

BRAINLIEST!!!
Given the two functions,

What is the rate of change of each function? (the graph & the equation)

g(x) = 4x - 2

Answers

For the equation, the rate of change would be four.
Now looking at the graph, look at each point of the line that hits perfectly on a grid. Count up four, over two. The rate of change for the graph would be 4/2, or 2. Hope this helps!
Hi there!

Graph:
The rate of change is 2.

If we take the points (3,2) and (1, -2) and use slope triangles to find the slope, 4 ÷ 2 = 2, so the slope is 2.

Function:
The rate of change is 4.
The rage of change in a function in slope intercept form is always the number before x.

Hope this helps!

What series of transformations to quadrilateral ABCD map the quadrilateral onto ​ quadrilateral EFGH to prove that ABCD≅EFGH ?




a reflection across x-axis, and then a translation 4 units left

a reflection across x-axis, and then a translation 4 units right

a reflection across y-axis, and then a translation 4 units right

a reflection across y-axis, and then a translation 4 units left

Answers

B:  a reflection across the x-axis followed by a translation 4 units right.

Comparing the points to their mapped images compares A to E, B to F, C to G, and D to H.  In each point, the y-coordinate switches signs and the x-coordinate is subtracted by 4.

Reflections across the x-axis will switch the sign of the y-coordinate, and reflections across the y-axis will switch the sign of the x-coordinate.  Since the y-coordinates are the ones whose sign changed, the points must have been reflected across the x-axis.

Translations to the left will cause the x-coordinate to increase, and translations to the right will case the x-coordinate to decrease.  Since the x-coordinate of every point was subtracted, this means that the translation must have been to the right.

The correct series of transformations is a reflection across the x-axis, and then a translation 4 units left.

Let's start by labeling the vertices of quadrilateral ABCD as follows:

A(2, 4)

B(4, 5)

C(5, 4)

D(4, 1)

If we reflect quadrilateral ABCD across the x-axis, the new coordinates of the vertices will be:

A'(2, -4)

B'(4, -5)

C'(5, -4)

D'(4, -1)

Now, if we translate quadrilateral A'B'C'D' 4 units left, the new coordinates of the vertices will be:

E(-2, -4)

F(0, -5)

G(1, -4)

H(0, -1)

These are the coordinates of the vertices of quadrilateral EFGH.

Therefore, it can prove that for the transformation to quadrilaterals ABCD≅EFGH by reflecting quadrilateral ABCD across the x-axis and then translating it 4 units left.

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Which module is not a function?

Answers

C would be your answer for this one my friend ☺
Choice C is not a function. The input of x = 2 leads to more than one output (y = -2, y = -1, y = 0, y = 1, y = 2). In order to have a function, any given input must have exactly one output. The other answers choices A, B, D represent this.



Janine wishes to conduct a poll to predict how many dance club members will vote for her for club president.

Which polling methods are likely to be biased?

Select each correct answer.

Janine chooses 5 members that plan on voting for her and asks each to select another 5 members. These 25 members are asked for whom they intend to vote.

Every 10th club member from a list of all members is selected and asked for whom the member intends to vote.

From a list of all club members, 25 members are selected at random and asked for whom they intend to vote.

Five of Janine's friends are selected and asked for whom they intend to vote.

Answers

the answer choice: Five of Jainie's friends are selected and asked for whom they intend to vote is the right answer because friends tend to be bias.

The polling methods likely to be biased are when Option d. Five of Janine's friends are selected and asked for whom they intend to vote.

When conducting a poll, it is important to ensure the sampling method is random and representative. Here are the methods and their potential biases:

Janine chooses 5 members that plan on voting for her and asks each to select another 5 members. These 25 members are asked for whom they intend to vote. — This method is likely to be biased because it relies on the initial selection of supporters, which creates a non-random and unrepresentative sample.Every 10th club member from a list of all members is selected and asked for whom the member intends to vote. — This method is less likely to be biased as it uses systematic sampling, which is more representative of the entire population.From a list of all club members, 25 members are selected at random and asked for whom they intend to vote. — This method is unlikely to be biased because it employs a simple random sample, ensuring each member has an equal chance of being selected.Five of Janine's friends are selected and asked for whom they intend to vote. — This method is likely to be biased due to the convenience sampling of her friends, which is not representative of the entire club.

Hence option D is likely to be biased.

Complete question:

Janine wishes to conduct a poll to predict how many dance club members will vote for her for club president.

Which polling methods are likely to be biased?

Select each correct answer.

a. Janine chooses 5 members that plan on voting for her and asks each to select another 5 members. These 25 members are asked for whom they intend to vote.

b. Every 10th club member from a list of all members is selected and asked for whom the member intends to vote.

c. From a list of all club members, 25 members are selected at random and asked for whom they intend to vote.

d. Five of Janine's friends are selected and asked for whom they intend to vote.

Yolanda participated In a walkathon in which each kilometer walked raised $10 for charity, her goal was to raise more more than $300 on Saturday and Sunday she raised $50 on Saturday which inequality is it?

Answers

x= amount of money needed on sunday

50+x(greater or equal to)300

Answer: The required inequality will be 50+x>$300

Step-by-step explanation:

Since we have given that

Amount raised for charity = $10

Amount raised on Saturday = $50

Amount raised on both Saturday and Sunday is more than $300.

Let the amount raised on Sunday be 'x'.

So, Inequality becomes,

Saturday + Sunday > $300

50+x>$300

x>$300-$50

x>$250

So, On Sunday he must raised more than $250.

Hence, the required inequality will be

50+x>$300

solve for x: A=2xy what is the answer

Answers

the answer is x= A/2y
x =A/2y
thats the only answer based on information you given

Shayla has 5 pets which is 3 more than half the number of pets Judy has. how many pets does Judy have

Answers

Judy has 4 pets
5+3=8
And If you cut that in half (8-4) it would be 4 :)
The answer to this is 4. 

What is the slope of this line?

Answers

Hello!

To find slope, calculate the change in y-values and divide it by the change in x-values:

y1 - y2 / x1 - x2

You have the coordinates (-4, 5), (0, 6), and (8, 8). You can use any combination of two of these points to calculate slope. I'll use (0, 6) and (8, 8).

6 - 8 / 0 - 8
-2 / -8
1/4

Answer:
The slope of the line is 1/4
Hello there! Slope is rise/run. The formula for finding slope is y2 - y1/ x2 - x1, where you subtract the first x and y-coordinates from the second s and y-coordinates. We will use the points (0, 6) and (8, 8). The values will represent each of these:

y2 = 8
y1 = 6
x2 = 8
x1= 0

That makes the problem 8 - 6/ 8 - 0. Let's subtract. 8 - 6 is 2. 8 - 0 is 8. 2/8 is 1/4 in simplest form. There. The slope of the line is 1/4.

Which of the following options is a better purchase for a microwave? A. $5 down with equal payments of $10 for 15 weeks B. $10 down with equal payments of $5 for 24 weeks C. $0 down with equal payments of $15 for 9 weeks D. $20 down with equal payments of $10 for 11 weeks

Answers

B. Option 1 is the better purchase

B. $10 down with equal payments of $5 for 24 weeks.

22. If triangle DEC equals about triangle BEC, which is true by CPCTC?

A. Angle EBC equals about angle EDC
B. Line AE equals about line EC
**C. Angle A equals about angle C
D. Line AE equals about line ED

I choose C but I’m Lost

Answers

D. Line AE equals about line ED because if you measure line AE it is the same length as line ED

Answer with explanation:

→Triangle DEC equals about Triangle B EC.

⇒The meaning of equal here,is that both the triangles that is,                  ΔDEC ≅ ΔB EC.

≡When Triangles are congruent,their corresponding sides and angles are equal .

Corresponding Sides which are equal by C P C TC:

1. BE = DE

2.BC =CD

3.EC, is Common.

Corresponding angles which are equal by C P C TC are:

1. ∠B EC=∠DEC

2. ∠ D CE=∠B CE

3.∠ E B C= ∠ E D C

Option A: ⇒Angle E BC equals about angle E DC

The sides of a triangle are 7, 4, n. If n is an integer, state the largest and smallest possible values of n.

smallest value-

largest value-

plz help

Answers

The smallest value it could be is 4 and the largest value it could be is 10.

The triangle inequality theorem states that any two sides of a triangle must have a sum greater than the third side.  Given the two sides we have, 7 and 4, the sum would be 11; this would mean that the missing side could be no more than 10.

If we take the unknown side and the smallest one we're given, we would have the inequality 
n+4>7

Subtracting 4 from both sides we would have n>3.  That means it would have to be the next integer up, which would be 4.

Smallest value and largest value of n is [tex]11 , 3[/tex].

The third side of a triangle has a range,

[tex]Sum\; of \;two\; other\; sides\geq n\geq Difference\; of\; the\; sides[/tex]

[tex]7+4\geq n \geq7-4[/tex]

[tex]11\geq n \geq 3[/tex]

Therefore

Largest[tex]=11[/tex]

Smallest[tex]=3[/tex]

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Four days before the 1997 500 Festival Parade, a fire destroyed 10 of the 14 floats. People wanted to know if the parade would be canceled. During the first two days after the fire, the Festival received an average of 22 incoming calls a minute. How many calls did the Festival receive in an hour? How many calls did the receive in 12 hours?

**The parade went off as planned four days later. More than 250,000 people lined the streets to view huge posters and replicas of the floats.

Answers

There are 1,320 calls every hour.. in 12 hours there are 14,760 calls.

The scatter plot shows the relationship between the weekly hours spent on social media and the weekly hours spent reading, by the students of a middle school:



What is the y-intercept of the line of best fit and what does it represent?

6 hours; the number of hours students read when they do not spend time on social media
6 hours; the number of hours students spend time on social media when they do not read
8 hours; the number of hours students read when they do not spend time on social media
8 hours; the number of hours students spend time on social media when they do not read

Answers

8 hours; the number of hours students spend on social media when they do not read.

Answer:

The correct answer is - 8 hours; the number of hours students spend on social media when they do not read.

Step-by-step explanation:

The y intercept is marked as hours spent on social media.

So, the answer is :

8 hours; the number of hours students spend on social media when they do not read.

Which values in this data set are outliers?

61,53,21,48,78,84,56,52,58,62,63

Answers

21 and 84
Hope this helps☺

Answer:

21, 84

Step-by-step explanation:

Hansel makes the following statement: "I have an 80% chance of being selected as the captain of the baseball team and a 10% chance of being elected student body president." What is the probability that Hansel will be selected as the captain of the baseball team and will be elected student body president?
4%
8%
70%
90%

Answers

Answer:

Its 8%

Step-by-step explanation:

turn the percentages into decimals and multiply them its will give you 8%.

Answer:

8%

Step-by-step explanation:

all i did was devide 80 by 10, im not sure its correct but it got the right answer apparantly :)

how many pairs of parallel sides does the quadrilateral appear to have

Answers

Where is the quadrilateral?
There are 4 parallel sides but has 2 pairs of parallel sides.

I'll give brainliest if you show your work. Plz answer quickly.
Which two numbers does Square root of 52 lie between on a number line?
7.0 and 7.1
7.1 and 7.2
7.2 and 7.3
7.3 and 7.4

Answers

7.2 and 7.3 and I honestly just did guess and check
Square root of 52 = 7.2111

That lies between 7.2 and 7.3

Hope this helped!

a large aquarium 18 inches deep holds 30 gallons of water. a small aquarium with the same shape holds 20 gallons of water. how deep is the small aquarium to the nearest inch?

Answers

20 so -10 from 30 so the 18 is -10 right hope dis helped

Please explain I don’t know how to do this‍♀️

Answers

[tex]V_{Cone} = \frac{1}{3} * \pi *radius^2 * height[/tex]
r = 1.2, h = 2.9
[tex]V_{Cone} = \frac{1}{3} * \pi *(1.2)^2*2.9 \\ V_{Cone} = \frac{1}{3} * \pi *4.176 \\ V_{Cone} = 4.37 in^3[/tex]

clothing store buys coats for $50 and then sells them for $80. what is the percent of increase om the price of the coat?

Answers

% Change Formula=
(new # - original #) ÷ original # x 100

= (80-50)/50 x 100
= 30/50 x 100
= 0.60 x 100
= 60%

ANSWER: There is a 60% increase on the price of the coat.

Hope this helps! :)

60% is the percent of increase om the price of the coat.

What is the percentage?

The ratio of two numbers that has no dimensions is what is known as a percentage. It may be used to determine how much one number exceeds another when comparing two figures, or it is used to compare the two statistics to a uniform grid.

The clothes are brought for $50

The selling price is $80

% Change Formula=

(Selling price / cost price ) ÷ cost price# x 100

= (80-50)/50 x 100

= 30/50 x 100

= 0.60 x 100

= 60%

The cost of the coat has increased by 60%.

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stacy has hired tom to build her a doll house. The doll house will be a scale model of her home, and the scale will be 2 inches:3ft. The living room in stacy's house is 18 feet by 12 feet and has wall-to-wall carpeting. Hiw many square inches of carpeting will Tom need for thevliving room in Stacy's doll house?

Answers

Final answer:

To find the area of the living room in Stacy's doll house, we need to use the given scale of 2 inches:3ft.

Explanation:

To find the area of the living room in Stacy's doll house, we need to use the given scale of 2 inches:3ft. First, we convert the dimensions of the living room from feet to inches. The dimensions of the living room in inches will be 18 feet * 12 inches/foot = 216 inches by 12 feet * 12 inches/foot = 144 inches.

Next, we multiply the dimensions by the scale factor of 2 inches:3ft. The dimensions of the living room in the doll house will be 216 inches * (2 inches/3ft) = 144 inches and 144 inches * (2 inches/3ft) = 96 inches.

Finally, we multiply the dimensions together to find the area: 144 inches * 96 inches = 13,824 square inches.

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Madison drove from Atlantic City to newmark. Madison drove for 284 miles at a constant speed of 58 mph how long did it take for Madison to get there?

Answers

4.89 Hours
284 divided by 58 is 4.89
You would divide 284 by 58 because she is going at a constant speed.
284 divided by 58 = 4.89 (approximately)
It took Madison 4.9 hours to get there.

I'll give brainliest if you show your work. Plz hurry.
Which statements are true? Check all that apply.
A square root of 1.8<1.8 (This 1.8 is not Square root)
A square root of 1.8>1 (This 1 is not a Square root)
A square root of 1.8< 1.9 (This 1.9 IS IS IS a square root)
1.3 A square root of 1.9+ the square root of 1.8>2
A square root of 1.9- the square root of 1.8>0.1

Answers

Answer:

Step-by-step explanation:

Given are some statements and we have to check which are true

I) True since [tex]\sqrt{1.8} =1.341<1.8[/tex]

2) True since [tex]\sqrt{1.8} =1.341>1[/tex]

3) True [tex]\sqrt{1.8} =1.341<\sqrt{1.9}[/tex]

4) True since [tex]\sqrt{1.9} +\sqrt{1.8} \\=1.378+1.341\\=2.719>2[/tex]

5) False since

[tex]\sqrt{1.9} -\sqrt{1.8} =1.378-1.341\\=0.037<0.1[/tex]

Answer:

1234

Step-by-step explanation:

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