Ahmad and Dante wash cars in the neighborhood and charge $5 per car. Last year, they worked very hard and were able to wash 450 cars in the year. They have done a little market research and found that for every $0.20 that the price is reduced, they can get 50 more customers.
2. a. Model the relationship between the number of $0.20 price decreases and the amount of money earned using an equation, table, and graph.
The model for the relationship between the number of $0.20 price decrease, x, to the amount of money earned, E, is presented by the following equation;
E = -10•x² + 160•x + 2250Please find attached the values of the model in the attached table and graph of the model.
How can the equation of the model be found?Let x represent the number of $0.20 price decrease and let E represent the total amount earned (the revenue), we have the following revenue equation;
E = Amount earned = Number of cars washed × The price to wash one carHowever;
When the number of cars washed = (450 + 50•x)
The price to wash one car = (5 - 0.2•x)
Therefore;
E = (450 + 50•x) × (5 - 0.2•x)Which gives the following equation;
E = -10•x² + 160•x + 2250Please find the attached table and graph created using the above equation for the amount earned per year.
From the graph, the maximum amount is earned when the price is reduced by $0.20, eight times to give;
Optimum price = 5 - 0.2×8 = 3.4
The optimum price = $3.4The number of cars washed at the optimum price = 850The maximum amount earned = $2890Learn more about how to find the revenue function here:
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(0,5, 1, 17)
What is the number of subsets
What is the number of proper subsets
Answer:
16
Step-by-step explanation:
n=4
subset=2^n
=2^4
=16
Find the value of x by filling the blanks in the provided statement-reason solutions
Answer:
no picture?
Step-by-step explanation:
I need help finding the slope, identifying the initial value and writing An equation for a linear function and finding the X answer Y intercept PLEASE HELP PLEASE
Answer/Step-by-step explanation:
✔️Slope (m) using the two points (2, 4.58) and (5, 4.28):
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4.28 - 4.58}{5 - 2} = \frac{-0.3}{3} = -0.1 [/tex]
Slope (m) = -0.1
✔️Initial Value = y-intercept = b
To find b, substitute x = 2, y = 4.58, and m = -0.1 into y = mx + b.
(Note: y is P(t) and x is t).
Thus:
4.58 = (-0.1)(2) + b
4.58 = -0.2 + b
Add 0.2 to both sides
4.58 + 0.2 = b
4.78 = b
b = 4.78
Initial value = 4.78
✔️Equation for the linear function:
Substitute b = 4.78, and m = -0.1 into P(t) = mt + b
Thus the equation would be:
P(t) = -0.1t + 4.78
✔️The y-intercept = initial value = 4.78
✔️The x-intercept = the value of t when P(t) = 0.
To get this, substitute P(t) = 0 into P(t) = -0.1t + 4.78.
Thus:
0 = -0.1t + 4.78
Add 0.1t to each side
0.1t = 4.78
Divide both sides by 0.1
t = 47.8
x-intercept = 47.8
At Mama’s Country Kitchen, they serve mashed potatoes and country fried steak. The average amount of mashed potatoes put on the plate is 4 oz. with a standard deviation of 0.2 ounces. If they decided to double their servings of mashed potatoes on each plate, what would be that standard deviation of a total of 10 servings of mashed potatoes?
a) 4
b) 10.24
c) 0.64
d) 3.2
e) 1.6
Answer:
b c
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
If the standard deviation for the original serving is .2, and they doubled the size, then the deviation would become .4. Then you multiply that by the ten servings to make 4.
Jim wants to save money to open a tutoring center. He buys an annuity with a quarterly payment of 56$ that pays 3.7 interest, compounded quarterly. Payments will be made at the end of each quarter. Find the total value of the annuity in 9 years.
Answer:
$78.01
Step-by-step explanation:
solve the equation 56(1+.037÷4)^4×9
ends up being 56(1.00925)^36
56(1.3930133899)
=78.0087
The total value of the annuity in 9 years is: $78.00
We have the following information available from the question is:
He buys an annuity with a quarterly payment of $56 that pays 3.7 interest, compounded quarterly.
Payments will be made at the end of each quarter.
We have to find the total value of the annuity in 9 years.
Now, According to the question:
The total value of the annuity in 9 years :
The equation will be :
[tex]= > 56(1+ \frac{3.7}{4} )^4^(^9^)[/tex]
=>56(1.3930)
=$78.00
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6. In Florida, 94% of people have a TV, 71% have a TV and a DVD player. What percent of people that have a TV also
have a DVD player? In other words, what is the probability a person has a DVD player given that they own a TV?
A. 66%
B. 70%
C. 76%
D. 83%
find a parameterization for a circle of radius 3 with center (-4,4,1) in a plane parallel to the yz plane. write your parameterization so the y component includes a positive cosine
Answer:
Following are the solution to the question:
Step-by-step explanation:
[tex]Radius= 3\\\\center= (-4,4,1)\\\\x(t)=-4\\\\y(t)=4+3 \cos \ t\\\\z(t)= 1+ 3 \sin \ t[/tex]
What is the equation of the line that is parallel to the line 5x + 2Y=12 and passesthrough the point (-2,4) ?
Answer:
y = [tex]-\frac{5}{2}[/tex]x - 1
Step-by-step explanation:
5x + 2y = 12
2y = -5x + 12
y = [tex]-\frac{5}{2}[/tex]x + 6
y = mx + b
4 = [tex]-\frac{5}{2}[/tex] ( -2 ) + b
4 = 5 + b
b = -1
y = [tex]-\frac{5}{2}[/tex]x - 1
how to make 6/12 in to decimal
Answer:
Step-by-step explanation:
If you have a calculator just put 6 / 12, and you will get your answer
If you don't have a calculator, do long division or you can simplify the fraction. Ex: 6/12 = 3/6 = 1/2; 1/2 = 0.5
Answer:
0.5
Step-by-step explanation:
You can reduce it to 1/2 which is equivalent to 50% or 0.5
Find the radius of a circle that has an area of 121 pi f2
Answer: r=11
Step-by-step explanation:
A=πr^2
A=121π
121π=πr^2
r^2=121
r=11
Given the function:
f (x) = (3 x + 4) minus (2 minus x)
Evaluate for f (5).
sum all the prime numbers less than 80 and write the answers.
Answer:
791
Step-by-step explanation:
Prime number is a number that is divisible only by itself and 1 .
prime numbers less than 80
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79
therefore,
2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79
=791
Answer:
791.
prime numbers less than 80 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79
sum of these numbers are
2+3+5+7+11+13+17+19+23+29+31+37+41+43+47+53+59+61+67+71+73+79
= 791
Charlotte is looking for seashells on the beach. She is only going to look for the seashells in a 14 feet by 4 feet rectangular area. What is the area of the rectangle in square feet? *
Answer:
The answer is 56 square feet. Don't forget the square or else the answer is invalid :). good luck
Step-by-step explanation:
What is the reduce form of 10/ab+x
1.
[tex] \frac{10}{2 {ab}^{2} } \times \frac{ {a}^{2} {b}^{2}}{5}[/tex]
[tex] = \frac{5}{2a {b}^{2} } \times {a}^{2} {b}^{2} [/tex]
[tex] = \frac{5}{2a} \times {a}^{2} [/tex]
[tex] = \frac{5 {a}^{2} }{2a} [/tex]
Find the distance between 6 and -2 on a number line
Answer:
8
Step-by-step explanation:
The distance between 6 and -2 is 8
(draw a number line and from 6 to -2 is 8 steps)
what is the measure of ABC?
Please answer the question as quickly as possible
Answer:
The answer would be x by 2 over the squared number.
d. (3+5i) (6-i) = Show your work.
Answer:
4i + 9 < simplified version
Step-by-step explanation:
3 + 5i + 6 - i =
4i + 9
Which statements about experimental probability are true? Select three options. Experimental probability has the total number of trials in the numerator and the number of times an event occurs in the denominator. Experimental probability is the same as theoretical probability. An experiment to determine probability will include a number of trials. A probability experiment will count the number of times an event occurs. Experimental probability can be written in the form of a ratio.
Answer:
C D E or 345
Step-by-step explanation:
Answer:
CDE
Step-by-step explanation:
30+(-46) =?
-45+(-25)=
Answer:
30+(-46)= -16
-45+(-25)= -70
Step-by-step explanation:
Shaela can solve 20 one-step equation problems in 3 minutes. How many seconds does it take her to solve one problem?
Answer:
.67 secounds
Step-by-step explanation:20/3
2/5 acres in 7/8 days
Given that,
A group of workers can plant 2/5 acres in 7/8 days.
To find,
The unit rate in acres/day.
Solution,
To find unit rate, divide acres and days as follows:
[tex]R=\dfrac{\dfrac{2}{5}}{\dfrac{7}{8}}\ \text{acres/days}\\\\=\dfrac{2}{5}\times \dfrac{8}{7}\\\\=0.45\ \text{acres/days}[/tex]
So, the unit rate is 0.45 acres/days.
Jessie can type 140 words every 4 minutes. Suppose she needs to type a report that will have 700 words. Write a proportion that could be used to predict the number of minutes it will take Jessie to type the report. Use x to represent the number of minutes.
Answer:
X = 20 minutes .
Step-by-step explanation:
One word: 4/140 = 1/35 minute .
700 words: X = 700x1/35 = 20 minutes .
(Multiplication)
Need this ASAP thanks
Answer:
the answer is A substitution
Mariette bought a 6 pack of donuts to share with her friends
at school. The donuts cost $18.00 all together.
What is the unit rate for the donuts in ?
donut
1
What is the unit rate for the donuts
Answer: The unite rate is $3 per pack.
Step-by-step explanation:
The unit rate will the the cost of one pack of donuts.
If 6 packs is equal to $18 dollars, then to find the unit rate we will divide 18 by 6.
18/6 = 3
This means one pack of of donut will cost $3.
ent.psonsvc.net/#/question/b1e947ad-6841-4a77-b0a5-7ea88c76f674/3df88b41-2ef2-4268-97a2-4dc1283afd2e
OB. (-2, 6)
Review
1 Unit 7.3 Checkpoint - Transformations in the Coordinate Plane(8.G.2.8.G.3.8.G.4)(22-23 / 4 of 10
O C. (2,-6)
Bookmark
OD. (6, 2)
XD
Rectangle WXYZ has coordinates at W(2, 2), X(2, 6), Y(4, 6), and Z(4, 2). If the rectangle was rotated 90° clockwise about the origin,
what would be the coordinates of X'?
The coordinates of X¹ will be (6,-2), if the rectangle was rotated 90° clockwise about the origin.
Given that, rectangle WXYZ has coordinates at W(2, 2), X(2, 6), Y(4, 6), and Z(4, 2) respectively. We have to calculate the coordinates of X¹ when the rectangle was rotated 90° clockwise about the origin.
Rotation generally helps us to align the figures in the direction along with a fixed point. To rotate the figure 90 degrees clockwise about a point, every point(x,y) will rotate to (y, -x). So, (y,-x) will be the rotation of the coordinates about 90° clockwise about the point.
So, we have to calculate the coordinate after rotation of X(2, 6). Let's suppose after rotation X changes to X¹ then, we have
X(2, 6)→X¹(6,-2) when the rectangle was rotated 90° clockwise about the origin.
Therefore, (6,-2) is the required answer.
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Jane took 10 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day at the same boat speed took her 5 min. If the current in that part of the river is 10 km per hr, what was her boat speed in still water?
Answer: B = 15 kph or 15 kph
step by step
(b-5)*10=(b+5)*5
10b-50=5b+25
5b=75
b=15 kph in still water
Evergreen Wildlife Preserve has 110 animals, and 66 of them are birds of prey. What percent of the animals are birds of prey?
Answer:
60%
Step-by-step explanation:
let ,x% is birds of prey
total animals=110
birds of prey=66
then,
x%of 110=66
x/100×110=66
110x/100=66
1.1x=66
x=66/1.1
x=60%
I'm not sure if this is correct.
Evaluate the following expression: (10 - 3y) - 1 , if y = 3.
Answer: =0
Step-by-step explanation:
(10 - 3*3) - 1
(10 - 9) - 1
1-1
=0