The profit function of the company is the difference between the cost and the revenue functions of the company
The expression of the profit function is [tex]- 0.5x^2 + 40x - 300[/tex]The two values of x that creates a profit of $50 are x = 10 and x = 70How to set up the profit functionThe given parameters are:
C(x) = 60x + 300 --- the cost function
R(x) = 100x - 0.5x^2 ---- the revenue function
The profit function is calculated as:
P(x) = R(x) - C(x)
So, we have:
[tex]P(x) = 100x - 0.5x^2 - 60x - 300[/tex]
Rewrite as:
[tex]P(x) = - 0.5x^2 + 100x - 60x - 300[/tex]
[tex]P(x) = - 0.5x^2 + 40x - 300[/tex]
This means that the expression of the profit function is [tex]- 0.5x^2 + 40x - 300[/tex]
The two values of x that creates a profit of $50This means that:
P(x) = 50
So, we have:
[tex]- 0.5x^2 + 40x - 300 = 50[/tex]
Subtract 50 from both sides
[tex]- 0.5x^2 + 40x - 350 = 0[/tex]
Multiply through by -2
[tex]x^2 - 80x + 700 = 0[/tex]
Expand
[tex]x^2 - 70x - 10x + 700 = 0[/tex]
Factorize
[tex]x(x - 70) - 10(x - 70) = 0[/tex]
Factor out x - 70
[tex](x - 10)(x - 70) = 0[/tex]
Solve for x
x = 10 or x = 70
Hence, the two values of x that creates a profit of $50 are x = 10 and x = 70
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Directions: Each of the following sets are similar real-life situations. Solve these problems accurately using the appropriate combinatorics.
1. You are tasked to take pictures of Dan, Ben, Yla, Jun, and May taking three of them at a time. How many possible ways can you photograph them completely?
2. You are tasked to choose three of your classmates from Dan, Ben, Yla, Jun, and May to be your group mates. How many possible groups will you have?
please my Question}:‑)
[1] 60 possible ways
There are 5 people with 3 "spots."
We can use the following formula to solve for the possible ways that they could be photographed. This calls for a "permutation."
-> n is the total number of people, 5
-> r is the sample, 3, we are taking a picture of at a time
n! / (n−r)!
5! / (5−3)!
5! / (2)!
120 / 2
60
[2] 10 different groups
There are 5 people with 3 "spots."
We can use the following formula to solve for the possible combinations your group mates could end up being. This calls for a "combination."
-> n is the total number of people, 5
-> r is the sample, 3, we are taking 3 people to be a part of our group at a time
n! / (r!(n−r)!)
5! / (3!(5−3)!)
5! / (3!(2)!)
5! / (3!(2)!)
120 / 12
10
What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the given point?
Answer:
answer is D
Step-by-step explanation:
y + 1 = 3(x + 1)
help me thank u alot <333
Answer:
N~U
P~V
Q~S
R~T
(im confused on the second picture, give me time to figure it out)
Step-by-step explanation:
In the diagram, what is the value of x?
Answer:
i believe its C
Answer:
D
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Which is the quotient of 1/4 ÷ 4 ? Use a number line to help.
Answer:
[tex]\frac{1}{16}[/tex]
Step-by-step explanation:
Given;
[tex]\frac{1}{4}\div \:4[/tex]
Solve;
[tex]\mathrm{Convert\:element\:to\:fraction}:\quad \:4=\frac{4}{1}[/tex]
[tex]=\frac{1}{4}\div \frac{4}{1}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]
[tex]\frac{1}{4}\times \frac{1}{4}[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}[/tex]
[tex]=\frac{1\times \:1}{4\times \:4}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:1\times \:1=1[/tex]
[tex]=\frac{1}{4\times \:4}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:4\times \:4=16[/tex]
[tex]=\frac{1}{16}[/tex]
Number line given below:
~Learn with Lenvy~
25 is 55% of what number
Answer:
45.45
Step-by-step explanation:
25 is 55% of What Number? - 25 is 55% of 45.45. 100% of 45.45 is 45.45, therefore 55 percent of 45.45 equals 25.
Answer:
x = 500/11
Step-by-step explanation:
look at the attached photo :)
the sum of 4.5 and a number K is 26.2
Answer:
Your answer should be K=21.7
You can find this by subtracting 26.2-4.5
Judy uses 9.7 pints of blue paint and white paint to paint her bedroom walls.3/5
of this amount is blue paint, and the rest is white paint. How many pints of white paint did she use to paint her bedroom walls?
Answer:
3.88 Pints
Step-by-step explanation:
First we need to find the amount of blue paint that was used. We can do that by multiplying 9.7 by 0.60 since that is 3/5 in decimal form
[tex]9.7*0.60=5.82[/tex]
Now we know how much blue paint was used, now we just need to find how much white paint was used. We can do that by subtracting our amount of blue paint from the total amount of paint used
[tex]9.7-5.82=3.88[/tex]
thus, 3.88 is the amount of white paint used
Graph A represents the exponential equation y=4(6) and graph B represents y=6(4). which statements are true about graph a and graph b
Answer:
Step-by-step explanation:The following statements are true about exponential functions:
-The domain is all real numbers.
- The input to an exponential function is the exponent.
- The base represents the multiplicative rate of change.
The reason why the other two options are wrong are explained below:
The range of exponential functions is not always includes negative numbers; on the contrary, the range is the set of all positive real numbers.
The graph of an exponential function does not have a horizontal asymptote at x = 0; contrarily, the equation of the horizontal asymptote of the graph of is y = 0, which is the x-axis.
Can someone please help me?
Answer:
[tex]\pi \times 4 \times 9 = 113 \\ 4 \times \pi = 12.5[/tex]
Which equation represents a line that passes through (–9, –3) and has a slope of –6?
y – 9 = –6(x – 3)
y + 9 = –6(x + 3)
y – 3 = –6(x – 9)
y + 3 = –6(x + 9)
Answer:
y+3= -6(x+9)
Step-by-step explanation:
Slope is represented as M
Name the numbers in bracket as y1 and x1
You have to use the formula which is:y-y1=m(x-x1)
Then you substitute the numbers into the formula
y--3=-6(x--9)
when two negatives meet the turn to positive
thats how we can conclude that the answer is y+3=-6(x+9)
PLEASE HELP ITS DUE THIS SUNDAY
its okay if you don't know the answer
Answer:
109.25 the answer is 109.25 you can right this or 109 1/4
Identify entry B13
Please help
Answer:
-1
Step-by-step explanation:
The first number indicates the row number and the second number indicates the column number. Therefore B13،That is, the first row and the third column. -1
A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. -1 is the value of B13.
What is Matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.
The given matrix is [tex]B=\left[\begin{array}{ccc}2&5&-1\\0&-3&8\end{array}\right][/tex]
We need to find the value of B13.
In B13 the number one represents the row 1 and 3 represents the columns 3.
So the element in B13 position is third element of first row or first element of the third column.
-1 is the third element of first row and first element of the third column
Hence -1 is the B13 of the matrix.
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#SPJ5
Write each expression as a difference.
1. 7+3
2. a+5
3. a+b
Step-by-step explanation:
I’ll assume that difference means “subtraction”
If that’s the case then you just make everything -(-)
a) 7 - (-3)
b) a - (-5)
c) a - (-b)
What is the perimeter of the triangle shown to the nearest tenths
Answer:
22 (I think)
Step-by-step explanation:
The picture is a lil blurry so I'm not sure if I counted the squares right. But basically, you count the squares from one dot to the next. For example, the one on the top that goes in a horizontal line is 6 squares. As for the other two lines, you count from the dot you're starting at and count VERTICALLY until you reach the same line as the point of the triangle. Like with the left side, it starts at point -5, 4 and you'll count how many squares it takes until you reach the same y-axis line as the tip of the triangle. So you should get to -5, -4 for the left side which counts to 8 squares. Same for the other side, also being 8 squares. Then just add it up. 8+8+6=22.
which graph represents the solution to the inequality 2x-y>-3
Answer:
graph c
Step-by-step explanation:
because-3 is lower than y and 2x
In the diagram, △TPR ∼ △XPZ. Find the length of the altitude PY.
Given that △TPR and △XPZ are similar triangles, the length of the altitude PY is: 24.
What are Similar Triangles?Similar triangles have corresponding sides that have the same ratio, i.e. their sides are proportional.
To find PY, we need to know PZ.
Since △TPR ∼ △XPZ, therefore:
TR/XZ = TP/PZ
Substitute
10/20 = 13/PZ
PZ = (13 × 20)/10
PZ = 26
Find PY using Pythagorean theorem:
PY = √(PZ² - YZ²)
PY = √(26² - 10²)
PY = 24
Therefore, given that △TPR and △XPZ are similar triangles, the length of the altitude PY is: 24.
Learn more about similar triangles on:
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1- The radius of a circle is equal to 12 cm. Find the length of the longest chord of the circle ?
2- Name the polygon whose perimeter is 35 cm and length of its side is 7 cm.
Please help me in this asp i need all the steps
Answer:
1. Longest chord is the diameter. Then answer is diameter is 12 and the radius is 6 CM.
Shay's net earnings per month are $4000. Shay's total monthly expenses are $3000. The biggest expense is rent at $1500. If Shay takes on a roommate who pays $500 per month, by what amount has Shay reduced total monthly expenses?
Group of answer choices
1/8 or 13%
1/6 or 17%
1/3 or 33%
1/2 or 50%
Answer:1/6 or 17%
Step-by-step explanation:
Explanation:
Ignore the net earnings of $4000 as it's extra unneeded info. The same goes for the $1500 rent.
Shay has monthly expenses of $3000. If the roommate chips in $500, then Shay saves 500/3000 = 5/30 = 1/6 of her money toward expenses.
Using a calculator, 1/6 = 0.17 = 17% approximately
12 people are watching the otters at the zoo. 7 people are watching the giraffes. How many more people are watching the otters?
Answer:
[tex]\displaystyle 5[/tex]
Explanation:
All you do is deduct the people watching giraffes from the total number of people at the zoo:
[tex]\displaystyle \boxed{5} = -7 + 12[/tex]
I am joyous to assist you at any time.
5 people’s are watching the otters …
Problem:12 people are watching the otters at the zoo. 7 people are watching the giraffes. How many more people are watching the otters ?
To find:How many more people are watching the otters ?
Let’s find: ( step-by-step explanation ):As question says ,→ At the zoo, 12 people are watching the otters & 7 people are watching the giraffes...
• So , you have to find how many people’s are watching otters more than the giraffes...
→ Then use , Subtraction to find How many more people are watching the otters..
So ,[tex]12 - 7 = 5[/tex]
• Therefore , 5 people’s are more peoples are watching the otters than the giraffes….
Hope this helps you... :)Liliana and Marcus are playing a word game. Liliana spells a word incorrectly and loses 18 points. Then Marcus spells a word correctly and has the opposite score. Which is the correct way to represent “the opposite of Liliana’s score is equal to Marcus’s score”?
Negative 18 = 18
Negative (negative 18) = negative 18
Negative (18) = negative 18
Answer:
Well if Liliana loses 18 points and Marcus get the correct one and gains 18 points
Step-by-step explanation:
So basically it's going to be negative because its saying what is the opposite of Liliana's core but in reverse order
How to be an expert on brainly?
Answer :
Most English queries can be answered with a search, and arithmetic problems can be solved with a calculator. The majority of individuals use Brainly to ask questions that have previously been answered.
Day 5
Now, in this part, your knowledge will be tested again. To assess
your understanding of our lesson for this week, answer the following
tasks: Learning Task 7: Identify and describe the triangles according
to their sides
and angles.
Triangles
Sides
Angles
1.
2.
3.
4.
5.
In this part
we can measure our learnings in identifying and describing
Answer:
1. 3, 3
2 3, 3
3 3, 2
4 3, 3
5 3, 3
Translate each sentence into an equation.
15. Fifty-three plus four times
c is as much as 21
Answer:
53+4c=21 = 53 + 4 x c =21
Step-by-step explanation:
Write an equation to represent the diagram on the left.
Answer:
3n + 10 = 28
Step-by-step explanation:
3n + 10 = 28
-10 -10
3n = 18
÷3 ÷3
n = 6
I hope this helps!
Answer:
3n = 18
Step-by-step explanation:
3n = 28-10
3n = 18
If u simplify this further you will get n value as 6
What is the answer for this question?
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
I just took an assignment on this
Please look at the picture and answer it. Thank you.
Answer: 140
Step-by-step explanation:
As you can see the angles are identical which means both sides are 140!
PLS HELP ME What effect will an animal have if it is introduced to a new environment?
It will be helpful if it spreads disease.
It will be harmful if it helps seeds disperse.
It will be harmful if it takes over the environment.
It will be helpful if it overpopulates. ITSscience
Answer:
It will be harmful if it takes over the environment.
Step-by-step explanation:
The reason for this is because, if the animal has no natural predators or controls, it can reproduce and quickly spread and multiply, taking over an area.
Also there are many invasive species that are the reasons for many other animals and plants becoming extinct. For example, they can reduce the habitat, fight with other animals for natural resources, and change the habitat.
Answer:
it is harmful
Step-by-step explanation:
hope this helps
Brody has a collection of 300 basketball and baseball trading cards. He has 180 baseball cards.
Answer:
The answer is 300 - 180= k
Step-by-step explanation:
Hope that helps!
Greetings to everyone! Can anyone be willing to help me in the word problems on Normal Distributions? I will forever be thankful and grateful to you!
Answer:
if some does this than this would happen
Step-by-step explanation: