A small company shows the profits from their business with the function P(x)0.01x^2+60x-500, where x is the number of units they sell and P is the profit in dollars.
a. How many units are sold by the company to earn the maximum profit?
b. Between which numbers of units sold does the company show a profit?
Answers
Answer:
A, 3,000 B 8,5992
Step-by-step explanation:
:)
The number of units is 3000 and the profit is $89500 if the profits from their business with the function P(x)= -0.01x²+60x-500, where x is the number of units they sell and P is the profit in dollars.
What are maxima and minima?Maxima and minima of a function are the extreme within the range, in other words, the maximum value of a function at a certain point is called maxima and the minimum value of a function at a certain point is called minima.
We are assuming the function is:
P(x) = - 0.01x²+60x-500
P'(x) = -0.02x + 60
P'(x) = 0
x = 3000
P''(x) = 0.02
P''(x) > 0 for all x
The function is maximum at x = 3000
Plug x = 3000 in the function;
P(3000) = $89500
Thus, the number of units is 3000 and the profit is $89500 if the profits from their business with the function P(x)= -0.01x²+60x-500, where x is the number of units they sell and P is the profit in dollars.
Learn more about the maxima and minima here:
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Related Questions
please help I will mark brainliest
The triangles below are similar.
Triangle S R P. Angle S is 54 degrees, R is 41 degrees, P is 85 degrees. Triangle X Y Z. Angle X is 54 degrees, Z is 41 degrees, and Y is 85 degrees.
Which similarity statements describe the relationship between the two triangles? Check all that apply.
Triangle P R S is similar to triangle X Y Z
Triangle R S P is similar to triangle Z X Y
Triangle S R P is similar to triangle X Z Y
Triangle P S R is similar to Triangle Z Y X
Triangle R P S is similar to triangle Z Y X
Triangle S P R is similar to triangle X Z Y
Answers
Answer:
Choice 1) no
Choice 2) yes
Choice 3) yes
Choice 4) no
Choice 5) yes
Choice 6) no
Answer:
2, 3, & 5
Step-by-step explanation:
How many solutions do the TWO equations have?
15y + 12x = 18 5y + 4x = 6
==========================
2x+ 3y= 12 -6y= 4x-24
^^^ SEPERATE EQUATIONS
Answers
Answer:
Below.
Step-by-step explanation:
15y + 12x = 18
5y + 4x = 6
The second equations is the first times 3 so they are basically the same.
Infinite Solutions.
2x+ 3y= 12
-6y= 4x-24 Rearranging the second equation:
-4x - 6y = -24 Multiplying the first equation by 2:
4x + 6y = 24
- we see that the last equation is -1 * previous equation.
So there are infinite solutions.
PPLLLLZZZZZ HHHEEELLLLPPPP
Answers
Answer:
11 1/3 sq yards
Step-by-step explanation:
4 1/4 x 2 2/3
change into improper fractions: 17/4 x 8/3 = 136/12 = 11 1/4
An item that costs $278.00 is marked 65% off. The store is offering an additional 10% off the discounted price. Sales tax for the item is 4%. What is the final price, including tax?
Answers
At a baseball game, a vender sold a combined total of 172 sodas and hot dogs. The number of sodas sold was 58 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.
Answers
S is sodas and H is hotdogs
You can get two equations from the statement
Total sold of 172= S + H
And S-58=H
Replace the H in the first equation with the second
So
172=S+(S-58)
230=S+S =2S
230/2=S=115
115-58=57=H
And to check 57+115=172 total again
Find the slope (-8,8) and (1,-10)
Answers
Answer:
Slope = - 2
Step-by-step explanation:
(-8,8) ; (1,-10)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x{1}}\\[/tex]
[tex]=\frac{-10-8}{1-[-8]}\\\\=\frac{-18}{1+8}\\\\=\frac{-18}{9}\\\\= -2[/tex]
Use the FOIL method to check your answer from part A.
Answers
Answer: (3x=2) (x+2)
Step-by-step explanation:
Factor by grouping
What is four fifths mines two thirds sorry for asking
Answers
Answer:
2/15
Step-by-step explanation:
4/5-2/3
Find the missing values in the ratio table.
Miles
28
84
Hours
Answers
Find the area of the given rectangle.
Answers
Answer:
D
Step-by-step explanation:
(3X-8)(X+6)
3X^(2)+(3X×6-8X)-(8×6)
3X^(2)+10x-48
A set of counters is numbered 1 through 12. Suppose you draw one counter without looking. What is the probability of choosing a number greater than 4?
Question 5 options:
2/3
1/12
1/3
1/6
Answers
8/12 = 2/3
the sum of 8 and a number
Answers
Answer:
x+ 8
Step-by-step explanation:
Find the missing values in each column.
Column A
Column 8
Column C
+3+=12
63 +7=
-63+(-7) = 9
-63-7=
Column D
21 + 7 = 3
-21-7) = 3
-21-7=3
21+(-7) = 3
- 24+4=-6
43 - (-4)= -12
Describe the pattern you see in each column's answers in Problem 1. relating it to the problems divisors and
dividends. Why is this so?
Describe the pattern you see between the answers for Columns A and B in Problem I les compare the first answer
in Column A to the first answer in Column B compare the second answer in Column A to the second answer in
Column B) Why is this so?
Describe the pattern you see between the answers for Columns C and Din Problem 1. Why is this so?
Answers
Answer:
because less
Step-by-step explanation:
Translate this phrase into an algebraic expression.
The sum of 17 and twice Greg's score
Use the variable g to represent Greg's score.
Answers
Answer:
17+2g
Step-by-step explanation:
Answer:
2g=17
Step-by-step explanation:
a bag has 4 red balls and 4 balls, what is the probability of getting a red ball randomly.
Answers
Answer:
1/2
Step-by-step explanation:
4/8 are red. If you simplify that you get 1/2.
Please help!!!!
Sometimes you need to use FOIL, in order to simplify a radical expression,
Multiplying binomial expressions is very similar to multiplying binomial radicals
Examples:
Answers
Answer:
c) ([tex](6-\sqrt{12} )(6+\sqrt{12} ) = 24[/tex]
d) ([tex](3+\sqrt{8} )(3-\sqrt{8} ) = 1[/tex]
Step-by-step explanation:
Step(i):-
Given that the binomial expression
([tex](6-\sqrt{12} )(6+\sqrt{12} )[/tex]
Multiply
( 36 + 6√12 -6√12 -(√12)²)
= ( 36 -12)
= 24
c) ([tex](6-\sqrt{12} )(6+\sqrt{12} ) = 24[/tex]
Step(ii):-
Given that the binomial expression
([tex](3+\sqrt{8} )(3-\sqrt{8} )[/tex]
Multiply
= 9 - 3√8 + 3√8 -(√8)²
= 9 - 8
= 1
d) ([tex](3+\sqrt{8} )(3-\sqrt{8} ) = 1[/tex]
PLEASE HELP 20 POINTS
The area of a rectangular trampoline is 84 ft^2. The length of the trampoline is 8 ft greater than the width of the trampoline. The
situation can be represented by the equation
w^2 + 8w- 84 = 0
What is the width of the trampoline in feet?
A) 7 feet
B) 6 feet
C) 14 feet
D) 8 feet
Answers
Answer:
the rectangle is 14x6, the width is 6ft
Step-by-step explanation:
Find the area of the shaded part (π=22/7)
Answers
Answer:
42cm square
Step-by-step explanation:
Frist find the area of the square. 14*14
Then find the Area of the circle.- (radius) one side of the square is the diameter so, diameter divided by 2 - 14/2=7
After that subtract the area of circle from the area of the square.
Answer:
first we find the area of the square.
area of square=side²
area of square =14²
area of square=196cm²
area of circle=pi×radius²
radius=14/2=7
area of circle=22/7×(7)²
area of circle =22/7×49
area of circle =154cm²
area of shaded region=area of square - area of circle
area of shaded= 196cm²-154cm²
area of shaded=42cm²
please i don't understand set theory in mathematics
please who will teach me through zoom
please indicate
will mark brainiest
Answers
Set theory is the mathematical theory of well-determined collections, called sets, of objects that are called members, or elements, of the set. ... The axioms of set theory imply the existence of a set-theoretic universe so rich that all mathematical objects can be construed as sets
For example, if A = {1, 2, 3} and B = {1, 2, 3, 4, 5} then A Í B (Í means is a subset of). If A = {1, 2, 4, 8}, then n(A) = 4. This is because n(A) means the number of members in set A. The universal set is the set of all sets.
Helpppppppppppppp!!!!!
Answers
Answer:
60°
Step-by-step explanation:
angle at a point is 360°
add your given angles and minus it from 360°
40°+105°+155°=300
360°-300°=60°
b1=4,b2=8,h=2 I NEED HELP THE ANSWERS YOU PUT IN DONT SHOW UNLESS I STAY ON :(
Answers
in that case the answer is 12
Integrating sums of functions
Answers
Answer:
(a) -12
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityCalculus
Integrals
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Property [Swapping Limits]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = -\int\limits^a_b {f(x)} \, dx[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Integration Property [Splitting Integral]: [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Step-by-step explanation:
Step 1: Define
[tex]\displaystyle \int\limits^6_4 {f(x)} \, dx = 5[/tex]
[tex]\displaystyle \int\limits^4_{10} {f(x)} \, dx = 8[/tex]
[tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx[/tex]
Step 2: Solve Pt. 1
[Integral] Rewrite [Integration Property - Addition]: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = \int\limits^{10}_6 {4f(x)} \, dx + \int\limits^{10}_6 {10} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4\int\limits^{10}_6 {f(x)} \, dx + 10\int\limits^{10}_6 {} \, dx[/tex]Step 3: Redefine
Manipulate the given integral values.
[Integrals] Combine [Integration Property - Splitting Integral]: [tex]\displaystyle \int\limits^6_4 {f(x)} \, dx + \int\limits^4_{10} {f(x)} \, dx = \int\limits^6_{10} {f(x)} \, dx[/tex][Integral] Rewrite: [tex]\displaystyle \int\limits^6_{10} {f(x)} \, dx = \int\limits^6_4 {f(x)} \, dx + \int\limits^4_{10} {f(x)} \, dx[/tex][Integral] Substitute in integrals: [tex]\displaystyle \int\limits^6_{10} {f(x)} \, dx = 5 + 8[/tex][Integral] Add: [tex]\displaystyle \int\limits^6_{10} {f(x)} \, dx = 13[/tex][Integral] Rewrite [Integration Property - Swapping Limits]: [tex]\displaystyle -\int\limits^{10}_6 {f(x)} \, dx = 13[/tex][Integral] [Division Property of Equality] Isolate integral: [tex]\displaystyle \int\limits^{10}_6 {f(x)} \, dx = -13[/tex]Step 4: Solve Pt. 2
[Integral] Substitute in integral: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10\int\limits^{10}_6 {} \, dx[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(x) \bigg| \limits^{10}_6[/tex][Integral] Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(10 - 6)[/tex][Integral] (Parenthesis) Subtract: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = 4(-13) + 10(4)[/tex][Integral] Multiply: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = -52 + 40[/tex][Integral] Add: [tex]\displaystyle \int\limits^{10}_6 {[4f(x) + 10]} \, dx = -12[/tex]Topic: AP Calculus AB/BC
Unit: Integration
Book: College Calculus 10e
What is the area of this quadrilateral?
20
31
27
O A. 24 square feet
O B. 20 square feet
OC. 80 square feet
D. 40 square feet
Answers
Answer:
The area is 40 square feet
Which is the minimum or maximum value of the given function?
51
4
3
21
1P
-5
-4
-3 -2
-1
0
1
21
31
4
5
-1
-3
-41
-5
Answers
Answer:
the minimum value of the given function is -4
Which words have vertical symmetry for all of the letters in the word? Check all that apply. MOM DIZZY HIT SEAT WAXY
Answers
Answer: 1, 3, 5
1.) MOM 3.) HIT 5.) WAXY
Step-by-step explanation: i hope this helps :)
The words in which all letters have vertical symmetry are MOM, HIT, and WAXY so options (A),(C), and (E) are correct.
What is symmetry?If two figures look an exact shape but their size could be small or big then both figures are called similar figures.
When anything has identical pieces facing one another or revolving around an axis, it is said to be symmetrical.
Vertical symmetry is the way by which a latter will completely coincide about a vertical axis.
For example word "A".
If we take a vertical axis in the mid of the word "A" then about this axis the whole word will coincide by left and right.
Thus, another words are M, O, T, Y, H, X.
The words containing the above letters are MOM, HIT, and WAXY.
Hence "The words in which all letters have vertical symmetry are MOM, HIT, and WAXY".
To learn more about symmetry,
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What explicit expression can be used to find any term of this sequence: 6, 9, 14, 21, ...
A) f(n) = 3n + 3
B) f(n) = n^2 + 5
C) f(n) = 2n^2 + 4
D) f(n) = n^2 + 3
Answers
Answer:1
Step-by-step explanation:
patrick mahomes threw 229 yards in the first quarter of the súper bowl. for the last 3 quarters of the game, he ended up throwing a total of 754 yards. write an equation to find how many yards he threw each of the last three quarters
Answers
Answer:
345 yards :)
Step-by-step explanation:
1. Order the steps to solving a system of equations word problem in the
proper sequence.
Answers
Answer:
The answer is below
Step-by-step explanation:
The steps to solving a system of the equations word problem in the proper sequence are as follows:
1. Identify the problem: since the word problem don't give the direct question that needs to be solved, the first step is to identify the problem from the statement
2. Gather information: here you gather all the relevant information from the statement
3. Create an Equation: use the information available to create an equation for the word problem
4. Solve the problem: put the relevant information into the equation and do the necessary calculation
5. Verify the answer: verify your answer through rough estimates, or principles guiding the equation used, and many more.
2 1/2 divided by 2 1/4 in its simplest form
Answers
Answer:
convert to improper first
5/2 divided by 9/4-------swap the numerator and denominator of the second
5/2 x 4/9
= 10/9 or 1(whole) 1/9
Step-by-step explanation:
Confession Time: What's the grossest thing you've done?
I fed my brother worms when I was little, nobody found out...
Anyway, you're welcome for the points.