For a certain company, the cost function for producing x items is C(x)=50x+100 and the revenue function for selling x items is R(x)=−0.5(x−90)2+4,050 . The maximum capacity of the company is 150 items.
Assuming that the company sells all that it produces, what is the profit function?
P(x)=
What is the domain of P(x) ?
The company can choose to produce either 40 or 50 items. What is their profit for each case, and which level of production should they choose?
Profit when producing 40 items =
Profit when producing 50 items =
Can you explain, from our model, why the company makes less profit when producing 10 more units?
The profit function is P(x) = −0.5x² + 40x - 100
The domain is 3 < x < 75Profit when producing 40 items = 700Profit when producing 50 items = 650The company makes less profit when they produce moreHow to determine the profit function?From the question, we have the following equations that can be used in our computation:
Cost function, C(x) = 50x + 100
Revenue function, R(x) = −0.5(x − 90)² + 4050
The profit function is the difference between the revenue and the cost
So, we have
P(x) = R(x) -CP(x)
Substitute the known values in the above equation, so, we have the following representation
P(x) = −0.5(x − 90)² + 4050 - 50x - 100
Evaluate the like terms
P(x) = −0.5(x − 90)² - 50x + 3950
Expand
P(x) = −0.5(x² − 180x + 8100) - 50x + 3950
Expand
P(x) = −0.5x² + 90x - 4050 - 50x + 3950
Evaluate the like terms
P(x) = −0.5x² + 40x - 100
The domain of the functionIn (a), we have
P(x) = −0.5x² + 40x - 100
Using a graphing calculator, the reasonable domain is
3 < x < 75
So, the domain is 3 < x < 75
The profit at each productHere, we have
x = 40 or 50
So, we have
P(40) = -0.5(40)² + 40(40) - 100 = 700
P(50) = -0.5(50)² + 40(50) - 100 = 650
Why the profit makes less profitIn (d), we have
P(40) = 700
P(50) = 650
This means that the profit reduces as they produce more
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DUE SOON! PLEASE SHOW WORK! JUST DONT KNOW WHERE TO START! BEEN STUCK ON THIS FOREVER ITS DUE SOON!!
Answer:
(0,-7)
Step-by-step explanation:
Plug in the X and Y's from the answer choices to get your answer. If the left of the equation (Y) is less than the right side (-1/2x - 6) it is correct!
Hope this helps!
29.7 divided by 12 i need a anwser
Answer:
2.475
Step-by-step explanation:
Answer:
2.475
Step-by-step explanation:
Could you please give me brainliest for this? Thanks!
Callan is making pizza using flour, tomatoes, and mozzarella cheese. This table gives the cost, per kilogram, of each ingredient, and the amount, in kilograms, that Callan uses: Ingredient Price per kilogram Amount Flour 0.800.800, point, 80 dollars per kilogram xxx kilograms Tomatoes 3.303.303, point, 30 dollars per kilogram yyy kilograms Mozzarella zzz dollars per kilogram 0.50.50, point, 5 kilograms The total amount Callan spends on ingredients is CCC dollars.
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The total amount spent on the ingredients is
80x + 30y + 5z
Where x is the amount of flour, y is the amount of tomatoes and z is the cost of Mozzarella per kg.
What is an expression?
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Ingredients Amount Cost per kg
Flour x $80
Tomatoes y $30
Mozzarella 5 $z
The total amount spent on the ingredients can be given by the expression.
= 80x + 30y + 5z
Where x is the amount of flour, y is the amount of tomatoes and z is the cost of Mozzarella per kg.
Thus,
The total amount spent on the ingredients is
80x + 30y + 5z
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Answer:
C=0.8x+3.3y+0.5z
Step-by-step explanation:
khan
you`re welcome :)
8 x 5 = (4 X 5) + (_______ x 5
8 X 5 = 20 +
8 X 5 =
Answer:
4
20
40
Step-by-step explanation:
Since the final line says 8 x 5, I know that the final answer is 40.
That means that the blank on the first line has to be 4
The second line is missing a 20 because 20 + 20 = 40
Write the number 476 in
each form.
Word:
Expanded:
Answer:four-hundred-seventy-six
400+70+6
Step-by-step explanation:
four-hundred-seventy-six
400+70+6
Which of the following shows an example of the identity property of 0?
Answer:is 1
identity property of 0 the definition is adding 0 to any number results in the number itself. and one 1 is have the same but other 3 is not.
A rectangular flowebed is 6.1 meters long.and 3.6 meters wide. What is the area of the flower bed? Use the area model to solve?
NEED HELP WITH GEOMETRY ASAP!!!
Answer:
LK = 5
LM ≈ 5.83
KM ≈ 7.28
NOT isosceles
Step-by-step explanation:
L(-7,4)
K(-4,8)
[tex]LK=\sqrt{(-7--4)^{2}+(4-8)^{2}}=\sqrt{(-3)^{2}+(-4)^{2}}=\sqrt{9+16}=\sqrt{25}[/tex]
M(-2,1)
[tex]LM=\sqrt{(-7--2)^{2}+(4-1)^{2}}=\sqrt{(-5)^{2}+(3)^{2}}=\sqrt{25+9}=\sqrt{34}[/tex]
[tex]KM=\sqrt{(-4--2)^{2}+(8-1)^{2}}=\sqrt{(-2)^{2}+(7)^{2}}=\sqrt{4+49}=\sqrt{53}[/tex]
Tom makes $200 per week working a part-time
job. He pays $300 per month for his share of the
rent where he lives. How much money does he
have left for other expenses in one year?
Answer:
$6000
Step-by-step explanation:
200 dollars a week
spends 300 dollars every month
200 dollars*4 weeks in a month = 800 a month
800 dollars a month - 300 dollars spent every month = 500 remaining after each month
500 dollars a month remaining*12 months in a year = 6000 dollars left for other expenses in one year.
Hope this helps!
Answer:$6000
Step-by-step explanation:
there are 4 weeks in a month and he makes $200 a week so i multiplied it by 4 which equals $800 then i subtracted $300 for the monthly rent then i multiplied that by 12 and that got me to a total of $6000
Which graph represents the function f(x)=3⋅5^x?
Answer:
C (the one under the first graph)
Step-by-step explanation:
if x = 0
3 * 5^0
3 * 1
y = 3
Convert 5 feet into inches.
*Note: you must use these exact conversion factors to
get this question right.
Answer:
60 inches.
Step-by-step explanation:
There are 12 inches in one foot:
12 x 5 = 60
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 5 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Answer:
60 inches
Step-by-step explanation:
(5 feet) = [tex]\frac{12inches}{1foot}[/tex] The word feet can cancel and you are left with
(5)(12 inches) = 60 inches.
twelve more than the product of 16 and 3
Answer:
60
Step-by-step explanation:
16(3)+12
=48+12
=60
Answer:
60
Step-by-step explanation:
Use the distributive properly to rewrite the expression -2[5+(-3)]
Answer:
the answer for the expression -2[5+(-3)] is -4
PLS HELP
During a 90-minute school play, the main character was on stage 80% of the time.
What amount of time in minutes was the main character on stage?
88.9 minutes
112.5 minutes
80 minutes
72 minutes
Answer:
72 minutes
Step-by-step explanation:
you convert the 80% to decimal form so its now 0.80.
then you multiply how long the school play was (90) times the 'percentage' of how long the main character was on the stage (0.80).
90 times .80 is 72.
hope this helped:)
Use properties of operations to write an expression equivalent to the expression below.
p6+(q+8)
A. p6+8q
B. 8(p6+q)
C. (p6+q)+8
D. 6p+q+8
The expression (p⁶ +q) + 8 is equivalent to the given expression. which is the correct answer would be an option (C).
What is the Commutative Property?The commutative property is associated with mathematical operations such as addition and multiplication. It indicates that switching the order or location of two integers while adding or multiplying them has no effect on the outcome. For example, 4 + 5 gives 9, and 5 + 4 also gives 9.
The expression is given in the question below as
p⁶ + (q + 8)
We have to determine the expression equivalent to the given expression.
As per the given question, we have
⇒ p⁶ + (q + 8)
Using the commutative property of addition, we get
⇒ (p⁶ +q) + 8
Thus, the expression (p⁶ +q) + 8 is equivalent to the given expression.
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Sage and Tom started the month with the same number of talk minutes on their cell phones. Sage talked for 7 minutes with her dad. Tom talked for 4 minutes with a friend and 3 more minutes with his mom. Do Sage and Tom have the same number of talk minutes left on their cell phone plans?
Part A:
Complete the model to represent Sage’s minutes.
Enter the correct answers in the boxes.
Part B
Complete the model to represent Tom’s minutes.
Enter the correct answers in the boxes.
Part C
Write an algebraic expression to represent the number of minutes Sage has left.
Enter the correct answer in the box.
Part D
Write an algebraic expression to represent the number of minutes Tom has left.
Enter the correct answer in the box.
Part E
Do Sage and Tom have the same number of talk minutes left on their cell phone plans? Explain your reasoning.
Select answers from the drop-down lists to correctly complete the explanation.
Part A: We can complete the model representing Sage's minutes by putting n and 7 in the box.
Part B: We can complete the model representing Tom's minutes by putting n and 7 in the box
Part C: An algebraic expression to represent the number of minutes Sage has left is S = n - 7, where S equals the remaining talk minutes for Sage and n is the initial number of talk minutes.
Part D. An algebraic expression to represent the number of minutes Tom has left is T = n - 7, where T equals the remaining talk minutes for Tom and n is the initial number of talk minutes.
Part E: Sage and Tom have the same number of talk minutes left on their cell phone plans because they started with the same amount and consumed the same amount at the end of the month.
What is an algebraic expression?An algebraic expression is a mathematical expression that consists of variables and constants, along with algebraic operations and equality or inequality symbols.
The basic algebraic operations include addition, subtraction, division, and multiplication.
Thus, algebraic expressions can be used to mathematically model or represent the number of minutes that Sage and Tom have left.
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The polynomial
p(x)=24x3−46x2+29x−6
has three real roots. One of them is x=2/3 Find the others and list them in increasing sequence:
The other roots of the cubic equation p(x) = 24·x³ - 46·x³ + 29·x - 6 are;
x = 1/2
x = 3/4
What is a cubic equation in mathematics?A cubic equation is an equation that has 3 as the highest index.
The specified polynomial in the question is presented as follows;
P(x) = 24·x³ - 46·x² + 29·x - 6
The solution of the equation is; x = (2/3)
Therefore, (x - 2/3) is a factor of the equation and we get;
(24·x³ - 46·x² + 29·x - 6) ÷ (x - 2/3) has a remainder of 0
Dividing the above expression using long division, we get;
24·x² - 30·x + 9
(x - 2/3) [tex]{}[/tex] |(24·x³ - 46·x² + 29·x - 6)
[tex]{}[/tex] 24·x³ - 16·x² + 29·x - 6
[tex]{}[/tex] -30·x²
[tex]{}[/tex] -30·x² + 20·x
[tex]{}[/tex] 9·x - 6
[tex]{}[/tex] 9·x - 6
The other real roots of the specified equation can be found as follows;
The equation for the roots is; P(x) = 24·x³ - 46·x² + 29·x - 6 = 0
From the above long division, therefore;
24·x³ - 46·x² + 29·x - 6 = (24·x² - 30·x + 9) × (x - 2/3) = 0
Which indicates; (24·x² - 30·x + 9) = 0 or (x - 2/3) = 0
The other solution are;
24·x³ - 30·x + 9 = 0
3·(·8·x² - 10·x + 3) = 0
8·x² - 10·x + 3 = 0
Solutions for the above equation in the form; a·x² + b·x + c = 0 can be obtained using the quadratic formula as follows;
The quadratic formula; x = [tex]\dfrac{-b\pm\sqrt{b^2 - 4\cdot a\cdot c} }{2\cdot a}[/tex]
By comparing the equation, 8·x² - 10·x + 3 = 0 to the equation, a·x² + b·x + c = 0, we get;
a = 8, b = -10, and c = 3
Therefore;
x = (10 ± √((-10)² - 4 × 8 × 3))/(2 × 8)
((-10)² - 4 × 8 ×3) = 2
Therefore;
x = (10 ± √((-10)² - 4 × 8 × 3))/(2 × 8) = (10 ± 2)/(16)
x = 3/4, and x = 1/2
Therefore, the other other roots in increasing sequence are;
x = 1/2 and x = 3/4
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what is 5 to the power of 3?
Answer:
5 to the power of 3 is 125, you get this b/c 5 times 5 is 25 & 25 times 5 is 125.
encuentra el producto: (2) (3) (-4) (-2)
ayuda porfa.
Answer:
48
Step-by-step explanation:
Start with 2 x 3 to get 6
then take 6 and multiply by -4 which is -24 (The negative stays from the four)
Last, take -24 and multiply by negative 2 to get 48. The negatives cancel out
X^2-9/2x+
Find the term to make the trinomial into a perfect square
Write and solve the equation that represents the sentence below.
The product of 18 and a number is 109.8 .
Which statements are correct? Select three options.
The linear equation we want to write is:
18*x = 109
And the solution is x = 6.06
How to write and solve the equation?Remember that the product between two numbers is just a multiplication A*B.
Here we know that the product of 18 and a number, is 109.
If we define the variable x as the number, then we can write the linear equation:
18*x = 109
Where the product between 18 and x is equal to the number 109.
Now, we want to find the value of x, to do that, we need to divide both sides of the equation by 18, then we will get:
18*x/18 = 109/18
x = 109/18 = 6.06
The solution of the linear equation is 6.06
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The base of a triangle is twelve more than twice its height. If the area of the triangle is 50 square centimeters, find its base and height.
The height of the triangle is 4.68 cm and base of the triangle is 21.36 cm.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
Given that,
Base of triangle is twelve more than twice its height.
Also, area of triangle = 50 square centimeters.
Let height of the triangle is x cm,
Therefore, the base of triangle will be 2x+12 cm.
The area of triangle = 50
1/2 × (2x+12) × x = 50
x (x+6) = 50
x² + 6x -50 = 0
By solving the equation,
x = -3 + √59 and -3 - √59
Length can not be negative,
Therefore, x = -3 + √59 or x = 4.68114
Height of triangle = 4.68 cm
Base of triangle = 21.36 cm
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If a boy grows 5 inches, he will be one half as tall as his sister , his sister is 68 inches tall. How tall is the boy?
Which is the best estimate of 756 ÷ 26?
The division between 756 and 26 can be represented as a fraction or decimal as 378/13 or 29.1 respectively
FractionsFractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
We can say the fraction of a number is a ratio between the numerator and denominator of two numbers.
Fractions are often as a result of dividing two numbers and they probably don't give a whole number.
In this case, the division between 756 and 26 will result in a fraction because both numbers are not completely divisible by one another.
To divide 756 by 26;
756 ÷ 26 =
Divide both sides by 2
756 ÷ 26 = 378 / 13
Both numbers are not divisible by one another from here, but we can represent this as a fraction of one another;
756 ÷ 26 = 29.076923
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Given the graph of f(x) above, find the following and write your answers using interval notation (Separate multiple intervals with a comma):
(a) Domain: 7
(b) Range:
(c) Interval(s) on which f(x) is increasing:
(d) Interval(s) on which f(x) is decreasing:
(e) Interval(s) on which f(x) is constant:
(f) Local maxima: 3
(g) Local minima: -5
Answer:
a) [-9,8)
b) [-5,5]
c) (-4,0), (1,6)
d) [-9,-4), (6,8)
e) [0,1]
f) just the y-value: 5; as a point: (-8,5)
g) just the y-value: -5; as a point: (-4,-5)
Step-by-step explanation:
a) Domain is all of the x-values that are defined in the function. The smallest x-value in the graph is -9, and the largest is 8. And all values in between are defined (have corresponding y-values). But notice that there's an open dot on (8,0).
b) Range is found the same way as Domain, but with the y-values. The smallest y-value of this function is -5, and the largest is 5.
For c-e, notice where the graph changes direction and draw a vertical line from the x-axis through the turning point. These lines are the boundaries between intervals of increasing/decreasing/constant. You should have vertical lines at x=-4, x=0, x=1, and x=6.
c) Interval(s) on which f(x) is increasing: Reading the graph from Left To Right, between which vertical lines is the graph going up?
d) Interval(s) on which f(x) is decreasing: Reading the graph from Left To Right, between which vertical lines is the graph going down?
e) Interval(s) on which f(x) is constant: Reading the graph from Left To Right, between which vertical lines is the graph staying flat?
f) Look for the highest non-infinity point on the graph
g) Look for the lowest non-infinity point on the graph
A saleswoman earns 40% commission on all the merchandise that she sells. Last month she sold $500 worth of merchandise. How much commission (in dollars) did she earn last month?
Answer:
Your answer is $200
Step-by-step explanation:
[tex]500[/tex] × [tex]0.4 = 200[/tex]
Jim made $165 for 11 hours of work. At the same rate, how much would he make for 7 hours of work?
$105
Earnings for 1 hour=165÷11=$15
Earnings for 7 hours=15×7=$105
x + 4y = 22
4x + y = 13
Solve by elimination
Using elimination method, the solution of the equation is as follows:
x = 2y = 5How to solve system of equation by elimination method?System of equation can be solved using different method such as elimination method, substitution method and graphical method.
Therefore, let's use elimination method to solve the equation as follows;
x + 4y = 22
4x + y = 13
multiply equation (i) by 4 to eliminate variable x.
Therefore,
4x + 16y = 88
4x + y = 13
subtract equation(ii) from equation(i)
15y = 75
divide both sides by 15
y = 5
x = 22 - 4y
x = 22 - 4(5)
x = 22 - 20
x = 2
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Use the information to complete the task.
A family is driving at a constant speed of 60 miles per hour on the second day of a trip. The expressions 60h + 300 and 60(h+ 5) are equivalent.
They represent the total number of miles the family has driven on the trip, where h is the number of hours they have driven on the second day.
Choose "True" or "False" for each statement.
Statement
The value 5 represents the speed the family drove on the first day.
The value 60 represents the miles the family drove on the first day.
The value 300 represents the miles the family drove on the first day.
True or False?
True False
True False
True
False
A
Answer:
False
False
True
Step-by-step explanation:
Knowing that they are traveling 60 miles per hour, 60h is equivalent to how many miles they are traveling. When adding 300 you know that would be the a1 term going along the rules of sequences.
Therefore 60h is the rate of increase.
300 is the miles traveled on the first day.
With this information in mind we can now answer the True and false statements.
1. 5 represents the hours they drove on the first day, therefore 1 is a false statement.
2. 60 represents the mph they are traveling on the second day, therefore 2 is a false statement.
3. 300 represents the miles they traveled on the first day, therefore 3 is a true statement.
Answer:
false
false
true
the person above is correct :)