For a certain company, the cost for producing x items is 50x+300 and the revenue for selling x items is 90x−0.5x2.
The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!
Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)
Part b: Find two values of x that will create a profit of $300.
The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1). The order of the list does not matter. To enter a−−√, type sqrt(a).
x=
Part c: Is it possible for the company to make a profit of $15,000?
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This is a typical model used in "microeconomics", the economic study of a firm.
In your Discussion post, don't just post your final answers. It's very important that you explain to your classmates how you arrived at those answers.
It helps to start by choosing good names for the variables. It would make sense here to have x be the number of items, C be the Cost of producing x items, R be the Revenue from selling x items, and P be the Profit from producing and selling x items.
Part a: Write expressions for C and R, the cost and revenue, in terms of the variable x. The profit P that a company makes is the revenue minus cost, or P=R−C. You need to write P also in terms of the variable x.
Part b: Finding two production/sales levels x that create a profit of $300 means solving the equation P=$300. Use your formula for P from Part a and apply what you learned about solving quadratic equations in Module 2 to solve for x. You saw several different methods (factoring, completing the square, quadratic formula, etc.) and can use whichever one you choose.
Part c: This is similar to Part b, but instead you need to solve the equation P=$15,000. Hint - the quadratic equation might be the easiest method for this part
Part a: To set up an expression for the profit from producing and selling x items, we need to find the difference between the revenue and cost functions. Cost function is given as C(x) = 50x + 300Revenue function is given as R(x) = 90x - 0.5x².
Profit function P(x) = R(x) - C(x)P(x) = [90x - 0.5x²] - [50x + 300]P(x) = -0.5x² + 40x - 300Therefore, the quadratic polynomial representing profit is P(x) = -0.5x² + 40x - 300.
Part b: To find two values of x that will create a profit of $300, we need to equate P(x) to 300 and solve for x.-0.5x² + 40x - 300 = 300-0.5x² + 40x - 600 = 0x² - 80x + 1200 = 0x² - 8x + 120 = 0( x - 6)( x - 20 ) = 0Therefore, x = 6 or x = 20 when profit is $300.
Part c: We need to check whether the company can make a profit of $15,000 or not by equating P(x) to 15000 and solving for x.-0.5x² + 40x - 300 = 15000-0.5x² + 40x - 15300 = 0x² - 80x + 30600 = 0.
Dividing both sides by 20, x² - 4x + 1530 = 0Since the discriminant, b² - 4ac = 4² - 4(1)(1530) = -6076 < 0, the equation does not have any real roots. Hence, it is not possible for the company to make a profit of $15,000.
Part a: The profit from producing and selling x items can be expressed as a quadratic polynomial P(x) = -0.5x² + 40x - 300.Part b: Two values of x that will create a profit of $300 are x = 6 or x = 20.Part c: It is not possible for the company to make a profit of $15,000.
For this question, we have to find the profit function of a company that is represented by the difference between the revenue and cost functions. The cost of producing x items is given as C(x) = 50x + 300 and the revenue from selling x items is given as R(x) = 90x - 0.5x².
Therefore, the profit P(x) can be expressed as P(x) = R(x) - C(x). After substituting the expressions for R(x) and C(x) in the formula for profit, we get P(x) = -0.5x² + 40x - 300, which is a quadratic polynomial. To find two values of x that will create a profit of $300, we need to set P(x) = 300 and solve for x. We get two values of x, x = 6 and x = 20. Finally, to find whether it is possible for the company to make a profit of $15,000 or not, we need to set P(x) = 15000 and solve for x. After simplifying, we get a quadratic equation x² - 4x + 1530 = 0, which does not have any real roots. Therefore, it is not possible for the company to make a profit of $15,000.
We have found the profit function, two values of x that will create a profit of $300, and checked whether the company can make a profit of $15,000 or not.
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Given the height of a giraffe (20 ft) how tall would it be if you added 40 more different giraffes? Please explain your answer.
Answer:
800 ft
Step-by-step explanation:
You would have to multiply one girraf by 40 (40 x 20), then you would get 800.
40
x20
00
+ 800
800
whats more likely to happen on dice?
roll 2 evens
or
roll 2 doubles
Answer:
2 evens
Step-by-step explanation:
Answer:
2 evens
Step-by-step explanation:
6. a Suppose the measure of an angle is 25°. What is the measure of its complementary angle?
Answer:
65
Step-by-step explanation:
a complementary angle is either of two angles whose sum is 90°.
90 - 25 = 65
Answer:
65°
Step-by-step explanation:
A pair of complementary angles' measurements combined is equal to 90° in measurement. One of the angles given is 25°. To find the other one, simply subtract 90 with 25:
90 - 25 = 65
65° is the measurement of the complementary angle.
~
Write an interpretation of the statement f(5)=25
Answer:
The answer is 5xf =25 f=5
Step-by-step explanation:
25 ÷ 5 = 5
what is the slope of a line perpendicular to y=-1/2x-2
m = -(1/2)
Step-by-step explanation:
[tex]y = - \frac{1}{2} x - 2[/tex]
The line is written in slope intercept form :
y = mx+b
Where ;
m = Slope
According to the equation,
[tex]m = - \frac{1}{2} [/tex]
So right now i'm doing "solving Inequalities" i need help with this question
3v-12>5v+10
Answer:
v < -11
Step-by-step explanation:
Combine like terms: 3v - 5v > 12 + 10Simplify: -2v > 22Divide each side by -2 to cancel out the -2 next to v. It should now look like this: v < -11I hope this helps!
20 PT PLZZ HELP ASAP
C=4.95+ 3.99b 3.99 per book plus 4.95 fee paid once a month
Create a graph of your equation
Answer:
see below
Step-by-step explanation:
C=4.95+ 3.99b
The slope is 3.99 and the y intercept is 4.95
The cruise ship has 2,067 passengers that will be boarding on Saturday. Each passenger is allowed to have 3 bags each. What is the maximum number of passenger bags that the cruise ship will be carrying?
Answer: 6201 bags
Step-by-step explanation:
2,067 passengers x 3 bags each = 6,201 bags
Answer:
6201
Step-by-step explanation:
No. of passengers = 2067
No. of bags each = 3
Therefore, total bags = 2067 × 3 = 6201
I need help!!!!!!!!!!!!!!!!!!
Answer:
just do what she needs to pay for the first year minus what her uncle gave her then divide by 12
Step-by-step explanation:
t took Mr. Phillips 1.6 hours to run the 13.2 miles. What was his average speed? *
Answer:
8.25 miles per hourStep-by-step explanation:
aver. speed = distance over time
where distance = 13.2 miles
time = 1.6 hours
plugin values into the formula+
speed = 13.2 miles
1.6 hours
= 8.25 miles per hour
What does x equal in the problem?
Answer:4
Step-by-step explanation:
Just look at it. Pretty sure it's 4. .-.
Please Help! Brainliest Answer!
Answer:
D
Step-by-step explanation:
Using sine rule
a/sin A ＝b/sin B
8/sin90° ＝ x/sin60°
8 * sin60° ＝ x
x ＝
[tex]4 \sqrt{3} [/tex]
Ayden spent 35 minutes studying for his math test. He scored a 72%. Olivia spent 75 minutes studying, and scored a 97%. Assume there is a linear relationship between these two quantities. Write an equation to represent the score a student got on the test as a function of the amount of time spent studying.
Answer:
s = 0.625t + 50.125
Step-by-step explanation:
Let the equation that represents the relation between the time of study and marks obtained is,
s = mt + b
Here 's' = marks scored by the students
m = marks obtained by the study per minute
t = duration of study
b = marks obtained without study
Slope of the line having points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope of the line passing through two points (35, 72) and (75, 97)
m = [tex]\frac{97-72}{75-35}[/tex]
m = [tex]\frac{25}{40}[/tex]
m = 0.625
Equation of the line will be,
y = 0.625t + b
Since this line passes through (35, 72),
72 = 0.625(35) + b
b = 72 - 21.875
b = 50.125
Therefore, equation representing duration of study and the score obtained will be,
s = 0.625t + 50.125
Help!! Please click on the photo for more info. You can just say A, B, or C.
Answer:
A
Step-by-step explanation:
Each time, you can get either heads or tails so you need to show all of the possibilities and B and C repeat possibilities
A soccer player kicks a ball downfield. The height of the ball increases until it reaches a maximum height of 8 yards, 20 yards away from the player. A second kick is modeled by y=x(0,4 – 0.008x). Which kick travels farther before hitting the ground? Which kick travels higher?
Answer:
second kick goes fartherfirst kick goes higherStep-by-step explanation:
Assuming the kick started from ground level, the path of the ball is assumed to be symmetrical about the high point. That is, the first kick will land 2×20 = 40 yards downfield.
The equation for the second kick can be rewritten as ...
y = 0.008x(50 -x)
The value of y will be zero at x=0 and at x=50. The second kick will land 50 yards downfield, a greater distance than the first kick.
At x=25, the height of the second kick is ...
y = 0.008(25)(50-25) = 5 . . . yards
The second kick travels farther (50 yds vs. 40 yds).
The first kick travels higher (8 yds vs. 5 yds).
What is the value of x in the equation below?
11.9 - 0.8x = 4.5
A
--6.6
B
9.25
С
17.2
D
20.5
Answer: B 9.25
Step-by-step explanation:
4,000 10,000 BAC = ? BCWS = ? BCWP = ? 12,000 4,000 6,000 TIME- -Today 6,000 LEGEND COMPLETED NOT COMPLETED 10,000
The project has a Budget at Completion (BAC) of $10,000, a Budgeted Cost of Work Scheduled (BCWS) of $12,000, and a Budgeted Cost of Work Performed (BCWP) of $4,000.
The information provided seems to be related to project management and uses the Earned Value Management (EVM) technique. EVM is a project control technique that integrates scope, schedule, and cost to measure project performance and progress. Let's analyze the given data:
BAC = Budget at Completion = $10,000
BCWS = Budgeted Cost of Work Scheduled = $12,000
BCWP = Budgeted Cost of Work Performed = $4,000
In EVM, these values represent the planned and actual costs of the work performed on the project. Here's a breakdown of the terms:
BAC (Budget at Completion) represents the total budgeted cost for completing the project. In this case, it is $10,000.
BCWS (Budgeted Cost of Work Scheduled) represents the budgeted cost for the work scheduled or planned to be performed. It indicates the planned value of the work at a specific point in time. In this case, it is $12,000. This suggests that the project has been delayed or additional work has been added, resulting in a higher planned cost compared to the original budget.
BCWP (Budgeted Cost of Work Performed) represents the budgeted cost for the work that has actually been performed or completed. It indicates the earned value of the work at a specific point in time. In this case, it is $4,000. This suggests that only a portion of the planned work has been completed, resulting in a lower actual cost compared to the planned cost.
Based on the given information, the project is behind schedule and has completed only a portion of the planned work. The BCWP of $4,000 is lower than both the BCWS of $12,000 and the BAC of $10,000, indicating that the project is not on track in terms of cost and progress.
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50 POINTS!!
The function f(x) = 5(2)* represents the number of bacteria, f(x), growing in a culture after x hours. How many bacteria are in the culture after 3 hours? Enter your response here: Only 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, .,-, and / are allowed in your answer. Answers that are mixed numbers must be entered as an improper fraction or a decimal.
Answer:
If it's
F(x)=5x
Then f(3)=15
Step-by-step explanation:
Fill in the missing term on each line. Simplify any fractions. 2s+13=17
Answer:
s = 2
Step-by-step explanation:
2s + 13 = 17
17 - 13 = 2s
17 - 13 = 4
2s / 2 = s
4 / 2 = 2
s = 2
As |a| increases, the parabola becomes
Answer:
1: Narrower
2: Wider
Step-by-step explanation:
The magnitude of 'a' increases, the parabola becomes more and more wider.
What is Parabola?A parabola is a curve where any point is at an equal distance from a fixed point (the focus), and a fixed straight line (the directrix).
Given is a parabola.
The parametric form of equation of parabola is given by -
y² = 4ax
Here, distance 'a' is called focus of parabola.
For a constant value of x - coordinate, take different values of 'a'. For constant x, we get the following relation -
y² [tex]\alpha[/tex] a
As the magnitude of 'a' increases, the y coordinate increases and parabola becomes more and more wider.
Therefore, the magnitude of 'a' increases, the parabola becomes more and more wider.
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3 times Marie’s age is equal to 50 plz show ur work need it now
Answer:
about 16.67 or 16 2/3
Step-by-step explanation:
just divide 50 by 3: 50/3= 16 2/3
Adding a number and its opposite is called
Answer:
additive inverse
Step-by-step explanation:
Linear functions are expressed by the graph and equation. Select all that apply.
The slope is positive for both functions.
The equation has a steeper slope than the line in the graph.
The y-intercept is the same for both.
The graph and the equation express an equivalent function.
Answer:
C and D
Step-by-step explanation:
Answer:
a and c
Step-by-step explanation:
You and some friends are going to the fair. Small rides costs 4 tickets and while big rides costs 7 tickets. You and your friends bought a total of 250 tickets. Write an inequality to represent the different combinations of small and big you can enter.
Answer:
4x+7y≤250
Step-by-step explanation:
Inequalities
Let's call:
x = number of small rides
y = number of big rides
Since each small ride costs 4 tickets, x rides cost 4x tickets.
Since each big ride costs 7 tickets, y rides cost 7y tickets.
The total number of tickets is the sum of both:
Total tickets = 4x+7y
The friends have 250 tickets, so the total tickets of the rides cannot be greater than the 250 tickets available, thus:
4x+7y≤250
You lose four points each time you attend gym class without sneakers. You forget your sneakers three
times. What integer represents the change in your points?
solve these last two
Answer: 24) B 25) B
Step-by-step explanation:
24. option B
When x = 8, y = 4
25. option B
When y = 4, x = 9 and x = 8
Sam is collecting pennies. On the first day of the month, Samnis given 16 pennies. Each day after that he gets 4 more pennies. Which of the following equations defines how many pennies he has after the nth day?
A. an = 16n + 4
B. an = 4n + 16
C. an = 4n + 16
D. an = 64n - 64
Answer:
The answer is 4n + 16
Step-by-step explanation:
N is the number of days that pass by. Each day Sam gets 4 more, meaning you would multiply the number of days by 4, before adding that number to the original number of pennies, which was 16.
The required equation that defined the pennies after nth day is 16 + (n - 1)4.
What is arithmetic progression?Arithmetic progression is the series of numbers that have common differences between adjacent values are same.
What is geometric progression?Geometric progression is a sequence of series whose ratio with adjacent values remains the same.
here,
Samnis gave 16 pennies. Each day after that he gets 4 more pennies.
So first term = 16
Common difference = 4
nth term is given as = a + (n - 1)d
nth term = 16 + (n - 1)4
Thus, the required equation that defined the pennies after nth day is 16 + (n - 1)4.
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1. Use the distributive property to multiply each expression.
2. Recall that i2=-1. Simplify each expression. Write any complex numbers in standard form, a+bi, and write binomials in standard quadratic form.
3. Compare and contrast the multiplication of real numbers and the multiplication of complex numbers.
6x(3+2x)=
6i(3+2i)=
Answer:
Step-by-step explanation:
The multiplication of 6x(3+2x) is 18x + 12x² and 6i(3+2i) is 18i - 12 because i² can be written as -1.
What is a complex number?It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.
It is given that:
The expression:
= 6x(3 + 2x)
After using distributive property:
= 18x + 12x²
= 6i(3+2i)
= 18i + 12i²
= 18i - 12
∵i² = -1
Real and complex numbers are multiplied in exactly the same way, with the exception that we can further condense the complex expression by substituting i² for -1.
Thus, the multiplication of 6x(3+2x) is 18x + 12x² and 6i(3+2i) is 18i - 12 because i² can be written as -1.
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The math club and the Latin club both ordered pizzas for their end-of-year banquets. After the banquets, the math club had 1 1/8 pizzas leftover and the Latin club had 2 3/8 pizzas leftover. Between the two clubs, how many total pizzas were leftover?
A. 1 1/8
B. 3 1/2
C. 1 1/4
D. 3 1/4
Answer: B. 3 1/2
Step-by-step explanation:
Hope this helps
