Find the marginal cost, marginal revenue, and marginal profit functions. Find all values of x for which the marginal profit is zero.
C(x) = 5x
R(x) = 8x − 0.001x^2
The marginal cost function is MC(x) = 5, the marginal revenue function is MR(x) = 8 - 0.002x, and the marginal profit function is MP(x) = MR(x) - MC(x). The quantity at which the marginal profit is zero is x = 1500.
Explanation:The marginal cost (MC) function represents the change in total cost when one additional unit is produced. It can be calculated by taking the derivative of the total cost function with respect to quantity (x). In this case, the total cost function is given as C(x) = 5x, so the marginal cost function is MC(x) = 5.
The marginal revenue (MR) function represents the change in total revenue when one additional unit is sold. It can be calculated by taking the derivative of the total revenue function (R(x)). In this case, the total revenue function is R(x) = 8x − 0.001x^2, so the marginal revenue function is MR(x) = 8 - 0.002x.
The marginal profit (MP) function represents the change in profit when one additional unit is produced and sold. It can be calculated by subtracting the marginal cost from the marginal revenue: MP(x) = MR(x) - MC(x).
To find all values of x for which the marginal profit is zero, set the marginal profit function equal to zero and solve for x: 0 = MR(x) - MC(x). In this case, 0 = (8 - 0.002x) - 5. Solving for x gives x = 1500, which is the quantity at which the marginal profit is zero.
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brad wants to buy flowers for a friend with 15 dollars daises are 1 dollar each and roses are 3 dollars a piece he buys 3 more daises than roses how much did the roses cost
Which expression represents, six times a number plus 8 times a number?
6a + 8
6 + 8 + a + b
48(ab)
6a + 8b
The answer is 6a+8b, so *D*, hope it helps!
Consider the sequence 2, 5, 10, 17, ...
What is the value of a4?
2
5
10
17
Answer:
The answer is [tex]a4=17[/tex]
Step-by-step explanation:
we have the sequence
[tex]2,5,10,17,...[/tex]
Let
a1-----> the first term
a2----> the second term
a3----> the third term
a4----> The fourth term
In this problem we have
[tex]a1=2[/tex]
[tex]a2=5[/tex]
[tex]a3=10[/tex]
[tex]a4=17[/tex]
therefore
the answer is
[tex]a4=17[/tex]
The equation y=1.2x+8.9 is a linear model for data comparing the ages of babies between 1 and 11 months old (x) and their average weights in pounds (y). About how much weight does a baby gain per month?
For all the people that actually have this question:
For babies between 1 and 11 months old, the equation y = 1.2x + 8.9 models the baby's weight when the baby is x months old. A baby in that age range weighs 17.5 lbs. What is the best estimate for the age of the baby?
Answer:
7 months
Step-by-step explanation:
1.2 * 7 + 8.9 = 17.3 & 17.3 is close to 17.5
I just took the test!
The weight that a baby gain per month is 1.2.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given is a linear equation,
y = 1.2x + 8.9
This equation compares the ages of babies between 1 and 11 months old (x) and their average weights in pounds (y).
This equation is in the slope intercept form, where 1.2 is the slope and 8.9 is the y intercept.
Slope is the change in y coordinates by change in x coordinates.
So, weight baby gain per month is 1.2.
Hence 1.2 is the weight that the baby gain per month.
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ricardo has a bag of mixed fruit snacks. in the bag, there are 8 cherry fruit snacks and 12 strawberry fruit snacks. what is the ratio of strawberry to cherry?
What is another name for the third quartile of a data set?
a. minimum
b.maximum
c. lower median
d. upper median ...?
Water flowing from a faucet can fill 1/4 of a tank in 3 minutes. How long does it take to fill the tank completely with water?
A cell phone company offers you a plan that charges a flat rate of $25 per month for 200 minutes of airtime. The rate of any time in excess of 200 minutes is $.12 per minute.
A. Write an expression for the monthly dollar amount spent for the cell phone service if you want to use x minutes of airtime in excess of 200 minutes.
B. Write an equation which indicates that you have budgeted no more than $40 per month to spend on the service.
C. Determine the maximum number of minutes you can use in excess of 200 minutes so that you do not exceed your $40 per month budget.
The expression for the monthly dollar amount spent is $25 + 0.12x. The equation for budgeting no more than $40 is $25 + 0.12x ≤ $40. The maximum number of minutes under the $40 budget is 125 minutes.
Explanation:A. The expression for the monthly dollar amount spent for the cell phone service if you want to use x minutes of airtime in excess of 200 minutes is: $25 + 0.12x. This accounts for the flat rate of $25 plus the additional charge of $0.12 per minute over 200 minutes.
B. The equation which indicates that you have budgeted no more than $40 per month to spend on the service is: $25 + 0.12x ≤ $40. This equation represents the total monthly cost being less than or equal to $40.
C. To determine the maximum number of minutes you can use in excess of 200 minutes so that you do not exceed your $40 per month budget, we solve the equation from B. Start by subtracting $25 from both sides to isolate the variable: 0.12x ≤ $40 - $25. Simplifying gives us: 0.12x ≤ $15. Then, divide both sides by 0.12 to solve for x: x ≤ $15/0.12. Simplifying further gives us: x ≤ 125. Therefore, the maximum number of minutes you can use in excess of 200 minutes is 125 minutes.
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Which expressions simplify to a rational answer?
A. √11 ⋅ √5
B. √9 ⋅ √16
C. 5√2 ⋅ √2
D. √3 ⋅ √2
Answer:
if your a k12 kid this is old and was once not a multip choice question but the answer is b
Step-by-step explanation:
-Former k12 kid
Identify the pair of alternate exterior angles.
A.
∠3 and ∠5
B.
∠2 and ∠8
C.
∠2 and ∠7
D.
∠1 and ∠8
i think B
The pair of alternate exterior angles is ∠2 and ∠8 in the context of two parallel lines intersected by a transversal.
The correct answer is option B.
When two parallel lines are intersected by a transversal, alternate exterior angles are pairs of angles that are on opposite sides of the transversal and outside the set of parallel lines. In the given options:
A. ∠3 and ∠5: These angles are on the same side of the transversal, not alternate exterior angles.
B. ∠2 and ∠8: These angles are on opposite sides of the transversal and outside the parallel lines, making them alternate exterior angles.
C. ∠2 and ∠7: These angles are on the same side of the transversal, not alternate exterior angles.
D. ∠1 and ∠8: These angles are on the same side of the transversal, not alternate exterior angles.
Therefore, the correct pair of alternate exterior angles is option B: ∠2 and ∠8.
Which function will produce the same graph as the function shown below?
y=(x+1)(x-3)
a. y+3=x(x-1)
b. y-3=(x-1)^2
c. y=x^2+2x+3
d. y=x^2-2x-3 Which function will produce the same graph as the function shown below?
y=(x+1)(x-3)
a. y+3=x(x-1)
b. y-3=(x-1)^2
c. y=x^2+2x+3
d. y=x^2-2x-3
Answer:
d
Step-by-step explanation:
if 5^-x=3 what does 5^3x equal?
A box that has a length of 2x + 2 and width of x - 2 has a perimeter of 90 centimeters. If the height of the box is x, what is the volume of the box?
please help?
For the function f(x) = -2x^2, if the domain is {-3, 0, 3}, find the range.
A) {0, -36}
B) {0, -18}
C) {-18, 0, 18)
D) {-36, 0, 36}
the mean height of a group of 500 nonsmoking college students is 74 inches and the standard deviation is 5 inches. what is the probability that in a random sample of 25 students from this group, the average height will be between 73 and 75 inches?
a person can pay $9 for a membership to the Science Museum then go to the museum for $1 per visit.For a member of the science museum,what is the total cost of 10 visits?
For a member of the science museum, the total cost of 10 visits is equals to $19.
What is cost?" Cost is defined as the amount paid for any purchase something or using any services."
According to the question,
Membership cost per person to the Science Museum = $9
Per visit cost for a member = $1
'x' represents the number of visits
'y' represents the total cost
As per the condition we get,
y = 9 + $1x
Therefore,
Total cost of 10 visits ,
y = 9 + 1(10)
= 9 + 10
= $19
Hence, for a member of the science museum, the total cost of 10 visits is equals to $19.
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Solve −4(x + 10) − 6 = −3(x − 2).
A. −40
B. −46
C. −52
D. 52
Answer:
x = -52
Step-by-step explanation:
-4(x+10)-6=-3(x-2)
Distribute -4 on the left side and -3 on the right side
-4x-40-6=-3x+6
Combine Like terms
-4x-46=-3x+6
Add 46 both sides
-4x=-3x+52
Add 3x to both sides
-1x=52
Divide by -1
x=-52
Hope this helps!!!! :)
You want to deposit $12,000 in a bank at an interest rate of 8 percent per year. What is the future value of this money after five years?
Answer: For Plato users the answer is
B . $ 17,631.94
Step-by-step explanation:
Kim, Laura and Molly share £385
The ratio of the amount of money Kim gets to the amount of money Mollley gets is 2:5
Kim gets £105 less than Molly gets
What percentage of the £385 does Laura get ?
With working out
To find out what percentage of the £385 Laura gets, we need to determine the amounts that Kim and Molly get. By solving equations and subtracting their amounts from the total, we find that Laura gets approximately 45.45% of the £385.
Explanation:To find out what percentage of the £385 Laura gets, we need to first find out the amounts that Kim and Molly get. Let's assume that Kim gets x amount. According to the ratio, Molly gets 5x amount. From the information given, we know that Kim gets £105 less than Molly, so we can write the equation: 5x - x = £105. Solving this equation, we get x = £35. Therefore, Kim gets £35 and Molly gets 5x £35 = £175. Now, to find out the amount Laura gets, we subtract the amounts of Kim and Molly from the total amount: £385 - £35 - £175 = £175. So Laura gets £175. To find out the percentage, we divide the amount Laura gets by the total amount (£385) and multiply by 100: (175 / 385) * 100 = 45.45%. Therefore, Laura gets approximately 45.45% of the £385.
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a dragon traveled at a rate of 35 miles per hour for 2.5 hours .what distance did the dragonfly travel?
The amount of rainfall in January in a certain city is normally distributed with a mean of 4.2 inches and a standard deviation of 0.5 inches. Find the value of the quartile Q1
Without Graphing, Is The System Independent, Dependent, Or Inconsistent? (Equation And Answer Choices Are In Comments!)
In statistics, the independent variable is plotted on the x-axis and the dependent variable on the y-axis of a scatter plot, which is used to analyze the relationship between variables. The correlation coefficient determines the strength and direction of this relationship, while the line of best fit predicts values of the dependent variable.
Explanation:In statistics, when analyzing a set of data that consists of two variables, we typically designate one variable as the independent variable and the other as the dependent variable. The independent variable is the one that is presumed to cause or explain changes in the other variable, which is the dependent variable. When these variables are plotted on a graph, the independent variable is placed on the x-axis (horizontal axis), and the dependent variable is placed on the y-axis (vertical axis).
To explore the relationship between two variables, creating a scatter plot is a common first step. This graph will show individual data points representing the pairs of values for the two variables. By inspecting the scatter plot, one might observe whether there is a clear pattern or trend that suggests a relationship. If the points tend to fall along a line, it indicates that there is a linear relationship between the variables.
The next step would be to calculate the line of best fit, also known as the least-squares line, using regression analysis. The equation of this line is typically in the form ŷ = a + bx, where 'a' is the y-intercept and 'b' is the slope. The line of best fit represents the linear relationship between the variables and is used to predict the value of the dependent variable, given a value of the independent variable.
Another important step is to determine the correlation coefficient, often denoted as 'r'. This coefficient measures the strength and direction of the linear relationship between the two variables. A correlation coefficient close to +1 or -1 indicates a strong correlation, while one close to 0 indicates little to no correlation.
How many kg in 1 gram?
The sum of the measures of the interior angles of a polygon is five times the sum of the measures of its exterior angles, one angle at each vertex. How many sides does the polygon have? ...?
The sum of exterior angles for any polygon is 360 degrees. Given that the sum of the interior angles is five times this, that's 1800 degrees. By using the formula (n-2)*180 = Sum of Interior angles, we can conclude that the polygon has 12 sides.
Explanation:This question revolves around the properties of interior and exterior angles of polygons. The sum of the exterior angles of any polygon is always 360 degrees. Now, given that the sum of the measures of the interior angles of the polygon is five times the sum of the measures of its exterior angles, this can be interpreted as the sum of the interior angles being 5*360 = 1800 degrees.
To find the number of sides the given polygon has, we can use the formula (n-2)*180 = Sum of Interior angles, where n is the number of sides. Rearranging the formula, n = sum of interior angles / 180 + 2 => n = 1800 / 180 + 2 = 12. Therefore, the polygon has 12 sides.
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The sum of two numbers is 48. If one third of one number is 5 greater than one sixth of another number, which of the following is the smaller number?
6
22
26
42
please just tell me the answer.
Answer:
b: 22
Step-by-step explanation:
what is 3/4 divided by 1/6 in its simplest form?
The value of the required division of [tex]\dfrac{3}{4}[/tex] and [tex]\dfrac{1}{6}[/tex] in the simplest form will be [tex]\dfrac{9}{2}[/tex].
The given fractions are [tex]\dfrac{3}{4}[/tex] and [tex]\dfrac{1}{6}[/tex].
It is required to get the simplest form of division of [tex]\dfrac{3}{4}[/tex] by [tex]\dfrac{1}{6}[/tex].
How to get the simplest form of fraction division?Firstly divide the fractions using algebra rules.Then, write the fraction in its simplest form.The given division can be solved as,
[tex]f=\dfrac{\frac{3}{4}}{\frac{1}{6}}\\f=\dfrac{3}{4}\times\dfrac{6}{1}\\f=\dfrac{9}{2}[/tex]
Therefore, the value of required division in the simplest form will be [tex]\dfrac{9}{2}[/tex].
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To find 3/4 divided by 1/6, multiply 3/4 by the reciprocal of 1/6 (which is 6/1), and simplify the resulting fraction to get 9/2, 4.5, or 4 1/2.
Explanation:To find 3/4 divided by 1/6, you need to multiply 3/4 by the reciprocal of 1/6. The reciprocal of 1/6 is 6/1. Here's a step-by-step explanation of the process.
Write the original division equation: (3/4) ÷ (1/6).Turn the division into multiplication by using the reciprocal of the second fraction: (3/4) × (6/1).Multiply the numerators together: 3 × 6 = 18.Multiply the denominators together: 4 × 1 = 4.Combine the numerators and denominators: 18/4.Simplify the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2: (18 ÷ 2) / (4 ÷ 2) = 9/2.The answer is 9/2, which can also be written as 4.5 or 4 1/2.
A point is moving along the graph of a given function such that dx/dt is 2 centimeters per second. Find dy/dt for the given values of x.
y = 9x2 + 5
(a) x = -1
dy/dt =____ cm/sec
(b) x = 0
dy/dt =____cm/sec
(c) x = 3
dy/dt =_____ cm/sec
...?
The rates of change in y for the given values of x are -36 cm/sec, 0 cm/sec, and 108 cm/sec respectively by using the derivative dy/dt = 18*x*dx/dt.
Explanation:This problem is a case of related rates in calculus. Given that dx/dt is constant at 2 cm/sec and the function y = 9x2 + 5, we need to differentiate the function with respect to t to find dy/dt. Solving for dy/dt, you get dy/dt = 18x * dx/dt.
When x = -1, dy/dt = 18*-1*2 cm/sec = -36 cm/sec.When x = 0, dy/dt = 18*0*2 cm/sec = 0 cm/secWhen x = 3, dy/dt = 18*3*2 cm/sec = 108 cm/secSo, the rates of change in y with respect to time for the given values of x are -36 cm/sec, 0 cm/sec, and 108 cm/sec respectively.
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Michelle finally landed her first job after college and it provides insurance. She had surgery on her knee that she was told would be covered by her insurance, but now she has received a bill from the hospital saying the insurance did not pay it. She called the insurance company and they said it has been paid, but the hospital billing department tells her they never received payment. Who should Michelle contact next for help with resolving this matter?
The correct answer is:
She should contact the person at her company that handles insurance policies, premiums, etc.
Explanation:
This person would have access to Michelle's insurance information, specifically the details of the policy.
The insurance representative at her company may also be able to directly contact the hospital and/or the insurance company on Michelle's behalf. If this is against policy, the representative would at the very least know which person Michelle should contact next.
give me an example of a unit rate used in a real world sutuation