At the optimal level of production (x = 3), the firm would break even, resulting in neither profit nor loss.
To find the optimal level of production and the profit function, we need to determine the quantity (x) at which marginal cost (MC) equals marginal revenue (MR).
MC = 4x + 30
MR = 60 - 6x
Cost of production of 80 units = $15,400
To find the optimal level of production, we set MC equal to MR and solve for x:
4x + 30 = 60 - 6x
Adding 6x to both sides:
10x + 30 = 60
Subtracting 30 from both sides:
10x = 30
Dividing by 10:
x = 3
The optimal level of production is 3 units.
To find the profit function P(x), we need to subtract the cost function from the revenue function:
Revenue function (R) = Price (P) * Quantity (x)
P(x) = MR = 60 - 6x
Cost function (C) = MC = 4x + 30
Profit function (P) = R - C
P(x) = (60 - 6x) - (4x + 30)
P(x) = 60 - 6x - 4x - 30
P(x) = 30 - 10x
The profit function is P(x) = 30 - 10x.
To find the profit or loss at the optimal level of production (x = 3), we substitute x = 3 into the profit function:
P(x) = 30 - 10x
P(3) = 30 - 10(3)
P(3) = 30 - 30
P(3) = 0
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What is 9 - 3 divided by 1/3 + 1
(Marking brainlest also doing random problems)
Answer:
the answer is 1 if i read this right
Step-by-step explanation:
Answer:
The answer is 1
Step-by-step explanation:
First Multiply and Divide (left to right)
3 divide by 1/3
Convert the element into a fraction:
=3/1 divided by 1/3
Apply the fraction rule:
=3/1 * 3/1
Apply rule a/1:
=3*3
Multiply the numbers: 3*3=9
=9
=9-9+1
Add and subtract (left to right):
9-9+1
9-9=0
=0+1
0+1=1
=1
to increase the mean of 4 numbers by 2, by how much would the sum of the 4 numbers have to increase? check image.
Answer:
8
Step-by-step explanation:
x=average
(x+x+x+x)/4=average
to increase x by 2 you add 2
x+2=average
(x+2+x+2+x+2+x+2)=4=(4x+8)/4=x+2
you'd have to increase the sum by 8 to make the numbers' averages' go up by 2
Are vertical lines negative?
Vertical lines do not have positive slopes or negative slopes. They have undefined slopes.
Now, According to the question :
What is Vertical line?
A vertical line is a line, parallel to y-axis and goes straight, up and down, in a coordinate plane. Whereas the horizontal line is parallel to x-axis and goes straight, left and right.
Is a vertical line positive or negative?
The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).
Hence, Vertical lines do not have positive slopes or negative slopes. They have undefined slopes.
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convert the following fraction to a decimal 3 15/16 to a decimal
A 2,5472
b. 3.156
c. 3.9375
d. 4.238
show work need it asap !
Answer:
C. 3.9375
Step-by-step explanation:
3 15/16
15/16
= 0.9375
0.9375+3
=3.9375
Answer:
C is correct
Step-by-step explanation:
a group consists of 10 kids and 2 adults. on a hike, they must form a line with an adult at the front and an adult at the back. how many ways are there to form the line?
a. 12/2!
b. 2 . 11!
c. 2 . 10!
d. 12!\
If a group consists of 10 kids and 2 adults, the number of ways are there to form the line are 2 * 10!. So, correct option is C.
To form a line with an adult at the front and an adult at the back, we need to consider the positions of the 10 kids within the line. The two adults are fixed at the front and back, so we have 10 positions available for the kids.
To calculate the number of ways to arrange the kids in these positions, we can use the concept of permutations. Since each position can be occupied by a different kid, we have 10 options for the first position, 9 options for the second position, 8 options for the third position, and so on, until the last position, where only 1 kid remains.
Therefore, the number of ways to form the line is:
10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 10!
However, the problem also mentions that there are 2 adults, so we need to consider the arrangements of the adults as well. Since there are only two adults, there are 2 ways to arrange them in the line (adult at the front and adult at the back or vice versa).
Therefore, the total number of ways to form the line is:
2 x 10! = 2 * 10!
Hence, the correct option is b. 2 * 10!, which accounts for both the arrangements of the kids and the adults.
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if z is a standard normal random variable, what is the probability that z is between -2.4 and 0.4?
The probability that a standard normal random variable z is between -2.4 and 0.4 is approximately 0.6472.
To find the probability that a standard normal random variable z is between -2.4 and 0.4, we can follow these steps:
Step 1: Look up the cumulative probability corresponding to -2.4 in the standard normal distribution table. The cumulative probability at -2.4 is approximately 0.0082.
Step 2: Look up the cumulative probability corresponding to 0.4 in the standard normal distribution table. The cumulative probability at 0.4 is approximately 0.6554.
Step 3: Subtract the cumulative probability at -2.4 from the cumulative probability at 0.4 to find the probability between the two values:
P(-2.4 < z < 0.4) = 0.6554 - 0.0082
= 0.6472.
Therefore, The probability that z is between -2.4 and 0.4, when z is a standard normal random variable, is approximately 0.6472. This means that there is a 64.72% chance that a randomly selected value from a standard normal distribution falls within the range of -2.4 to 0.4.
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Write a life situation for the inequality x<2
Answer:
see below (I hope this helps!)
Step-by-step explanation:
A real-life situation for this inequality could be "Tom runs a lemonade stand. His profit is x. If Tom knows that his profit is less than 2 dollars, what inequality represents this situation?"
Please please help me please
Tracy walked for 3 1/2 miles . How many feet did she walk ?
Answer:
18,480 feet
Step-by-step explanation:
Answer
18480
Step-by-step explanation
im smart
WHAT IS THE REMAINDER WHEN \(32^{37^{32} }\) IS DIVIDED BY 9?
Recall Euler's theorem: if \(\gcd(a,n) = 1\), then
\(a^{\phi(n)} \equiv 1 \pmod n\)
where \(\phi\) is Euler's totient function.
We have \(\gcd(9,32) = 1\) - in fact, \(\gcd(9,32^k)=1\) for any \(k\in\Bbb N\) since \(9=3^2\) and \(32=2^5\) share no common divisors - as well as \(\phi(9) = 6\).
Now,
\(37^{32} = (1 + 36)^{32} \\\\ ~~~~~~~~ = 1 + 36c_1 + 36^2c_2 + 36^3c_3+\cdots+36^{32}c_{32} \\\\ ~~~~~~~~ = 1 + 6 \left(6c_1 + 6^3c_2 + 6^5c_3 + \cdots + 6^{63}c_{32}\right) \\\\ \implies 32^{37^{32}} = 32^{1 + 6(\cdots)} = 32\cdot\left(32^{(\cdots)}\right)^6\)
where the \(c_i\) are positive integer coefficients from the binomial expansion. By Euler's theorem,
\(\left(32^{(\cdots)\right)^6 \equiv 1 \pmod9\)
so that
\(32^{37^{32}} \equiv 32\cdot1 \equiv \boxed{5} \pmod9\)
-26a-19-35=-84 . show work!!
Step-by-step explanation:
-26a-19-35=-84
-26a-19+(19)-35=-84+(19)
-26a-35=-65
-26a-35+(35)=-65+(35)
-26a=-30
-26a/26=-30/26
Juan made 24 hamburger patties that were 6 ounces each. How many pounds of beef did he use?
Answer:
9 pounds
Step-by-step explanation:
Gabriel makes a model of a pyramid with the dimensions shown.
A square pyramid. The square base has side lengths of 12 inches. The triangular sides have a height of 11 inches.
Gabriel wants to paint the model. How much paint will he need?
The area of the square base is
in.2.
The area of each triangular face is
in.2.
Gabriel will need
in.2 of paint.
please explain the method used
Answer:
The Area of the square base is 114 In .2
The Area of each triangle face is 66 in .2
Gabriel will need 408 in .2 of paint
Answer:
Step-by-step explanation:
The area of the square base is 144 in.2.
The area of each triangular face is 66 in2.
Gabriel will need 408 in2. of paint.
Last year there were 80 members in chess club this year membership decreased by 20% how many members are there? Sorry
Answer:64 people
Step-by-step explanation: total no. of members=80
%decrease=20
20/100 x 80=16(people that left)
people rem.=80-16
Match the equations of parabolas with the x-intercepts of the parabolas.
Each of the equations of parabolas should be matched with the x-intercepts of the parabolas as follows;
(-2, 0), (7, 0) ⇒ y = -x² - 5x + 14(-4, 0), (3, 0) ⇒ y = x² + x - 12.(-4, 0), (-1, 0) ⇒ y = x² + 5x + 4(-3, 0), (8, 0) ⇒ y = x² - 5x - 24What is the x-intercept?In Mathematics and Geometry, the x-intercept of any function refers to the point at which the graph of a function crosses the x-coordinate and the y-value of "f(x)" is equal to zero (0).
Next, we would determine the x-intercept of each of the equations of parabolas (quadratic functions) as follows;
y = x² + x - 12
0 = x² + x - 12
0 = x² + 4x - 3x - 12
0 = (x + 4)(x - 3)
Therefore, the x-intercept are (-4, 0) and (3, 0).
y = x² + 5x + 4
0 = x² + 5x + 4
0 = x² + 4x + x + 4
0 = (x + 4)(x + 1)
Therefore, the x-intercept are (-4, 0) and (-1, 0).
y = x² - 5x - 24
0 = x² - 5x - 24
0 = x² - 8x + 3x - 24
0 = (x - 8)(x + 3)
Therefore, the x-intercept are (-3, 0) and (8, 0).
y = -x² - 5x + 14
0 = -x² - 5x + 14
0 = -x² - 7x + 2x + 14
0 = (x - 7)(x + 2)
Therefore, the x-intercept are (-2, 0) and (7, 0).
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Eric can run I mile in
6.5 minutes. How long
will it take him to run
3.5 miles?
Answer:
it will take Eric 22.75 minutes to run 3.5 miles
Step-by-step explanation:
Tickets to a school dance cost $5. Ninety tickets have already been sold. How many more tickets x must be sold to earn at least $700? Write your answer as an inequality.
Step-by-step explanation:
5x90=450
700-450=250
250/5=50
50 more tickets.
i don't know if that's in an inequality form or not. but that's how many tickets
Where is the horizontal center of mass of the entire upper extremity?
Answer:
can you tell me please
Step-by-step explanation:
nicest
the chance of rain on a given day in seattle is 70%. if it rains, the chance that a food truck will incur a loss on that day is 80%. if it does not rain, then the chance of loss is 10%. on a randomly chosen day if the food truck has not incurred a loss, what is the probability that it had not rained that day?
The probability of incurring a loss when it rains is:P (loss | raining) = 80%So, there is a 20% chance that the food truck will not have incurred a loss when it rains.
The P (not raining | not loss) = 90% × 30% = 27%.Thus, the probability that it had not rained on that randomly selected day given that the food truck did not incur a loss is 27%.
The chance of not raining on a given day in Seattle can be calculated as follows:When it does not rain, there is a 10% probability that the food truck will incur a loss, as given in the statement. Similarly, when it rains, there is an 80% chance that the food truck will incur a loss on that day.
To calculate the probability that the food truck will not have incurred a loss on that day, we must first calculate the probability that the food truck will have incurred a loss on that day.Suppose the probability of rain is 70%, so the chance that it won't rain will be: P (not raining) = 100% - 70% = 30%When it rains, there is a 80% probability that the food truck will have incurred a loss, as given in the statement.
The probability of not incurring a loss when it does not rain is:P (not loss | not raining) = 100% - 10% = 90%The probability of not raining when the food truck does not incur a loss can be calculated as follows:P (not raining | not loss) = P (not loss | not raining) × P (not raining)P (not loss | not raining) = 90%P (not raining) = 30%
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Leanna has a rectangular price of fabric The fabric is 24 inches wide and 40 inches long leanna folds the piece of fabric along its diagonal to form a triangular scarf. what is the area in square inches
The rectangular pice has a wide of 24 inches and 40 inches long so we can calculate the area of the rectangle:
\(\begin{gathered} A=24\cdot40 \\ A=960 \end{gathered}\)Now they say that Lenna folds the piece of fabric along its diagonal so the triangle will have halve of the area of the triangle, so que so we can divide the area of the trangle by 2
\(A_{\text{triangle}}=\frac{960}{2}=480\)So the triangle has an area o
653500 to the nearst thousand
Answer:
654000Step-by-step explanation:
653500
5 and over makes the number to the left 1 number
654000
Step-by-step explanation:
654,000 is the answe
can somone please give me answer me and my bestie dont know it
Answer:
20
Step-by-step explanation:
top = 4*2 = 8
bottom = 5*2=10
middle = (4+4-2)*2 = 12
total 20
Subjects who participate in a study of patients with inflammatory bowel disease are described as the:a. accessible population. b. element. c. sample. d. target population.
The target population is the population of interest that researchers aim to generalize their findings to.
The correct answer is c. sample.
In a research study, the population of interest is often too large or too difficult to access entirely. Therefore, researchers select a representative subset of the population to study, which is called a sample. In this case, patients with inflammatory bowel disease are the population of interest, and those who participate in the study are the sample.
The accessible population refers to the portion of the population that is accessible to the researcher. For example, if a researcher is studying the prevalence of a disease in a certain region, the accessible population would be the individuals living in that region.
An element refers to a single member of the population or sample.
The target population is the population of interest that researchers aim to generalize their findings to.
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what are the three elements of the project triangle?
The Project Triangle is also known as the triple constraints model and consists of three elements: cost, time and scope.
The Project Triangle is also known as the Iron Triangle or Triple Constraints and is a graphical representation of the connection between project costs, schedule, and scope. It is one of the key principles of project management, and it is utilized to help organizations and project managers understand and handle trade-offs between different objectives of a project.
The three elements of the Project Triangle are:
Cost: It is one of the three elements of the project triangle that refers to the money spent on project resources, including equipment, materials, and labor. It is the financial resources required to complete the project on time and within budget.Time: It is the second element of the project triangle that refers to the schedule of the project, including deadlines, milestones, and delivery dates. It is the amount of time that is required to complete the project within the predetermined scope.Scope: It is the third and final element of the project triangle that refers to the requirements and objectives of the project. It is the scope that outlines the goals and objectives of the project and defines the deliverables that are expected at the end of the project.To know more about Project Triangle, visit:
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Apples are prepared in a process with two resources. The first resource has a capacity of 2.1 apples per hour. The capacity of the second resource is 4.4 apples per hour. The first resource has 1 worker and the second resource has 4 workers. Demand for this process is 1.6 apples per hour. Wages are $8 per hour.
What is the cost of direct labor (in $)?per unit
The cost of direct labor per unit is $5.628 per apple.
To calculate the cost of direct labor per unit, we need to determine the total labor hours required to produce one unit of output and then multiply it by the wage rate.
Let's denote the labor hours required for the first resource as "L₁" and the labor hours required for the second resource as "L₂".
The first resource has a capacity of 2.1 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the first resource per unit of output are:
L₁ = 1 apple / (2.1 apples/hour) = 0.4762 hours/apple (rounded to 4 decimal places)
The second resource has a capacity of 4.4 apples per hour, and the demand is 1.6 apples per hour. Therefore, the labor hours required for the second resource per unit of output are:
L₂ = 1 apple / (4.4 apples/hour) = 0.2273 hours/apple (rounded to 4 decimal places)
Now, let's calculate the total labor hours required per unit:
Total labor hours per unit = L₁ (first resource) + L₂ (second resource)
= 0.4762 hours/apple + 0.2273 hours/apple
= 0.7035 hours/apple (rounded to 4 decimal places)
Finally, to calculate the cost of direct labor per unit, we multiply the total labor hours per unit by the wage rate:
Cost of direct labor per unit = Total labor hours per unit * Wage rate
= 0.7035 hours/apple * $8/hour
= $5.628 per apple (rounded to 3 decimal places)
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For f(x) = 4x+1, what is the output for the input 5?
Answer: f(x) = 21 .The output is 21 when the input is 5.
Step-by-step explanation:
f(x) = 4x+1 Substitute the input, 5, for x on the right side f(x) is the equivalent of y, the output you are looking for
f(x) = 4(5) + 1
f(x) = 20 +1
f(x) = 21
The output for the input 5 is f(5) = 21.
What is a function?A function can be regarded as a computer, which is helpful.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.
Given the function,
f(x) = 4x+1
Here x is called the independent variable or input of the function and f(x) is called the dependent variable or output of the function.
So,
At x = 5
f(5) = 4(5) + 1 = 21
Hence "The output for the input 5 is f(5) = 21".
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2^2018+2^2019-2^2020/2^2020-2^2021-2^2022
Answer:NaN
Step-by-step explanation:
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giving the following NaN.
PLEASE
The simple interest formula is I=Prt, where I is the interest, P is the principal, r is the interest rate, and t is the time.
What is the interest rate if the principal is $25,000, the interest is $10,875, and the time is 15 years?
Answer:
$40781250
Step-by-step explanation:
Okay so the formula for simple interest is: I = P x T x R divided by 100
25000 x 10875 x 15 = 4078125000 / 100 = $40781250
If you have the multiple choice answers:
A. $160
B. $200
C. $1600
D. $16,000
the answer is C. $1600
here's why:
The principal is $10,000, the interest rate is 2%, and the time is 8 years.
I = Prt
= $10,000 · 2% ⋅ 8
= 10,000 ⋅ 0.02 ⋅ 8
= 1600
So, the interest earned is $1600.
Solve the given differential equation:
xy''+y'=0
usually if it was the form (x^2)y''+xy'+5y=0, you could then assume (r^2)+(1-1)r+5=0
how do i start/solve this?
The solution to the given differential equation is \(y = a_0x^{[0]} + a_1x^{[1]} + a_2x^{[2]}\), where a_0, a_1, and a_2 are constants.
How to solve the differential equationTo fathom the given differential equation, xy'' + y' = 0, we will begin by expecting a control arrangement of the frame y = ∑(n=0 to ∞) a_nx^n, where a_n speaks to the coefficients to be decided.
Separating y with regard to x, we get:
\(y' = ∑(n=0 to ∞) a_n(nx^[(n-1))] = ∑(n=0 to ∞) na_nx^[(n-1)]\)
Separating y' with regard to x, we get:
\(y'' = ∑(n=0 to ∞) n(n-1)a_nx^[(n-2)]\)
Presently, we substitute these expressions for y and its subsidiaries into the differential condition:
\(x(∑(n=0 to ∞) n(n-1)a_nx^[(n-2))] + (∑(n=0 to ∞) na_nx^[(n-1))] =\)
After improving terms, we have:
\(∑(n=0 to ∞) n(n-1)a_nx^[(n-1)] + ∑(n=0 to ∞) na_nx^[n] =\)
Another, we compare the coefficients of like powers of x to zero, coming about in a boundless arrangement of conditions:
For n = 0: + a_0 = (condition 1)
For n = 1: + a_1 = (condition 2)
For n ≥ 2: n(n-1)a_n + na_n = (condition 3)
Disentangling condition 3, we have:
\(n^[2a]_n - n(a_n) =\)
n(n-1)a_n - na_n =
n(n-1 - 1)a_n =
(n(n-2)a_n) =
From equation 1, a_0 = 0, and from equation 2, a_1 = 0.
For n ≥ 2, we have two conceivable outcomes:
n(n-2) = 0, which gives n = or n = 2.
a_n = (minor arrangement)
So, the solution to the given differential equation is \(y = a_0x^{[0]} + a_1x^{[1]} + a_2x^{[2]}\), where a_0, a_1, and a_2 are constants.
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Nathan decides to research the relationship between the length in inches and theweight of a certain species of catfish. He measures the length and weight of a numberof specimens he catches then throws back into the water. After plotting all his data,he draws a line of best fit. What is the meaning of the x-value on the line wheny = 44?* The expected weight of a catfish that is 44 inches long* Nathan caught a catfish that weighed 44 pounds* Nathan caught a catfish 44 inches long* The expected length of a catfish that weighs 44 pounds
Since the line of best fit represents the best linear model given the data, we can see that if y = 44 (pounds), then we are looking at the expected length of a catfish that weighs 44 pounds.