This prompt involves calculating total revenue, marginal revenue, total cost, and marginal cost for a competitive firm and finding the profit maximizing quantity of dog coats sold. The analysis is done by constructing a table and graphing relevant curves to identify where marginal revenue equals marginal cost.
Explanation:The question regards the calculation of total revenue, marginal revenue, total cost, and marginal cost for a perfectly competitive firm, Doggies Paradise Inc., and the identification of the profit maximizing quantity of dog coats sold. To find these values, a table must be constructed with output levels from one to five units. The price per unit is $72, and fixed costs are $100, with variable costs increasing with each additional unit produced. The total revenue (TR) is the price multiplied by the quantity sold, while the marginal revenue (MR) is the additional revenue from selling one more unit. Total cost (TC) is the sum of fixed costs and variable costs at each output level, and marginal cost (MC) is the change in total costs when production is increased by one unit. The profit maximizing quantity is determined where MR equals MC or where the additional cost of producing one more unit no longer yields an additional profit.
Total Revenue and Total Cost Curves
Sketching these curves will show the relationship between the cost of producing dog coats and the revenue generated from sales at different production levels. The TR curve shows a steady increase as more units are sold, while the TC curve reflects the fixed costs and the upward slope as variable costs increase with higher output.
Marginal Revenue and Marginal Cost Curves
Graphing MR against MC allows for visual determination of the profit maximizing output, which is the point where the two curves intersect. This indicates that producing any more units beyond this point will not increase profit.
Find the mode of this set of data 18,27,28,44,44,50,67
Answer:
44
Step-by-step explanation:
the mode of a set of data is the value that occurs most often, in this case it is 44
44 would be the mode of the data.
The mode of the data is the number that occurs the most. It is always best to put the numbers in order from least to greatest so we can see what number appears more than once.
18,27,28,44,44,50,67
When we look at this set of numbers, we can see that 44 appears more than any other number. Therefore, the mode of these numbers is 44.
Tania analyzed the relationship between student test scores and the number of hours studied. She calculated the trend line to be y = 6.8x + 60, where x is the number of hours studied and y is the score. Which closet is to the score for a student who studied 3 hours?
A 80
B 85
C 90
D 95
Answer:
A: 80
Step-by-step explanation:
As we know that the trend line is [tex]y=6.8x+60[/tex], we can plug in x=3 in order to find out the estimated score for 3 hours of studying
[tex]y=6.8x+60\\\\y=6.8(3)+60\\\\y=20.4+60\\\\y=80.4[/tex]
y=80.4 is closest to A: 80
Answer:
Option A, 80
Step-by-step explanation:
Trend line is given by y = 6.8x + 60
where x = number of hours she studied
y = score
Now we have to calculate the score for a student for studied for 3 hours.
y = 6.8 × 3 + 60
= 20.4 + 60
= 80.40
≈ 80
Option A will be the answer.
The sum of two integers is -8.if one integer is 12 then the other is?
Answer:
2 and -10
Step-by-step explanation:
let the two integers be x and y.
so, x+y=-8---‐-------(1)
and,
x=y+12-------‐-----(2)
from (1) and (2),
(y+12)+y=-8
or, 2y=-8-12
or, y=-20/2
or, y=-10
substitutting the value of y in (2),
x=-10+12=2
therefore the required integers are 2 and -10.
Answer:
-20
Step-by-step explanation:
→ The sum of two integers is -8.
⇒ One will be called "x" and the other will be called "y"
→ One integer is 12 ( "y" )
Let's set up an equation x = ? and y = 12 so,
→ x + y = -8
( Substitute y for 12 )
→ x + 12 = -8
( -12 from both sides to isolate x )
→ x = -20
The perimeter of a rectangular herb garden is 74 feet. If the length is 5 feet longer then 3 times it’s width what is the gardens width?
Answer:
width = 8 feet and length = 29 feet
Step-by-step explanation:
perimeter of a rectangle P = 2(L + W)
width W = x
length L = 3x + 5
P = 74 feet
74 = 2(3x + 5 + x)
37 = 3x + 5 + x
37 = 4x + 5
4x = 37 -5
4x = 32
x = 8
W = 8 feet
15 POINTS
Using Euler's Formula: F+V=E+2
A geometric solid has thirty-two faces and ninety edges. Find the number of vertices.
SHOW WORK
Answer:
V -E +F = 2
Vertices = 2 + Edges -Faces
Vertices = 2 + 90 -32
Vertices = 60
Step-by-step explanation:
Multiply and simplify.
(x + 3)(x - 8)
A) 2x - 24
B) x2 - 5x + 24
C) x2 - 5x - 24
D) x2 - 8x - 24
Answer:
x^2-5x-24
Step-by-step explanation:
Final answer:
The product of the binomials (x + 3)(x - 8) is simplified using the FOIL method to get x² - 5x - 24. We multiply each term in the first parenthesis by each term in the second and combine like terms.
Explanation:
To multiply and simplify the expression (x + 3)(x - 8), we will use the FOIL method (First, Outer, Inner, Last). This method involves multiplying each term in the first parenthesis by each term in the second parenthesis.
First: x times x = x²
Outer: x times -8 = -8x
Inner: 3 times x = +3x
Last: 3 times -8 = -24
Next, combine like terms (-8x and +3x):
x² - 8x + 3x - 24 = x² - 5x - 24
The simplified form of the given expression is x² - 5x - 24, which corresponds to option C).
If f(x)=2x and g(x)= 1/x, what is the domain of (f*g) (x)
Answer:
The domain of (f*g) (x) is the set of all real numbers; ( -∞, ∞)
Step-by-step explanation:
(f*g) (x) simply means we obtain the product of f(x) and g(x). We are given that;
f(x)=2x
g(x)= 1/x
(f*g) (x) = f(x) * g(x)
(f*g) (x) = 2x * 1/x = 2
This is a horizontal line defined everywhere on the real line. The domain of (f*g) (x) is thus ( -∞, ∞)
Answer:
All real numbers
Step-by-step explanation:
Given : [tex]f(x)=2x[/tex]
[tex]g(x)= \frac{1}{x}[/tex]
To Find : the domain of (f*g) (x)
[tex]f(x)=2x[/tex]
[tex]g(x)= \frac{1}{x}[/tex]
[tex](f\cdot g)(x)=2x \times \frac{1}{x}[/tex]
[tex](f\cdot g)(x)=2[/tex]
Since the value of [tex](f\cdot g)(x)=2[/tex]
So, the domain of the function is [tex](f\cdot g)(x)[/tex] is all real numbers .
In triangle JKL, m of angle J = 90, m of angle K = 30, and m of angle L = 60. Which of the following statements about triangle JKL are true? Check all that apply.
A) KL= root 3 (JL)
B) KL= 2(JL)
C) JK= root 3 (JL)
D) JK= 2(JL)
E) JL= root 3/2 (KL)
F) JK= root 3/2 (KL)
Answer:
# Answer B is true ⇒ KL = 2(JL)
# Answer C is true ⇒ JK = √3(JL)
# Answer F is true ⇒ JK = √3/2(KL)
Step-by-step explanation:
* Lets explain the ratio between the sides of the triangle
- In Δ JKL
∵ The measure of angle J is 90°
∴ KL is the hypotenuse
∵ The measure of angle K is 30°
∴ JL is the opposite side to angle 30°
∵ The measure of angle L is 60°
∴ JK is the opposite side to the angle 60°
- There is a fact in the triangle which has angles 30° , 60° , 90°
# The length of the side opposite to the angle of measure 30° is
half the length of the hypotenuse
∵ KL is the hypotenuse
∵ JL is the opposite side to the angle of measure 30°
∴ JL = 1/2 KL OR KL = 2 JL
# The length of the side opposite to the angle of measure 60° is
√3 the length of the opposite side to the angle 30°
∵ JK is the opposite side to the angle of measure 60°
∵ JL is the opposite side to the angle of measure 30°
∴ JK = √3 JL
# The length of the side opposite to the angle of measure 60° is also
half √3 the length of the hypotenuse
∵ JK is the opposite side to the angle of measure 60°
∵ KL is the hypotenuse
∴ JK = √3/2 KL
- From the relation above
# Answer B is true ⇒ KL = 2(JL)
# Answer C is true ⇒ JK = √3(JL)
# Answer F is true ⇒ JK = √3/2(KL)
Answer:
It is a and B in C & D
Step-by-step explanation:
These are the closest answers
a Potter uses 3/5 of a pound of clay to make a bowl how many bowls could the Potter make from 10 lb of clay
Answer:
16
Step-by-step explanation:
Let's say x is the number of bowls. If each bowl needs 3/5 pound of clay, then the total clay needed is 3/5 * x. We know the total amount is 10 pounds. Therefore:
10 = 3/5 x
Divide:
x = 10 / (3/5)
To divide by a fraction, we need to multiply by the reciprocal:
x = 10 * (5/3)
x = 50/3
x = 16 ⅔
We can't have part of a bowl, so we must round down. The potter can make 16 bowls.
what is the other binomial?
Answer:
11x² -3x
Step-by-step explanation:
We have the product of a sum, of two binomials and one of the initial binomials but we'd like to know the other one.
It's very much like A + B = C, and we have both B and C, but looking to find A.
What would you do in the ABC scenario?
You'd isolate A by transforming the equation to: A = C - B
In this case, C = 12x² - 5x and B = x² - 2x...
A = (12x² - 5x) - (x² - 2x) = 12x² - 5x - x² + 2x
A = 11x² -3x
Find negative square root of 36. ±6 −6 6 18
Answer:
The answer is -6
Step-by-step explanation:
Hope it helped you!
Answer:
B. [tex]-6[/tex]
Step-by-step explanation:
We are asked to find the negative square root of 36.
We can write our given problem as [tex]-\sqrt{36}[/tex].
We can write 36 as 6 to second power.
[tex]-\sqrt{36}=-\sqrt{6^2}[/tex]
Using radical rule [tex]\sqrt[n]{a^n}=a[/tex], we will get:
[tex]-\sqrt{6^2}=-6[/tex]
Therefore, the negative square root of 36 is negative six and option B is the correct choice.
Perform the indecated operation. 5 over 9 times 3 over 7
Answer:
[tex]\frac{5}{21}[/tex]
Step-by-step explanation:
[tex]\frac{5}{9}[/tex] × [tex]\frac{3}{7}[/tex] = [tex]\frac{15}{63}[/tex] = [tex]\frac{5}{21}[/tex]
Answer:
5/63
Step-by-step explanation:
that would be:
5 3 5
----- * ------ = (after reduction) ----------- = 5/63
9 7 3(21)
Find the value of each variable. For the circle, the dot represents the center.
Answer:
Part 1) The measure of angle d is 65°
Part 2) The measure of angle c is 89°
Part 3) The measure of arc a is 131°
Part 4) The measure of arc b is 47°
Step-by-step explanation:
we know that
In an inscribed quadrilateral, opposite angles are supplementary
step 1
Find the measure of angle d
∠d+115°=180°
∠d=180°-115°=65°
step 2
Find the measure of angle c
∠c+91°=180°
∠c=180°-91°=89°
step 3
Find the measure of arc a
we know that
The inscribed angle measures half that of the arc comprising
115°=(1/2)[99°+arc a]
230°=[99°+arc a]
arc a=230°-99°=131°
step 4
Find the measure of arc b
we know that
The inscribed angle measures half that of the arc comprising
∠c=(1/2)[arc a+arc b]
substitute the values
89°=(1/2)[131°+arc b]
178°=[131°+arc b]
arc b=178°-131°=47°
A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
An arc is one of the portions of a circle. It is basically a part of the circumference of a circle.
The measure of the ∠d is 65 degrees.
The measure of the ∠c is 89 degrees.
The measure of the arc a is 131 degrees.
The measure of arc b is 47 degrees.
We have to determineThe value of each variable. For the circle, the dot represents the center.
What is the angle?A figure which is formed by two rays or lines that shares a common endpoint is called an angle.
What is an arc?
An arc is one of the portions of a circle. It is basically a part of the circumference of a circle.
1. The measure of ∠d is;
∠d+ 115°= 180°
∠d= 180°-115°= 65°
The measure of the ∠d is 65 degrees.
2. The measure of ∠c is,
∠c+ 91°= 180°
∠c =180°-91° =89°
The measure of the ∠c is 89 degrees.
3. The measure of arc a is,
The inscribed angle measures half that of the arc comprising;
[tex]\rm 115=\dfrac{1}{2}[99+arc \ a]\\\\230=[99+arc a]\\\\arc \ a = 230-99\\\\arc \ a= 131[/tex]
The measure of the arc a is 131 degrees.
4. The measure of arc b is,
The inscribed angle measures half that of the arc comprising;
[tex]\rm 89=\dfrac{1}{2}[131+arc \ b]\\\\178=[131+arc \ b]\\\\arc \ b = 178-131\\\\arc \ b = 47[/tex]
The measure of arc b is 47 degrees.
To know more about Angle and Arc click the link given below.
https://brainly.com/question/9177423
paige and her family went to the movies. They bought 4 tickets and paid $12 for popcorn. They spent $40. How much did each ticket cost?
____________________________________________________
Answer:
7 dollars
____________________________________________________
Step-by-step explanation:
To make solving this equation easier, lets turn the the information we got in the question into an actual equation.
Key information:
4 tickets
$12 popcorn
Spent a TOTAL of $40.
With the information above, we can use it to make an equation.
We would use the equation: y = mx + b
Since our "y" value would represent our total value, our total value is 40, so we would plug 40 into y.
Your equation should look like this:
40 = mx + b
Our "b" value represents our start value, and our start value would be 12 because we started with one $12 popcorn.
Your equation should look like this:
40 = mx + 12
Our "m" value would represent how many tickets we bought, so we would plug in 4 in m.
Our equation would be:
40 = 4x + 12
Now we can solve the equation:
We would move the 12 over to the left side of the equal sign by subtracting, then we would divide by 4.
[tex]40=4x+12\\\\28=4x\\\\7=x[/tex]
We should get ther answer of 7, that means that each ticket cost $7 dollars.
7 dollars should be your FINAL answer.
____________________________________________________
Answer:
One ticket = $7
Step-by-step explanation:
Forming the equation,
→ 4x + 12 = 40
Now the value of x will be,
→ 4x + 12 = 40
→ 4x = 40 - 12
→ x = 28/4
→ [ x = 7 ]
Hence, the value of x is 7.
Find the simple interest paid one $600 is borrowed for three years at 6% per
Answer:
Principal amount= $600
Time= 3 years
Rate of Interest = 6%
SI= PRT/100
= 600x6x3/100
= $108
Interest is $108
Step-by-step explanation:
Each of 6 students reported the number of movies they saw in the past year. This is what they reported. 15,9,13,18,9,6, find the mean and median numbers of the movies that students saw.
Answer:
mean = 11.66666
median = 11
Step-by-step explanation:
To find the mean, add up all the numbers, then divide by how many numbers
mean = (15+9+13+18+9+6) / 6 = 70/6 = 11 .6666666
To find the median, put the numbers from smallest to largest. then take the middle number. Since there is an even number, take the two middle numbers and average them
6,9,9,13,15,18
The two middle numbers are 9 and 13
(9+13)/2 = 22/2 = 11
What is the circumference of a circle with a diameter of 21 m? (use for pi)
Answer:
21π m, or ≈ 65.94 m
Step-by-step explanation:
Remember that π is the ratio between a circle's circumference and its diameter, or, in equation form:
[tex]\pi=\frac{c}{d}[/tex]
where c is the circumference and d is the diameter. If we want to find the circumference, we can just multiply that equation by d on both sides to get
[tex]c=\pi d[/tex]
Here, our d = 21 m, so our circumference would be
[tex]c=21\pi[/tex] m, or approximately 21(3.14) = 65.94 m
Solve for X in this equation
Answer: x=e
Step-by-step explanation:
x= ln(e^e)
using ln(e^x)= x x ln (e), transform the expression
x= e x ln (e)
the natural logatithm of e equals 1
x=e x 1
any expression multiplied by 1 remains the same
x=e alternative form: x= 2.71828
ANSWER
[tex]x = e[/tex]
EXPLANATION
The given logarithmic equation
[tex]x = ln_{e}(e) [/tex]
Note that
[tex] ln(e) = 1[/tex]
Using the power rule of logarithms,
[tex]x =e \ln(e)[/tex]
This gives us:
[tex]x =e (1)[/tex]
Simplify to get:
[tex]x = e[/tex]
Barry is 8 years older than his sister. In 3 years, he will be twice as old as she will be then. How old is each now?
Final answer:
Barry is currently 13 years old and his sister is 5 years old. This is determined by setting up a system of equations based on the given information and solving for their current ages.
Explanation:
The question involves solving a system of equations to find the current ages of Barry and his sister. Let's let B represent Barry's current age and S represent his sister's current age. According to the problem, Barry is 8 years older than his sister (B = S + 8). In 3 years, Barry will be twice as old as his sister will be then (B + 3 = 2(S + 3)).
Write down the two equations: B = S + 8 and B + 3 = 2(S + 3).
Substitute B from the first equation into the second equation: (S + 8) + 3 = 2(S + 3).
Simplify and solve for S: S + 11 = 2S + 6.
Rearrange the equation to find S: S = 5.
Substitute the value of S back into the first equation to find B: B = 5 + 8, so B = 13.
Therefore, Barry is currently 13 years old and his sister is 5 years old.
If f(x) = 5x - 2 and g(x) = 2x + 1, find (f + g)(x)
Answer:
(f + g)(x) = 7x - 1
Step-by-step explanation:
Given : f(x) = 5x – 2 and g(x) = 2x + 1
We have to find (f + g)(x)
Consider (f + g)(x) = f(x) + g(x)
Also, given f(x) = 5x – 2 and g(x) = 2x + 1
Substitute, we have,
f(x) + g(x) = 5x - 2 + 2x + 1
Like Terms are terms having same variable with same degree.
Simplify by adding like terms, we have,
f(x) + g(x) = 5x + 2x - 2 + 1
f(x) + g(x) = 7x - 1
Thus, (f + g)(x) = 7x - 1
Answer:
Thus, (f + g)(x) = 7x - 1
Step-by-step explanation:
(f + g)(x) = 7x - 1
Step-by-step explanation:
Given : f(x) = 5x – 2 and g(x) = 2x + 1
We have to find (f + g)(x)
Consider (f + g)(x) = f(x) + g(x)
Also, given f(x) = 5x – 2 and g(x) = 2x + 1
Substitute, we have,
f(x) + g(x) = 5x - 2 + 2x + 1
LIKE TERMS are terms having same variable with same degree.
Simplify by adding like terms, we have,
f(x) + g(x) = 5x + 2x - 2 + 1
f(x) + g(x) = 7x - 1
Thus, (f + g)(x) = 7x - 1
See attached question below
ANSWER
A. 10,000
EXPLANATION
The given rational function is
[tex]f(x) = \frac{1}{x - 2} [/tex]
This function is not defined at x=2.
But as we are picking x-values that are closer and closer to 2, the functional values grows bigger and bigger positively or negatively without bounds.
Therefore a possible value of f(x) as x is close to 2 is 10,000.
The correct answer is A.
Need whole answer please
Answer: Audrey is less than 17 years old (possible answers 16,15,14,13...)
Answer in inequality: x<17
Step-by-step explanation:
3x + 9 < 60
3x + 9 - 9 < 60 - 9
3x < 51
x<17
Answer: x<17
EXPLAIN
ekfnkw
Determine whether the piece of paper can be used to wrap the rectangular prism exactly once without any gaps or overlaps.
Answer:
No, because they do not have the same area.
Step-by-step explanation:
For the piece of paper to cover once without overlap or gaps, it must have the same area as the the total surface area of the prism.
The total surface area of the rectangular prism is: [tex]2(3.5\times2+3.5\times1.5+2\times1.5)=30\frac{1}{2}in^2[/tex]
The area of the rectangular sheet is:[tex]5\times 8=40in^2[/tex]
Since the area of the piece of paper is more than the surface area of the rectangular prism there will be an overlap.
ASAP RIGHT NOW NEW FOR ME
Answer:8m+20
Step-by-step explanation:
U have too add the perimeter than multiple area
how to factor 6x^2+7x-10
Answer:
(6x-5)(x+2)
Step-by-step explanation:
6x²+7x-10
= (6x-5)(x+2)
the perimeter of a rectangle is 68 cm. the length is 4 cm less than three times ots width. write a system of equation to find the dimensions of the rectangle.
2L + 2w = 68 & L = 3w-4
2(3w-4) = 68
6w-8= 68
6w = 60
W= 10
L = 3*10-4
L= 30-4= 26
9 pounds of ground beef cost $40.32. What is the price per ounce?
The price per ounce of ground beef, when 9 pounds cost $40.32, is $0.28.
Calculating Price per Ounce of Ground Beef
To calculate the price per ounce for ground beef when given the price for 9 pounds, we will first need to know how many ounces are in 9 pounds. Since there are 16 ounces in 1 pound, 9 pounds is equivalent to 144 ounces (9 pounds × 16 ounces/pound).
Next, we divide the total cost of the 9 pounds of ground beef by the total number of ounces to find the price per ounce. The total cost given is $40.32.
Price per ounce = Total cost \/ Total number of ounces
Price per ounce = $40.32 \/ 144 ounces
Price per ounce = $0.28
Therefore, the price per ounce of ground beef is $0.28.
Which of the following digits could replace the □ in the tens place to make this statement true? 88,5□1 rounds to 88,500 if we round to the nearest hundred.
chose all answers that apply:
:0
:2
:4
To make 88,5□1 round down to 88,500, the digit that replaces □ must be less than 5; therefore, the replacements could be :0, :2, or :4.
potential
Explanation:The given number is '88,5□1' and we want to find the digit that replaces the □ and rounds the number to '88,500' when we round to the nearest hundred. An important point to remember about rounding is that if the digit in the tens place is less than 5, we round down, while if it's 5 or above, we round up. Since we want to round down to 88,500, the digit that replaces □ in the tens place must therefore be less than 5. So, the possible digits could be :0, :2, or :4.
Learn more about Rounding Numbers here:https://brainly.com/question/28562556
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If 5 x 6 = 20 + y, what is the value of y?
5*6=20+y
30=20+y
30-20=20-20+y
10=y
Check answer by using substitution method
5*6=20+y
30=20+10
30=30
Answer is y=10
5 x 6 = 30
y + 20 = 30
y + 20 - 20 = 30 - 20
y = 10
A flat screen television has a 50 inch diagonal and a height of 25 inches. How wide is the television rounded to the nearest tenth?
(Use the Pythagorean Theorem)
Answer
inches
Answer:
The wide of television is [tex]43.3\ in[/tex]
Step-by-step explanation:
Let
x----> the wide of television
we know that
Applying the Pythagoras Theorem
[tex]50^{2}=x^{2}+25^{2}[/tex]
Solve for x
[tex]x^{2}=50^{2}-25^{2}[/tex]
[tex]x^{2}=1,875[/tex]
[tex]x=43.3\ in[/tex]