Find the break - even points for company X, which sells all it produces, if the variable cost per unit is $3, fixed costs are $2 and YT R = 5√q, where q is the number of thousands of units of output produced.
Given:
The variable cost per unit is $3, fixed costs are $2.
The revenue function is:
[tex]Y_{TR}=5\sqrt{q}[/tex]
where q is the number of thousands of units of output produced.
To find:
The break - even points for company X.
Solution:
The variable cost per unit is $3, fixed costs are $2.
So, the cost function is:
Total cost = Fixed cost + Variable cost × Quantity
[tex]Y_{TC}=2+3q[/tex]
The revenue function is:
[tex]Y_{TR}=5\sqrt{q}[/tex]
At break - even points the profit is zero. It means the cost and revenue are equal.
[tex]Y_{TC}=Y_{TR}[/tex]
[tex]2+3q=5\sqrt{q}[/tex]
Squaring both sides, we get
[tex](2+3q)^2=(5\sqrt{q})^2[/tex]
[tex]2^2+2(2)(3q)+(3q)^2=25q[/tex]
[tex]4+12q+9q^2-25q=0[/tex]
[tex]4-13q+9q^2=0[/tex]
Splitting the middle term, we get
[tex]4-4q-9q+9q^2=0[/tex]
[tex]4(1-q)-9q(1+q)=0[/tex]
[tex](4-9q)(1-q)=0[/tex]
Using zero product property, we get
[tex]4-9q=0[/tex] and [tex]1-q=0[/tex]
[tex]q=\dfrac{4}{9}[/tex] and [tex]q=1[/tex]
[tex]q\approx 0.444[/tex] and [tex]q=1[/tex]
Therefore, the break even points are 0.444 and 1.
Select ALL the correct answers.
For AABC, which two relationships are true?
0
0
sin (0) = AE =
cos (0)
cos (8) = A
cos (6)
cos (6)
ACC = sin (90 - 0)
sin (90 - 0)
sin (0)
cos (906)
cos (90 - 0)
=
=
BOCC
sin
(0) = C
sin (0) = A
=
=
=
=
B
(90-8)
Therefore , the solution ot the given problem of trigonometry comes out to be Option (A) and (F) are the correct answers since sin = BC/AC = cos(90 - ∅), and cos = AB/AC = sin(90 - ∅).
Describe the trigonometric function.The right triangle's angle serves as the domain input value for the six basic trigonometric operations, which produce a range of numbers as their results.Understanding the trigonometric functions of the four quadrants' graphs, domains, differentiation, and integration will be achievable.
Here,
Sinx = perp./hypo.
Cosx equals base/hypo.
So,
Sin = B/C
A= cos(90 -∅ ) = BC/AC
So,
Cos(90 -∅ ) = Sin(BC/AC)
And,
cos = AC/AB
AB/AC = sin(90 -∅ )
So,
cos AB/AC = sin (90 -∅ )
Therefore , the solution ot the given problem of trigonometry comes out to be Option (A) and (F) are the correct answers since sin = BC/AC = cos(90 -∅ ), and cos = AB/AC = sin(90 - ∅).
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write down the value of 10^-3
Answer:
value of 10^-3= 0.001
hope it helps.
Answer:
Step-by-step explanation:
10^(-3) is equivalent to
1
--------- which in turn is equivalent to 1/1000, or 0.001.
10^3
EASY MATH!!! GIVING BRAINLIEST!!!
math. f(x)=8x-7;f(x)=9
Answer:
65
Step-by-step explanation:
We are given f(x) = 9
Substitute 9 for x in f(x) = 8x - 7
f(x) = 8 (9) - 7
f(x) = 72 - 7
f(x) = 65
In the triangle below, with right angle R, suppose that m is Angle Q=(5x-13) and m is Angle S=(4x-5) Find the degree measure of each angle in the triangle.
Answer:
Degree measure of each angle is 90⁰, 47⁰ and 43⁰
Step-by-step explanation:
since the triangle is right angled, we assume that Q and S are the other angles of this triangle R
Thus using the concept that angles inside a triangle add up to 180⁰ and we already have one angle as 90⁰( since the triangle is right angled). we therefore know that Q + S = 90⁰
5x - 13 + 4x - 5 = 90⁰
9x = 108
x = 12
We now replace x in Q and S to get the angles
Q = 5(12) -13
= 47⁰
S = 4(12) - 5
= 43⁰
Find the quartiles and interquartile range of the following data. 6, 15, 8, 13, 3, 18, 0, 5, 5, 12
Answer:
Q1 - 5
Q3 - 12.75
Interquartile Range = 7.75
(i think)
Step-by-step explanation:
use an identity to explain how to find the value of sin (0+90°). (this is a writing thing answer)
Answer:
0+90=90 thank me later
Step-by-step explanation:
What is an example of ordered pair function?
An ordered pair function is a type of mathematical function that associates certain pairs of elements (called ordered pairs) with a single output. For example, the function f(x,y) = x+y associates the ordered pair (2,3) with the output 5.
What is function?A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, Python gives you many built-in functions such as print(), etc. but you can also create your own functions. These functions are called user-defined functions.
This is because 2+3 = 5. Another example is the function f(x,y) = x×y,
which associates the ordered pair (3,4) with the output 12, since 3×4 = 12.
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What i the cartoonit' purpoe in thi cartoon?
to convince people that fungal band are dangerou for beetle
to convince people that beetle are damaging to tree
to make people laugh at a play on word
to make people believe that longhorn beetle hate fungi
The cartoonist's purpose of the given cartoon is C: "to make people laugh at a play on the words".
Though the cartoon in the picture is designed based on the concept that fungal bands are an effective way of the biological control of Asian longhorn beetles, the core purpose of the cartoonist in designing this cartoon is to portray the idea in a comical way, indicating how these fungi actually form a music band called 'the fun guy' and they remove the beetles by playing their music, that awful racket as the beetle says.
Thus, the cartoonist's purpose of this cartoon is to make people laugh at a play on the words.
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Geoff purchased an annual golf pass for a municipal golf course in his town. He pays a flat fee for the annual golf pass and then each round he plays he must pay the additional cost for a golf cart. A linear model of this situation contains the values (25 , 1,167) and (41 , 1,407), where x represents the number of times he plays each year, and y equals the total amount he spends on golf in one year. What is the flat fee for the annual golf pass? A. $15 B. $1,032 C. $792 D. $807
To find the flat fee for the annual golf pass, we need to find the y-intercept of the linear model. The y-intercept is the point at which the line crosses the y-axis, which in this case represents the flat fee for the annual golf pass.
The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept.
We can find the slope of the line using the two points given: (25, 1,167) and (41, 1,407). The slope is (1,407 - 1,167) / (41 - 25) = 240 / 16 = 15.
Now that we know the slope, we can use either of the two points given to find the y-intercept. Let's use the point (25, 1,167). Plugging the values into the equation y = mx + b, we get 1,167 = 15 * 25 + b. Solving for b, we find that b = 1,167 - 15 * 25 = -300.
The y-intercept is -300, so the flat fee for the annual golf pass is $300. The correct answer is therefore D, $807.
The rectangular floor of a classroom is 36 feet in length and 27 feet in width.A scale drawing of the floor has a length of 12 inches.What is the area, in square inches, of the floor in the scale drawing?
The area of the scale drawing is 108 square inches.
I know this because I divided 36 by 13 to get 3. Then I took 27/3 and got 9. So I knew that the scale drawing was 9 by 12 and so then I just multiplied 9 by 12 and got 108
Can x = 2i be a "solution" for (x+3)^2 =5
Answer:
the x =2 cant be a solution for (x+3)^2 =5.
hope it helps.
Write the terms in standard form. Then state the degree of the polynomial and the leading coefficient (LC).
On solving the provided question, we can say that - the answer of the following sequence 1.9, 3x , 8x will be 13.78x
what is a sequence?A sequence is a collection of numerals (referred to as "terms"), for example, 2, 5, 8. A specific pattern that some sequences follow may be leveraged to make them infinitely long. To continue the series, add 3 and use the example of 2,5,8. Formulas that show where to look for words inside a sequence can be found there. Informally, a sequence in mathematics is a collection of items that are in some order (or events). It has components, much like a set (also called elements or terms). The length of the sequence refers to the total, potentially unlimited number of ordered items. arranging two or more objects in a logical sequence. Chronological.
sequence 1.9, 3x , 8x
answer is = 13.78x
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2. Lyda is taking a test worth 50 points. Her goal is to score 80%.
Write a proportion to figure out how many points she needs to accomplish her goal.
Answer: Lyda wants to score 80% on a test that is worth 50 points. To figure out how many points she needs to accomplish her goal, we can set up a proportion using her desired percentage as the proportion of points she wants to score over the total number of points on the test.
score / total points = percentage / 100
To figure out the number of points Lyda needs to score, we can use the proportion above and cross-multiply:
score * 100 = percentage * total points
We know that percentage=80 and total points =50, so we can substitute these values:
score * 100 = 80 * 50
score = (80*50) / 100 = 40
So Lyda needs to score 40 points to accomplish her goal of 80%.
The proportion would be score / total points = x/100 = percentage/100 = 40/50 = 8/10
It's worth to mention that scoring 80% on a test means she scored 40 points on a test worth 50, the minimum score to pass is 30 so she got a good grade already.
Step-by-step explanation:
Help please??!!!!!!!!!
Answer:
c
Step-by-step explanation:
the answer is c
hope it helps
Find the area of the shaded region
On solving the provided question we can say that - surface area of the following figure cuboid will be - 148cm²
what is surface area ?An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).
Total Surface Area = 2(lw + bw + lb)
Total Surface Area = [tex]2(24 + 30 + 20)[/tex]
Total Surface Area = [tex]148cm^2[/tex]
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On solving the provided question we can say that - surface area of the following figure cuboid will be - 148cm²
what is surface area ?
An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).
Total Surface Area = 2(lw + bw + lb)
Total Surface Area = - 148cm²
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The circumference of a circle is 56.52 feet. What is the circle's radius?
C=56.52 ft
Use 3.14 for .
Answer:
If we substitute pi as 3.14 we would be doing -
56.52/3.14 = 18
18/2 = 9.
So the circle's radius would be 9.
BUT if you want it with PI. . .
The answer would be 8.995437385
On Monday, Lexi rode 3 miles on a bike. On Tuesday, she rode 3 times more than she did Monday. On Wednesday, she rode an additional 4 miles.
How many miles has Lexi ridden so far this week?
Answer:
she has rode 16 miles this week
Step-by-step explanation:
3 miles on monday 3 times that many on tuesday plus 4 miles one wensaday add them all up
3 times 3 is 9 plus 3 is 12 plus 4 is 16 there fore 16 miles in totale
sorry for my speling erros
She rode a total distance of 16 miles this week.
An expression in mathematics is a combination of terms both constant and variable. For example, we can write the expressions as -
2x + 3y + 5
2z + y
x + 3y
The distance rode by Lexi per day is mentioned below -
Monday - Lexi rode 3 miles on a bike.
Tuesday - Lexi rode 3 times more than she did Monday.
Wednesday - Lexi rode an additional 4 miles.
We can write the expression to find the total distance in miles covered by Lexi as -
d = d{M} + d{T} + d{W}
d = 3 + (3 + 3) + 4
d = 3 + 6 + 4
d = 13 miles
Therefore, she rode a total distance of 16 miles this week.
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10.
Write the linear inequality shown in the graph. The gray area represents the shaded region.
A. y ≥ 3x + 4
B. y ≥ 3x – 4
C. y ≤ 3x – 4
D. y ≤ 3x + 4
Answer:
B. y ≥ 3x – 4
Step-by-step explanation:
Mr. Pratt was building a house. A ladder that is 10 ft. long is leaning against the side of a building. If the angle formed between the ladder and the ground is 65 degrees, how far is the bottom of the ladder from the base of the building? Round to one decimal place.
Answer:
[tex]\huge\boxed{\text{4.2 feet}}[/tex]
Step-by-step explanation:
In order to solve this problem, we can use the basic trigonometric functions.
Let's first start to break down the triangle scenario we're given.
We know that the ladder is 10 ft tall. Given that it is slanted, it's likely the hypotenuse.We know the angle formed between the ladder and the ground is 65°. Since the ladder will form a 90° angle with the ground, the last angle will have to follow the triangle rule.The triangle rule is that all angles within a triangle will add up to 180°. Using this logic, we can find the measure of the third angle from the other two[tex]90+65+x=180[/tex], [tex]155+x=180[/tex], [tex]x=25[/tex]Now we know the three angles of the triangle and one side.
We can find the other two sides (or just the base side, in our case), using trigonometric functions such as sin, cos, and tan. We can substitute in their formulas and find lengths based on angle measures.
We know using SOH CAH TOA the relationships between opposites, adjacents, and hypotenuses with these functions. SOH CAH TOA states that:
Sin = Opposite/HypotenuseCosine = Adjacent/HypotenuseTangent = Opposite/AdjacentUsing the triangle, we want to find a relationship that has the base we need as an opposite/adjacent that can use the hypotenuse (since it's the only side length we know.
Well, we can take the sin of the 25 degree angle - it's opposite is the base leg and the hypotenuse is 10.
We can then represent this using an equation:
[tex]\text{sin}(25) = \frac{\text{opposite}}{\text{hypotenuse}}[/tex] [tex]\text{sin}(25) = \frac{\text{opposite}}{10}[/tex] (Since we know the hypotenuse is 10)[tex]\text{sin}(25) \cdot 10 = \text{opposite}[/tex] We know that sin(25) is roughly 0.4226 because of our. calculator. We can then multiply that by 10 to recieve 4.226. This rounds to 4.2 (to the nearest 10th).Therefore, the length of the base leg is 4.2 feet
Hope this helped!
Answer:
4.2 feet
Step-by-step explanation:
.................
Please answer correctly I’ll mark you brainlist!
Answer:
area=12cm
perimeter=16 cm
Step-by-step explanation:
a=bh/2
a=6(4)/2
a=24/2
a=12 cm
p=5+5+6
p=16 cm
Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answer:
Option D. {7 + i√71 / 20, 7 – i√71 / 20}
Step-by-step explanation:
10m² – 7m + 3 = 0
Using formula method, the solution to equation can be obtained as follow:
10m² – 7m + 3 = 0
Coefficient of m² (a) = 10
Coefficient of –7m (b) = –7
Constant (c) = 3
m = –b ±√(b² – 4ac) / 2a
= – –7 ±√((–7)² – 4 × 10 × 3) / 2 × 10
= 7 ±√(49 – 120) / 20
= 7 ±√(–71) / 20
Recall:
–17 = –1 × 17
Thus,
7 ±√(–71) / 20 = 7 ±√(–1 × 71) / 20
Recall:
√–1 = i
Thus,
7 ±√(–1 × 71) / 20 = 7 ± i√71 / 20
= 7 + i√71 / 20 or 7 – i√71 / 20
Therefore, the solutions to the equation are:
{7 + i√71 / 20, 7 – i√71 / 20}
Jack split 25 jellybeans between his brother and himself so that his brother has one more than twice the number Jack has. How many jellybeans does each have?
Answer:
Jack has 8 jellybeans and his brother has 17 jellybeans
Step-by-step explanation:
Jack+Jack's Brother= total
x+(2x+1)=25
3x+1=25
3x=24
x=8
2*8+1=16+1=17
Jack has 8 jellybeans and his brother has 17 jellybeans.
What is an equation?"It is a statement which consists of equal symbol between two mathematical expressions."
What is system of equations?"It is a finite set of equations for which we find a common solution."
For given example,
Let Jack has 'x' jellybeans and his brother has 'y' jellybeans.
Jack split 25 jellybeans between his brother and himself.
⇒ x + y =25 ...........................(1)
his brother has one more jellybean than twice the number Jack has.
⇒ y = 2x + 1 ...........................(2)
So, we get system of equations,
x + y =25
y = 2x + 1
Now, substitute the value of y [from equation (2)] in the equation (1),
⇒ x + (2x + 1) = 25
⇒ 3x + 1 = 25
⇒ 3x = 24
⇒ x = 8
Substitute this value of 'x' in the equation (2),
⇒ y = 2(8) + 1
⇒ y = 17
Therefore Jack has 8 jellybeans and his brother has 17 jellybeans.
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(MATH PROBLEM) v + w at v = 2, w = 5
pls helpp me
uwu
Answer:
7
Step-by-step explanation:
hope this helps:))))))
Write a STORY PROBLEM for the following equation: 4x+(-3)=-11
Answer:
X = - 2
John had solve the equation 4x+(-3)=-11, he said's his answer is x = 2.
Is he wrong or correct? If wrong plz show the steps on how to get the right answer.
Step-by-step explanation:
4x+(-3)= -11
-11 + 3
= -8
We got x by itself
now solve for x
4x = -8
Solution
X = -2
Please find the perimeter of this irregular shape
Answer:
30
Step-by-step explanation:
i’ll give brainliest please help
Answer:
m=4
Step-by-step explanation:
Answer:
m= 4
Step-by-step explanation:
i hope this helps :)
hey i need help a sap
Answer:
1. f(x)=1-1/2
4. y=10x
5. yes
Step-by-step explanation:
1)
f(x) = 4(2 + 3x) + 3 is a linear function.
2)
The slope of the function is 6.
3)
The linear function is (1/2)x - 4.
4)
y = x² + 2 is not a linear function.
5)
No, it is not a linear function.
6)
Graph D does not represent a linear function.
7)
Graph B does not represent a linear function.
8)
Table D is a linear function.
9)
Table B is not a linear function.
10)
3x + 2y = 6 is a linear function.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
1)
f(x) = 4(2 + 3x) + 3
f(x) = (1/2)x² - 5
f(x)= 5 - x²
f(x) = 1 - 1/x
The graph of each function is given below.
The red line in the graph represents f(x) = 4(2 + 3x) + 3.
This is a straight line which means it is a linear function.
2)
f(x) = 2(3x - 7)
f(x) = 6x - 14
It is in the form of y = mx + c where m is the slope.
So,
m = 6
3)
f(x) = (1/2)x - 4
f(x) = x³ - 2
The graph is given below.
The red line represents f(x) = (1/2)x - 4.
This is a linear function.
4)
y = 3x + 12
y = x² + 2
y = 10x
y = 9
The graph is shown below.
The green curve is y = x² + 2.
This is not a linear function.
5)
y = 2x² - 6
This is not a linear function because we have x².
The graph is given below.
6)
Graph D represents a non-linear function.
7)
Graph B represents a non-linear function.
8)
If the rate of change between two (x, y) from the graph is the same then it is a linear function.
Table D has the same rate of change.
Rate of change = (y(2) - y(1)) / (x(2) - x(1))
= (4 - 7) / (-1 + 2)
= -3/1
= -3
Table D is a linear function.
9)
If the rate of change between two (x, y) from the graph is the same then it is a linear function.
Table B does not have the same rate of change.
Rate of change = (y(2) - y(1)) / (x(2) - x(1))
Table B is not a linear function.
10)
The green line on the graph represents a straight line.
The green line is a linear function.
The green line is 3x + 2y = 6.
Thus,
The answers are given above.
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3. Select a ratio that is equivalent to 6:4
a. 16:12
b. 8:12
c. 18:12
d. 24:12
Answer:
C
Step-by-step explanation:
6:4=8:12
6x3=8
4x3=12