To reach the revenue needed to cover expenses and begin turning a profit, or 120x = 120(92) = $11,040, the business must sell at least 92 guitars.
To start making a profit, the music company needs to generate enough revenue to cover its costs. The revenue function is given by r(x) = 120x, where x is the number of guitars manufactured and sold.
The cost function is given by c(x) = 100x + 1840, where 1840 represents the fixed cost (such as rent, salaries, etc.) associated with setting up the manufacturing process.
To determine the total revenue required to start making a profit, we need to find the break-even point where the revenue generated is equal to the total cost incurred:
r(x) = c(x)
Substituting the given functions, we get:
120x = 100x + 1840
Solving for x, we get:
20x = 1840
x = 92
Therefore, the company needs to sell at least 92 guitars to generate a revenue of 120x = 120(92) = $11,040, which is the amount required to cover its costs and start making a profit. If the company sells fewer than 92 guitars, it will not be able to cover its costs and will incur a loss.
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100 points please help!!
We locate the [tex](5x+4)(x+7)[/tex] in order to solve this trinomial problem.
How do you formulate a trinomial's equation?The quadratic trinomial formula inside one variable has the general form ax2 + bx + c, where a, b, and c are constant terms and none of them are zero. If b2 - 4ac > 0, we're able to factor a quadratic trinomial for any value of a, b, and c. It denotes that, where h and k are real values,
How can you tell if a given equation has a trinomial?A single-term expression is referred to as a monomial, a two-term expression as a factorial, and a three-term expression as a trinomial. a phrase that contains more than three terms is identified only by the quantity of its terms.
Given, [tex]5 x^{2} + 4 x + 35 x + 28[/tex]
Regroup terms into two proportional parts [tex](5 x^{2} + 4 x) + (35 x + 28)[/tex]
Factor Greatest Common Factors out [tex]x (5 x + 4) + 7 (5 x + 4)[/tex]
Factor Greatest Common Factors out [tex](5 x + 4) (x + 7)[/tex]
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This trapezoid has been divided into two right triangles and a rectangle. how can the area of the trapezoid be determined using the area of each shape? enter your answers in the boxes. the area of the triangle on left is in², the area of the triangle on the right is in², and the area of the rectangle is in². the area of the trapezoid is the sum of these areas, which is in².
A trapezoid has been divided into two right triangles and a rectangle, see the above figure. Area of the triangle on left is 9 in². The area of the triangle on the right is 9 in², and the area of the rectangle is 108 in². The area of the trapezoid is the sum of these areas, which is 126 in².
We have a trapezoid, ABCD see in above figure has been divided into two right triangles, i.e., ∆BEC, ∆DAF and a rectangle, ABEF. We have to determine the area of trapezoid. Now, as we know area of a figure divides into pieces is equals to the sum of areas of each piece of figure. So, the area of trapezoid, ABCD is sum of area of two right triangles, i.e., ∆BEC, ∆DAF and a rectangle, ABEF. From above figure, In case of right triangles,
The base length of the triangle BEC= 2 in
height of triangle BEC = 9 in
Area of triangle BEC = (1/2)× base× height
=> Area of ∆BEC = (1/2)× 9× 2
= 9 in² Similarly, Area of triangle DAF = 9 in²
Therefore, the required area is 2×( Area of the triangle), A₁ = 2× 9 sq. in
= 18 in²
Now, length of rectangle ABEF, l = 12 in
width of rectangle, w = 9 in
Area of rectangle ABEF, A₂ = l×w
= 12× 9 = 108 in²
Thus, the required area = A₁ + A₂
= 18 in² + 108 in² = 126 in²
Hence required area is 126 in².
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Complete question:
This trapezoid has been divided into two right triangles and a rectangle, see the above figure. how can the area of the trapezoid be determined using the area of each shape? enter your answers in the boxes. the area of the triangle on left is ___ in², the area of the triangle on the right is___ in², and the area of the rectangle is__ in². the area of the trapezoid is the sum of these areas, which is___ in².
Anna’s new baby sister weighs 2076 grams. How many kilograms does the baby weigh
-8(6y-2x-5) Use the distributive property to remove the parentheses.
Answer: -48y+6x+40
Step-by-step explanation: when you multiply two minuses that is +.
•
Read the following and answer the adjoining questions.
John's family is planning a road trip to Florida.
John is using the following information to help plan the trip:
- total distance (one way): 1,023 miles
- average driving speed: 60 miles per hour
- driving time on first day: 10 hours.
The question is, write an equation John can use to represent the relationship between distance traveled, in miles, d, and driving time, in hours, t
The relationship between distance traveled, in miles, d, and driving time, in hours, t. The Equation is 60 miles × 10 hours = 1023 miles
Distance:
Distance is a numerical or sometimes qualitative measurement of the distance between objects or points. In physics or common usage, distance can refer to a physical length or an estimate based on other criteria. Since spatial cognition is a rich source of conceptual metaphors in human thought, the term is also often used metaphorically to refer to a measure of the amount of difference between two similar objects or some degree of separation.
Most of these concepts of distance, whether physical or metaphorical, are formalized in mathematics using the concept of metric spaces.
According to the Question:
total distance (one way): 1,023 miles
average driving speed: 60 miles per hour
driving time on first day: 10 hours.
Now,
Average driving speed = 60 miles per hour
Driving time on first day = 10 hours.
Total distance on first day = 60 miles × 10 hours
= 600 miles/ Hour.
and,
The relationship obtained from the Given equation is:
60 miles + 10 hours = 1023 miles
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Quick Check 13.13-3.11 Find the difference. list (3y^(2)+11y-5)/(y^(2)-2y-24)-(2y^(2)+4y-17)/(y^(2)-2y-24)
Answer: pic please so i know some more info thanks
Step-by-step explanation: pic please so i know some more info thanks
Find the zeros of \( f(x) \), and state the multiplicity of each zero. (Order your answers from smallest to largest \( x \) first by real \[ f(x)=x^{4}+12 x^{2}-64 \] \[ x= \] with multiplicity \[ \be
To determine the zeros of f(x) and state the multiplicity of each zero, the following steps should be followed:
Step 1: Determine the roots of the polynomial
To solve for the roots of f(x), use the quadratic formula. f(x) = x⁴ + 12x² - 64
a = 1, b = 12, c = -64
Using the quadratic formula, we have:
x = (-b ± √(b² - 4ac)) / 2a
x = (-12 ± √(12² - 4(1)(-64))) / 2(1)
x = (-12 ± √400) / 2
x = (-12 ± 20) / 2
x₁ = -16
x₂ = 4
x₃ = x₄ = 0
Step 2: State the multiplicity of each zero
After determining the roots of f(x), determine the multiplicity of each root by using the concept of multiplicity. A root has a multiplicity of p if and only if f(x) has a factor of (x - r)ᵖ.
From the quadratic equation above, we have:
x₁ = -16 (multiplicity 1)
x₂ = 4 (multiplicity 1)
x₃ = x₄ = 0 (multiplicity 2)
Therefore, the zeros of f(x) and their multiplicities are: x = -16 (multiplicity 1), x = 4 (multiplicity 1), and x = 0 (multiplicity 2).
The final answer is as follows:
x = -16 with multiplicity 1
x = 0 with multiplicity 2
x = 4 with multiplicity 1.
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Twenty-six less than the product of 5 and a number is 69. What is the number?
Answer:
19
Step-by-step explanation:
Product of 5 and a number is 5a
5a - 26 = 69
Add 26 to both sides
5a = 69+26
5a = 95
Divide both sides by 5
A = 19
Check
(5× 19) - 26 = 65
help whats the missing side lengths!
Answer:
x = y = 2[tex]\sqrt{3}[/tex]
Step-by-step explanation:
the triangle is a 90- 45- 45 isosceles triangle with congruent legs, that is
x = y
using Pythagoras' identity in the right triangle
x² + y² = (2[tex]\sqrt{6}[/tex] )² , that is
x² + x² = 24
2x² = 24 ( divide both sides by 2 )
x² = 12 ( take square root of both sides )
x = [tex]\sqrt{12}[/tex] = [tex]\sqrt{4(3)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex] = 2[tex]\sqrt{3}[/tex]
then
x = y = 2[tex]\sqrt{3}[/tex]
Question one, please help
An equation that represents the relationship is y = 0.01x.
What is a proportional relationship?In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios. Also, it passes through the origin (0, 0) and it can be modeled by the following mathematical expression:
y = kx
Where:
x and y represents the variables or data points.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 1/90
Constant of proportionality, k = 0.01.
Therefore, the required equation is given by:
y = kx
y = 0.01x
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Please only comment if your going to help me thanks!
The volume of the rectangular prism is 36 cubic centimeters.
How to find the volume of a rectangular prism?For a rectangular prism of height H, length L and width W, the volume is given by the product between these 3 quantities, here we will get:
V = H*L*W
On the image we can see a rectangular prism with the dimensions:
Height = 6cm
Length = 3cm
Width = 2cm
Then we can replace these values in the volume formula so we will get:
V= 6cm*3cm*2cm
V = 36 cm³
The volume of the prism is 36 cm³
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Complete question.
"The volume of a prism is the product between the dimensions, find the volume of the rectangular prism below".
The weight of the eggs produced by a certain breed of hen are normally distributed with a mean of 65 grams and standard deviation of 5 grams. What is the probability that a sample of 12 eggs will have a mean weight of more than 68 grams?
There is a 0.0838 or 8.38% chance that a sampling of 12 eggs has a weighted mean greater than 68 grammes.
The Central Limit Theorem, which asserts that group means of a large sample size from every population, irrespective of its distribution, will be roughly distributed normally with an average equal to the inhabitants imply and a variance equal to the standard deviation of the population multiplied by the square root of the random sample, must be used to solve this problem.
As a result, there is a 0.0838 or 8.38% chance that a sampling of 12 eggs has a weighted mean greater than 68 grammes. When n is the sample size, x is the sample mean, is the population mean, and seems to be the population standard deviation.
In this instance, n = 12 eggs, x = 68 grammes, = 65 grammes, = 5 grammes. When these values are added to the formula, you obtain:[tex]z = (68 - 65) / (5 / √12) = 1.385[/tex]
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For the complex number z = 12 + i, what is Modifying above z with bar?
The conjugate of the complex number z = 12 + i is [tex]\hat{z}=12-i[/tex]
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
Complex number are in the form a + bi, where a is the real part and b is the imaginary part. Both a and b are real numbers
The conjugate of a complex number z = a + bi is [tex]\hat{z}=a-ib[/tex]
Given that z = 12 + i
The conjugate of z is [tex]\hat{z}=12-i[/tex]
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what tips can you share with the group? check all that apply. select the survey population carefully limit the number of questions explain why the survey is necessary select the survey population randomly ask as many questions as possible
It is important to carefully select the survey population and explain why the survey is necessary. It is also important to limit the number of questions and ask them in a clear and concise manner.
Select the survey population carefully: This means selecting a group of people who are representative of the target population and have the relevant knowledge or experience to answer the survey questions. For example, if the survey is about customer satisfaction with a product, the survey population should be customers who have used the product.
Limit the number of questions: It's important to keep the survey short and focused to reduce the risk of respondent fatigue and increase the response rate. A shorter survey also makes it easier to analyze the data.
Explain why the survey is necessary: This helps to increase the response rate by providing a clear explanation of why the survey is being conducted, what the data will be used for, and how it will benefit the target population.
Select the survey population randomly: Random selection helps to ensure that the survey results are representative of the target population and minimize the risk of bias in the sample.
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what tips can you share with the group? check all that apply.
Select the survey population carefullyLimit the number of questionsExplain why the survey is necessarySelect the survey population randomlyy = 4x - 3
y =-2x + 9
Radio, diameters, and chords of O are shown. State the measure of angle 1.
Therefore , the solution of the given problem of circle comes out to be 110°
is the angle 1.
Circle – what is it?Each area of a plane with a specific distance from this additional spot forms a circle (center). Thus, it comprises of curved spots that are separated from one another and separated by the surface. Additionally, it rotates evenly around the centre from all sides. Every set of endpoints in a circular, constrained double sphere is uniformly spaced apart from the "centre."
Here,
Given :
To find: the angle of 1
So,
From the diagram , we can see it is showing 110 degree
So ,
Angle 1 comes out to be 110°
So, rest of circle angle is = 360° - 110° = 250°
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In a factory, three machines, J, K and L, are used to make biscuits. Machine J makes 25% of the biscuits. Machine K makes 45% of the biscuits. The rest of the biscuits are made by machine L. It is known that 2% of the biscuits made by machine J are broken, 3% of the biscuits made by machine K are broken and 5% of the biscuits made by machine L are broken. A biscuit is selected at random. Calculate the probability that the biscuit is made by machine J and is not broken.
B. Probability that the biscuit is made by machine and is not broken is:
1-(25% × 2%)
= 50%
c. The probability of breakage: 2% + 3% + 5% = 10%
d. Probability that biscuit is not made by machine = 1-5% = 95%
What do you mean by probability?Probability is the concept that describes the likelihood of an event occurring. In real life, we frequently have to make predictions about how things will turn out. About an event's outcome, we might be certain or uncertain.
When this occurs, we state that there is a possibility that the event will occur. In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence.
Now from the question,
The probability that the biscuit is made by machine and not broken:
1 - 25% × 2%
= 50%
Now not broken probability = 1- 25% × 2%
Now next, the probability of breakage: 2% + 3% + 5% = 10%
Finally, the probability that biscuit is not made by machine = 1-5% = 95%
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Please help ASAP!!
Will mark brainlest
Assignment due at 12:00
Answer:
(1,5)?
Step-by-step explanation:
Thabelo buys R350 worth of electricity .he gets 152,84 units (kwh) , what is the price per unit ?
The price per unit is equal to R2.29 per unit.
How to determine the unit price?Generally speaking, a unit price is sometimes referred to as price per unit or unit rate and it can be defined as the price that is being charged by a seller for the sale of a single unit of product.
In this scenario, we would determine the unit price for number of unit of electricity by using the following mathematical expression;
Unit price = Cost of electricity/Number of units
Substituting the given parameters into the unit price formula, we have the following;
Unit price = R350/152.84
Unit price = R2.29 per unit.
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NEED HELP ASAP WILL MARK BRAINLIST !!
Todd and Eric went to the book store. Eric spent $15 less than three times the
amount that Todd spent. If the shoppers spent a total of $197 in books, How much
did Eric spend?
$34
$53
$65
$71
$29
$59
$48
Using an equation, the amount Eric spent at the bookstore was $45.50.
What is an equation?An equation is a mathematical statement of the equality or equivalence of two or more algebraic expressions.
Equations are depicted using the equal symbol (=).
Let the amount that Todd spent in the bookstore = 3x
Let the amount that Eric spent in the bookstore = x - 15
The total amount spent by the two shoppers = $197
Equation:197 = 3x + x - 15
182 = 4x
45.5 = x
Check:
Amount spent by Eric = $45.50
The amount spent by Todd = 45.50(3) + 15 = $151.50
The total amount spent by the two shoppers = $197 ($45.50 + $151.50)
Thus, the equation shows that Eric spent $45.50 which is $15 less than three times the amount that Todd spent or $151.50.
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A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (if an answer does not exist, enter dne. ) f(t) = t3 − 8t2 + 25t
f(t) = t3 − 8t2 + 25t + 10. When all the parts are put together, the equation represents a combination of the 3 components, representing a law of motion for a particle.
This equation represents a law of motion, where t is measured in seconds and s in feet. This equation can be broken down into 3 parts; t3, -8t2 and 25t + 10. The t3 part of the equation represents a cubic function, which is usually associated with acceleration. The -8t2 part is a quadratic function, which is typically associated with velocity. Finally, the 25t + 10 is a linear function, which is usually associated with displacement. When all the parts are put together, the equation represents a combination of the 3 components, representing a law of motion for a particle.
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Pla help algebra1 pls
Answer:
A. 2(4a^3 - 49a)
In this case, you would simply multiply the numbers and leave the a value and exponents alone.
B. 2a(4a^2 - 49)
First, you would distribute(multiply) 2 with the numbers inside the parentheses just like you did for answer A. Then, you would distribute a with the other a values inside the parentheses, you would add this values instead of multiplying it.
F. 2a(2a - 7)(2a + 7)
You would distribute 2a inside the FIRST set of parentheses just like you did before. Then multiply that set of parentheses with the other set of parentheses.
Step-by-step explanation:
Find the value of x for which PQ and RS are parallel
The value of x for which PQ and RS are parallel, is 83°.
The two parallel lines PQ and RS are stretched from Q to M and S to N, respectively, in the accompanying figure.
In addition, a line from T to O is drawn parallel to PQ and RS.
Now, in the illustration,
∠MPT = 180° - 135°
∠MPT = 45°
The parallel lines MQ and OT are divided by the transversal line PT.
∠MPT = ∠PTO = 45°
∠TRN = 180° - 142°
∠TRN = 38°
A transversal line TR splits the parallel lines NS and OT.
Then, ∠TRN = ∠OTR = 38°
∠PTO + ∠OTR = x
x = 45° + 38°
x = 83°
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can anyone help me with this because its due tomorrow!
Write a proportion for each set of similar polygons. Solve for the unknown side.
Type the FULL Answer for both questions.
Pls Answer!
Step-by-step explanation:
The proportion of similar triangles are
[tex] \frac{3}{4} = \frac{9}{r} [/tex]
Solving for r
[tex] \frac{4}{3} = \frac{r}{9} [/tex]
[tex] \frac{9 \times 4}{3} = r[/tex]
[tex]12 = r[/tex]
A manufacturer buys a new machine that costs $50,000. The estimated useful life for the machine is ten years. The
achine can produce 1,000 units per month. If the machine ran at its capacity for ten years, what would be the fixed cost per unit based on
e cost of the machine per part manufactured? (Round to the nearest penny)
oooo
a) $. 42 / unit
b) $1. 00/unit
c) $4,167 / unit
d) $5,000/unit
The fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit.
What is multiplication ?
Multiplication is a mathematical operation that involves finding the product of two or more numbers or quantities. It is a way of adding a number to itself multiple times. The symbol used to represent multiplication is an "x" or a dot "·". For example, in the expression 5 x 6 = 30, 5 and 6 are multiplied together to give the product of 30. Multiplication can also be represented using parentheses, such as (5)(6) = 30. In addition, multiplication can be done with decimals, fractions, variables, and matrices.
To find the fixed cost per unit based on the cost of the machine per part manufactured, we need to calculate the total number of units produced by the machine over its estimated useful life, and then divide the cost of the machine by that number.
The machine runs at its capacity of 1,000 units per month for 10 years, so the total number of units produced by the machine is:
10 years x 12 months/year x 1,000 units/month = 120,000 units
The cost of the machine is $50,000, so the fixed cost per unit based on the cost of the machine per part manufactured is:
$50,000 ÷ 120,000 units = $0.4167 per unit
Rounding this to the nearest penny gives us the final answer of:
$0.42 per unit (option a)
Therefore, the fixed cost per unit based on cost of the machine per part manufactured is $0.42 per unit.
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1) What will the time be 90 minutes after 11:15 in the morning
2) What will the time be 135 minutes after 11:15 in the morning
Answer:
the answers are 1. 12:45 pm 2. 1:30 pm
Find the exact value, in terms of a, of each of the following. (HINT: Don't let the variable a scare you! The same strategy you used in Problem 2 still works - draw a point on a circle, assign it coordinates, and find the appropriate trig function’s value.)
a. sin (tan^-1(2/a))
b. cot (cos^-1(a))
Answer:
a. i dk how to do this qn
b. cot (cos^-1(a))
let cos^-1(a) = θ
implies, cosθ = a
from the figure, cotθ = [tex]\frac{x}{\sqrt{1 -x^{2} } }[/tex]
pls mrk me brainliest
The expression (6x+5)/(x+7) written in the form quotient +( remainder )/( divisor ) is
6x + 5 + ( -2 )/( x + 7 ), The expression can be written as the quotient of 6x + 5 divided by x + 7, plus the remainder of -2, all divided by the divisor of x + 7.
To calculate (6x+5)/(x+7), first we must add x to both the numerator and the denominator to get (6x+x+5)/(x+7+x), which simplifies to (7x+5)/(2x+7). Then, divide the numerator by the denominator to get (7x+5)/(2x+7) = 3.5x + 2.5. To find the remainder, subtract 3.5x and 2.5 from both the numerator and denominator, which gives us (7x+5)-(3.5x+2.5) = 3.5x + 2.5 - (3.5x + 2.5) = 3.5x - 2.5. Lastly, divide the remainder by the divisor (2x+7) to get (3.5x-2.5)/(2x+7). Therefore, the answer is 3.5x + 2.5 + (3.5x - 2.5)/(2x+7).
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the common ratio of -1, 4, -7, 10
In response to the given question, we can state that We may infer that there is no common ratio for this sequence because the ratios change for each computation. As a result, it is not a geometric sequence.
what is a sequence?A sequence is a collection of numbers (or "terms"). Examples of words are 2, 5, and 8. Certain sequences may be made infinitely long by takes advantage of a specific pattern they follow. To continue the sequence, use the case of 2,5,8 or add 3. There are formulae that show where to seek for words in a sequence. A sequencing in mathematics is a collection of items that are in some order (or events). It is similar to a set in that it has components (also called elements or terms). The length of a sequence is defined as the total, possibly unlimited number of ordered items. the act of arranging two or more elements in a logical sequence.
To get the common ratio of a geometric series, divide any phrase by the term before it.
Let us divide the second term by the first term:
4 ÷ (-1) = -4
Let us now divide the third term by the second term:
(-7) ÷ 4 = -1.75
Lastly, let us divide the fourth term by the third term:
10 ÷ (-7) = -1.42857142857 (rounded to 11 decimal places) (rounded to 11 decimal places)
We may infer that there is no common ratio for this sequence because the ratios change for each computation. As a result, it is not a geometric sequence.
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