a) The break-even quantity (in units) is 59 units.
b) If the company is selling no more than 34 units, A. The product should not be produced because it will lead to a loss of $625.
What is the break-even point?The break-even point is the production and sales point at which the total costs equal the total revenue.
At the break-even point, there is no profit or loss.
Total units produced = x
Let the cost of production = C
Let the revenue = R
C = 84x+1,475
R = 109x
At the break-even point, 109x = 84x + 1,475
109x - 84x = 1,475
25x = 1,475
x = 59 units
If x = 34 units:
Total cost = 84x+1,475
= 84(34) + 1,475
= 2,856 + 1,475
= $4,331
Total revenue = 109x
= 109(34)
= $3,706
Loss = $625 ($3,706 - $4,331)
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Question Completion:(a) Find the break-even quantity units (Simplify your answer.)
(b) Decide whether the product should be produced on the basis of whether it will earn a profit. (Profit = Revenue - Cost.)
Choose the correct answer below and, if necessary, in the answer box to complete your choice.
A. The product should not be produced because it will lead to a loss of B. The product should be produced because it will lead to a profit of
Is anyone able to solve this?
Answer:
2.4
Step-by-step explanation:
The bottom is a right triangle. You know the 2 legs, you need the hypotenuse.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]1^{2}[/tex] + [tex]1^{2}[/tex] = [tex]c^{2}[/tex]
1 + 1 = [tex]c^{2}[/tex]
2 = [tex]c^{2}[/tex]
[tex]\sqrt{2}[/tex] = [tex]\sqrt{c^{2} }[/tex]
[tex]\sqrt2[/tex] = c
Now we know the 2 legs for the larger triangle on top.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]
[tex]\sqrt{2} ^{2}[/tex] + [tex]2^{2}[/tex] = [tex]c^{2}[/tex]
2 + 4 = [tex]c^{2}[/tex]
6 = [tex]c^{2}[/tex]
[tex]\sqrt{6}[/tex] = [tex]\sqrt{c^{2} }[/tex]
[tex]\sqrt{6}[/tex] = c
[tex]\sqrt{6}[/tex] rounded to the tenths place is 2.4
does it mean the common multiples?
The expressions given in the questions mean that the least common denominator is the least common multiple.
According to the question,
We have the following information:
We have three questions of fractions which are either in addition or subtraction.
Now, we will only look at the denominators of these fractions. And note that the least common multiple is same as the least common denominator.
For first one, it is 6 and 4:
Each multiple of 6: 2*3
Multiples of 4:2*2
The least common multiple of 6 and 4: 12
The least common denominator is 12.
For second one, it is 7 and 3.
Each multiple of 7: 7
Multiple of 3: 3
The least common multiple of 7 and 3: 21
The least common denominator of 7 and 3: 21
For third one, it is 8 and 2.
Multiples of 8: 2*2*2
Multiples of 2: 2
The least common multiple of 8 and 2: 8
The least common denominator is 8.
Hence, the expressions given in the questions mean that it is the least common multiple.
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somebody please help me
Answer:
I got (-1,-4) and (3,0) When I graphed with Desmos. I do no see that solution.
Step-by-step explanation:
4.5 3.9 4.25 3.75 4.2 in lest to greatest
The order of least to greatest of given decimal numbers is 3.75, 3.9, 4.2, 4.25, 4.5.
The given decimal number are 4.5, 3.9, 4.25, 3.75, 4.2
What is the order of decimal numbers?Numerical order is a way of arranging a sequence of numbers. This could be in ascending or descending order.
Ascending order: Ascending order means to arrange numbers in increasing order, that is, from smallest to largest.
The order of decimal numbers
Now, least to greatest of decimal numbers is
3.75<3.9<4.2<4.25<4.5
Therefore, the order of least to greatest of given decimal numbers is 3.75, 3.9, 4.2, 4.25, 4.5.
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What is the equation of the line that passes through the point
(
6
,
2
)
(6,2) and has a slope of
−
1
2
−
2
1
?
The equation of the line that passes through the point (-6, 2) and has slope of -1/2 is y = (-1/2)x - 1
The slope of the line = -1/2
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line
The slope intercept form
y = mx + b
Where m is the slope of the line
b is the y intercept form
The coordinates of the point = (-6, 2)
Substitute the values in the equation
2 = (-1/2)(-6) + b
2 = 3 +b
b = 2 -3
b = -1
The equation will be
y = (-1/2)x - 1
Hence, the equation of the line that passes through the point (-6, 2) and has slope of -1/2 is y = (-1/2)x - 1
The complete question is :
What is the equation of a line that passes through (-6, 2) and has a slope of -1/2 ?
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Find the value of x.
( please help! Dude today!)
Answer: tell me the soulation like how do you solve it then I can help
Step-by-step explanation:
11. This table shows the items sold by an ice cream ship in the first hour after opening.
Cup 6
Cone 4
Milkshake 3
Sundae 1
What is the experimental probability that the next customer will order a cone?
Answer:
2:7 or [tex]\frac{2}{7}[/tex]
Step-by-step explanation:
The cone total is 4 and the total orders is 14
[tex]\frac{4}{14}[/tex] = [tex]\frac{2}{7}[/tex]
Please help I was sick and missed out on class.Thank you
Answer:
m = -5/3
Step-by-step explanation:
Slope is defined as the change in y / change in x or [tex]\frac{y2-y1}{x2-x1}[/tex]
The order of the points don't matter so we can do:
[tex]\frac{-1-(-6)}{5-8}=\frac{-5}{3}[/tex]
-5/3 is as simple as the fraction can be.
A small welding shop employs four welders and one secretary. A workers' compensation insurance policy charges a
premium of $10.51 per $100 of gross wages for the welders and $1.33 per $100 of gross wages for the secretary. If each welder earns $33,000 per year, and the secretary earns $26,000 per year, what is the total annual premium for this insurance?
The total annual premium for this insurance will be $14,219.
Define premium.
An amount that the insured pays on a regular basis to the insurer to cover his risk is known as a premium. In terms of finance, a premium is the sum of the costs associated with an option or the distinction between the higher price paid for a fixed-income instrument and the relevant face amount. For many different insurance policies, including health, homeowner's, and rental insurance, premiums are typically paid. Automobile insurance is a typical example of an insurance premium.
Solution explained:
A/Q, as we calculate,
Annual Premium for one worker is = [tex]33000 X \frac{10.51}{100}[/tex] = $3468.3
Annual Premium for four workers is = 4 X 3468.3 = $13873.2
Annual Premium for the secretary is = 26000 X [tex]\frac{1.33}{100}[/tex] = 345.8
Therefore, the total annual premium for this insurance will be
= 13873.2 + 345.8 = 14219
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Express the sample proportion as a percent:
Out of 1150 insurance applicants, 837 have no citations on their driving record.
%
solve by factoring 6^2 − x - 12 = 0
[tex]{ \purple{ \tt{x = 3}}}[/tex]
[tex]{ \blue{ \sf{ {6}^{2} - x - 12 = 0}}}[/tex]
[tex]{ \blue{ \sf{36 - x - 12 = 0}}}[/tex]
Take 12 as common
[tex]{ \blue{ \sf{ \cancel{12}(3 - x) { \cancel{-12} = 0}}}}[/tex]
[tex]{ \blue{ \sf{3 - x = 0}}}[/tex]
[tex]{ \red{ \boxed{ \green{ \tt \overbrace{ \underbrace{x = 3}}}}}}[/tex]
A company hired 20 new graduates. The mean salary of the newly hired employees is 38 in thousands of dollars, where Σ(x - 38)² = 64. Which is the population variance of the given data ?
The population variance of the given data is 3.2.
Given Σ(x - 38)² = 64 .
We know that the population variance of the data is the square of the standard deviation.
Now the standard deviation for the population is given by
σ =√(Σ(x - 38)² / N)
Again variance = σ ²
Let us first calculate σ .
σ = √(64/20) = √3.2
variance
= σ ²
= (√3.2)²
= 3.2
Therefore the variance of the population is 3.2
In probability theory and statistics, variance is the predicted squared variation of a random variable from its population mean or sample mean. Dispersion, or how far apart from the mean a set of data are from one another, is measured by variance.
A few ideas that use variance include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling.
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I need help solving this problem
Answer:
1/2
Step-by-step explanation:
u replace x with -3
=4(2)-³
=4(0.125)
=0.5
=1/2
Which of the following would be the numerator of the fraction
Answer:
The numerator is the top number of a fraction.
your welcome! <3
Answer:
Numerator is on the the top of the fraction
Step-by-step explanation:
x
_ x is the numerator
y
Question 12(Multiple Choice Worth 1 points)
(02.04 MC)
Write an equation of a line that is perpendicular to y = 4x + 8 and passes through (-8, 4).
y = -1/4x - 7
y = -1/4x + 2
y = 4x + 24
y = 4x + 36
The equation of a line is y=-1/4x-7, (option 1)
What is the equation of a line?A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.
How do you find the equation of a line?Write the equation in the form y = mx + b to find the slope m and the y-intercept. This will allow you to graph the equation using the slope and y-intercept.
Given:-
Equation of the line is y=4x+8
The point through which the line passes (-8,4).
here the slope of the line is m1=4
To find the perpendicular line we know the formula
m1*m2=-1
By putting the value of m1 we get m2= -1/4
By using the one-point formula of the line we have
=>(y-y1)=m2*(x-x1)
By putting the values of y1 and x1 we get
(y1,x1)=(-8,4)
=>(y+8)=-0.25*(x-4)
y+0.25x+7=0
Hence the desired equation of the line is y=-1/4x-7
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Jeremy bought a $60 pair of sneakers on sale for 15% off. Then, he used a coupon that gave him an additional 10% off. How much did Jeremy spend on the sneakers?
Answer:
45.90
Step-by-step explanation:
$60.00 15% off = $51.00
$51.00 10% off = 45.90
7x²(2x - 3) 3z3 + 4 in word form?
Answer:
seven multiplied by x to the second power multiplied by the difference of two multiplied by x subtract 3 multiplied by the product of three multiplied by z multiplied by 3 add four.
Step-by-step explanation:
This is a useless question, word form isn't in any sort of ACTUAL GLOBAL TEST. So don't stress over this.
Romeo applies a 300 N force on a 25 kg object. What is the acceleration of the object?
Answer: Force = 300 NewtonsMass = 25 kgAcceleration = Force / Mass = 300 Newtons / 25 kg = 12 metres / second^2.
Second law of Newton
Romeo applies a 300 N force on a 25 kg object. What is the acceleration of the object?Data:
m = 25kgF = 300NNewton's second law formula
F = m * a
We clear for acceleration
[tex]\boldsymbol{\sf{\dfrac{F}{m}=\dfrac{\not{m}*a}{\not{m}} \iff \ \dfrac{F}{m}=a \longmapsto \ a=\dfrac{F}{a} }}[/tex]
[tex]\boldsymbol{\sf{a=\dfrac{300 \ N}{25 \ kg} }}[/tex]
We know very well that to find the acceleration, we decompose N= Kg*m/s^2.
[tex]\boldsymbol{\sf{a=\dfrac{300 \not{kg}*\frac{m}{s^2} }{25 \not{kg}} }}[/tex]
[tex]\boldsymbol{\sf{a=12 \ \dfrac{m}{s^{2}} }}[/tex]
The acceleration of the object is 12 m/s^2.(3x + 5y)^5
Rewrite the following expression in expanded form and simplify completely.
Answer: 243x^5 + 2025x^4y + 6750x^3y^2 + 11250x^2y^3 + 9375xy^4 + 3125y^5
Step-by-step explanation:
1. To find each term, use BINOMIAL EXPANSION THEOREM (best to look up theorem on your own).
2. Expand the summation (after finding each term).
3. Simplify the exponents for each term.
> 1 • (3x)^5 • (5y)^0 + 5 • (3x)^4 • (5y)^1 + . . . + 1 • (3x)^0 • (5y)^5
4. Simplify.
Question 1 4 pts Rhoda pays for Internet access each month. The graph shows the relationship between the total amount she has paid and the amount of time, in months. How can Rhoda show that the slope of the line is constant? What does a constant slope mean? Explain your reasoning.
By examining the slope at different points, we can see that the slope is constant.
What is a slope?The term slope has to do with a measure of how steep the line of best fit is for a relationship that exists between two variables. In this case, we are considering the relationship between the amount paid and the time taken.
A straight line graph is expected to have a constant slope. To show that the slope is constant, let us look at two points on the graph; (0, 0) (9, 675) and (0, 0) (7, 525)
In the first case;
m = [tex]y_{2} - y_{1} /x_{2} - x_{1}[/tex]
m = 675 - 0/9 - 0
m = 75
In the second case;
m = [tex]y_{2} - y_{1} /x_{2} - x_{1}[/tex]
m = 525 - 0/7 - 0
m = 75
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Suppose that the mean GRE score for the United States is 500 and the standard deviation is 75. Use the 68-95-99.7 (empirical) rule to determine the percentage of students likely to get a score below 275? Is a score below 275 significantly different from the mean
1) The percentage of students who will get a score below 275 is; 0.15%
2) Yes, any score below 275 is significantly different from the mean.
How to use the Empirical rule in statistics?
The empirical rule states that for a normal distribution, 68% of the distribution are within one standard deviation from the mean, 95% are within two standard deviation from the mean and 99.7% are within three standard deviations from the mean.
The formula for z-score is;
z = (x' - μ)/σ
where;
x' is sample mean
μ is population mean
σ is standard deviation
1) We are given;
Population mean; μ = 500
Sample mean; x' = 275
standard deviation; σ = 75
Thus;
z = (275 - 500)/75
z = -3
This is 3 standard deviations from the mean. Thus;
The percentage of students who will get a score below 275 is;
(100 - 99.7)/2 = 0.15%
2) Yes, any score below 275 is more than 3 standard deviations away from the mean and can be considered significantly different from the mean.
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The locker's combination code
consists of one letter and 3 digits.
How many possible different codes
exist, if the letter can be A or C and
must come first, and the digits can
be repeated?
The number of different codes as the letters A or C must come first and digits can be repeated is 2000
Permutation and Combination:Permutations and combinations are a subset of the study of finite, discrete structures that are known as combinatorics. Combinations include the selection of items without respect to order, whereas permutations are precise selections of elements within a set where the order of the elements is significant.
Here we have,
The locker combination code consists of one letter and 3 digits
Here we need to find the number of different codes If the letter A or C must come first and digits can be repeated.
Given that the first letters are A and C
Here number of ways that A and C can be chosen at first = 2
As we know Number of digits = 10 [ including 0, 0 to 9 ]
Number of arrangements that can be chosen from 10 digits
= 10 × 10 ×10 [ Since repetition is allowed ]
Therefore,
The possible number of different codes = 2 × 10 × 10 ×10 = 2000
Therefore
The number of different codes as the letters A or C must come first and digits can be repeated is 2000
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help on this maths
im confuse and dont know what to do
Answer:
30-2=28+542=570
Step-by-step explanation:
Which property is used in the following calculation?
(64⋅25)⋅464⋅(25⋅4)64⋅(100)6400
Commutative Property of Multiplication
None of these
Associative Property of Multiplication
Distributive Property
Identity Property of Multiplication
A property which is used in the calculation above is: Commutative Property of Multiplication.
What is the Commutative Property of Multiplication?The Commutative Property of Multiplication states that when three (3) numbers are multiplied, the end result (output) would always be the same regardless of the way the numbers are arranged and grouped.
This ultimately implies that, re-arranging or regrouping the order of numbers that are being multiplied does not change the end result (output) or product.
Mathematically, the Commutative Property of Multiplication is represented by this mathematical expression:
a · (b) = b · (a)
By applying the Commutative Property of Multiplication to the calculation, we have:
(64⋅25)⋅4 = 6400
64⋅(25⋅4) = 6400
64⋅(100) = 6400
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The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $5, sales will reach 7000 Fun Noodles per day during the summer. Raising the price to $6 will cause the sales to fall to 3000 Fun Noodles per day.
Assume that the relationship between sales price, x, and the number of Fun Noodles sold, y, is linear. Use ordered pairs of the form (sales price, number sold).
1. Write an equation in a slope-intercept form describing this relationship.
2. Predict the daily sales of Fun Noodles if the price is $5.50
1. The equation in a slope-intercept form describing the relationship is y = -4000x + 27000.
2. The daily sales of Fun Noodles at the price of $5.50 is 5000.
How to represent linear equation in slope intercept form?The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $5, sales will reach 7000 Fun Noodles per day during the summer. Raising the price to $6 will cause the sales to fall to 3000 Fun Noodles per day.
The relationship between sales price, x, and the number of Fun Noodles sold, y, is linear. The ordered pair are (5, 7000) and (6, 3000).
The equation in slope intercept form describing the relationship is as follows:
1. y = mx + b
where
m = slopeb = y-interceptTherefore,
m = 3000 - 7000 / 6 - 5
m = - 4000
Let's find the y-intercept using (6, 3000)
3000 = -4000(6) + b
3000 + 24000 = b
27000 = b
Hence, the equation is y = -4000x + 27000
2. The daily sales of Fun Noodles at the price of $5.50 can be computed as follows;
y = -4000(5.5) + 27000
y = -22000 + 27000
y = 5000
Therefore, the daily sales is 5000.
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PLS HELP Me guys is for today plsssss I will give branlist who assert it first pls Emily wants to buy tomatoes and a loaf of bread. Tomatoes are $1.20 a pound, and a loaf
of bread is $2.00. If she spends $8.00 how many pounds of tomatoes can she buy.
a. Write an equation modeling the problem. Let x represent the number of pounds.
b. Solve the equation from part a and determine how many pounds of tomatoes Emily
can buy. Write your answer as a full sentence. Show your work.
Answer:
Below
Step-by-step explanation:
If she buys a loaf of bread she has only 6 dollars for tomatoes
$ 6 / 1.20 $/POUND = 5 POUNDS OF TOMATOES
(8-2) / 1.20 = # TOMATOES
You have 72 square feet of material to build a rectangular box.
The length is twice the width and there is no top.
What values for W and L and H will create a box that encloses the maximum volume using the material you have?
W = ?
L = ?
H = ?
For the given conditions, the length of box=6.92 feet, width of box=3.46 feet and height of box=2.31 feet.
What is volume?Each object in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's boundaries in three dimensions is referred to as its volume. It is also referred to as the object's capacity.
Here,
area of material=72 feet²
V=lbh
l=2b
72=lb+2lh+2bh
substitute l as 2b,
72=2b²+4bh+2bh
36=b²+3bh
3bh=36-b²
h=(36-b²)/3b
v=lbh
v=2b*b*(36-b²)/3b
v=2b*(36-b²)/3
=(72b-2b³)/3
differentiate the v,
v'=1/3(72-6b²)
v'=0
72-6b²=0
6b²=72
b²=12
b=√12
b=3.46 feet
l=2b=6.92 feet
h=(36-b²)/3b
=(36-12)/3*3.46
h=2.31 feet
The box measures 6.92 feet long, 3.46 feet wide, and 2.31 feet tall under the specified circumstances.
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Answer:
[tex]W=2\sqrt{3}=3.46\; \sf ft\;(2\;d.p.)[/tex]
[tex]L=4\sqrt{3}=6.93\; \sf ft\;(2\;d.p.)[/tex]
[tex]H = \dfrac{4\sqrt{3}}{3}=2.31\; \sf ft\;(2\;d.p.)[/tex]
Step-by-step explanation:
If the length is twice the width:
W = widthL = 2W = lengthH = heightSurface area of the box
[tex]\implies SA = WL + 2WH + 2LH[/tex]
[tex]\implies SA = W(2W) + 2WH + 2(2W)H[/tex]
[tex]\implies SA = 2W^2 + 2WH + 4WH[/tex]
[tex]\implies SA = 2W^2 + 6WH[/tex]
If the surface area is 72 ft²:
[tex]\implies 2W^2 + 6WH = 72[/tex]
[tex]\implies 6WH = 72 - 2W^2[/tex]
[tex]\implies H = \dfrac{72 - 2W^2}{6W}[/tex]
[tex]\implies H = \dfrac{36 - W^2}{3W}[/tex]
Volume of the box
[tex]\implies V = LWH[/tex]
[tex]\implies V = (2W)WH[/tex]
[tex]\implies V = 2W^2H[/tex]
Substitute the found expression for H into the formula for volume:
[tex]\implies V = 2W^2\left(\dfrac{36 - W^2}{3W}\right)[/tex]
[tex]\implies V = \dfrac{2W^2(36 - W^2)}{3W}[/tex]
[tex]\implies V = \dfrac{2W(36 - W^2)}{3}[/tex]
[tex]\implies V = \dfrac{72W - 2W^3}{3}[/tex]
[tex]\implies V =24W-\dfrac{2}{3}W^3}[/tex]
To find the value of W when the volume is at its maximum, first differentiate the equation for volume with respect to W:
[tex]\implies \dfrac{\text{d}V}{\text{d}W}=24-2W^2[/tex]
Now set the derivative to zero and solve for W:
[tex]\implies 24-2W^2=0[/tex]
[tex]\implies 2W^2=24[/tex]
[tex]\implies W^2=12[/tex]
[tex]\implies W=\sqrt{12}[/tex]
[tex]\implies W=2\sqrt{3}[/tex]
As length is twice the width:
[tex]\implies L=2 \cdot 2\sqrt{3}[/tex]
[tex]\implies L=4\sqrt{3}[/tex]
To find H, substitute the found value of W into the expression for H:
[tex]\implies H = \dfrac{36 - W^2}{3W}[/tex]
[tex]\implies H = \dfrac{36 - (2\sqrt{3})^2}{3(2\sqrt{3})}[/tex]
[tex]\implies H = \dfrac{36 - 12}{6\sqrt{3}}[/tex]
[tex]\implies H = \dfrac{24}{6\sqrt{3}}[/tex]
[tex]\implies H = \dfrac{4}{\sqrt{3}}[/tex]
[tex]\implies H = \dfrac{4\sqrt{3}}{3}[/tex]
What is the length of a rectangle that has an area of 12½ square feet and a width of 2½ feet?
Answer:
Step-by-step explanation:
l = length
w = width = 2.5
a = area = 12.5
l = a/w = 12.5/2.5 = 5
so the answer is l = 5
Solve for x. Round to the nearest tenth, if necessary.
Answer:
27.64
Step-by-step explanation:
As the triangle is right-angle triangle,take another 29° and take sin29°You will get sin29°=x/57-- as(p/h)then x=57*sin29°=27.64An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 1050 feet apart. As the
airplane passes over the line joining them, each observer takes a sighting of the angle
elevation to the plane, as indicated in the figure. If A = 30 degrees and B = 40 degrees how high is the
airplane?
If the angle elevation to the plane A = 30 degrees and B = 40 degrees , then the Airplane is 359.11 feet high .
In the question ,
it is given that
the distance between the two observer = 1050 feet
the measure of angle A is = 30°
the measure of angle B is = 40°
By angle sum property angle C is = 180 - (30 + 40)
= 180 - (70)
= 110
By Sine Law .
Sin(110)/1050 = Sin(30)/a = Sin(40)/b
Using , Sin(110)/1050 = Sin(30)/a ,
we get ,
Sin(110)/1050 = 0.5/a
a = 558.69
Using Sin(110)/1050 = Sin(40)/b
b = 718.24
By using Sine Law
Sin(40)/h = Sin(90)/558.69
h = 359.11
Therefore , If A = 30 degrees and B = 40 degrees , then the Airplane is 359.11 feet high .
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