The correct answer is option b which is the break-even quantity will be 20217 units.
What is the break-even point?
The point at which the company will not have any profit and loss on the products they manufactured they only get the amount they invested in manufacturing the product is called the break-even point.
Given that:-
If fixed costs are $281,000, the unit selling price is $33, and the unit variable costs are $21, the break-even sales (units) if fixed costs are reduced by $38,400.
The formula for calculating break-even quantity will be given as:-
[tex]BEQ = \dfrac{FC}{SP-VC}[/tex]
Here,
FC = Fixed cost = $281000
SP = Selling price = $33
VC = Variable cost = $21
The fixed cost is reduced by $38400 so the fixed cost now:-
FC = $281000 - $38400
FC = $242600
[tex]BEQ = \dfrac{242600}{33-21}[/tex]
BEQ = 20217 units
Therefore the correct answer is option b which is the break-even quantity will be 20217 units.
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What is the volume of a cone with a height of 22 and a radius of 6
Answer:
3041.06
Step-by-step explanation:
The formula of a cone is [tex]\pi r^{2} \frac{h}{3}[/tex] , so plugging both the height and radius will result in the answer!
what is (4-¹)(2³-4-2) 4 - ¹ ) ( 2³ - 4-2 )
Answer:
[tex](4-¹)(2³-4-2) 4 - ¹ ) ( 2³ - 4-2 )[/tex]
[tex]4 {}^{ - 2} (2 {}^{3 } - 4 - 2)(2 {}^{3} - 4 - 2)[/tex]
[tex]4 {}^{ - 2} (2 {}^{3} - 4 - 2) {}^{2} [/tex]
[tex] \frac{1}{16} (8 - 4 - 2) {}^{2} [/tex]
[tex] \frac{1}{16} (4 - 2) {}^{2} [/tex]
[tex] \frac{1}{16} \times 4[/tex]
[tex] \frac{1}{4} [/tex]
St^2 e^-10t dt
Evaluate the intergral
It looks like you're talking about the indefinite integral
[tex]\displaystyle \int t^2 e^{-10t} \, dt[/tex]
Integrate by parts:
[tex]\displaystyle u\,dv = uv - \int v\,du[/tex]
Let
[tex]u = t^2 \implies du = 2t \, dt[/tex]
[tex]dv = e^{-10t} \, dt \implies v = -\dfrac1{10} e^{-10t}[/tex]
Then
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} + \frac15 \int t e^{-10t} \, dt[/tex]
Integrate by parts again, this time with
[tex]u = t \implies du = dt[/tex]
[tex]dv = e^{-10t} \, dt \implies v = -\dfrac1{10} e^{-10t}[/tex]
Then
[tex]\displaystyle \int t e^{-10t} \, dt = -\frac1{10} t e^{-10t} + \frac1{10} \int e^{-10t} \, dt[/tex]
Putting everything together, we get
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} + \frac15 \int t e^{-10t} \, dt[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} + \frac15 \left(-\frac1{10} t e^{-10t} + \frac1{10} \int e^{-10t} \, dt\right)[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} - \frac1{50} t e^{-10t} + \frac1{50} \int e^{-10t} \, dt[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} - \frac1{50} t e^{-10t} + \frac1{50} \left(-\frac1{10} e^{-10t}\right) + C[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} - \frac1{50} t e^{-10t} - \frac1{500} e^{-10t} + C[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = \boxed{-\frac{e^{-10t}}{500} \left(50t^2 + 10t + 1\right) + C}[/tex]
What are the roots of x In-10x2 + 12x-9=0? OA. 61√6 -1 10 31√6 10 OB. O C. 31√24 10131/24 OD. ti√24 OE. 1, 2:√6 51 10 What are the roots of x In - 10x2 + 12x - 9 = 0 ? OA . 61√6 -1 10 31√6 10 OB . O C. 31√24 10131/24 OD . ti√24 OE . 1 , 2 : √6 51 10
Answer:
9=0
Step-by-step explanation:
9=0
The roots of x in the equation -10x² + 12x - 9 = 0 are:
x = (3/5) + (3/5)√(6)i
x = (3/5) - (3/5)√(6)i
What is a quadratic equation?For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.
To find the roots of x in the equation -10x² + 12x - 9 = 0, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation in standard form (ax² + bx + c).
In this case, a = -10, b = 12, and c = -9. Substituting these values into the quadratic formula, we get:
x = (-12 ± √(12² - 4(-10)(-9))) / 2(-10)
x = (-12 ± √(144 - 360)) / (-20)
x = (-12 ± √(-216)) / (-20)
Substituting this into the expression for x, we get:
x = (-12 ± 6√(6)i) / (-20)
Simplifying the expression further, we get:
x = (3/5) ± (3/5)√(6)i
Therefore, the roots of x in the equation -10x² + 12x - 9 = 0 are:
x = (3/5) + (3/5)√(6)i
x = (3/5) - (3/5)√(6)i
These roots are complex conjugates of each other.
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find X :))))))))))))))
Answer:
X + 35° = 70° ( this is one of the property of triangle in which the sum of two interior angles of a triangle is equal to its other angle)
X = 70 - 35
X = 35°
It costs $164.34 to rent a standard-size car for 5 days. Find the price per day to rent this car.
What are the following expressions simplified?
(11 √40) (9 √5)
(2 √6) (10 √8)
5 √6 ÷ √7 - √5 ÷ √6
The simplified expressions are
1. 990√2
2. 80 √3
3. 30- √35 / √42
What is expression?An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
(11 √40) (9 √5)
= 11*9* √40*√5
= 99*√200
= 99* 10√2
= 990√2
(2 √6) (10 √8)
= 2*10 * √6 * √8
=20* √48
= 20* 4 √3
= 80 √3
5 √6 ÷ √7 - √5 ÷ √6
=30- √35 / √42
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Suppose that prices of recently sold homes in one neighborhood have a mean of $220,000 with a standard deviation of $7450. Using Chebyshev's Theorem, what is the minimum percentage of recently sold homes with prices between $197,650 and $242,350? Round your answer to one decimal place.
The minimum percentage of recently sold homes with prices between $197,650 and $242,350 is 88.9%.
What is Mean ?Mean is the ratio of the sum of all the data points to the number of data points.
It is given that
mean of $220,000 with a standard deviation of $7450.
The range is given , let the range is represented by x - --y
It is given that x = 197650 and y = 242350
Let the number of homes sold is k
To determine the value of k
upper level = (y-mean)/standard deviation = (242350-220000)/7450 = 3
lower level = (mean-x)/standard deviation = (220000-197650)/7450 = 3
probability = 1-(1/k²)
k= 3
= 1 - (1/3^2)
= 1 - 1/9
= 0.889 or 88.9%
So, the minimum percentage of recently sold homes with prices between $197,650 and $242,350 is 88.9%.
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What is the equation of the line that has a slope of -4 and passes through the point (2, 3)?
If [tex]m=-4[/tex]
and a point is [tex](2,3)[/tex]
[tex]y=mx+b[/tex]
[tex]3=(-4)(2)+b[/tex] using the point and the slope
[tex]3=-8+b[/tex]
[tex]b=8+3[/tex]
[tex]b=11[/tex]
Therefore, the equation of the line will be [tex]y=-4x+11[/tex]
The measures of the angles of a triangle are shown in the figure below. Solve for x.
83 ⁰
to
59°
The value of x is 38 degree.
What is a Triangle ?A triangle is a polygon with three sides , three angles and three sides .
The sum of all angles in a triangle is equal to 180 degree
The angles of the triangle given are
83 degree and 59 degree and x degree
83 + 59 + x = 180
x = 38 degree
Therefore the value of x is 38 degree.
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Samantha invests $11,000 at 6% simple interest for 25 years.
Round your answers to the nearest cent.
Answer:
$27,500.00
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 6%/100 = 0.06 per year.
Solving our equation:
A = 11000(1 + (0.06 × 25)) = 27500
A = $27,500.00
The total amount accrued, principal plus interest, from simple interest on a principal of $11,000.00 at a rate of 6% per year for 25 years is $27,500.00.
the table shows the length of time in hours ,some children spent watching tv last week
The histogram of the distribution plotted on the y - axis and the interval for the length of time on the x - axis is attached below.
How to denote the histogram?The first bar denotes the length of time between 0 and 10 having a frequency of 8. The second bar denoted the interval between 10 and 15 with a frequency of 15
The third bar denoted the interval between 15 and 20 with a frequency of 10. The fourth bar denoted the interval between 20 and 30 with a frequency of 11
Therefore, the histogram of the distribution is attached below.
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What is the value of y?
Answer:
Step-by-step explanation:
I can give you the meaning of Y
Y is the vertical value in a pair of coordinates. In other words how far up or down the point is. The Y coordinate is always written second in an ordered pair of coordinates (x,y) when used. A example from the internet is:
write the quadratic equation whose roots are -3 and 3, and whose leading coefficient is 5
Answer:
5x²- 1.8
Step-by-step explanation:
roots are -3 and 3, put them in brackets
(x - 3)(x + 3)
x² + 3x - 3x - 9
x² - 9
5x = -9
x = -1.8
5x² - 1.8
just to check:
5x² - 1.8
x² - 9
(x - 3)(x - 3)
x = -3 and 3.
25. (01.05)
Given the point (2, 3) and the slope of 4, find y when x = 22. (1 point)
I 78
O83
O88
091
Answer: 83
Step-by-step explanation:
The equation of the line in point-slope form is
[tex]y-3=4(x-2)[/tex]
Substituting in x = 22,
y - 3 = 4(22-2) [substitution]y -3 = 80 [simplify right hand side]y = 83 [add 3 to both sides]The Pythagorean Identity states that: (sin x)^2 + (cos x)2 = 1
Given sin 0 = 2/5, find cos 0.
cos 0 = ?/?
Answer:
[tex]\cos \theta =\dfrac{\sqrt{21}}{5}[/tex]
Step-by-step explanation:
Given:
[tex]\sin \theta=\dfrac{2}{5}[/tex][tex](\sin x)^2+(\cos x)^2=1[/tex]Substitute the given value of sin θ into the given identity and solve for cos θ:
[tex]\begin{aligned}(\sin x)^2+(\cos x)^2 & =1\\\implies (\sin \theta)^2+(\cos \theta)^2 & =1\\\left(\dfrac{2}{5}\right)^2+(\cos \theta)^2 & =1\\\left(\dfrac{2^2}{5^2}\right)+(\cos \theta)^2 & =1\\\dfrac{4}{25}+(\cos \theta)^2 & =1\\(\cos \theta)^2 & =1-\dfrac{4}{25}\\(\cos \theta)^2 & =\dfrac{21}{25}\\\cos \theta & =\sqrt{\dfrac{21}{25}}\\\cos \theta & =\dfrac{\sqrt{21}}{\sqrt{25}}\\\cos \theta & =\dfrac{\sqrt{21}}{5}\end{aligned}[/tex]
Question 1(Multiple Choice Worth 4 points)
Which set of line segments could create a right triangle?
O24, 30, 35
O 12, 18, 30.
O 18, 24, 30
O 18, 24, 35
Answer: 18, 24, 30
Step-by-step explanation:
For the segments to create a right triangle, they must satisfy the Pythagorean theorem.
The only set which satisfies the Pythagorean theorem, is 18, 24, 30, since [tex]18^{2}+24^{2}=30^{2}[/tex]
Use point-slope form − 1 = ( − 1) to find the equation of the line that passes through the point (−3,5) and has slope = −2 . Write the answer in slope-intercept form = + .
Answer:
y - 5 = -2(x + 3)
Step-by-step explanation:
When you write an equation in point-slope form, you only need two things: a point and a slope.
Given:
point: (-3, 5)
slope (m): -2
The standard point-slope equation is
y - y₁ = m(x - x₁)
Plug in what you know.
y - (5) = -2(x - (-3))
Simplify.
y - 5 = -2(x + 3)
This is your equation.
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Which trig expression can be used to find the height on the tree where the top guy wire attaches if the base of the wire is four feet from the base?
The trigonometric expression that can be used to find the height of the tree where the top guy wire attaches is tan(45 + 30)
How to use trigonometric rations to find height?The height of the tree can be found using trigonometric ratios.
Therefore,
tan ∅ = opposite / adjacent
Hence,
for the higher wire
tan 75 = h / 4
4 tan 75 = h
This can be express as follows:
tan 75 = tan(45 + 30)
Hence,
4 × 3.73205080757 = 14.9282032303 ft = 14.9ft
Hence, the trigonometric expression that can be used to find the height of the tree where the top guy wire attaches is tan(45 + 30)
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Sarah conducted an experiment regarding the effectiveness of two mathematics tutoring programs: Math Master and Excel. She randomly selected 20 students from her high school and assigned 10 students to the Math Master program. Sarah then assigned the remaining 10 students to the Excel program.
Finding the percent increase, it is found that the correct option is given by:
C. The Master Program and the Excel Program are both effective, but Math is more effective because of the greater percent increase.
What is the percent increase?The percent increase is given by the difference between the final and the initial score, divided by the initial score and multiplied by 100%.
Researching the problem on the internet, we have that:
In the Master program, the average score increased from 75 to 87.In the Excel program, the average score increased from 73 to 81.The percent increases are given as follows:
M = 12/75 x 100% = 16%,E = 8/73 x 100% = 10.96%.Hence the correct option is given by:
C. The Master Program and the Excel Program are both effective, but Math is more effective because of the greater percent increase.
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Fill in the blank. In the triangle below, x=?. Round your answer to two decimal places.
Answer:
Hello
DiinoMahFill in the blank. In the triangle below, x=?. Round your answer to two decimal places.
crash test results the insurance institute for highway safety crashed the 2010 ford fusion four times at 5 miles per hour. the costs of repair for each of the four crashes were $2529,$1889,$2610,$1073 $2529,$1889,$2610,$1073
compute the mean, median, and mode cost of repair.
Answer:
We know that
The costs of repair for each of the four crashes were
$2529, $1889, $2610, $1073
Here we have to compute the mean, median, and mode cost of repair.
Mean = total cost
the no of crashes
Mean = $2529 + $1889 +$2610 +$1073
4
Mean = $2025.25
Therefore the mean = 2025.25
Then we have to find median.
Now first we have to arrange the data in ascending order (smallest to highest).
$1073,$1889,$2529,$2610
Add the two middle numbers and then divide by two, to get the average:
$1889+$2529 = $4418
Median = $4418/2 = $2209
Therefore the median = $2209
Here there is no mode cost.
Simplify the expression -3z(1.8z-2.2).
-5.4z² + 6.6z
-5.4z²-6.6z
-1.2z²+5.2z
-1.2z²-5.2z
Mark this and return
Save and Exit
Next
Submit
Answer:
[tex] - 5.4z {}^{2} + 6.6z[/tex]
Step-by-step explanation:
Given:
[tex]-3z(1.8z-2.2)[/tex]
Solution:
Applying Distributive property,we obtain
[tex](−3z)(1.8z)+(−3z)(−2.2)[/tex]Simplifying using PEMDAS:
[tex] - 5.4z {}^{2} + 6.6z[/tex]Done!
Answer:A
Step-by-step explanation:
ASSIGNMENTS
COURSES
2.(-4)2
3.42
Assignment 5. Solving Equations with Exponents
Attempt 10 of 7
Evaluate each expression. Determine if the final simplified form of the expression is positive or negative
1.-42
NEXT QUESTION
SECTION
Answer:
-16, 16, 16
Step-by-step explanation:
1) -16
2) 16
3) 16
pls asap need it rn.
Similar triangles are those triangles whose corresponding sides are in the same ratio. The correct option is A.
What are similar triangles?Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same.
Since for the two of the given triangle, the measure of all the corresponding angles is the same. Also, all the corresponding sides are in a common ratio.
9/3 = 12/4 = 15/5 = 3
Therefore, the two of the given triangles are similar triangles.
Hence, the correct option is A.
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find the least common denominator 3/2x+4 and -11/3x+6
Answer: 6x+12
Step-by-step explanation: Both denominators can be multiplied to create 6x + 12.
2x + 4
2x(3) + 4(3)
6x+12
3x + 6
3x(2) + 6(2)
6x+12
I hope this helps!
Write 1 3/4 as a decimal and as a percent
Answer:
Decimal: 1.75
Percentage: 175%
Hey there!
1 3/4
= 1 * 4 + 3 / 4
= 4 + 3 / 4
= 7 / 4
= 7 ÷ 4
= 1.75
= 1.75 * 100
= 175%
Therefore, your answer should be:
• 1.75 (as your decimal form)
• 175% (as your percentage form)
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Can y’all help me with ! I need correct anwsers ! Please
Answer:
Im pretty sure its B, 1.75. Not exactly sure though
Step-by-step explanation:
Select the correct interpretation of the following expression.
2(3x+1)(9x-5)
A.
double the sum of 3x + 1 and 9x - 5
B.
the sum of 2, 3x, 1, 9x, and -5
C.
the product of 2, 3x + 1, and 9x - 5
D.
the product of 2, 3x, 1, 9x, and -5
Answer:
C
Step-by-step explanation:
you are multiplying so it is the product of the three
2 ( ... ) ( ... )
and you must solve the brackets first so C and not D
DOES THE THE NUMBER LINE GOES ON FORVEVER
Answer:
Yes.
Step-by-step explanation:
In mathematics, a number line ends in arrows on both sides, signifying it going infinite in the positive and negative directions.
Answer:
Yes.
Step-by-step explanation:
A number line is infinite in both directions it faces. This means left or right there is a infinite amount of numbers.
