1. The master budget variance for July was $3,900, and this variance was favorable.
2. The July sales volume variances in terms of contribution margin and operating income are $2,800 F and $3,900 F, respectively.
3. The July flexible-budget variances in terms of contribution margin and operating income are $5,550 F and $6,650 F, respectively.
4. Flexible budgets for the following output levels are:
3,560 units 3,980 units
Sales revenue $53,400 $59,700
Variable manufacturing costs 14,240 15,920
Fixed manufacturing costs 12,460 13,930
Variable selling and
administrative expenses 7,120 7,960
Fixed selling and
administrative expenses 9,100 9,100
Operating Income $10,480 $12,790
Data and Calculations:Actual Master Budget Per Unit Variance
Units 3,500 4,000 500 U
Sales revenue $ 54,300 $ 60,000 $15.00 $ 5,700 U
Variable manufacturing costs 10,000 16,000 4.00 6,000 F
Fixed manufacturing costs 13,000 14,000 3.50 1,000 F
Variable selling and
administrative expenses 6,500 8,000 2.00 1,500 F
Contribution margin $24,800 $22,000 $2,800 F
Fixed selling and
administrative expenses 8,000 9,100 1,100 F
Total costs $37,500 $47,100
Operating income $16,800 $12,900 $3,900 F
Sales volume variance:
Revenue per unit $15.51 $15.00 $0.51 F
Flexible-budget:Actual Master Budget Variance
Units 3,500 3,500 U
Sales revenue $ 54,300 $ 52,500 $ 1,800 F
Variable manufacturing costs 10,000 14,000 4,000 F
Fixed manufacturing costs 13,000 12,250 750 U
Variable selling and
administrative expenses 6,500 7,000 500 F
Contribution margin $24,800 $19,250 $5,550 F
Fixed selling and
administrative expenses 8,000 9,100 1,100 F
Operating income $16,800 $10,150 $6,650 F
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3a²+ab²-b² x a²-2ab²-3b²
/a+b
Answer:
It might be - c² or b³ *SORRY IF IM WRONG HAVE A GOOD DAY :D)
Step-by-step explanation:
I agree with the person above ^^^
The length and width of a rectangle must have a sum of 60. Find the dimensions of the rectangle that will have the maximum area. [Hint: Let x and 60-x be the length
and width. The area can be described by the function f(x)=x(60-x).]
The length is… and the width is…
If the sum of the length and width of rectangle is 60 and rectangle is having maximum area then the dimensions are 30 units each.
Given that the sum of length and breadth of rectangle is 60.
We are required to find the dimensions of the rectangle that will have the maximum area. Area is basically how much part of surface is being covered by that particular shape or substance.
Let the length of rectangle be x.
According to question the breadth will be (60-x).----2
Area of rectangle=Length *Breadth
A=x(60-x)
A=60x-[tex]x^{2}[/tex]
Differentiate A with respect to x.
dA/dx=60-2x
Again differentiate with respect to x.
[tex]d^{2} A/dA^{2}[/tex]=-2x
-2x<0
So the area is maximum because x cannot be less than or equal to 0.
Put dA/dx=0
60-2x=0
60=2x
x=30
Put the value of x in 2 to get the breadth.
Breadth=60-x
=60-30
=30
Hence if the sum of the length and width of rectangle is 60 and rectangle is having maximum area then the dimensions are 30 units each.
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louizah baked 8 dozen muffins and sold them all at the school for R5,50. if louizah bought the ingredients for R12,50. Determine louizahs profit
Answer:
3550
Step-by-step explanation:
C.P=Rs 1250
S.P=8(12)(50)
Rs4800
P=S.P-C. P
=Rs4800-Rs1250
= Rs3550
Explain insurable interest and give an example
The examples of insurable interest is an employer under certain arrangements.
Insurable interest is a investment that protects anything subject to a financial loss. A person or entity has an insurable interest in an item, event, or action when the damage or loss of the object would cause a financial loss or other hardshapes. In order to have an insurable interest a person or entity would take out an insurance policy protecting the person,item, or event in question. The insurance policy is able to mitigate the risk of loss if something happens to the asset-like becoming damaged or lost.
Examples of insurable interest are:
YourselfYour spouse or former spouseYour children or grandchildrenA special needs adult childAn aging parentAn employer (under arrangements)Hence the examples of insurable interest is an employer under certain arrangements.
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Answer: Insurable interest means you must have a financial stake in the risk being insured. You can’t claim insurance for a risk that you don’t face directly.
If Rob’s dad’s car is stolen, his father will receive the insurance money, not Rob.
Step-by-step explanation: Edmentum
What must be true for line EF to not intersect plane L?
Answer:
If line EF is parallel to line CD, it will not intersect plane L.
please help urgently
Answer: no real solution
Thus, the function has no x- intercept
Step-by-step explanation:
Which answer choice shows that the set of irrational numbers is not closed under addition? π+(-π)=0
1/2+(-1/2)=0
π+π=2π
1/2+1/2=1
Answer:
(a) π + (-π) = 0
Step-by-step explanation:
You want a counterexample for the statement that irrationals are closed under addition.
Closed setA set is closed under addition if adding members of the set always results in a member of the set.
π + (-π) = 0This shows that adding members of the set can result in a rational number. This is the counterexample you're looking for.
(1/2) + (-1/2) = 0Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.
π + π = 2πAn example of a sum that is an element of the set. This is not a counterexample.
(1/2) +(1/2) = 1Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.
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Why are angles opposite each other when two lines cross called vertical angles? (
Angles is known to be opposite each other when two lines cross called vertical angles due to the fact that they are opposite each other at a vertex.
What angles are opposite to each other when two lines cross?Vertical Angles are known to be often called Vertically Opposite Angles and this is described as the scenario when two lines intersect one another, then the opposite angles, is made as a result of the intersection which is known to be called vertical angles or what we say as vertically opposite angles.
Note that A pair of vertically opposite angles are said to be often always equal to one another.
Hence, based on the scenario above, Angles is known to be opposite each other when two lines cross called vertical angles due to the fact that they are opposite each other at a vertex.
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From the sample space S={1,2,3,4,...,15} a single number is to be selected at random. Given the following events, find the indicated probability.
A. the selected number is even
B. the selected number is a multiple of 4.
C. the selected number is a prime number.
P(BIA)
The probabilities of the given events are:
A. P(even) = P(A) = 7/15
B. P(multiple) = P(B) = 3/15
C. P(prime) = 6/15
D. P(B|A) = 3/7
What is probability?Probability is defined as the ratio of the number of favorable outcomes of an event to the total number of possible outcomes.
P(E) = n(E)/n(S)
Calculation:The given sample space is S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
So, n(S) = 15
A. The selected number is even:
Consider the event as A.
The set of even numbers in the given sample is {2,4,6,8,10,12,14}
So, n(A) = 7
Then, the required probability is
P(A) = n(A)/n(S)
= 7/15
B. The selected number is a multiple of 4:
Consider the event as B.
The set of multiples of 4 in the given sample is {4,8,12}
So, n(B) = 3
Then, the required probability is
P(B) = n(B)/n(S)
= 3/15
C. The selected number is prime:
Consider the event as C.
The set of prime numbers in the given sample is {2,3,5,7,11,13}
So, n(C) = 6
Then, the required probability is
P(C) = n(C)/n(S)
= 6/15
D. calculate P(B|A):
Since events B and A are dependent events of the same sample,
n(A∩B) = 3 and the set is {4,8,12}. Then, P(B|A) is
P(B|A) = n(A∩B)/n(A)
⇒ P(B|A) = 3/7
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Please put answer as a mixed number! :)
1 and 3/8* 1.5 + 5 and 5/8 ÷ 0.4 =
Answer: 7 1/16 and 1 9/16
Step-by-step explanation: 1 3/8 x 1.5 is 1 3/8 x 1 5/10 11/8 x 15/10 which is 165/80. We divide it by 5/5 to get 33/16. This as a mixed number is 2 1/16. We add 5 to get 7 1/16.
5/8 divided by 0.4 is 5/8 divided by 2/5. We divide this by first finding the reciprocal of 2/5 which is 5/2. 5/8 x 5/2 = 25/16. This as a mixed number is 1 9/16.
Find the equation of the line that passes through point (6,1) with the x-intercept of 2.
Answer:
y=1/4x-1/2
Step-by-step explanation:
Round 219.371 to the nearest one tenth and hundredths
Answer:
219.4
Step-by-step explanation:
Find the number in the tenth place 3 and look at the one place to the right for rounding digit 7. Round up if this number is greater than or equal to 5 and round down if it is less than 5. So the answer is 219.4
question in image
ddddddddddddddddd
Step-by-step explanation:
"congruent" for lines simply means they are equally long.
15. yes. AB = EF = 3
16. yes. BD = DF = 8
17. no. AC = 5, CD = 6
18. yes. AC = DE = 5
19. no. BE = 13, CF = 14
20. no. CD = 6, DF = 8
Evaluate each expression given the variable. 3x+7, when x=2
Answer:
13
Step-by-step explanation:
3x + 7
x = 2
3 × 2 + 7 = 6 + 7 = 13
Hi there.
3x+7
x=2 :
3(2)+7
6+7
13
That's it.
mrs smith had 46$more than mrs wilson at first mrs wilson spent 4/7 of her money on some clothes and mrs smith spent 3/5 of her on household items after that they had an equal amount of money left find the total amount of money the two ladies spent.
please solve it as soon as posible
Using a system of equations, it is found that the total amount of money the two ladies spent was of $782.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Amount Mrs. Smith had initially.Variable y: Amount Mrs. Wilson had initially.Mrs smith had $46 more than Mr.s Wilson at first, hence:
x = y + 46.
Mrs Wilson spent 4/7 of her money on some clothes and, and Mrs. Smith spent 3/5 of her on household items, then they remained with an equal amount, so:
[tex]\frac{2}{5}x = \frac{3}{7}y[/tex]
Since x = y + 46, we have that:
[tex]\frac{2}{5}(y + 46) = \frac{3}{7}y[/tex]
14(y + 46) = 15y
y = 14 x 46
y = $644
x = 644 + 46 = $690
Hence the amount they spent is given as follows:
[tex]\frac{3}{5}x + \frac{4}{7}y = \frac{3}{5} \times 690 + \frac{4}{7} \times 644 = 782[/tex]
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(-4,2) (5,0) midpoint
Answer:
[tex]M = (0.5, 1)[/tex]
Step-by-step explanation:
The midpoint can be found using the formula: [tex]x, y = (\frac{x_2+x_1}{2}, \frac{y_2 + y_1}{2})[/tex]
So plugging in the values we get: [tex]M = (\frac{-4+5}{2}, \frac{2+0}{2})\\M = (\frac{1}{2}, \frac{2}{2})\\M = (0.5, 1)[/tex]
Answer: [tex]\Large\boxed{Midpoint~=~(\frac{1}{2} ,~1)}[/tex]
Step-by-step explanation:
Given information
(x₁, y₁) = (-4, 2)
(x₂, y₂) = (5, 0)
Given formula for midpoint
[tex]Midpoint~=~(\frac{x_1~+~x_2}{2} ,~\frac{y_1~+~y_2}{2} )[/tex]
Substitute values into the formula
[tex]Midpoint~=~(\frac{-4~+~5}{2} ,~\frac{2~+~0}{2} )[/tex]
Simplify by addition
[tex]Midpoint~=~(\frac{1}{2} ,~\frac{2}{2} )[/tex]
Simplify fractions if necessary
[tex]\Large\boxed{Midpoint~=~(\frac{1}{2} ,~1)}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Please help me quick. I don’t understand please give me the answer
Answer:
m = -2
Step-by-step explanation:
to find the answer you must put rise over run
rise is (y2 - y1) and run is (x2 - x1)
lets use the bottom two points for thisd
y2 is 0 and y1 is 2
x2 is 1 and x1 is 0
0 - 2 = -2
1 - 0 = 1
-2/1 = -2
that is the slope
Please help me this is due Monday!
Answer:
1.
2. Additive Identity
3. Associative Property
4. Multiplication Inverse Property
5. Multiplication Property of 0
6. Commutative Property
7.
8.
Step-by-step explanation:
which description from the list below accurately describe the relationship between QRS and TUV? check all that apply
Triangle QRS was translated to form triangle TUV, hence both triangles have the same shape, same size and are congruent.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Triangle QRS was translated to form triangle TUV, hence both triangles have the same shape, same size and are congruent.
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Answer: All of the above
Step-by-step explanation:
I did the test
Find the surface area of the cone in terms of pie 18 height 12 radius
144π cm²
Answer:
Solution given:
diameter (d)= 12cm
radius (r)=12/2=6 cm
slant height(l)=18cm
Now
Total surface area of cone=πr(r+l)π*6(6+18)=144π cm²
3. What is the measure of angle B from the right triangle below?
Answer:
angle B = 78.46°
Step-by-step explanation:
Use the cosine ratio
[tex]cosB=\frac{2}{10} =0.2[/tex]
[tex]B=cos^{-1} (0.2)=78.46^{0}[/tex]
Hope this helps
(x+ 3/8 ) 2 + y 2 =1
what is the radius & units?
The radius of the circle of the circle equation (x + 3/8)^2 + y^2 = 1 is 1 unit
How to determine the radius of the circle?The circle equation of the graph is given as:
(x + 3/8)^2 + y^2 = 1
The general equation of a circle is represented using the following formula
(x - a)^2 + (y - b)^2 = r^2
Where the center of the circle is represented by the vertex (a, b) and the radius of the circle is represented by r
By comparing the equations (x - a)^2 + (y - b)^2 = r^2 and (x + 3/8)^2 + y^2 = 1, we have the following comparison
(x - a)^2 = (x + 3/8)^2
(y - b)^2 = y^2
1 = r^2
Rewrite the last equation as follows:
r^2= 1
Take the square root of both sides of the equation
√r^2 = √1
Evaluate the square root of 1
√r^2 = 1
Evaluate the square root of r^2
r = 1
Hence, the radius of the circle of the circle equation (x + 3/8)^2 + y^2 = 1 is 1 unit
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I NEED HELP ASAP PLS!!!
Answer:
C looks most correct
Step-by-step explanation:
Given: LM ∥ KN
LP ⊥ KN , KL = MN
KN = 30, LM = 20
m∠KLM=126°
Find: LP
An angle is produced at the point where two or more lines meet. Thus the value of LP required in the question is approximately 14.
Two lines are said to be perpendicular when a measure of the angle between them is a right angle. While parallel lines are lines that do not meet even when extended to infinity.
From the question, let the length of LP be represented by x.
Thus, from the given question, it can be deduced that;
LM ≅ PN = 20
KP = KN - PN
= 30 - 20
KP = 10
LP = x
Also,
<MLP is a right angle, so that;
< KLP = < KLM - <PLM
= 126 - 90
<KLP = [tex]36^{o}[/tex]
So that applying the Pythagoras theorem to triangle KLP, we have;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan 36 = [tex]\frac{10}{x}[/tex]
x = [tex]\frac{10}{Tan 36}[/tex]
= [tex]\frac{10}{0.7265}[/tex]
x = 13.765
Therefore the side LP ≅ 14.
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can someone help me on this question with step by step explaination
and reasoning
Answer: Same
Step-by-step explanation:
Given formula
[tex]Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%[/tex]
Given information
Troop A:
Original (2010) = 14New (2011) = 16Troop B:
Original (2010) = 21New (2011) = 24Substitute values into the formula (Troop A)
[tex]Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%[/tex]
[tex]Percent~of~change~=~\Large\frac{(16)~-~(14)}{(14)}*100\%[/tex]
Simplify the fraction
[tex]Percent~of~change~=~\Large\frac{2}{14}*100\%[/tex]
[tex]Percent~of~change~=~\Large\frac{1}{7}*100\%[/tex]
[tex]Percent~of~change~\approx~14.29\%[/tex]
Substitute values into the formula (Troop B)
[tex]Percent~of~change~=~\Large\frac{New~-~Original}{Original}*100\%[/tex]
[tex]Percent~of~change~=~\Large\frac{(24)~-~(21)}{(21)}*100\%[/tex]
Simplify the fraction
[tex]Percent~of~change~=~\Large\frac{3}{21}*100\%[/tex]
[tex]Percent~of~change~=~\Large\frac{1}{7}*100\%[/tex]
[tex]Percent~of~change~\approx~14.29\%[/tex]
Compare the two percent of change
[tex]Troop~A~v.s.~Troop~B[/tex]
[tex]14.29\%~=~14.29\%[/tex]
Therefore, they are [tex]\Large\boxed{Same}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The answer is same.
Finding the percentage of change for Troop A :
New - Original / Original × 100%
16 - 14 / 14 × 100%1/7 × 100%14.29%Finding the percentage of change for Troop B :
24 - 21 / 21 × 100%1/7 × 100%14.29%Both the troops have the same percent change in membership.
I neeeeed heeeelp please
Answer:
10b/y^2
Step-by-step explanation:
Hope this helps! :)
Rebecca drew a graph with these key features:
The function is decreasing.
The left end is approaching a constant.
Which function could be represented by Rebecca’s graph?
Answer that was correct for me was: f(x) =-2(5/4)^x+3
The function that could be represented by Rebecca’s graph is f(x) =-2(5/4)^x+3
How to determine the function that could be represented by Rebecca’s graph?The properties are given as:
The function is decreasing.The left end is approaching a constant.For an exponential function to keep decreasing, one or more the following must be true:
The rate is less than 1The leading factor is negative and the rate is greater than 1For the left end of an exponential function to approach a constant, the following must be true:
The leading factor is negative and the rate is greater than 1The equation that has the above properties is f(x) =-2(5/4)^x+3
Hence, the function that could be represented by Rebecca’s graph is f(x) =-2(5/4)^x+3
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If s(x) = 2 - x and t(x) = 3x, which value is equivalent to (s•f)(-7)?
Answer:
Step-by-step explanation:
t(-7)= 3(-7)= -21
s(-21)= 2-(-21)= 2 + 21= 23
What is the area of the actual square window
shown in the scale drawing?
Answer:
2.25m²
Step-by-step explanation:
if 1in = 2m then 0.5in = 1m
so 0.75in = 1.5m
area = 1.5 x 1.5
a = 2.25m²
An electrician plans to install solar panels on a rectangular section of roof with an area 180m2. This width of this section of roof is 7 1/5 m across. What is the length of this section of roof?
The length of the rectangular section of the roof is 25 m
Calculating areaFrom the question, we are to determine the length of the section of the roof
From the given information,
The area of the rectangular section = 180 m²
The width of the rectangular section = 7 1/5 m = 7.2 m
Using the formula for area of a rectangle
A = l × w
Where A is the area
l is the length
and w is the width
Then,
180 = l × 7.2
l = 180/7.2
l = 25 m
Hence, the length of the rectangular section of the roof is 25 m
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Answer:
25
Step-by-step explanation:
Just did it on Khan Academy.
