The maximum volume of the cylinder in exact form is; V_max = 2560π/27
How to maximize the volume of a cylinder?Let us define the variables as:
Radius of cone = r
Radius of cylinder = x
Height of Cone = h
Height of Cylinder = y
The general equation for volume of the cylinder is;
V = πx²y
Taking a strip of both figures and relating x, y, r & h as well as using ratios of similar triangles, we have:
Height of triangle above cylinder/Base of Triangle above cylinder = Height of full triangle/Base of full triangle
This gives;
(h - y)/2x = h/2r
Making y the subject gives us;
h – y = hx/r
y = h – hx/r
y = h(1 – x/r)
Plug in y into our Volume equation:
V(x) = πx²h(1 – x/r)
V(x) = πh(x² - x³/r)
To get maximum volume, find the derivative of the volume and solve for when the derivative equals zero:
V'(x) = πh(2x - 3x²/r)
V'(x) = 0
Thus;
(2x - 3x²/r) = 0
x( 2r – 3x) = 0
Thus;
x = 0 or x = 2r/3
Put x = 2r/3 in our volume equation to find V_max
V_max = πh((2r/3)² – (2r/3)³/r)
V_max = πh(4r²/9 - 8r²/27)
V_max = πh(12r²/27 - 8r²/27)
V_max = 4πhr²/27
Thus, at r = 8 and h = 10, we have;
V_max = 4π(10)8²/27
V_max = 2560π/27
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Use the Fundamental Counting Principle to solve.
There are 9 performers who will present their comedy acts this weekend at a comedy club. One of the performers
insists on being the last stand-up comic of the evening. If this performer's request is granted, how many different
ways are there to schedule the appearances?
There are ways to schedule the appearances.
(Simplify your answer.)
GECOD
[tex]number \: of \: performances = 9 \\ note = \\ one \: insists \: on \: being \: last \\ number \: of \: flexible \: performances = 9 - 1 = 8 \\ \\ c( \gamma ) = 8P8 \times 1 \\ c( \gamma ) = 8! \\ c( \gamma ) = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \\ c( \gamma ) = 40320 \: ways[/tex]
Put y-x=-8 of a line into slope-intercept form, simplifying all fractions.
Answer: [tex]y= x-8[/tex]
Step-by-step explanation:
Slope intercept form has a general formula of [tex]y=mx +b[/tex]m represents the slope of the lineb represents the value of the lines y-intercept the equation must be rearranged into the general formula by isolating for 'y'[tex]y-x=-8[/tex]
to remove the x from the left side of the equation the opposite operation must be done to both sides[tex]y-x+x=-8+x[/tex]
the negative and positive x cancel out on the left side, leaving us with the equation with y by itselfnow you can rearrange to put the equation into [tex]y=mx+b[/tex]Final Answer: [tex]y=x-8[/tex]
A. What are the coordinates of R’ if R (-2, 7) is dilated around the origin with k=3?
B. What are the coordinates of T’ if T (4,-1) is dilated by a scale factor of ½ with R as the center of the dilation?
A: The coordinates of the point R' are (- 6, 21).
B: The coordinates of the point T' are (1, 3).
How to generate new points by definition of dilation
In this question we must make use of rigid transformations to find the location of new points, rigid transformations are transformations used in geometric loci such that Euclidean distance is conserved. In this case, we need to use a kind of rigid transformation known as dilation, which is defined below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)] (1)
Where:
O(x, y) - Center of dilationk - Dilation factorP(x, y) - Original pointP'(x, y) - Resulting pointPart A - If we know that O(x, y) = (0, 0), R(x, y) = (- 2, 7) and k = 3, then the coordinates of point R' are:
R'(x, y) = (0, 0) + 3 · [(- 2, 7) - (0, 0)]
R'(x, y) = (- 6, 21)
Part B - If we know that O(x, y) = (- 2, 7), T(x, y) = (4, - 1) and k = 1/2, then the coordinates of point T' are:
T'(x, y) = (- 2, 7) + (1 / 2) · [(4, - 1) - (- 2, 7)]
T'(x, y) = (- 2, 7) + (1 / 2) · (6, - 8)
T'(x, y) = (- 2, 7) + (3, - 4)
T'(x, y) = (1, 3)
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What are the leading coefficient and degree of the polynomial?
2+18u^4+9u-u^8
Leading coefficient:
Degree:
Answer:
-1 and degree 8
Step-by-step explanation:
the highest degree carry the leading coefficient, and the highest power take the highest degree
Find the value of x.
Answer:
x = 106 degrees
Step-by-step explanation:
x + 104 + 40 + 110 = 360
x + 254 (No more 254)
- 254 (Again no more 254)
x = 106
Twelve different video games showing drugs were observed. The duration times of drugs were recorded, with the times (seconds) listed below. Assume that these sample data are used with a 0.01 significance level in a test of the claim that the population mean is greater than 75 sec. If we want to construct a confidence interval to be used for testing that claim, what confidence level should be used for a confidence interval? If the confidence interval is found to be -34.1 sec < μ < 238.3 sec, what should we conclude about the claim?
88 15 537 53 0 52 197 40 182 0 2 59
1.) The confidence level should be _____%
2.) What should we conclude about the claim?
The given confidence interval __(contains / does not contain)___ the value of 75 sec, so there ___( is / is not )___ sufficient evidence to support the claim that the mean is greater than 75 sec.
_____________________________________________
NOTE: Please explain like I'm five. I'm not understanding why the confidence level should be anything but 90% and I don't know *why* we would conclude what we would conclude about this claim.
The answers to the questions are:
1. The confidence level is 99 percent.
2. We have to conclude that there is no sufficient evidence available to support this claim because the Confidence interval contains 75 sec.
How to solve for the confidence level1. The confidence level here should be
1- 0.01 = 0.99
= 99 percent
Given that, 99% confidence interval for population mean (μ) is (-34.1 sec u< u < 264.1 ) seconds.
We are to test the claim that the population mean is greater than 75 sec.
2.
The given confidence interval contains the value of 75 sec, so there is not sufficient evidence to support the claim that the mean is greater than 75 sec.
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Write a polynomial that has a GCF of 7m and another with a GCF of 2ab squared.
The polynomial that has a GCF of 7m is 14mn - 21m + 49m²n + 7mn²
The polynomial that has a GCF of 2ab² is 6a²b² - 8ab³ + 4a³b² + 2a³b³
Writing PolynomialsFrom the question, we are to write a polynomial that has a GCF of 7m
That is,
We are to write a polynomial that has a greatest common factor of 7m
Writing the polynomial
14mn - 21m + 49m²n + 7mn²
The polynomial above has a greatest common factor of 7m. That is, 7m is the greatest factor that can divide each of the terms
We are to write a polynomial with a GCF of 2ab²
Writing the polynomial
6a²b² - 8ab³ + 4a³b² + 2a³b³
The polynomial above has a greatest common factor of 2ab². That is, 2ab² is the greatest factor that can divide each of the terms
Hence,
The polynomial that has a GCF of 7m is 14mn - 21m + 49m²n + 7mn²
The polynomial that has a GCF of 2ab² is 6a²b² - 8ab³ + 4a³b² + 2a³b³
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mary is making a batch of chocolate chip cookies the recipe calls for 9 cups of flour and 2 4/7 cups of sugar she isshort on flour cuts the recipe down to 7 cups if flour how much sugar should she add
Mary added [tex]$24 \frac{1}{2}[/tex] cups of sugar.
How to estimate how much sugar should Mary add?The ratio of flour to sugar exists at 9 cups: 2 4/7 cups
Utilizing equivalent ratios, given that 7 cups of sugar was utilized,
Let cups of flour needed = x such that our equation becomes
flour/sugar[tex]$ =\frac{9}{2\frac{4}{7} }=\frac{x}{7}[/tex]
[tex]$ \frac{9}{2\frac{4}{7} }=\frac{x}{7}[/tex]
Convert mixed numbers into improper fractions
[tex]$2 \frac{4}{7}= \frac{18}{7}[/tex]
simplifying the above equation, we get
[tex]$\frac{9}{\frac{18}{7} } = \frac{x}{7}[/tex]
= [tex]$24 \frac{1}{2}[/tex]
x = 24.5
The value of x = 24.5.
Therefore, [tex]$24 \frac{1}{2}[/tex] cups of sugar exist required.
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Which of the following demonstrates the correct calculation for simple interest?
The statement that demonstrates the correct calculation for simple interest is " A principal balance of $10,000 at 5% interest earns $500 each year as interest.
What is a simple interest?Simple interest is based on the principal amount of a loan or the first deposit in a savings account.
Simple interest does not compound interest on an interval basis. For instance quarterly, semi annually, annually etc. This are carried out in the case of compound interest.
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
Hence base don the explanation above, the statement that demonstrates the correct calculation for simple interest is " A principal balance of $10,000 at 5% interest earns $500 each year as interest.
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(g) Every student of class IV donated as much money as their number to make a fund for landslide, If there are 68 students in class IV how much money did they collect?
Answer:$2346
Step-by-step explanation: Assuming that the students' numbers start at 1, we have 1+2+3+4.....+65+66+67+68 as the total amount of money raised. We can see that 1+68 = 69 and 2+67 also equals 69. So, we can use this method to figure out how many 69s are in the sum. Since 68 divided by 2 is 34, there are 34 69s in the sum. 34x69 = 2346.
Will mark brainliest
A table of values of an increasing function f is shown.
x 10 14 18 22 26 30
f(x)
−14
−8
−1
1
4
7
The upper estimate and lower estimate become R5 = 16 and L5 = −64
According to the statement
we have given that the some values of the increasing function f and we have to find the lower estimate and upper estimate values.
So, For this purpose, we know that the
the values of x is 10 14 18 22 26 30
And the values of f(x) is −14 −8 −1 1 4 7
So,
Δx = 4 because
L5 = 4(−12 − 6 − 2 + 1 + 3) = −64,
And
R5 = 4(−6 − 2 + 1 + 3 + 8) = 16.
And from these functions we see that the
The function being increasing, the Riemann sum with left endpoint L5 = −64 is a lower estimate,
And while the sum with right endpoints R5 = 16 is an upper estimate.
So, The upper estimate and lower estimate become R5 = 16 and L5 = −64
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After descending 8.25 feet, a bird is now
at a height of 16.5 feet. What was the initial
height of the bird?
A farmer finds there is a linear relationship between the number of bean stalks, n , she plants and the yield, y , each plant produces. When she plants 30 stalks, each plant yields 25 oz of beans. When she plants 32 stalks, each plant produces 24 oz of beans. Find a linear relationship in the form y=mn+b that gives the yield when n stalks are planted.
Answer:
y = -1/2n +40
Step-by-step explanation:
We are given two ordered pairs (stalks, ounces) and asked for the slope-intercept form equation of the line through them.
SlopeThe slope of the desired line can be found from the formula ...
m = (y2 -y1)/(x2 -x1)
For the given points (30, 25) and (32, 24), the slope is ...
m = (24 -25)/(32 -30) = -1/2
Y-interceptThe y-intercept of the desired line can be found from the formula ...
b = y -mn
b = 25 -(-1/2)(30) = 25 +15 = 40
Slope-intercept equationThe slope-intercept equation of a line is ...
y = mn +b . . . . . line with slope m and y-intercept b
y = -1/2n +40 . . . . . . line with slope -1/2 and y-intercept 40
The linear relationship between stalks (n) and yield (y) is ...
y = -1/2n +40
Find the ratio of the number of days with no fire incidents to the number of days with more than 5 fire incidents .
Answer:
ratio = 4
Step-by-step explanation:
According to the given table:
• the number of days with no fire incidents
= 16
• the number of days with more than 5 fire incidents
= 2 + 2
= 4
Conclusion :
the ratio of the number of days with no fire incidents
to the number of days with more than 5 fire incidents is :
16 to 4 (16 : 4)
Then
The ratio = 4
a. Based on the picture, what properties can you be sure this figure has? Think about angles, lines, and points.
b. Does ray l bisect ∠ABC? Explain your thinking.
c. What would you need to do to prove that ray l bisects ∠ABC?
The angle measures ABD = 45, DBC = 45 and ABC = 90 imply that ray l bisect ∠ABC?
The properties of the figureFrom the figure, we have the following highlights:
The lines AB and BC are perpendicular lines i.e. the angle at B =90Ray I bisects the angle ABC (because 45 + 45 = 90)Angles ABD and DBC are adjacent anglesThis means that the points ABC can be joined to form a right triangle
Does ray l bisect ∠ABC?Yes, it does.
This is so because it divides the angle ABC into equal segments.
i.e.
ABC = 90
DBC = 45
So, we have
ABD = 90 - 45
ABD = 45
The angle measures ABD = 45, DBC = 45 and ABC = 90 imply that ray l bisect ∠ABC?
What would you need to do to prove that ray l bisects ∠ABC?You would need the measures of ABC and ABD
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1+1-1(2)+1=?
A,0
B,1
C,2
D,3
Answer:
B. 1
Step-by-step explanation:
-1*2 = -2
-2+1 = -1
-1+1 = 0
0+1 = 1
Two jets leave an air base at the same time and travel in opposite directions. One jet travels 80 mi/h faster than the other. If the two jets are 11392 miles apart after 8 hours, what is the rate of each jet
The rate of the slower jet is 672 miles per hour.
The rate of the slower jet is 752 miles per hour.
How to find the rate of the jets?Two jets leave an air base at the same time and travel in opposite directions.
One jet travels 80 mi/h faster than the other.
let
x = rate of the slower jet
faster jet = 80 + x
Therefore,
rate = distance / time
The two jets are 11392 miles apart.
(80 + x)8 + 8x = 11392
640 + 8x + 8x = 11392
640 + 16x = 11392
16x = 11392 - 640
16x = 10752
divide both sides by 16
x = 10752 / 16
x = 672 miles per hour
rate of the faster jet = 80 + 672 = 752 miles per hour
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At the beach, Nardia collected triple the number of seashells that Pierre did. Together, they collected 52 seashells. Which equations represents p, the number of seashells that Pierre collected.
3 p + p = 52
3 + p = 52
52 + p = 3 p
52 + p = 3
Answer:
A
Step-by-step explanation:
p = Pierre shells
Nardia shells = 3p
3p + p = 52
Answer:
a
Step-by-step explanation:
Please help i cant seem to figure this out
Answer:
A
Step-by-step explanation:
First we need to solve the inequality: -3b-15>-24
-3b-15>-24
-3b>-9
b<3 (we divided by a negative so we flip the sign)
This means that we have an empty circle and the arrow pointing left
[tex]\boldsymbol{\sf{-3b-15 > -24 }}[/tex]
Add 15 to both sides.
[tex]\boldsymbol{\sf{-3b > -24+15 \ \longmapsto \ \ \ [Add \ -24+15] }}[/tex]
[tex]\boldsymbol{\sf{ -3b > -9}}[/tex]
Divide both sides by −3. Since −3 is < 0, the inequality direction is changed.
[tex]\boldsymbol{\sf{b < \dfrac{-9}{-3} \ \ \longmapsto \ \ [Split] }}[/tex]
[tex]\red{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ \ b < 3}}}}[/tex]
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Use the graphing tool to find the local minimum and the local maximum for the given function.
Over the interval [-3, -1], the local minimum is
A) -3
B) -2
C) -1
D) 0
Over the interval [-1, 0], the local maximum is
A) -1
B) 0
C) 1.5
D) 4.39
Over the interval [0, 3], the local minimum is
A) -40
B) -32
C) -18
D) 0
The local minimum over the interval [-3,-1] is 0, the local maximum over the interval [-1,0] is 4.39, local minimum over the interval[0,3]is -32.
Given a graph of a function.
We are required to find:
A)Local minimum over the interval [-3,-1],
B) Local maximum over the interval [-1,0],
C) Local minimum over the interval [0,3].
We know that local maximum is a point after which the value of function starts decreasing and the local minimum is a point after which the value of function starts increasing.
When we see the graph from x=-3 to x=-1 we can find that the highest point is where the value of f(x) is minimum and after which the graph is increasing is at x=-2 and y=0, so the value of local minimum will be 0.
When we see the graph from x=-1 to x=0 we can find that the highest point is where the value of f(x) is maximum and after which the graph is decreasing is at y=4.39, so the value of local maximum will be 4.39.
When we see the graph from x=0 to x=3 we can find that the highest point is where the value of f(x) is minimum and after which the graph is increasing is at y=-32, so the value of local minimum will be -32.
Hence the local minimum over the interval [-3,-1] is 0, the local maximum over the interval [-1,0] is 4.39, local minimum over the interval[0,3]is -32.
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What is the equation of the circle that has its center at -26,120 and passed through the origin
well, first off let's check those two points, we know it's centerd at (-26 , 120) and we also know it passes through (0 , 0), so the distance between those two points is its radius
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{-26}~,~\stackrel{y_2}{120})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{(~~-26 - 0~~)^2 + (~~120 - 0~~)^2} \implies r=\sqrt{(-26)^2 + (120 )^2} \\\\\\ r=\sqrt{( -26 )^2 + ( 120 )^2} \implies r=\sqrt{ 676 + 14400 } \implies r=\sqrt{ 15076 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-26}{h}~~,~~\underset{120}{k})}\qquad \stackrel{radius}{\underset{\sqrt{15076}}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-26) ~~ )^2 ~~ + ~~ ( ~~ y-120 ~~ )^2~~ = ~~(\sqrt{15076})^2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (x+26)^2+(y-120)^2 = 15076~\hfill[/tex]
A car traveled at an average speed of 80 km/h for 5 hours. What was
the distance traveled?
Answer:
400 km
Step-by-step explanation:
Distance = rate times time
Distance = 80(5)
Distance = 400
Which one of the following linear inequalities is graphed in the xy plane above
The linear inequality that is graphed in the xy plane is: C. 2x + 3y ≤ 4.
How to Write the Linear Inequality of a Graph?Values in the shaded part are the solution of a a linear inequality. Thus, a dotted or dashed line is used on the graph when the inequality sign is either "<" or ">". On the other hand, when a line that is not dotted or dashed is used when the inequality sign is either "≤" or "≥". These lines, dotted or not are the boundary lines.
Also, when the shaded area is above the boundary line, the sign "≥" or ">" is used. When the shaded part is beneath the boundary line, "≤" or "<" is used in the linear inequality.
The graph given has a boundary line that is not dashed or dotted, and also, the shaded part is beneath the boundary line. Therefore, the inequality sign to use is "≤".
Find the slope:
Slope (m) = rise/run = -4/3 / 2 = -4/6
m = -2/3
y-intercept (b) = 4/3.
Substitute m = -2/3 and b = 4/3 into y ≤ mx + b:
y ≤ -2/3x + 4/3
Rewrite
3y ≤ -2x + 4
2x + 3y ≤ 4
The answer is: C. 2x + 3y ≤ 4.
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How many workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days?
Considering the simple inverse rule of three, 12 workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days.
Inversely proportional relationshipTwo variables are related when a change in one of them causes a change in the other.
Two variables have an inversely proportional relationship when an increase in one variable causes the other to decrease or, analogously, a decrease in one causes the other to increase.
In other words, two magnitudes are inversely proportional when as one increases, the other decreases in the same proportion, and as the first decreases, the second increases in the same proportion.
Simple inverse rule of threeThe simple inverse rule of three is used when the problem deals with two inversely proportional magnitudes where the amount of one of a magnitude corresponding to a given amount of the other magnitude must be calculated.
To carry out an inverse rule of three, it must be taken into account that if for a value A of one magnitude, there is a value B of the other magnitude, while for a value of C of the first magnitude, the second magnitude is will correspond a value of X:
A → B
C → X
So: [tex]X=\frac{AxB}{C}[/tex]
Amount of workers neededThe number of people who perform a task is inversely proportional to the time it takes: a greater number of workers corresponds to less time to perform the task. Then:
9 days → 8 workers
6 days → amount of workers
So:[tex]amount of workers=\frac{9 daysx8 workers}{6 days}[/tex]
amount of workers= 12 workers
Finally, 12 workers will be needed to complete a task in 6 days, given that 8 workers can complete the same task in 9 days.
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Try it
How many true, real number solutions does the equation n + 2 = √-16-5n have?
solution(s)
Answer:
none
Step-by-step explanation:
The domain of the equation can be found by looking at the requirements ...
the square root is non-negativethe argument of the square root is non-negative.DomainFor n+2 ≥ 0, we find ...
n ≥ -2 . . . . . . . . subtract 2 from both sides
For -16-5n ≥ 0, we find ...
-16 ≥ 5n . . . . . add 5n
-3.2 ≥ n . . . . . divide by 5
Together, these domain restrictions require that ...
n ≥ -2
n ≤ -3.2
These intervals do not overlap, so there are no values of n that can satisfy this equation.
__
Additional comment
The solutions would appear on the attached graph as points where the curves intersect above the x-axis. They do not intersect, hence the equation has zero solutions.
__
If we were to solve this without regard to domain restrictions, we would square both sides to get ...
(n +2)² = -16 -5n
n² +9n +20 = 0 . . . . . put in standard form
(n +4)(n +5) = 0 . . . . . factor
n = {-5, -4} . . . . . . . . . both are extraneous solutions.
These "solutions" do not satisfy the requirement that the square root be positive.
Name a line that does not appear to intersect plane L.
Answer:
BE
Step-by-step explanation:
A line and a plane will not intersect if they are parallel. A line is named by naming any two points on it, in any order.
LineThe line containing points B, E, F appears to be parallel to plane L. As such, it will remain at the same distance from plane L throughout its infinite length. The line can be named by 2 points in any of 6 different ways.
Line BE is parallel to plane L.
__
Additional comment
Other names for the same line include ...
BF, EF, EB, FB, FE.
if im taking a 32 hour course and ive completed 73% of it how much time do i have left
Answer:
8.64 hours, so
8 hours, 38 mins, 24 seconds
Just find that 27% you have left, then find how much that 27% is in terms of time.
It might be wrong so double check it please.
Answer:
8.64 hours
which is 8hrs 38mins and 24secs
Step-by-step explanation:
If you've completed 73% then you have 27% left to go still. (100-73 = 27)
27% of 32
= .27×32
= 8.64 hours left
That is 8hrs and .64 of an hour .64×60=38.4 mins
which is 38 mins and .4 of a minute.
.4×60 = 24secs
Probably you will just round this answer.
832 x156 show your work
Answer:
129792
Step-by-step explanation:
156
× 832
----------
312
468
+ 1248
---------------
129792
Rock Solid Bank and Trust (RSB&T) offers only checking accounts. Customers can write checks and use a network of automated teller machines. RSB&T earns revenue by investing the money deposited; currently, it averages 7.00 percent annually on its investments of those deposits. To compete with larger banks, RSB&T pays depositors 0.50 percent on all deposits. A recent study classified the bank’s annual operating costs into four activities.
Activity Cost Driver Cost Driver Volume
Using ATM Number of uses $ 4,200,000 5,600,000 uses
Visiting branch Number of visits 2,520,000 420,000 visits
Processing transaction Number of transactions 18,480,000 224,000,000 transactions
Managing functions Total deposits 16,800,000 $ 1,050,000,000 in deposits
Total overhead $ 42,000,000
Data on two representative customers follow.
Customer A Customer B
ATM uses 100 200
Branch visits 5 20
Number of transactions 40 1,500
Average deposit $ 6,000 $ 6,000
Required:
a. Compute RSB&T's operating profits.
b. Compute the profit from Customer A and Customer B, assuming that customer costs are based only on deposits. Interest costs = 0.50 percent of deposits; operating costs are 4 percent (= $42,000,000/$1,050,000,000) of deposits.
c. Compute the profit from Customer A and Customer B, assuming that customer costs are computed using the information in the activity-based costing analysis.
A) RSB&T's operating profits are 2,625,000.
B) The profit from Customer A = 42 and Customer B=42.
C) The profit from Customer A=77.7 and Customer B=-207.75(loss)
What does mean by profit?Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity outweighs the costs, costs, and taxes incurred to maintain the activity in question.A business's financial gain when revenue exceeds costs and expenses is frequently referred to as profit. One cup of lemonade, for instance, costs a child at a lemonade stand one quarter. She then charges $2 for the beverage. She made $1.75 in profit on the cup of lemonade.All costs are first deducted from sales, and the result is then divided by sales. This creates the profit formula, which is expressed as a percentage. (Sales - Expenses) Sales = Profit is the formula.Data on two representative customers follow.
[A] Compute RSB&T's operating profits.
Computation of Operating Profits:-
Revenue 19,500,000
Interest to Depositors (1,875,000)
Overheads (15,000,000)
Total operating Profit 2,625,000
[B] Costs are based only on Deposits
Particulars A B
Revenue 312 312
Interest Cost -30 -30
Operating Cost -240 -240
Profits 42 42
[C] As per Activity based costing
Particulars A B
Revenue 312 312
Interest Cost -30 -30
ATM Uses -75 -150
Branch Visit -30 -120
Processing Transaction -3.3 -123.75
Managing Function -96 -96
Profits/Loss 77.7 -207.75
Therefore,
A) RSB&T's operating profits are 2,625,000.
B) The profit from Customer A = 42 and Customer B=42.
C) The profit from Customer A=77.7 and Customer B=-207.75(loss)
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The percentage of each transaction contributed to the total transactions in the same Account. Use BASE_EQUIV_AMT as the unit.
The percentage that each transaction contributed to the total transactions in the same account (Cash Account and Service Revenue) is computed as follows:
Cash Account:1. Service Revenue $900 = 8%
2. Owner's Equity, Barbara Hanson $2,200 = 19.8%
3. Accounts Receivable $750 = 6.8%
5. Note Payable $6,000 = 54.1%
6. Unearned Revenue $1,250 = 11.3%
Total cash receipts = $11,100
Service Revenue:1. Cash $900 = 70.6%
4. Accounts Receivable $375 = 29.4%
Total $1,275
How is the percentage computed?The percentage that each transaction contributed to the total transactions in the same account can be computed by taking the dollar value of the transaction over the total value of transactions in the same account and then multiplying by 100.
Percentage values show the degrees of relationship among variables.
The formula for computing percentage in this scenario is transaction value/total transactions value × 100%.
Transaction Analysis:1. Cash $900 Service Revenue $900
2. Cash $2,200 Owner's Equity, Barbara Hanson $2,200
3. Cash $750 Accounts Receivable $750
4. Accounts Receivable $375 Service Revenue $375
5. Cash $6,000 Note Payable $6,000
6. Cash $1,250 Unearned Revenue $1,250
Question Completion:The following transactions occurred during July:
1. Received $900 cash for services provided to a customer during July.
2. Received $2,200 cash investment from Barbara Hanson, the owner of the business.
3. Received $750 from a customer in partial payment of his account receivable, which arose from sales in June.
4. Provided services to a customer on credit, $375.
5. Borrowed $6,000 from the bank by signing a promissory note.
6. Received $1,250 cash from a customer for services to be rendered next year.
Use the transactions to compute the percentage of each transaction relative to the total transactions in the same account.
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