ACCOUNTING
Differential Analysis for a Discontinued Product
A condensed income statement by product line for Lavonia Beverage Inc. indicated the following for Vim Cola for the past year:
Line Item Description Amount
Sales $235,000
Cost of goods sold (111,000)
Gross profit $124,000
Operating expenses (143,000)
Operating loss $(19,000)
It is estimated that 15% of the cost of goods sold represents fixed factory overhead costs and that 20% of the operating expenses are fixed. Because Vim Cola is only one of many products, the fixed costs will not be materially affected if the product is discontinued.
a. Prepare a differential analysis dated November 2 to determine whether Vim Cola should be continued (Alternative 1) or discontinued (Alternative 2). If an amount is zero, enter "0". If required, use a minus sign to indicate a loss.
Answers
Based solely on financial considerations, Vim Cola should be discontinued.
We have,
Differential analysis to determine whether Vim Cola should be continued or discontinued:
Differential Analysis:
Continue vs. Discontinue Vim Cola table is given below.
The differential analysis shows that if Vim Cola is continued (Alternative 1), the company will have sales of $235,000, a cost of goods sold of $111,000, and operating expenses of $143,000.
This will result in a gross profit of $124,000 and an operating loss of $19,000.
If Vim Cola is discontinued (Alternative 2), the company will have no sales or cost of goods sold related to Vim Cola, but will still have $25,000 of fixed operating expenses.
This will result in an operating loss of $25,000.
The difference between the two alternatives is an operating income(loss) of ($6,000).
Since the difference is negative, discontinuing Vim Cola would result in a better financial outcome for the company.
Therefore,
Based solely on financial considerations, Vim Cola should be discontinued.
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Here's a differential analysis for Lavonia Beverage Inc. to decide whether Vim Cola should be continued or discontinued:
Differential Analysis
Alternative 1: Continue Vim Cola
Alternative 2: Discontinue Vim Cola
Sales revenue $235,000 $0
Cost of goods sold:
Variable costs (111,000) 0
Fixed factory overhead costs (16,650) 0
Total cost of goods sold (127,650) 0
Gross profit $107,350 $0
Operating expenses:
Variable expenses (114,400) (28,800)
Fixed expenses (28,600) 0
Total operating expenses (143,000) (28,800)
Operating income (loss) $(35,650) $(28,800)
The analysis shows that if Lavonia Beverage Inc. continues to sell Vim Cola, it will generate sales revenue of $235,000 and incur total variable costs of $111,000.
Additionally, 15% of the cost of goods sold, or $16,650, is fixed factory overhead costs. Total cost of goods sold for Vim Cola is $127,650 ($111,000 + $16,650).
On the other hand, if Vim Cola is discontinued, the company will lose the sales revenue of $235,000 but will also save on the variable and fixed costs associated with the product.
Variable operating expenses are estimated to be 20% of total operating expenses, or $28,800. Fixed operating expenses associated with Vim Cola are estimated to be 20% of total fixed operating expenses, or $28,600.
Thus, based on the analysis, it appears that Vim Cola is generating a loss of $35,650 if it continues to be sold, while discontinued it would result in a loss of $28,800. Therefore, it may be advisable to discontinue Vim Cola.
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Related Questions
1. The law of demand predicts that
a. the more consumers purchase a good, the greater the demand for the good
b. consumers are willing to buy more of a good at a lower price than at a higher price
c. as prices go up, the quantity of a particular good that consumers will buy also rises
d. consumers are willing to buy more of a good at a higher price than at a lower price
2. The function of price in a market system
a. is a way of adjusting the balance between the forces of supply and demand
b. acts as an incentive to producers to either increase or decrease the quantity supplied
c. is a means of rationing the available supply among those who demand it
d. all of these
3. A key advantage of the corporate form of business organization is
a. that the business lives on even if the owners of the business die
b. limited liability of stockholders
c.
the ability to raise significant amounts of financial capital
d.
all of these
Answers
1) consumers are willing to buy more of a good at a lower price than at a higher price Option B
2) All of these
3) All of these
What is the law of demand?An economic theory known as the law of demand states that, all other things being equal, if a good or service's price rises, consumers will demand fewer units of it, and vice versa.
Price and quantity demanded are inversely related, to put it another way. This is a fundamental concept in economics and plays a key role in shaping market behavior and pricing strategies.
The price system is a way of adjusting the balance between the forces of supply and demand. A key advantage of the corporate form of business organization is the ability to raise significant amounts of financial capital.
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(Factorize) p2 + 2p - 8-q2-6q
Answers
Factor of the equation are,
⇒ p (p + 2) - q (q + 6) - 8
We have to given that;
The expression is,
⇒ p² + 2p - 8 - q² - 6q
Now, We can factor as;
⇒ p² + 2p - 8 - q² - 6q
⇒ p (p + 2) - 8 - q (q + 6)
⇒ p (p + 2) - q (q + 6) - 8
Thus, Factor of the equation are,
⇒ p (p + 2) - q (q + 6) - 8
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Which point is collinear to the point (0, 0)? ○ A) (1,0) OB) (3,2) OC) (4,1) OD) (1,3)
Answers
Answer:
A) (1, 0)
Step-by-step explanation:
The point (0, 0) lies on the x-axis and y-axis, so any point that lies on either axis will be collinear to it. Therefore, the answer is A) (1, 0).
Hope this helps!
In a certain video game, players can create environments and populate them with a variety of characters. One player creates a magical park in which the unicorn population triples each day. The starting unicorn population is 5. What will the unicorn population be after the 4th day?
Answers
Using the laws of multiplication, we can find that after the 4th day the unicorn population of the park is 405.
Define multiplication?The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors.
In the question,
Let the unicorn population be = x.
Now as per the question,
It triples every day.
The function will be = 3x.
The starting unicorn population is 5.
After the 1st day it will get tripled and become 3 × 5 = 15.
After the 2nd day the unicorn population will be 3 × 15 = 45.
After the 3rd day, 3 × 45 = 135.
Finally, after the 4th day, the unicorn population will be = 3 × 135 = 405.
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abc is dilated by a scale factor of 4 with a center of dilation at the origin to form a’b’c’ then a’b’c’ is dilated by a scale factor of 3 over 4 with a center of dilation at the origin to create a’’b’’c’’ what are the coordinates of a’’b’’c’’
Answers
The coordinates of the vertices of the triangle A''B''C'' after the two successive dilations are (3 times the x-coordinate and 3 times the y-coordinate of the original triangle's vertices).
To find the coordinates of the vertices of the dilated triangle A''B''C'' after two successive dilations, first with a scale factor of 4 and then with a scale factor of 3/4.
Firstly, Apply the first dilation with a scale factor of 4 to the original triangle ABC, with a center of dilation at the origin. This can be done by multiplying each coordinate of the original triangle by 4.
The coordinates of the dilated triangle A'B'C' after the first dilation would be;
A' = (4 × x-coordinate of A, 4 × y-coordinate of A)
B' = (4 × x-coordinate of B, 4 × y-coordinate of B)
C' = (4 × x-coordinate of C, 4 × y-coordinate of C)
Now, we apply the second dilation with a scale factor of 3/4 to the dilated triangle A'B'C', again with a center of dilation at the origin. This can be done by multiplying each coordinate of A'B'C' by 3/4.
The coordinates of the dilated triangle A''B''C'' after the second dilation would be;
A'' = ((3/4) × x-coordinate of A', (3/4) × y-coordinate of A')
B'' = ((3/4) × x-coordinate of B', (3/4) × y-coordinate of B')
C'' = ((3/4) × x-coordinate of C', (3/4) × y-coordinate of C')
Plugging in the values of A', B', C' obtained from the first dilation, we get;
A'' = ((3/4) × 4 × x-coordinate of A, (3/4) × 4 × y-coordinate of A)
B'' = ((3/4) × 4 × x-coordinate of B, (3/4) × 4 × y-coordinate of B)
C'' = ((3/4) × 4 × x-coordinate of C, (3/4) × 4 × y-coordinate of C)
Simplifying further, we get;
A'' = (3 × x-coordinate of A, 3 × y-coordinate of A)
B'' = (3 × x-coordinate of B, 3 × y-coordinate of B)
C'' = (3 × x-coordinate of C, 3 × y-coordinate of C)
Therefore, the coordinates of the vertices of the triangle A''B''C'' after the two successive dilations are (3 times the x-coordinate and 3 times the y-coordinate.
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Nicole is looking for the best deal on a tablet that regularly costs $749. Help her compare the price of the tablet at a store
with the price on the store's website by completing the following.
(a) The store's website is offering the tablet at a 60% discount off the regular price. Ignoring tax and shipping, how
much would she pay for the tablet on the store's website?
$0
(b) The store is having a sale, offering a 50% discount off the regular price of the tablet. Nicole also has an
in-store-only coupon for an additional 10% off the sale price. Ignoring tax, how much would she pay for the tablet
at the store?
(c)
Check
Select the true statement.
Nicole would pay more for the tablet on the website.
Nicole would pay more for the tablet at the store.
Nicole would pay the same amount at the store and on the website.
Answers
Answer:
a) $299.60
b) $337.05
c) Nicole would pay more at the store
Step-by-step explanation:
a) 10% of $749 = $74.90
60% = ($74.90 x 6) = $449.40
$749 - $449.40 = $299.60
b) 10% = $74.90
50% = $374.50
$749 - $374.50 = $374.50
10% of $374.50 = $37.45
$374.50 - $37.45 = $337.05
Complete the table for the following function y = 3 Superscript x x -3 -2 -1 0 1 2 3 y One-third 1 3 Graph the function and describe what the graph looks like. a. Increases in Quadrant III b. Increases from left to right c. Decreases from left to right d. Decreases in Quadrant II
Answers
The correct answer is to increase from left to right. The correct option is B.
To complete the table for the function [tex]y = 3^x - 3[/tex],
x y
-3 1/27
-2 1/3
-1 0
0 2
1 6
2 18
3 54
To graph the function, we can plot the points from the completed table on a coordinate plane and connect them with a smooth curve.
The graph of the function [tex]y = 3^x - 3[/tex] looks like an exponential function that increases from left to right, passing through the point (0, 2) on the y-axis. The graph is concave up and approaches the x-axis but never touches it.
Therefore, the correct answer is to increase from left to right. The correct option is B.
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Kylie, a youth leader at a summer camp, is making clear slime for an activity with the kids. She is placing the slime in 2-ounce plastic containers with lids. If Kylie can mix up the slime and fill 75 containers in 50 minutes, how long will it take her to make the slime and fill up 450 of the 2-ounce plastic containers?
A. 6 hours
B. 5 hours
C. 4 hours
D. 9 hours
Answers
Therefore, the answer is (B) 5 hours. We can start by finding out how long it takes Kylie to fill one 2-ounce container. we can get by forming equation .
what is equation ?
In mathematics, an equation is a statement that two expressions are equal. An equation can contain variables, constants, and mathematical operations like addition, subtraction, multiplication, division, exponents, and roots.
In the given question,
We can start by finding out how long it takes Kylie to fill one 2-ounce container. To do this, we can set up a proportion:
75 containers / 50 minutes = 1 container / x minutes
Solving for x, we get:
x = (50 minutes) / (75/1) = 0.67 minutes per container
Now we can use this information to find how long it will take Kylie to fill 450 containers:
450 containers × 0.67 minutes per container = 301.5 minutes
So it will take Kylie 301.5 minutes to make the slime and fill up 450 containers. We can convert this to hours by dividing by 60:
301.5 minutes / 60 minutes per hour = 5.025 hours
Rounding to the nearest hour, we get 5 hours.
Therefore, the answer is (B) 5 hours.
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Find the value of x. Assume that segments that appear to be tangent are tangent.
x =
(50 POINTs will give BRAINIEST FOR EFFORT)
Answers
pythagorean theorem:
26^2 + 9^2 = 757
square root of 27.514
Give a recursive defintition for the following set or ordered pairs of positive integers (a|b means that a is a factor of b): [tex]S =[/tex]{[tex](a,b)|a[/tex]∈[tex]Z^+, b[/tex]∈[tex]Z^+, a + b[/tex] is odd}
Answers
[tex](2,1)[/tex], [tex](1,2)[/tex] is your base step
if [tex](a,b)[/tex] is in the set [tex](a+1,b+1)[/tex] will be in the set
if [tex](a,b)[/tex] is in the set [tex](a+2,b)[/tex] will be in the set
if [tex](a,b)[/tex] is in the set [tex](a,b+2)[/tex] will be in the set.
Think about how to solve this problem in general. How can you assure that the sum [tex]a+b[/tex] is odd?
Think about this, what happens when you sum two even numbers? The result is even or odd?
[tex]2+6 = 8 \ \text{(even)}[/tex]
[tex]10+12 = 22 \ \text{(even)}[/tex]
And what happens when you sum two odd numbers ? The result will be even or odd? Look
[tex]3+7 = 10 \ \text{(even)}[/tex]
[tex]5+11 = 16 \ \text{(even)}[/tex]
Therefore to assure that [tex]a+b[/tex] is odd, one of them has to be odd and one of them has to be even, that is why
[tex](2,1)[/tex], [tex](1,2)[/tex] is your base step
if [tex](a,b)[/tex] is in the set [tex](a+1,b+1)[/tex] will be in the set
if [tex](a,b)[/tex] is in the set [tex](a+2,b)[/tex] will be in the set
if [tex](a,b)[/tex] is in the set [tex](a,b+2)[/tex] will be in the set.
I need help understanding tree diagrams
Answers
The probability that she will hire a woman for the two positions is given as follows:
1/4.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
From the last node, the total number of outcomes is given as follows:
4.
The desired outcomes are Women on the first node and women on the second node, which is one outcome. (the last outcome).
Hence the probability is given as follows:
p = 1/4.
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The tolerance for a ball bearing is 0.01. if the true diameter of the bearing is be 2.0 inches and the measured value of the diameter is x inches, express the tolerance using absolute value notation.
Answers
The value of the absolute difference can be expressed as | x - 2 | ≤ 0.01.
What is the expression of the tolerance?
The tolerance for the ball bearing is given as 0.01 inches.
Let x = measured value of the diameter in inches
The absolute difference between x and the true diameter of 2 inches of the ball bearing must be less than or equal to the tolerance of 0.01 inches.
The value of the absolute difference can be expressed using absolute value notation as follows;
| x - 2 | ≤ 0.01
Thus, the inequality above, express the absolute value of the difference between x and 2, which is less than and equal to 0.01.
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HELP FAST
What is the volume of the rectangular prism?
A rectangular prism with a length of 7 meters, a width of 4 meters, and a height of 3 meters.
19 m3
25 m3
31 m3
84 m3
Answers
The volume is D) 84[tex]m^3[/tex].
What is volume?
The space taken up by any three-dimensional solid constitutes a volume, to put it simply. A cube, cuboid, cone, cylinder, or sphere can be one of these solids. Cubic units are used to measure the volume of solids. The volume will be given in cubic metres, for instance, if the dimensions are given in metres.
Here the given rectangular prism length = 7m , Width = 4m and Height = 3m.
Now using Volume of rectangular prism formula then,
V = lwh cubic unit.
=> V = 7×4×3
=> V = 84[tex]m^3[/tex]
Hence the volume is D) 84[tex]m^3[/tex].
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How do you write 9.6522 as a percentage
Answers
Answer:
965.22%
Step-by-step explanation:
To write 9.6522 as a percentage, we can multiply it by 100 and add the percent symbol (%):
9.6522 * 100% = 965.22%
Therefore, 9.6522 is equal to 965.22% as a percentage.
Hope this helps!
Answer:
Step-by-step explanation:
41.67 is the answer brainlist and verifed answer
HELP DOING CORRECTIONS DUE IN A HOUR GIVING BRAINLIEST AND 20 POINTS
Answers
x = 12 times square root 2 (45 45 90 triangle)
y = 6 times square root 2 (30 60 90 triangle)
A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer choices – a, b, c, d, e – and only one correct answer. What is the probability that she answered both of the problems correctly? Write your answer as a fraction in simplest form
Answers
The probability that the student, who ran out of time on a multiple choice exam and randomly guessed the answers for two problems, answered both of the problems correctly is ⁹/₂₅.
What is the probability?Probability refers to the likelihood of an expected outcome occurring out of many possible outcomes.
Probability is computed as the quotient of expected outcome over total outcomes.
The number of questions left = 2
The number options of for each question = 5
Since there are 5 options for each question, 4 of which are wrong, the probability of getting both wrongs is:
⁴/₅ x ⁴/₅ = ¹⁶/₂₅ = 0.64 or 64%
Therefore, probability of getting both questions correct is 36% (1 - 64%) or ⁹/₂₅ (1 - ¹⁶/₂₅).
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The number of bacteria P(h) in a certain population increases according to the following function, where time h is measured in hours.
P(h)=2800e^0.09h
How many hours will it take for the number of bacteria to reach 3500?
Round your answer to the nearest tenth, and do not round any intermediate computations.
Answers
It will take 2.48 hours for the number of bacteria to reach 3500.
How many hours to reach 3500?In order to find number of hours to take for the number of bacteria to reach 3500, we can set the function equal to 3500 and solve for h.
The function given is P(h) = 2800e^(0.09h). So, plugging the values of 3500, we will get:
3500 = 2800e^(0.09h)
Dividing both sides by 2800, we get:
e^(0.09h) = 3500/2800
Taking the natural logarithm of both sides, we get:
0.09h = ln(3500/2800)
h = (ln(3500/2800))/0.09
h = 0.22314355131/0.09
h = 2.47937279233
h = 2.48 hours
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the box plots show the target heart rates of men 20-40 years old and men 50-70 years old. which statement is best supported by the information in the box plots.
Answers
The statement that best supports the information in the box plots is: D. the interquartile range value of the data for men 20 - 40 years old is greater than that of men of 50 - 70 years old.
How to Find the Interquartile Range from a Box Plot?The interquartile range of a data set is the difference between the values that are located on both edges of the rectangular box that is displayed in a box plot.
Interquartile range for the men between 20 - 40 years old = 150 - 110 = 40
Interquartile range for the men between 50 - 70 years old = 125 - 95 = 30
This shows that, D. the interquartile range value of the data for men 20 - 40 years old is greater than that of men of 50 - 70 years old.
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The mean absolute deviation of Mr. Zimmerman's class is 0.46. What does this mean?
Answers
Answer:
is a measure of the average absolute distance between each data value and the mean of a data set.
Solve and reduce the result to lowest fr
not a decimal.
4
3
+ +2- +5-
5 10
Answer:
58
II
미ㄷ
VŨ Vũ (D)
(89)
Answers
Answer:
8[tex]\frac{29}{40}[/tex]
Step-by-step explanation:
The least common multiply is 40
[tex]\frac{4}{5}[/tex] x [tex]\frac{8}{8}[/tex] = [tex]\frac{32}{40}[/tex]
2 [tex]\frac{3}{10}[/tex] x [tex]\frac{4}{4}[/tex] = 2 [tex]\frac{12}{40}[/tex]
5 [tex]\frac{5}{8}[/tex] x [tex]\frac{5}{5}[/tex] = 5 [tex]\frac{25}{40}[/tex]
Now that we have a common denominator, add these numbers together
[tex]\frac{32}{40}[/tex] + 2 [tex]\frac{12}{40}[/tex] + 5 [tex]\frac{25}{40}[/tex]
7 [tex]\frac{69}{40}[/tex]
7 + [tex]\frac{40}{40}[/tex] + [tex]\frac{29}{40}[/tex] I broke up [tex]\frac{69}{40}[/tex] because I know that [tex]\frac{40}{40}[/tex] equals 1
8 [tex]\frac{29}{40}[/tex]
Helping in the name of Jesus.
When abraham was born his parents put 2000 into an account that yielded 1.2%
Answers
When abraham was born his parents put 2000 into an account that yielded 1.2%, Abram will receive $2,213.10 on his 16th birthday.
To calculate how much Abram will receive on his 16th birthday, we need to use the compound interest formula:
A = [tex]P(1 + r/n)^{(nt)[/tex]
Where:
A = the amount Abram will receive
P = the principal amount (initial investment) = $2,000
r = the annual interest rate = 1.2% = 0.012
n = the number of times the interest is compounded per year = 2 (semi-annually)
t = the number of years = 16/2 = 8 (since interest is compounded twice a year)
Plugging in the values, we get:
A = $2,000(1 + 0.012/2)¹⁶
A = $2,000(1.006)¹⁶
A = $2,000(1.10655)
A = $2,213.10
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Complete question is:
When Abram was born, his parents put $2,000 into an account that yielded 1.2% interest, compounded semi-annually. When he turns age 16, his parents will give him the money to buy a car. How much will Abram receive on his 16th birthday?
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answers
The answers are A = 46% and B = 20%.
Given that, a table of data, each cell in the table shows the number of cars in that category.
A) The probability that the car's total repair cost is less than $10000 =
86 / (86+35+67) x 100 = 86/188 x 100 = 46%
B) The probability that the car's purchase was more than $40,000 =
40 / (40+86+71) x 100 = 40/197 x 100 = 20%
Hence, the answers are A = 46% and B = 20%.
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Barb is saving money to buy a house in ten years. This is an example of a(n) goal. O A. medium-term OB. short-term OC. unrealistic O D. long-term
Answers
Answer: long term
Step-by-step explanation: I got it right on the test
If one flyer is 3.0 × 10-3 inches thick, how thick is a stack of 1.25 × 103 flyers
Answers
If one flyer is 3.0 × 10⁻³ inches thick, the stack of 1.25 × 10³ flyers has a thickness of 3.75 inches.
To find the thickness of a stack of flyers, we need to multiply the thickness of a single flyer by the number of flyers in the stack. In this case, the thickness of a single flyer is given as 3.0 × 10⁻³ inches, and the number of flyers in the stack is 1.25 × 10³.
So, the thickness of the stack can be calculated as:
Thickness of stack = Thickness of a single flyer x Number of flyers in the stack
Thickness of stack = 3.0 × 10⁻³ inches x 1.25 × 10³
Thickness of stack = (3.0 x 1.25) × (10⁻³ × 10³) inches
Thickness of stack = 3.75 inches
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Calculate for the percentages. Show your solutions.
100% of 30
40% of 60
20% of 80
40% of 50
80% of 20
50% of 30
60% of 80
60% of 10
90% of 70
90% of 60
help please. thank youu!!
Answers
Percentage = (Part/Whole) x 100
Where "Part" is the value we are trying to find the percentage of and "Whole" is the total value.
Let's use this formula to solve the given problems:
1. 100% of 30
Percentage = (Part/Whole) x 100
Percentage = (30/30) x 100
Percentage = 100%
Therefore, 100% of 30 is 30.
2. 40% of 60
Percentage = (Part/Whole) x 100
Percentage = (40/100) x 60
Percentage = 24
Therefore, 40% of 60 is 24.
3. 20% of 80
Percentage = (Part/Whole) x 100
Percentage = (20/100) x 80
Percentage = 16
Therefore, 20% of 80 is 16.
4. 40% of 50
Percentage = (Part/Whole) x 100
Percentage = (40/100) x 50
Percentage = 20
Therefore, 40% of 50 is 20.
5. 80% of 20
Percentage = (Part/Whole) x 100
Percentage = (80/100) x 20
Percentage = 16
Therefore, 80% of 20 is 16.
6. 50% of 30
Percentage = (Part/Whole) x 100
Percentage = (50/100) x 30
Percentage = 15
Therefore, 50% of 30 is 15.
7. 60% of 80
Percentage = (Part/Whole) x 100
Percentage = (60/100) x 80
Percentage = 48
Therefore, 60% of 80 is 48.
8. 60% of 10
Percentage = (Part/Whole) x 100
Percentage = (60/100) x 10
Percentage = 6
Therefore, 60% of 10 is 6.
9. 90% of 70
Percentage = (Part/Whole) x 100
Percentage = (90/100) x 70
Percentage = 63
Therefore, 90% of 70 is 63.
10. 90% of 60
Percentage = (Part/Whole) x 100
Percentage = (90/100) x 60
Percentage = 54
Therefore, 90% of 60 is 54.
Sure, I'd be happy to help you calculate these percentages! Here are the solutions:
- 100% of 30 = 30
- 40% of 60 = 0.4 x 60 = 24
- 20% of 80 = 0.2 x 80 = 16
- 40% of 50 = 0.4 x 50 = 20
- 80% of 20 = 0.8 x 20 = 16
- 50% of 30 = 0.5 x 30 = 15
- 60% of 80 = 0.6 x 80 = 48
- 60% of 10 = 0.6 x 10 = 6
- 90% of 70 = 0.9 x 70 = 63
I hope that helps! Let me know if you have any other questions.
Exercise 1.4
A. Mark the periods with commas according to the two place value systems and write the numbers in words in each system.
1. 2365358 2. 34282627 4. 90150028 5. 81552101 3. 87013569 6. 99160001
Answers
Step-by-step explanation:
2,36,53,58
Two place value system:
Twenty-three lakh, sixty-five thousand, three hundred and fifty-eight
Three place value system:
Two crore, thirty-six lakh, fifty-three thousand, three hundred and fifty-eight
3,42,82,627
Two place value system:
Thirty-four million, twenty-eight thousand, six hundred and twenty-seven
Three place value system:
Three crore, forty-two lakh, eighty-two thousand, six hundred and twenty-seven
8,70,13,569
Two place value system:
Eighty-seven million, thirteen thousand, five hundred and sixty-nine
Three place value system:
Eight crore, seventy-one lakh, thirty-five thousand, five hundred and sixty-nine
9,01,50,028
Two place value system:
Ninety million, one lakh, fifty thousand, twenty-eight
Three place value system:
Nine crore, one lakh, fifty thousand, twenty-eight
8,15,52,101
Two place value system:
Eighty-one million, five hundred and fifty-two thousand, one hundred and one
Three place value system:
Eight crore, fifteen lakh, fifty-two thousand, one hundred and one
9,91,60,001
Two place value system:
Ninety-nine million, one lakh, sixty thousand, one
Three place value system:
Nine crore, ninety-one lakh, sixty thousand, one
Choose any dataset (from any online resource). Describe any variable on the dataset where you can apply CLT for mean and CLT for proportions.
Answers
Here is a possible dataset with variables for which the central limit theorem could be applied:
A dataset of customer spending at different retail stores.
Variable for which CLT for mean could be applied:
Average monthly spending per customer. As the number of customers at each store increases, the sample mean spending will approach a normal distribution.
Variable for which CLT for proportions could be applied:
Proportion of customers who spend over $200 per month. Even with a small number of customers at each store, the proportion will be approximately normally distributed as the sample size increases due to the CLT for proportions.
The central limit theorem states that the sampling distribution of the sample mean and sample proportion will be normally distributed for large sample sizes, regardless of the original distribution. So these variables from the retail dataset would satisfy that condition. Please let me know if you would like any clarification or have a different dataset in mind. I can provide additional examples.
For CLT for mean:
We can take random samples of age from the dataset and calculate the mean age of each sample. If we repeat this process many times, the distribution of sample means will tend towards a normal distribution, as long as the sample size is large enough. This is because the mean age of the population is likely to be normally distributed, and as we take more samples, the sample means will become more and more representative of the population mean.
For CLT for proportions:
We can look at the proportion of passengers who survived (the "Survived" variable) within different age groups. If we take random samples of passengers from the dataset, we can calculate the proportion of survivors in each sample for each age group. If we repeat this process many times, the distribution of sample proportions will tend towards a normal distribution, as long as the sample size is large enough. This is because the proportion of survivors in the population is likely to be normally distributed, and as we take more samples, the sample proportions will become more and more representative of the population proportion.
Si al 15% del 20% de 5N le agregamos el 30% del 50% de 2N obtenemos 270. Calcula N.
Answers
The value of N in the algebraic equation is 600.
How to calculate N in the algebraic equation?An algebraic equation is when two expressions are set equal to each other, and at least one variable is included.
If to 15% of 20% of 5N we add 30% of 50% of 2N we get 270. We have:
(15/100 * 20/100 * 5N) + (30/100 * 50/100 * 2N) = 270
0.15N + 0.3N = 270
0.45N = 270
N = 270/0.45
N = 600
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Question in English
If to 15% of 20% of 5N we add 30% of 50% of 2N we get 270. Calculate N.
What is the range of the function y=e^4x?
O Y <0
O Y > O
O y <4
O y>4
Answers
The range of the function y=e⁴ˣ is y>0
The range of the function y=e⁴ˣ is the same as the range of any exponential function:
y > 0
The function can take on any positive value, but will never be 0 or negative.
It has a horizontal asymptote of y=0.
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The equation of the line is
Answers
Answer:
y = -x +3
Step-by-step explanation:
You want the slope-intercept equation of the line with the same intercept as -3y = -9 +3x, and the same slope as -2x -2y = -8.
Slope-intercept formThe slope-intercept form of the equation of a line is ...
y = mx +b . . . . . where m is the slope, and b is the y-intercept
For the given equations, we can put them in this form to find the desired parameters.
-3y = -9 +3x
y = -x +3 . . . . . . . . . . divide both sides by -3
We observe that the y-intercept is +3, which we will need for our answer.
The slope-intercept form of the second equation is ...
-2x -2y = -8
x + y = 4 . . . . . . . . . . divide by -2
y = -x +4 . . . . . . . . . . subtract x
We observe that the slope (coefficient of x) is -1, which we will need for our answer.
Desired equationWe want the equation of the line with slope -1 and y-intercept 3. It is ...
y = -x +3 . . . . . . . . . . same as the equation of the first line
__
Additional comment
The slope-intercept equation (green) is plotted using dots, so that you can see it is coincident with the line described by the first equation (red). Parallel lines have the same slope, so our desired line must be parallel to the blue line. (It is.)