The company can expect to earn $5 per product sold if they offer a warranty, compared to an expected loss of $13 per product sold if they do not offer a warranty. It is a profitable decision for the company to offer the warranty.
What is binomial distribution?In a binomial probability distribution, the number of "Successes" in a series of n experiments is represented as either success/yes/true/one (probability p) or failure/no/false/zero (probability q = 1 p), depending on the outcome's boolean value.
Assuming that the failure of the flagship product follows a binomial distribution with a probability of 1% of failure within 2 years of purchase, let's calculate the expected cost to the company without a warranty and with the warranty.
Without the warranty, the expected cost to the company is given by:
Expected cost without warranty = 0.01 x $1300 = $13
With the warranty, the expected cost to the company is given by:
Expected cost with warranty = $5 - (0.99 x $0) = $5
Therefore, the company can expect to earn $5 per product sold if they offer a warranty, compared to an expected loss of $13 per product sold if they do not offer a warranty. It is a profitable decision for the company to offer the warranty.
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Triangle DEF has vertices D(1,1), E(2,0), and F(0,4). It is transformed by a rotation 180 degrees about the origin followed by a dilation with a scale factor of 3. Find the coordinates of the vertices of triangle D”E”F”.
Check the picture below.
ASAP The vertices of a rectangle are plotted in the image shown.
A graph with the x-axis and y-axis labeled and starting at negative 8, with tick marks every one unit up to positive 8. There are four points plotted at negative 4, 4, then 3, 4, then negative 4, negative 3, and at 3, negative 3.
What is the perimeter of the rectangle created by the points?
49 units
56 units
14 units
28 units
The perimeter of the rectangle created by the given points (-4, 4), (3, 4), (-4, -3), and (3, -3) is 28 units. The length of each side is calculated, and the sum of all four sides gives the perimeter. Option D.
To find the perimeter of the rectangle created by the given points, we need to calculate the sum of the lengths of all four sides.
Let's calculate the length of each side:
Side 1: The distance between (-4, 4) and (3, 4) along the x-axis is 3 - (-4) = 7 units.
Side 2: The distance between (-4, 4) and (-4, -3) along the y-axis is 4 - (-3) = 7 units.
Side 3: The distance between (-4, -3) and (3, -3) along the x-axis is 3 - (-4) = 7 units.
Side 4: The distance between (3, -3) and (3, 4) along the y-axis is 4 - (-3) = 7 units.
Now, let's sum up the lengths of all four sides:
Perimeter = Side 1 + Side 2 + Side 3 + Side 4
Perimeter = 7 + 7 + 7 + 7
Perimeter = 28 units
Therefore, the perimeter of the rectangle created by the given points is 28 units. Option D is correct.
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The graph of f(x) = |x| is reflected across the y-axis and translated to the left 5 units. Which statement about the domain and range of each function is correct? Both the domain and range of the transformed function are the same as those of the parent function. Neither the domain nor the range of the transformed function are the same as those of the parent function. The range of the transformed function is the same as the parent function, but the domains of the functions are different. The domain of the transformed function is the same as the parent function, but the ranges of the functions are differe
Both the domain and range of the transformed function are the same as those of the parent function.
What are Range and Domain?
The collection of all potential output values that a function can generate given its domain is known as its range.
The set of all potential input values for which a function is specified is referred to as its domain.
The function that results from translating the left 5 units and reflecting the function f(x) = |x| across the y-axis is g(x) = |-x + 5|.
Since any real number's absolute value is always non-negative, the original function's domain is all real numbers, or f(x) = |x|.
A function's domain remains unaffected when it is reflected across the y-axis. Since all real numbers fall within the domain of the modified function g(x) = |-x + 5|, this is also true.
Since each real number's absolute value is always non-negative, the original function's range is also all non-negative real numbers, f(x) = |x|.
A function's sign is reversed when it is reflected across the y-axis. Since all non-negative real numbers fall within this range, the transformed function g(x) = |-x + 5| also has this range as well
So, the correct statement about the domain and range of each function is: Both the domain and range of the transformed function are the same as those of the parent function.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer: C. 3/(t-1)
Step-by-step explanation:
Answer:
[tex] \dfrac{3}{t - 1} [/tex]
Step-by-step explanation:
[tex] \dfrac{t^2 - 2t - 3}{t^2 - 1} \cdot \dfrac{3t - 3}{t^2 - 4t + 3} = [/tex]
Start by factoring every numerator and denominator.
[tex] = \dfrac{(t - 3)(t + 1)}{(t + 1)(t - 1)} \cdot \dfrac{3(t - 1)}{(t - 3)(t - 1)} [/tex]
Every factor that exists in both a numerator and denominator can be eliminated.
[tex] = \dfrac{1}{t - 1} \cdot \dfrac{3}{1} [/tex]
Multiply numerators together. Multiply denominators together.
[tex] = \dfrac{3}{t - 1} [/tex]
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The evaluations of the given expressions are:
(a) ln e⁻³ = -3
(b) e^(ln 5) = 5
(c) e^(ln √3) = √3
(d) ln (1 / e⁵) = -5
Evaluating an expressionFrom the question, we are to evaluate the given expressions.
The given expressions contain natural logarithm and exponential functions.
The natural logarithm is the inverse of the exponential function.
Thus,
ln eˣ = x
Likewise
e^(ln x) = x
Applying these rules to the given expressions, we get
(a) ln e⁻³ = -3
(b) e^(ln 5) = 5
(c) e^(ln √3) = √3
(d) ln (1 / e⁵)
This can be written as
ln (e⁻⁵) = -5
Thus,
ln (1 / e⁵) = -5
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ATU COVID-19 team of Marshalls has 13 lecturers, 15 students, 10 administrative staff and 12 modicul personnel. An executive committee of 16 is to be formed to strategize for their mode of operations to help contain the vinus on campus. What is the probability of foming this committee, if there should be equal representation on it?
The probability of forming this committee with equal representation is approximately 0.570 or 57.0%.
The total number of individuals in the ATU COVID-19 team of Marshalls is 50 (13+15+10+12). To form an executive committee of 16 with equal representation, we need to choose 4 individuals from each group (4 lecturers, 4 students, 4 administrative staff, and 4 medical personnel).
Using the combination formula, we can calculate the number of ways to choose 4 individuals from each group:
C(13,4) × C(15,4) × C(10,4) × C(12,4) = 715 × 1,455 × 2,385 × 4,095 = 7,976,476,875
Therefore, there are 7,976,476,875 possible ways to form the executive committee with equal representation.
To calculate the probability of forming this committee, we need to divide the number of possible ways by the total number of ways to choose any 16 individuals from the ATU COVID-19 team of Marshalls:
C(50,16) = 13,983,816
The probability of forming the executive committee with equal representation is:
7,976,476,875 / 13,983,816 = 0.570
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|-13.5-(-4 1/5)| times 1.4 plus (-2) to the power of 2
In summary |-13.5 - (-4 1/5)| × 1.4 + (-2)²2 is equal to 17 3/5.
How to solve?
|-13.5 - (-4 1/5)| = |-13.5 + 4 1/5| [Subtracting a negative is equivalent to adding a positive]
= |-9 4/5|
= 9 4/5
Now, we can substitute the values and simplify the expression:
|-13.5 - (-4 1/5)| × 1.4 + (-2)²2
= 9 4/5 × 1.4 + (-2)²2
= 13 3/5 + 4
= 17 3/5
Therefore, |-13.5 - (-4 1/5)| × 1.4 + (-2)²2 is equal to 17 3/5.
An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), connected by an equal sign (=).
For example, the equation 3x + 5 = 14 is an equation that shows that the expression 3x + 5 is equal to the expression 14. This equation can be solved for x to find the value of x that makes the equation true.
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The value of s in the given logarithmic functions is 19683.
What is logarithm equation?
A logarithmic equation is an equation that involves logarithmic functions.
Logarithms are the inverse functions of exponential functions and are used to solve for an unknown variable that appears as an exponent in an exponential equation.
For the given logarithm function, the value of s is calculated by applying the following steps;
log₃s = 9
rewrite the equation in exponential form:
3⁹ = s
3⁹ = 19683
So, the value of s is 19683.
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PLEASE HELP 100 POINTS + BRAINLEST!
Answer: B
Step-by-step explanation:
The external angle is = to the sum of the other 2 angles so <x=125
and <y=55 Because of the supplemental rule.
So answer is B
Write the following as an algebraic expression. Simplify if possible.
Subtract 5x−2 from x−1.
Answer:
The algebraic expression for "Subtract 5x−2 from x−1" is:
(x - 1) - (5x - 2)
Simplifying this expression:
x - 1 - 5x + 2
= -4x + 1
Therefore, the simplified algebraic expression is -4x + 1.
A rectangle has vertices at these coordinates.
(0, 8), (5, 8), (5, 0)
What are the coordinates of the fourth vertex of the rectangle?
Enter the coordinates in the boxes.
Answer:
Step-by-step explanation:
(0,0)
i hope this helps
HELPP!!!Show all work to identify the asymptotes and state the end behavior of the function f of x is equal to 3x divided by the quantity of x minus 9 end quantity.
CAN SOMEONE PLEASEEE HELPP MEEE
What is the area, in square meters, of the shape below?
Answer:
A = 15.87 m²
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 6.9 and h = 4.6 , then
A = [tex]\frac{1}{2}[/tex] × 6.9 × 4.6 = 3.45 × 4.6 = 15.87 m²
Determine whether f(x)=x9+43
and g(x)=9x+12
are inverses. Explain your reasoning.
Answer:
the abswer is D
Step-by-step explanation:
[f○g](x)=(9x+12)/9+8/3=x+8/3
[g○f](x)=9(x/9 + 4/3)+12=x+24
so for the same x they are not inverses
Answer questions based on this graph. Will give brainlest!!!
1.What percent of students got less than a 60% on their math quiz? Round to the nearest whole percent
2.What percent of students got higher than a 70% on their test?Round to the nearest whole percent.
3. How many students scored an 86% or better on their quiz?
4 .?What percentage of students got a 100% on their math quiz? Round to the nearest whole percent?
5. If an 85% score forgot to be added to the graph what would the mean be now? Round to the nearest percent
6. What is the mean of the math pop scores? Round to the nearest percent.
7. What percentage of students scored a 90% on their quiz? Round to the nearest percent
8. What is the range of the math quiz scores?
9. How many students scored better than a 60% on their quiz?
10. What is the median math pop score?
Answer:4
4 What percentage of students got a 100% on their math quiz? Round to the nearest whole percent?
Step-by-stepStep-by-stepStep-by-step explanation: 4 What percentage of students got a 100% on their math quiz? Round to the nearest whole percent?
9207 divided by 4 long division
Answer:
9207 divided by 4 = 2301 with a remainder of 3
Step-by-step explanation:
(check the attached document)
Which of the following is the fourth vertex needed to create a rectangle with vertices located at (−15, 3), (−15, −6), and (25, −6)?
(−6, 25)
(−25, −3)
(6, −25)
(25, 3)
The missing fourth vertex needed to create a rectangle is (25, 3) option D.
Define the term vertices?Vertices (singular: vertex) are the corners or points where two or more lines, edges, or curves intersect and form an angle.
Here, the width of one side of the rectangle;
⇒ +3 - (-6) = 9 unit (left side y-coordinates)
Similarly the length of the rectangle;
⇒ 25 - (-15) = 40 unit (up-side x-coordinates)
Since a rectangular shape has two sets of equal sides of equivalent width (y-coordinates) and length (x-coordinates), we realize that the missing fourth vertex should be 9 units and 40 units over the point (25, -6). and (-15, 3)
So, we add 9 to the y-coordinate of (25, -6) and add 40 to the x-coordinate of (-15, 3) to get the missing vertex:
⇒ (25, -6+9) = (25, 3)
⇒ (-15+40, 3) = (25, 3)
Therefore, the missing fourth vertex is (25, 3)
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Athletes from Seneca nation practice lacrosse every Monday, Wednesday ,and Friday each practice lasts 1 3/4 hours what is the total number of hours the athletes spend at lacrosse practice each week
Upon answering the query Thus, the athletes devote a total of 21/4 equation hours, or 5 1/4 hours, to lacrosse practise each week.
What is equation?An equation in math is an expression that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between each of the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The sign and only one variable are frequently the same. as in, 2x - 4 equals 2, for instance.
On Monday, Wednesday and Friday, the Seneca Nation athletes practise lacrosse for 1 3/4 hours daily.
[tex]1 3/4 hours + 1 3/4 hours + 1 3/4 hours1 3/4 = 7/4\\7/4 + 7/4 + 7/4\\7/4 + 7/4 + 7/4 = (7+7+7)/4 = 21/4\\[/tex]
Thus, the athletes devote a total of 21/4 hours, or 5 1/4 hours, to lacrosse practise each week.
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Tyler invests $9700 in two different accounts. The first account paid 10 %, the second account paid 9 % in interest. At the end of the first year he had earned $931 in interest. How much was in each account?
Tyler invested $5800 in the first account and $3900 in the second account.
What is simple and compound interest?Simple interest is interest that is calculated solely on a loan's or investment's principal amount, without taking into account any interest that has accrued over time. For instance, regardless of how long you keep the money in the account, if you deposit $1,000 in a savings account that offers 5% simple interest annually, you will make $50 in interest each year. Contrarily, compound interest accounts for both the original principal and the interest that has accrued over time. This means that interest is calculated on the new, higher balance after the interest collected during each period is applied to the principal amount.
Let us suppose the amount invested in first account = x.
The amount in second account = y.
Thus, according to the statements we have:
x + y = 9700 (total amount invested is $9700)
0.10x + 0.09y = 931
Now from the first equation we can write:
y = 9700 - x
Substituting the value of y we have:
0.10x + 0.09(9700 - x) = 931
0.10x + 873 - 0.09x = 931
0.01x = 58
x = 5800
Now, substituting the value of x we have:
y = 9700 - 5800
y = 3900
Hence, Tyler invested $5800 in the first account and $3900 in the second account.
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Please help meeeee !!!
The chart shows the number of students who participate in various sports.
A 2-column table with 5 rows. Column 1 is labeled Sport with entries flag football, tennis, dance, basketball, cheer. Column 2 is labeled Number of Students with entries 35, 27, 43, 33, 26.
What is the ratio of students who dance to the total number of students?
StartFraction 43 Over 95 EndFraction
StartFraction 43 Over 121 EndFraction
StartFraction 43 Over 164 EndFraction
StartFraction 43 Over 175 EndFraction
what is the answer to this?
-2/5-(-9/15)
Answer:
1/5
Step-by-step explanation:
-2/5 - (-9/15) make like denominators
-6/15 - (-9/15) negative and negative make positive
-6/15 + 9/15 solve
3/15 simplify
1/5
10PTS pleas help what is the answer
From the given dimensions, it seems like the figure is a trapezoid.Therefore, the surface area of the figure is 300 square feet.
What is surface area?Surface area is the measure of the total area that the surface of an object occupies. It is calculated by adding the area of all the faces or surfaces of the object.
What is trapezoid?A trapezoid is a four-sided geometric shape that has one pair of parallel sides. It is also called a trapezium. The parallel sides are called bases and the non-parallel sides are called legs.
According to the given information:
To calculate the surface area of the figure, we need to split it into smaller shapes and then calculate their individual areas. From the given dimensions, it seems like the figure is a trapezoid.
The formula for the surface area of a trapezoid is (1/2) × (a + b) × h, where a and b are the lengths of the two parallel sides and h is the height.
Using this formula, we can calculate the surface area of the trapezoid:
Surface Area = (1/2) × (15 + 9) × 15 + 2 × 15 × 4
= (1/2) × 24 × 15 + 2 × 15 × 4
= 180 + 120
= 300ft²
Therefore, the surface area of the figure is 300 square feet.
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Price of Airfare
900
800
700
600
500
400
300
200
100
0
0
Distance Traveled vs. Price of Airfare
from NYC
500
1000
Blank 1:
Blank 2:
Blank 3:
Blank 4:
Blank 5:
y = 200+ 0.30x
1500
Distance
Traveled
Word Bank:
200 800 1000 30 y=50+0.30x y=30+0.50x
2000
Consider the data shown on the graph:
The y-intercept represents the base price of $
The slope represents a cost of
cents per mile traveled.
According to the equation given, someone who traveled 2000 miles from NYC
would pay $
for their airfare
2500
According to the equation given, someone who paid $500 for airfaire from NYC
would have traveled
miles.
for airfare from NYC..
If the base cost for airfare changed to $50 and the cost per mile is unchanged, the
new equation would be
Answer:
The completed statements are:
The y-intercept represents the base price of $200.
The slope represents a cost of 30 cents per mile traveled.
According to the equation given, someone who traveled 2000 miles from NYC would pay $800 for their airfare. (y = 200 + 0.30x, where x is the distance traveled in miles)
According to the equation given, someone who paid $500 for airfare from NYC would have traveled 1,000 miles. (500 = 200 + 0.30x, solving for x gives x = 1,000)
If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be y = 50 + 0.30x. (The slope remains the same, while the y-intercept changes to 50.)
Note that the statement "According to the equation given, someone who traveled 2000 miles from NYC would pay $2500 for their airfare" is incorrect. The correct calculation using the given equation y = 200 + 0.30x is:
y = 200 + 0.30(2000) = 800
Therefore, someone who traveled 2000 miles from NYC would pay $800 for their airfare.
Solve for x. 11=3+4x
To solve for x, we need to isolate the variable (x) on one side of the equation. We can do that by first subtracting 3 from both sides of the equation to get:
11 - 3 = 4x
Simplifying the left side gives:
8 = 4x
Finally, dividing both sides by 4 gives:
x = 2
Therefore, the solution to the equation 11=3+4x is x=2.
the solution to the equation [tex]11=3+4x[/tex] 11=3+4x is [tex]x = 2[/tex] X = 2.
The equation [tex]11=3+4x[/tex] 11=3+4x is a linear equation in one variable [tex](x)[/tex](x) with coefficients and constants that are real numbers.
It can be simplified by performing basic algebraic operations, such as isolating the variable term [tex](4x)[/tex] (4x) and solving for the value of [tex]x[/tex] x.
to solve for x in the equation [tex]11=3+4x[/tex] 11=3+4x, we will follow the steps of algebraic manipulation:
First, we will isolate the variable term [tex](4x)[/tex] (4x) by subtracting 3 from both sides of the equation:
[tex]11 - 3 = 4x[/tex] 11 - 3 = 4x
[tex]8 = 4x[/tex] 8 = 4x
Next, we will isolate x by dividing both sides by 4:
[tex]8/4 = x[/tex] 8/4 = x
[tex]2 = x[/tex] 2 = x
Therefore, the solution to the equation [tex]11=3+4x[/tex] 11=3+4x is [tex]x=2[/tex] x=2.
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Find the measure of angle x in the figure below:
35 degrees
47 degrees
51 degrees
62 degrees
Answer:
x= 51°
Step-by-step explanation:
Fist find the measure of angle y.
A straight angle measures 180°
180 - 57 - 61 = 60
y = 62
The sum of the interior angles of a triangle also equals 180
180 - 62 - 67 = 51
x= 51°
Helping in the name of Jesus.
Maricopa's Success scholarship fund receives a gift of $ 95000. The money is invested in stocks, bonds, and CDs. CDs pay 4.75 % interest, bonds pay 4.2 % interest, and stocks pay 11.2 % interest. Maricopa Success invests $ 35000 more in bonds than in CDs. If the annual income from the investments is $ 6845 , how much was invested in each account?
Maricopa Success invested $18,000 in CDs, $32,000 in bonds, and $24,000 in stocks.
What is investment?
Property acquired or invested in to build wealth and save hard-earned income or appreciation is called investment.
Let's start by assigning variables to represent the amounts invested in each type of account:
Let x be the amount invested in CDs.
Let y be the amount invested in bonds.
Let z be the amount invested in stocks.
From the problem statement, we know that:
Here total invested amount is $95,000,
So, we have
[tex]x + y + z = 95,000.[/tex]
The amount invested in bonds is $35,000 more than the amount invested in CDs,
So we have
[tex]y = x + 35,000.[/tex]
The annual income from the investments is $6,845, which we can express as:
0.0475x + 0.042y + 0.112z = 6,845........ (1)
Now we can use the system of equations formed by the three equations above to solve for x, y, and z. First, we can substitute [tex]y = x + 35,000.[/tex] into the equation [tex]x + y + z = 95,000[/tex] to get,
[tex]x + (x + 35,000) + z = 95,000[/tex]
Simplifying this equation, we get:
2x + z = 60,000........ (2)
Next, we can substitute y = x + 35,000 and simplify the equation (1) using equation (2) to get:
[tex]0.0475x + 0.042(x + 35,000) + 0.112z = 6,845[/tex]
Simplifying and rearranging this equation, we get:
0.0895x + 0.112z = 8,545 ..........(3)
Let's use substitution by solving equation (2) for z and substituting into equation (3):
Now, z = 60,000 - 2x
So, 0.0895x + 0.112(60,000 - 2x) = 8,545
Simplifying and solving for x, we get:
x = 18,000
Substituting this value of x into equation (2) to solve for z, we get:
2(18,000) + z = 60,000
z = 24,000
Finally, we can use equation (1) to solve for y:
[tex]0.0475(18,000) + 0.042(y) + 0.112(24,000) = 6,845[/tex]
Simplifying and solving for y, we get:
y = 32,000
Therefore, Maricopa Success invested $18,000 in CDs, $32,000 in bonds, and $24,000 in stocks.
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The management of Ballard MicroBrew is considering the purchase of an automated bottling machine for $74,000. The machine would replace an old piece of equipment that costs $19,000 per year to operate. The new machine would cost $9,000 per year to operate. The old machine currently in use is fully depreciated and could be sold now for a salvage value of $31,000. The new machine would have a useful life of 10 years with no salvage value.
Required:
1. What is the annual depreciation expense associated with the new bottling machine?
2. What is the annual incremental net operating income provided by the new bottling machine?
3. What is the amount of the initial investment associated with this project that should be used for calculating the simple rate of return?
4. What is the simple rate of return on the new bottling machine? (Round your answer to 1 decimal place i.e. 0.123 should be considered as 12.3%.)
1. Depreciation expense = $7,400 per year
2. Incremental net operating income = $10,000 per year
3. The initial investment associated with this project is the cost of the new bottling machine, which is $74,000.
4. The simple rate of return on the new bottling machine is 13.5%.
What is investment?Investment refers to the act of allocating money or resources to acquire an asset or property, with the expectation of generating income, profit, or appreciation in value over time. It involves forgoing the use of funds in the present, in order to potentially receive a greater benefit in the future.
Annual Depreciation Expense:
The new bottling machine would have a useful life of 10 years, and no salvage value. Therefore, the annual depreciation expense associated with the new bottling machine is:
Depreciation expense = (Cost of the machine - Salvage value) / Useful life
Depreciation expense = ($74,000 - $0) / 10 = $7,400 per year
Annual Incremental Net Operating Income:
To calculate the annual incremental net operating income provided by the new bottling machine, we need to compare the annual operating costs of the old machine and the new machine.
Annual operating cost of the old machine = $19,000
Annual operating cost of the new machine = $9,000
Incremental net operating income = Annual operating cost of the old machine - Annual operating cost of the new machine
Incremental net operating income = $19,000 - $9,000 = $10,000 per year
Initial Investment:
The initial investment associated with this project is the cost of the new bottling machine, which is $74,000.
Simple Rate of Return:
The simple rate of return is the ratio of the annual incremental net operating income to the initial investment. We have already calculated the annual incremental net operating income in step 2, and the initial investment in step 3.
Simple rate of return = Annual incremental net operating income / Initial investment
Simple rate of return = $10,000 / $74,000 = 0.1351 or 13.5% (rounded to one decimal place)
Therefore, the simple rate of return on the new bottling machine is 13.5%.
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1. Depreciation expense = $7,400 per year
2. Incremental net operating income = $10,000 per year
3. The initial investment associated with this project is the cost of the new bottling machine, which is $74,000.
4. The simple rate of return on the new bottling machine is 13.5%.
What is investment?
Investment refers to the act of allocating money or resources to acquire an asset or property, with the expectation of generating income, profit, or appreciation in value over time. It involves forgoing the use of funds in the present, in order to potentially receive a greater benefit in the future.
Annual Depreciation Expense:
The new bottling machine would have a useful life of 10 years, and no salvage value. Therefore, the annual depreciation expense associated with the new bottling machine is:
Depreciation expense = (Cost of the machine - Salvage value) / Useful life
Depreciation expense = ($74,000 - $0) / 10 = $7,400 per year
Annual Incremental Net Operating Income:
To calculate the annual incremental net operating income provided by the new bottling machine, we need to compare the annual operating costs of the old machine and the new machine.
Annual operating cost of the old machine = $19,000
Annual operating cost of the new machine = $9,000
Incremental net operating income = Annual operating cost of the old machine - Annual operating cost of the new machine
Incremental net operating income = $19,000 - $9,000 = $10,000 per year
Initial Investment:
The initial investment associated with this project is the cost of the new bottling machine, which is $74,000.
Simple Rate of Return:
The simple rate of return is the ratio of the annual incremental net operating income to the initial investment. We have already calculated the annual incremental net operating income in step 2, and the initial investment in step 3.
Simple rate of return = Annual incremental net operating income / Initial investment
Simple rate of return = $10,000 / $74,000 = 0.1351 or 13.5% (rounded to one decimal place)
Therefore, the simple rate of return on the new bottling machine is 13.5%.
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the length of two sides of a triangle are 5.3 and 0.4. find the length of the third side if it is an integer.
Answer: It is not possible for the length of the third side of a triangle to be an integer when the lengths of the other two sides are not integer.
Step-by-step explanation:
When the other two sides of a triangle are 5.3 and 0.4 in length, the third side cannot possibly have an integer length. This is so because any two sides of a triangle must have lengths that are greater than the length of the third side. In this instance, 5.3 + 0.4 = 5.7, which still falls short of any integer number for the third side's length.
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Answer: 5
Step-by-step explanation:
5.3+0.4=5.7
5.3-0.4=4.9
4.9<x<5.7
The only possible integer between these two numbers is 5, so the correct answer is 5.
