Let's start by calculating the initial concentration of salt in the tank:
4 kg of salt is dissolved in 100 L of water, so the initial concentration of salt in the tank is:
4 kg / 100 L = 0.04 kg/L
We want to increase the concentration of salt in the tank to 0.25 kg/L by adding a salt solution of 0.6 kg/L at a constant rate of 10 L/min.
Let's assume that t is the time in minutes that the faucet has been open. During this time, the volume of water that has been added to the tank is 10t liters.
The amount of salt that has been added to the tank during this time is:
0.6 kg/L x 10 L/min x t min = 6t kg
The total amount of salt in the tank after t minutes is:
4 kg + 6t kg
The total volume of water in the tank after t minutes is:
100 L + 10t L
The concentration of salt in the tank after t minutes is:
(4 kg + 6t kg) / (100 L + 10t L)
We want this concentration to be 0.25 kg/L, so we can set up the following equation:
(4 kg + 6t kg) / (100 L + 10t L) = 0.25 kg/L
Simplifying this equation, we get:
16 kg + 24t kg = 25 L + 2.5t L
21.5t = 9 L
t = 9 L / 21.5 = 0.42 hours = 25.2 minutes (rounded to the nearest minute)
Therefore, you need to close the faucet after approximately 25 minutes to achieve a concentration of 0.25 kg/L in the tank.
a group of students was to clean up to two areas in their school. area a was 1 1 2 times of area b. in the morning (half of a day), the number of students cleaning area a was 3 times that of the number of students in area b. in the afternoon (another half of a day), 7 12 of the students worked in area a while the rest of them in area b. at the end of the day, area a was done, but area b still needed 4 students to work one more day before it was done. how many were there in this group of students?
the total number of students in the group is (5/17)12B. We don't have a specific value for B, so we can't give a specific answer for the number of students,
How to solve the problem?
Let's use the following variables to represent the unknowns in the problem:
Let A be the area of area A
Let B be the area of area B
Let x be the number of students working in area B in the morning
Let 3x be the number of students working in area A in the morning
Let y be the total number of students in the group
From the problem statement, we know that A = 1.5B (since area A is 1.5 times area B). We also know that in the morning, the number of students working in area A is 3 times the number of students working in area B. This can be expressed as:
3x = y/2 (since half of the students work in the morning)
In the afternoon, 7/12 of the students work in area A, so the number of students working in area B is:
(1-7/12)y = 5/12y
At the end of the day, area A is done and area B still needs 4 more students to work for another day. This means that the amount of work done by the students in area B is (y/2 - 3x) + (5/12y - 4B) = B, since the total work needed to be done in area B is B and the amount of work done by the students in area A is y/2 - 3x.
Substituting A = 1.5B and 3x = y/2, we can solve for y:
(y/2 - 3x) + (5/12y - 4B) = B
y/2 - 3(y/2)/3 + 5/12y - 4B = B
y/2 - y/2 + 5/12y = 5B
17/12y = 5B
y = (5/17)12B
Therefore, the total number of students in the group is (5/17)12B. We don't have a specific value for B, so we can't give a specific answer for the number of students, but we can say that the number of students is proportional to the area of area B. If we know the area of area B, we can use the equation above to find the total number of students in the group.
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PLS REPLY FAST NO EXPLAINATION NEEDED
Tony solved the equation below by completing the square, but he got the incorrect solution. In which step did Tony first make an error?
Step 1 : x 2 + 4 x = 77
Step 2 : x 2 + 4 x + 4 = 81
Step 3 : ( x + 2 ) 2 = 81
Step 4 : x + 2 = ± 81
Step 5 : x = 79 , x = − 83
The error made by Tony is in Step 4, where he wrote "x + 2 = ± 81". The correct step should be:
Step 4: Take the square root of both sides to solve for x.
√((x + 2)^2) = √81
In this step, Tony should have taken the square root of both sides, but he made the mistake of only taking the square root of the right-hand side and neglected to take the square root of the left-hand side correctly.
The correct step should be:
x + 2 = ±9
Step 5: Solve for x.
x + 2 = 9 or x + 2 = -9
Step 6: Subtract 2 from both sides to isolate x.
x = 9 - 2 or x = -9 - 2
This will give the correct solutions:
x = 7 or x = -11
So, the error made by Tony occurred in Step 4 where he only took the square root of the right-hand side and neglected to take the square root of the left-hand side correctly.
Hope this helps!
The probability that a certain state will be hit by a major tornado (category F4 or F5) in any single year is
parts (a) through (d) below.
1/20
Complete
(Simplify your answer. Round to five decimal places as needed.)
- What is the probability that the state will be hit by a major tornado in three consecutive years?
(Simplify your answer. Round to five decimal places as needed.)
What is the probability that the state will not be hit by a major tornado in the next ten years?
(Round to three decimal places as needed.)
What is the probability that the state will be hit by a major tornado at least once in the next ten years?
(Round to three decimal places as needed.)
the probability of a major tornado in three consecutive years is 1/8000. the probability of not having a major tornado in the next ten years is approximately 0.328. he probability of having at least one major tornado in the next ten years is approximately 0.672.
How to the probabilities in the question(a) The probability of a major tornado in any single year is 1/20. To find the probability of a major tornado in three consecutive years, we multiply the probabilities together:
P(major tornado in 3 consecutive years) = (1/20) * (1/20) * (1/20) = 1/8000
So the probability of a major tornado in three consecutive years is 1/8000.
(b) The probability of not having a major tornado in any single year is 19/20. To find the probability of not having a major tornado in the next ten years, we raise this probability to the power of 10:
P(no major tornado in next 10 years) = (19/20)^10 ≈ 0.328
So the probability of not having a major tornado in the next ten years is approximately 0.328.
(c) To find the probability of having at least one major tornado in the next ten years, we can subtract the probability of having no major tornadoes in the next ten years from 1:
P(at least one major tornado in next 10 years) = 1 - P(no major tornado in next 10 years)
P(at least one major tornado in next 10 years) = 1 - (19/20)^10 ≈ 0.672
So the probability of having at least one major tornado in the next ten years is approximately 0.672.
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The cost that a recycling company charges is directly proportional to the number of recycling bins collected. The cost is $33 for each bin.
A: Write a direct variation equation to represent the cost.
B: How many bins can a customer pay the company to collect the bins for $500? Write and solve the equation.
C: Suppose the customer plans to tip the recycling company $30, how many bins can the customer get removed for $500 now? Write and solve the equation.
a) The direct variation equation is y = 33x.
b) The customer can pay the company to collect 15 bins.
c) The customer can get approximately 16 bins (rounded to the nearest whole number) removed for $500 with a $30 tip included.
A) The direct variation equation to represent the cost would be y = kx, where y represents the cost, x represents the number of bins collected, and k is the constant of proportionality. In this case, since the cost is $33 for each bin collected, the value of k is 33. Therefore, the direct variation equation is y = 33x.
B) To find the number of bins a customer can pay the company to collect for $500, we can set the cost (y) equal to $500 and solve for x (the number of bins). Thus, we have:
y = 33x
500 = 33x
x = 500/33
x ≈ 15.15
Therefore, the customer can pay the company to collect 15 bins (rounded to the nearest whole number) for $500.
C) If the customer plans to tip the recycling company $30, the total cost would be $500 + $30 = $530. We can set the cost (y) equal to $530 and solve for x:
y = 33x + 30
530 = 33x + 30
500 = 33x
x ≈ 15.91
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Function f has a vertex. Can the function be increasing over its entire domain? Can it be decreasing over its entire domain? Explain.
Choose the correct answer below.
A. A function with a vertex is always increasing if the y-coordinate of the vertex is positive and is always decreasing if the y-coordinate of the vertex is negative.
B. A function with a vertex is constant. So, the function can neither be increasing nor decreasing.
C. A function with a vertex must switch from increasing to decreasing or vice versa at the vertex. So, the function cannot be only increasing or only decreasing over its
entire domain.
D. A function with a vertex can be always increasing as long as the function approaches positive infinity in both directions and can be always decreasing as long as the
function approaches negative infinity in both directions.
A function with a vertex must switch from increasing to decreasing or vice versa at the vertex. So, the function cannot be only increasing or only decreasing over its entire domain.
Given data ,
A function with a vertex, also known as a vertex form of a quadratic function, is a function of the form f(x) = a(x-h)^2 + k, where (h, k) represents the vertex of the parabola. The vertex is the point on the parabola where it changes direction from increasing to decreasing or vice versa.
It is impossible for a function with a vertex to increase continuously if its whole domain shows an increase in the function. Similar to the last example, a function with a vertex cannot decrease throughout its whole domain because that would imply that the function is constantly decreasing.
Hence , a function with a vertex must switch from increasing to decreasing or vice versa at the vertex, and it cannot be only increasing or only decreasing over its entire domain.
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can someone help please it’s due at 12
angle 1 = 180 - 74 the angle on a straight line is given as 180
= 106 degrees
What are alternate angles?Alternate angles are a pair of angles formed by a transversal intersecting two parallel lines. These angles are located on opposite sides of the transversal and on opposite sides of the parallel lines.
The alternate angles are congruent, which means they have the same measure or degree. In other words, if one alternate angle measures x degrees, then its corresponding alternate angle will also measure x degrees.
angle 2 = angle 1
They are vertical angles hence they are equal
angle 3 = 74 degrees
They are vertical angles as well
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I am confused on how to solve the table and find the velocity
Answer:
Step-by-step explanation:
y = 5x^3 - x
Slope of a secant
= (y2 - y1)/(x2-x1) where (x1, y1) and (x2, y2) are the 2 points.
Slope for the interval (1, 2)
= [5(2)^3 - 2)- (5(1)^3 - 1)] / (2-1)
= 34
Slope for interval (1, 1.5)
= [5(1.5)^3 - 1.5)- (5(1)^3 - 1)] / (1.5-1)
= 22.75
In the same way we get the slopes of the intervals:
(1, 1.1):- 15.55
(1, 1,01):- 15.15
(1, 1.001):- 15.015
So the answer is 15.
Given the functions f(x)=1x+2 and g(x)=x2−2x, what is the domain of the composition (f∘g)(x)?
Responses
x≠−2 and x≠0
x is not equal to negative 2, and , x is not equal to 0
x≠0
x is not equal to 0
all real numbers
all real numbers
x≠−2
x is not equal to negative 2
Considering both functions, there are no restrictions or exclusions for any real number values in the domain. Therefore, the domain of the composition (f∘g)(x) is all real numbers.
To determine the domain of the composition (f∘g)(x), we need to consider the domains of both functions f(x) and g(x) and determine any restrictions.
The function f(x) =[tex]1x + 2[/tex] does not have any explicit restrictions on its domain. It is defined for all real numbers.
The function g(x) = [tex]x^2 - 2x[/tex] is a quadratic function. Quadratic functions are defined for all real numbers, so there are no restrictions on the domain of g(x).
When we compose functions, we need to ensure that the output of the inner function is within the domain of the outer function. In this case, the composition (f∘g)(x) means we substitute g(x) into f(x), resulting in f(g(x)).
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Tom and Philip were given the graph of a linear function and asked to find the slope. Tom says that the slope is 12 while Philip says that the slope is 2.
Which reason correctly justifies Tom's answer?
Probability problem pls help me
Where is the question?
What is the solution to the system of equations graphed below?
3
2
68 x
The solution of the system of equations is given by the point of intersection of all the equations that compose the graph.
How to obtain the solution to the system of equations?In this problem, the graph of the system of equations is given, hence we use it to obtain the solution.
The solution of the system of equations is given by the point of intersection of all the equations that compose the graph, that is, the point where all the curves cross each other.
The point of intersection represents the solution of the system of equations as it is the input values for which all the equations have the same output value.
Missing InformationThe problem is incomplete, hence the procedure to obtain the solution of the system of equations from the graph is presented.
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Write an expression in factored form for the polynomial of least possible degree graphed below.
An expression in factored form for the polynomial of least possible degree is y(x) = (x-2)(x+2).
What is polynomial?
Polynomials can be represented in various forms, including standard form, factored form, and expanded form. Standard form is where the polynomial is written with the terms in descending order of degree, with coefficients in front of each term. Factored form is where the polynomial is written as a product of linear factors, and expanded form is where the polynomial is written out in full, with all the terms multiplied together.
A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using addition, subtraction, and multiplication operations. The variables are raised to non-negative integer powers, and the highest power of the variable is called the degree of the polynomial.
For example, the polynomial 2x³ + 3x³ - 4x + 1 has degree 3, as the highest power of x is 3. The coefficients in this polynomial are 2, 3, -4, and 1.
Here, the curve touch two points (-2,0) and (2,0).
So, we can say (-2) and 2 are the root of the polynomial.
We know of a and b are two root of any polynomial then the polynomial will be (x-a)(x-b).
So, the expression is y(x) = (x-2)(x+2).
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A triangle has a base of 12 cm and an area of 18 cm².
Find the height of the triangle:
Height = cm
Answer:
3cm
Step-by-step explanation:
triangle formula is height times base divided by two and divide base by two. then its 6 and divide 6 from 18. so the answer is 3cm
matrix A = 2 -7 matrix B = -9 5
6 1 1 -1
If X - A = B, what is X?
Lisa will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $55 and costs an additional $0.13 per mile driven. The second plan has an initial fee of $48 and costs an additional $0.15 per mile driven.
For what amount of driving do the two plans cost the same?
What is the cost when the two planes cost the same?
Answer:
Step-by-step explanation:
To find the point at which the two plans cost the same, we can set their total costs equal to each other:
55 + 0.13x = 48 + 0.15x
Simplifying and solving for x, we get:
0.02x = 7
x = 350
Therefore, the plans will cost the same when Lisa drives 350 miles.
To find the cost at this point, we can substitute x=350 into either equation. Let's use the first plan:
Total cost = 55 + 0.13(350) = $97.50
Therefore, if Lisa drives 350 miles, the cost for either plan will be $97.50.
The accompanying data represent women's median earnings as a percentage of men's median earnings for recent years beginning with 1989. Is there a trend? How does it appear to affect women? Construct a time-series graph. Median Earnings Year Median Earnings 1989 1990 1991 1992 1993 1994 1995 1996 1997 59.2 60.1 62.3 61.7 62.5 61.7 61.7 65.0 67.0 Year 1998 1999 2000 2001 2002 2003 2004 2005 Median Earnings 65.6 62.9 63.3 61.5 65.2 63.9 66.7 68.8 Full data set 0 www X C. Median Earnings 70- 64- 584 1989 1997 Year 2005 Clear all Final check
Time Series Graph: Plot A
Based on the above plot, earnings first rise till 1997, and then start falling till 2001. After 2001, earnings start rising again. So overall there is an upward trend.
Why is option A the answer?Based on these observations, the answer is Option A, which says:
Option A: There is a general upward trend though there have benn some down years. An upward trend would be helpful to women so that their earnings become equal to those of men.
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Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several models and compare the values of R2.
y = 11.46 e1.107x
y = 0.45x1.903
y = –109.41 + 14.59x
y = –477.38 + 237.66 ln x
The regression equation that fits the scenario will be y = 11.46 e1.107x
How to explain the equationUtilizing this method with the provided information, we attain the regression equation:
ln y = 2.4502 + 0.0515x
It should be noted that to find the exponential equation, we can elevate both sides of the equation:
y = e^(2.4502 + 0.0515x) = 11.46 * e^(1.107x)
Consequently, the mathematical model that is most suitable for the mentioned data is:
y = 11.46 * e^(1.107x)
The coefficient of determination (R-squared) for said model is 0.994, thus indicating an incredibly strong fit.
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answer this please and thank you
Answer:
2800=1.4tons
Step-by-step explanation:
2000Ib=1ton
If JK is tangent to circle L, find x.
x =
(60 POINTs will give BRAINIEST FOR EFFORT)
Answer:
x ≈ 11.87 units-----------------------
Tangent line is perpendicular to radius at the point of tangency.
Hence we have:
MJ ⊥ KJTherefore ΔMKJ is a right triangle.
Radius is 11, so diameter is 22, this is one of legs and its hypotenuse is 25 units.
Use Pythagorean theorem to find the missing leg:
x² = 25² - 22²x² = 141x = √141x ≈ 11.87 units (rounded)If the difference of two numbers is less than the sum of the numbers, which of the following must be true.
F. Neither number is positive
G. At least one of the number is positive
H. Exactly one of the number is positive
J. Both numbers are positive
K. None of these statement must be true
True, option (G) is which is - at least one of the numbers is positive.
Define term positive integer number?A positive integer is a whole number greater than zero, i.e., any number that can be expressed without fractions or decimals, and is greater than zero.
If the difference of two numbers is less than the sum of the numbers, it is always true that at least one of the numbers is positive. As a result, "At least one of the numbers is positive" is the response, which is (G).
Here we assume that x and y are two numbers. The difference between the two numbers is |x - y|, which is always positive.
Now, according to the given condition:
|x - y| < x + y
Simplifying this inequality, we get:
-x + y < x + y
2y > 0
Dividing both sides by 2, we get:
y > 0
Therefore, we can conclude that at least one of the numbers (y) is positive. Note that it is possible for both numbers to be positive or for one number to be positive and the other to be zero.
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trell is working in a lab testing bacteria populations. After starting out with a population of 404 bacteria, he observes the change in population and notices that the The population doubles every 36 minutes. tep 1 of 2: Find the equation for the population P in terms of time t in minutes.
We can actually see here that the equation for the population P in terms of time t in minutes will be: P = 404 × 2^(t/36).
How we arrived at the solution?We can see here that looking at the change in population, we can use the following:
P = P₀ × 2^(t/Δt).
Where:
P₀ = initial population = 404 bacterias
t = time elapsed (in minutes).
Δt = time it takes for the population to double (36 minutes).
Thus, we see that substituting this, we have:
P = 404 × 2^(t/36).
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What is the solution of log(f-3)-log(17-40)?
04
05
O 15
O 20
The solution of the given logarithm function log(f-3)-log(17-40) is
f < 3.
So no option is correct.
What is a logarithm function?A logarithm function is a mathematical function that describes the relationship between a given number (called the argument or input) and a specified base. The logarithm of a number x with respect to a base b is the power to which b must be raised to give x.
In other words, if we have the equation y = log_b(x), then y represents the power to which the base b must be raised to get x. For example, if b=2, then log_2(8) = 3 because 2 raised to the power of 3 equals 8.
According to the given informationThe given expression is:
log(f-3)-log(17-40)
We can simplify this expression using the property of logarithms:
log(a) - log(b) = log(a/b)
So, we get:
log((f-3)/(17-40))
Now, for this expression to have a real solution, the argument of the logarithm must be positive, so we have:
(f-3)/(17-40) > 0
Solving for f, we get:
f - 3 < 0 (since 17-40 is negative)
f < 3
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The sum of two numbers exceeds a third number by four. If the sum of the three numbers is at least 20 and 28,find any three intgral values satisfying the inequality .
Answer:
Let the three numbers be x, y, and z.
We are given that x + y = z + 4.
We are also given that x + y + z >= 20 and x + y + z <= 28.
Combining these two inequalities, we get:
z + 4 + z >= 20
2z >= 16
z >= 8
Since z is an integer, z can be 8, 9, 10, 11, 12, 13, 14, 15, 16, or 17.
For each value of z, we can find the corresponding values of x and y using the equation x + y = z + 4.
For example, if z = 8, then x + y = 12.
So, the three integral values satisfying the inequality are 8, 4, and 0.
Another example is z = 15.
In this case, x + y = 19.
So, the three integral values satisfying the inequality are 15, 2, and 2.
There are many other possible solutions.
Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Enter the correct answer.
DONE
The equation of this graphed line is equal to y = x/2 - 5.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-1 + 5)/(8 - 0)
Slope (m) = 4/8
Slope (m) = 1/2.
At data point (0, -5) and a slope of 1/2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-5) = 1/2(x - 0)
y + 5 = x/2
y = x/2 - 5
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sqrt y^6 where y is greater than or equal to 0
Simplifying the expression √y⁶ for y is y³
Simplifying the expression for yFrom the question, we have the following parameters that can be used in our computation:
sqrt y^6
Rewrite the expression using numbers and mathematical symbol
So, we have
√y⁶
Take the square root of both sides
So, we have
√y⁶ = y³
Hence, the solution to the expression √y⁶ is y³
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Denzel used the spinner shown below to compare theoretical probability and experimental probability. He spun the spinner 180 times and recorded the letter that it landed on each time. The results are shown in the table..
Which statement correctly compares the theoretical probability and experimental probability for one of the letters on the spinner?
A. The theoretical probability of landing on a C is greater than the experimental probability of landing on an C.
B. The theoretical probability of landing on a D is greater than the experimental probability of landing on an D.
C. The theoretical probability of landing on a B is less than the experimental probability of landing on an B.
D. The theoretical probability of landing on an A is less than the experimental probability of landing on an A.
Answer:
C
Step-by-step explanation:
The theoretical probability of landing on A, B, C, or D is all 1/4. This would also mean the theoretical probability is 45/180. Statement C is the only one that is true.
Quadrilateral EFGH is a rhombus which addition fact would prove that EFGH is a square
the answer choices are in the photo below I will give brainlyest to right answer
Option C) EG bisects ZFEH would prove that EFGH is a square.
What is quadrilateral?In geometry, a quadrilateral is a polygon with four sides and four vertices (corners). It is a two-dimensional shape with four straight sides, and the sum of its interior angles is equal to 360 degrees. Some common types of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses. Each type of quadrilateral has its own unique set of properties, such as congruent sides and angles, parallel sides, or perpendicular diagonals. Quadrilaterals are used in many areas of mathematics, as well as in engineering, architecture, and other fields.
Here,
A rhombus has opposite sides congruent, but its angles are not necessarily right angles. However, if the diagonals of a rhombus are perpendicular bisectors of each other, then the rhombus is a square.
If EG bisects ZFEH, then the opposite angles of the rhombus are congruent and the diagonals of the rhombus are perpendicular bisectors of each other. This means that EFGH is a square, and all its sides and angles are congruent.
Options A), B), and D) do not provide any information about the shape of EFGH.
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2.2.3 quiz: angle theorems what is the value of y? OA.50
its c please mark me as a brainliest
Sonic Corporation purchased and installed electronic payment equipment at its drive-in restaurants in San Marcos, TX, at a cost of $37,800. The equipment has an estimated residual value of $2,400. The equipment is expected to process 261,000 payments over its three-year useful life. Per year, expected payment transactions are 62,640, year 1; 143,550, year 2; and 54,810, year 3.
Complete a depreciation schedule for each of the alternative methods.
1. Straight-line.
2. Units-of-production.
3. Double-declining-balance.
Annual depreciation = ($37,800 - $2,400) / 3 years = $11,800 per year
Depreciation per unit = ($37,800 - $2,400) / 261,000 = $0.139 per unit
Depreciation rate = 2 / 3 = 0.667 or 66.7%
Complete a depreciation schedule for each of the alternative methods.Method of the straight line:
Annual depreciation = (Cost - Residual value) / Useful life
Annual depreciation = ($37,800 - $2,400) / 3 years = $11,800 per year
Schedule of depreciation: shown in the below table
Units-of-production method:
Depreciation per unit = (Cost - Residual value) / Total units of production
Depreciation per unit = ($37,800 - $2,400) / 261,000 = $0.139 per unit
Depreciation schedule:
Double-declining-balance method:
Depreciation rate = 2 / Useful life
Depreciation rate = 2 / 3 = 0.667 or 66.7%
Depreciation schedule: shown in the below table
Learn more about the rate here:
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Given that a line has a slope of 1/2 and
its y-intercept is the point (0, 7), write
the equation of the line in slope-
intercept form, y = mx + b.
A. y= (1/2)x
B. 7 = (1/2)x+ 0
C. y= (1/2)x+ 7
D. y= 7x+ ½