1. The Cost of Ending Inventory and the Cost of Goods Sold under LIFO, FIFO, and Weighted-Average, are as follows:
LIFO FIFO Weighted-Average
Ending inventory $425 $691 $573
Cost of goods sold $492 $226 $344
How do the inventory methods differ?FIFO (First-in, First-out) assumes that the physical flow of goods sold follows the chronological order of acquisition.
LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.
The weighted-average method uses the average cost of goods to compute the ending inventory and the cost of goods sold.
LIFO:
Ending inventory = $425 ($917 - $492)
Cost of goods sold = $492 (12 x $20 + 12 x $21)
FIFO:
Ending inventory = $691 (9 x $11 + 17 x $20 + 12 x $21)
Cost of goods sold = $226 ($917 - $691)
Weighted Average:
Ending inventory = $573 (40 x $14.33)
Cost of goods sold = $344 (24 x $14.33)
Inventory Table:Units Unit Cost Total Cost
Jan. 1 Beg. Inventory 20 $8.00 $160
May 10 Purchases 15 $11.00 $165
June 30 Purchases 17 $20.00 $340
Dec. 10 Purchases 12 $21.00 $252
Total 64 $917
Units sold 24
Ending inventory 40 (64 - 24)
Average cost = $14.33 ($917/64)
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Write the equation of the line in fully simplified slope-intercept form.
Answer: y = -x - 8
Step-by-step explanation:
Slope-intercept form is given in y = mx + b where m is the slope and b is the y-intercept.
We can see our b, the y-intercept, is -8 since the line intercepts the y-axis at (0, -8).
For our slope, we can see that the line moves down one and right one for a slope of 1/1=1. Since it's moving downwards, the slope is -1.
Now, we will write the full equation:
y = -x - 8
tan(tan^-1x)=x where?
Tan of arc tan x is equal to x when the angle x is 0 degrees
What is tan as used in math?Tangent is the ratio of the side opposite the angle we know or want to know over the side adjacent to that angle, and is sometimes abbreviated as tan.
In a right angle triangle, the formula for tan is as below
Tangent (tan) = opposite / adjacent
Arc tan (tan^(-1)) is the inverse of tan = adjacent / opposite
Arc tan is equal to tan when the angel is zero degree
therefore, tan (tan^(-1) x) = x
when x = 0
tan^(-1) 0 = 0
tan 0 = 0
tan (tan^(-1) 0)
tan (0)
0
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complete question
At what point does tan(tan^-1(x))=x
Given f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity, which of the following is true?
f(x) is decreasing for all x < 6
f(x) is increasing for all x > 6
f(x) is decreasing for all x < 3
f(x) is increasing for all x < 3
The correct statement of the expression (x + 6) / ( x² - 9x + 18 ) is f(x) is increasing for all x > 6
How to determine the correct statementInformation given in the question
f of x is equal to the quantity x plus 6 end quantity divided by the quantity x squared minus 9x plus 18 end quantity
This is written as (x + 6) / ( x² - 9x + 18 )
factorizing the denominator gives
(x + 6) / {( x - 6)( x - 3)}
In the denominator
At x = 6 and at x = 3 the equation will result to infinity which is a very high value. hence:
f(x) is decreasing for all x < 6: contains x = 3 and result to a higher value
f(x) is decreasing for all x < 3: will result to negative numbers which will end up increasing
f(x) is increasing for all x < 3: contains values which will be decreasing like x = 4
Therefore the correct option is f(x) is increasing for all x > 6
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Simplfy and solve 13+7x66
assume that the box confains 11 balls: 5 red, 3 blues, and 3 yellow. as in the text, you draw one ball, note its color, and if its yellow rrplace it. if it is not yellow you do not replace it. you then draw a second ball and note its color
The probability that the second ball drawn is yellow is of:
0.2926 = 29.26%.
What is a probability?The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
In this problem, the possible outcomes to obtain a yellow ball on the second draw are:
Yellow (3/11 probability) then yellow (3/11 probability). -> yellow on the first is replaced.Non-yellow (8/11 probability) then yellow (3/10 probability) -> non yellow on the first is not replaced.Then the probability of an yellow ball on the second draw is given as follows:
p = (3/11) x (3/11) + (8/11) x (3/10) = 0.2926 = 29.26%.
Missing InformationThe problem asks for the probability that the second ball drawn is yellow.
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HELP!! WILL MARK BRAINLIEST!!
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer:
1/4
Step-by-step explanation:
rise/run you can count it but it doesn't always work
If you want to know the mathematical way of doing it it's:
m(slope) = y2-y1/x2-x1 Choose any two points I chose (-4,5) & (0,6)
m = 6-5/0-(-4) Then subtract 6 - 5 and 0-(-4)
m = 1/4
janet and andy bowled three games. Janets scores were 119, 96, and 145. Andys scores were 127, 74, and 88. How much greater was janets total score for the three games that andys total score
Answer:
64
Step-by-step explanation:
119+89+145=353-289=127+74+88
^
64
For the equation (x) = –3x2 + 2x – 1, explain if the graph will be pointing upward or downward. **20 POINTS**
Answer:
Step-by-step explanation:
the answer is "downward". If you say "why", it is because of the degree coefficient.
in the equation, the latest degree is 2 (which is quadratic equation) so from the degree its coefficient is -3. If it is negative, it should be downward like -3. But if it is positive it should be upward like 3, 1, 44.
In chapters 5-8 of Frankenstein, Victor feels, for the first time in a long time, a sense of joy and calm. What causes these feelings
A. A visit from his father
B. A letter from Elizabeth
C. The arrival of Henry Clerval
D. An award for creating the monster
Answer:
C______________4_⁴________
Huilan is 11 years older than Thomas. The sum of their ages is 61. What is Thomas's age?
Answer:
25
Step-by-step explanation:
Let the age of Thomas be x.
Huilan is 11 years older than Thomas,
Huilan = x + 11
The sum of their ages is 61.
x + x + 11 = 61
2x + 11 = 61
2x = 61 - 11
2x = 50
x = 50/2
x = 25
Hence,
Thomas's age is 25.
Which is the BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3?
A) 2
B) 3
C) 4
D) 6
The BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3 is 2 so option A is correct.
Given:
1 ≤ x ≤ 3
we know x is between 1 and 3 so the best estimate is 2 even though the answer could also be 3 but that will be skewed.
1 ≤ 2 ≤ 3 is the best estimate.
Therefore the BEST estimate of the average rate of change for the function graphed, over the interval 1 ≤ x ≤ 3 is 2 so option A is correct.
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Find the equation of the line tangent to the curve defined by f(x) = x^2+1 / square root x at the point (1,2). Show all your work.
Answer:
[tex]y=x+1[/tex]
Step-by-step explanation:
I am assuming that, given the nature of the curve, you know what a derivative is, and you know how to compute the derivative of the ratio of two functions.
[tex]f'(x) = \frac1{(\sqrt x)^2}[(2x+0)\sqrt x-(x^2+1)(\frac1{2\sqrt x})][/tex]
Could be rewritten in a nicer form? Probably, do we care? No, let's just evaluate it for [tex]x=1[/tex]:
[tex]f'(1)=\frac11 [(2)(1)-(1+1)\frac12]=1[2-1]=1[/tex]
We're almost done. We got the point, we have the slope, we can rewrite the tangent line as
[tex]y-y_0=f'(x_0)(x-x_0)\\y-2=1(x-1) \rightarrow y=x+1[/tex]
simplify your answer 5+2i/4i
1/2 - 5i/4 is the simplified form of the expression ( 5 + 2i ) / 4i.
What is the simplified form of the expression?Given the expression in the question;
( 5 + 2i ) / 4i
To simplify, multiply the numerator and denominator by the conjugate of 4i
( 5 + 2i ) / 4i
( 5 + 2i ) × i / 4i × i
( 5 + 2i )i / 4ii
Apply distributive property
( 5i + 2ii ) / 4ii
Not that i × i = i² = -1
( 5i + 2i² ) / 4i²
( 5i + 2( -1 ) ) / 4( -1 )
( 5i - 2 ) / -4
( -2 + 5i ) / -4
Split the fraction
-2/-4 + 5i/-4
1/2 - 5i/4
Therefore, the simplified form is 1/2 - 5i/4.
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Once the fence is installed, Jason uses 6 gallons 3 quarts of paint. How many quarts does he use?
Answer:
Jason used 27 quarts of paintStep-by-step explanation:
We know that:
1 gallon = 4 quartsThen 6 gallons is:
6 gallons = 6*4 quarts = 24 quartsAdd 3 quarts to get total:
24 + 3 = 27 quartsAnswer:
27 quarts
Step-by-step explanation:
Now we have to,
→ find how many quarts does 6 gallons 3 quarts of paint measure.
Formula we use,
→ 1 gallon = 4 quarts
Now the required solution will be,
→ (6 × 4) + 3
→ 24 + 3
→ 27 quarts
Hence, the answer is 27 quarts.
Consider the equation and the following ordered pairs: (4,y) and (x,2).
y=−2x+4
Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation.
Answer
Keyboard Shortcuts
Complete the table below.
x y
row 14 Answer
row 2 Answer
2
The missing x and y values in the ordered pair of the equation are:
x = 1
y = -4
How to Find the Ordered Pairs of an Equation?Given the ordered pair (x, y) of an equation, y = mx + b, we can find their values by plugging in the given value of either of the x or y coordinates to find the other coordinate value.
The ordered pairs of y = -2x + 4 are given as:
(4, y) and (x, 2)
To find the value of y, substitute x = 4 into the equation y = -2x + 4:
y = -2(4) + 4
y = -8 + 4
y = -4
The value of y is -4.
To find the value of x, substitute y = 2 into the equation y = -2x + 4:
2 = -2x + 4
2 - 4 = -2x
-2 = -2x
-2/-2 = x
1 = x
x = 1
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If you cut a sheet of paper in half, stack one piece on top of the other, cut those in half, stack all the pieces together, repeating this process 20 times, how high will the stack of paper be?
The stack of paper will have the height of 1048576 papers
How to determine how high the stack of paper will be?
The first cut will produce 2 papers, the second cut will produce 4 papers, the third cut will produce 8 papers and the fourth cut will produce 16 papers.
If you examine the stages of cut and the number of papers, the relationship between them is:
1st cut: number of papers = 2¹ = 2
2nd cut: number of papers = 2² = 4
3rd cut: number of papers = 2³ = 8
4th cut: number of papers = 2⁴ = 16
nth cut: number of papers = 2ⁿ
So if the process is repeated 20 times, the number of papers will be:
Number of paper = 2²⁰ = 1048576
Therefore, the stack of paper will be as high as 1048576 papers
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Determine the period.
2 y
-2
1
10
Answer:
8
Step-by-step explanation:
You want the period of a sinusoidal function that has a graph with peaks at x=1 and x=9.
PeriodThe period is the difference between x-values where the function repeats itself. Typically, we can determine the period from corresponding recognizable features of the graph.
Here, the graph has peaks at x=1 and x=9. The period is the difference between these x-values:
period = 9 - 1 = 8
The period of the function is 8 units.
__
Additional comment
In more formal terms, the period p of a function is the smallest value of p such that f(x -p) = f(p).
THE FIRST ANSWER GETS THE BRAINLIEST!
Which lists the distances between towns in order from greatest to least?
(picture of problem below)
Answer:
Step-by-step explanation:
the side opposite to greater angle is greater.
72>60>48
AB>AC>BC
A=Afton
B=Badeton
C=Capeton
On April 1, 2022 the balance in inventory is 220 units at $50 each
April 5, 2022 purchased 100 units at $60 each
Purchased 50 units at $45 each on April 10, 2022
Sold 300 units at $80 each on April 16, 2022
Sold 20 units at $95 each on April 25, 2022
Purchased 200 units at $40 each on April 30, 2022
The calculation of the ending inventory and the cost of goods sold using FIFO and LIFO methods for ABC Inc. is as follows:
FIFO LIFO
Ending inventory $10,250 $12,800
Cost of goods sold $17,000 $14,450
How does FIFO differ from LIFO?FIFO (First-in, First-out) assumes that the physical flow of goods sold depends on the chronological order of acquisition.
LIFO (Last-in, First-out) assumes that the cost of goods sold should be based on the latest inventory purchases.
Date Description Units Unit Costs Total Cost
April 1 Beginning inventory 220 $50 $11,000
April 5 Purchases 100 $60 6,000
April 10 Purchases 50 $45 2,250
April 16 Sales -300 $80
April 25 Sales -20 $95
April 30 Purchases 200 $40 8,000
Total 570 $27,250
Units sold 320
Ending inventory 250
FIFO:
Ending Inventory = $10,250 (200 x $40 + 50 x $45)
Cost of goods sold = $17,000 ($27,250 - $10,250)
LIFO:
Ending Inventory = $12,800 (220 x $50 + 30 x $60)
Cost of goods sold = $14,450 ($27,250 - $12,800)
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Question Completion:Calculate Ending Inventory And COGS Using FIFO And LIFO Methods For ABC Inc.
1. (03.03 MC)
The subtotal for Abdiel's takeout order is $24.30. What will Abdiel's total be if he uses a coupon for 12% off the subtotal and leaves a 25% tip before the discount? (2 points)
O $26.73
$27.46
$33.02
$33.29
Abdiel's total if he uses a coupon for 12% off the subtotal and leaves a 25% tip before the discount is $27.46
The correct answer option is option B
What is Abdiel's total?Abdiel's subtotal = $24.30Abdiel's coupon = 12%Tip = 25%Amount of total after discount = 12% × $24.30
= 0.12 ×24.30
= $2.916
Amount of abdiel's tip = 25% × $24.40
= 0.25 × 24.30
= $6.075
Abdiel's total after discount before tip = (Amount of abdiel's tip + Abdiel's subtotal) - Amount of total after discount
= (6.075 + 24.30) - $2.916
= $30.375 - $2.916
= $27.459
Approximately,
$27.46
Therefore, the total amount Abdiel paid after discount before tip is $27.46
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Solve for x.
giving 20 points for the right answer
Answer:
m∠D = 54°
Step-by-step explanation:
The sum of the measures of the interior angles of a triangle is 180°.
The sum of the measures of an interior angle and its corresponding exterior angle is 180°.
With this knowledge, we can construct the equation:
50° + (3x + 18)° + (180 - (8 + 8x))° = 180°
and solve for x.
50° + (3x + 18)° + (180 - 8 - 8x)° = 180°
(50 + 18 + 180 - 8)° + (3x - 8x)° = 180°
240° - 5x° = 180°
5x° = 240° - 180°
5x° = 60°
x° = 12°
Now, we can solve for m∠D by plugging in the x value that we solved for.
m∠D = (3x + 18)°
m∠D = 3(12)° + 18°
m∠D = 36° + 18°
m∠D = 54°
the artist was hired to decorate 40 in 3 hours he completed 3/8 of the pots at that rate how long will it take the artist to decorate 25 clay pots?
The artist will take 5 hours to decorate 25 clay pots.
Given,
Number of pots to be decorated in 3 hours =40
Number of pots he decorated in 3 hours =[tex]\frac{3}{8}*40=3*5=15[/tex]
So, the artist took 3 hours to decorate 15 pots instead of 40 pots.
It means to decorate 1 pot he took time=[tex]\frac{Total time}{Number of pots decorated} =\frac{3}{15} =\frac{1}{15} hour[/tex]
So, to decorate 25 pots he need time,
[tex]time=\frac{1}{5}*25= 5 hours[/tex]
Thus, the artist need 5 hours to decorate 25 clay pots.
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The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute (rpm))
and the cube of the diameter. If the shaft of a certain material 2 inches in diamter can transmit 16 hp at 120 rpm,
what must the diameter be in order to transmit 30 hp at 150 rpm?
The Diameter of the cube would be 3 inches
What is Variation?
A variation is a relationship that exists between a set of values for one variable and a set of values for other variables.
Solution:
We know that,
Horse Power is directly proportional to RPM * Diameter
So, we can write
Horse Power = k * RPM * Diameter
here, k is any constant
From the first case given, we can find the value of k
16 = k * 2 * 120
k = 1/15
Putting the value of k in second case,
30 = 1/15 * 150 * Diameter
Diameter = 3 inches
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Year No. of cars sold
in (hundreds)
2000 45
2002 51
2004 53
2006 60
2008 77
A car manufacturer's sales figures for 2000 to 2008 are shown in the table. Estimate the average rate of change in the number of cars the manufacturer sold between 2002 and 2006.
A.
450 cars per year
B.
225 cars per year
C.
2,900 cars per year
D.
600 cars per year
Answer: In photo below
You're Welcome :)
The average rate of change in the number of cars the manufacturer sold between 2002 and 2006 is B. 225 cars per year.
What is the average rate of change?The average rate of change shows the slope line over the stated interval.
We can find the average rate of change by dividing the change in y-values by the change in x-values.
Year No. of cars sold
in (hundreds)
2000 45
2002 51
2004 53
2006 60
2008 77
The total number of cars sold between 2002 and 2006 = 16,400
The number of cars sold in 2002 = 5,100
The number of cars sold in 2006 = 6,000
The increase in car sold between 2002 and 2006 = 900 (6,000 - 5,100)
OR:
Increase in the number of cars sold in 2004 = 200 (5,300 - 5,100)
Increase in the number of cars sold in 2006 = 700 (6,000 - 5,300)
Total change in y-values = 900 (6,000 - 5,100)
Total change in x-values = 4 (2006 - 200)2
Average rate of change = 225 (900/4)
Thus, we can conclude that for 4 years, car sales increased on, average, by 225 each year.
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Why should there be a number corresponding to the length of every line we draw?
Number lines are significant because they depict numbers as they appear in daily life.
What is number line?
A number line is a representation of a graduated straight line in elementary mathematics that serves as a visual representation of the real numbers. It is assumed that every point on a number line corresponds to a real number, and that vice versa.
Research has revealed that number lines are crucial because they foster sound mental number sense and arithmetic procedures.
They assist in providing a mental approach for addition and subtraction. Number lines are crucial, we can all agree on that.
Number lines are significant because they depict numbers as they appear in daily life.
Primarily because they make it possible for negative integers to be represented in a meaningful fashion.
The ability to display all real numbers, even enigmatic irrational numbers such π, -π, √2, -√ 2, etc., was a secondary but no less significant result.
Hence, number lines are significant because they depict numbers as they appear in daily life.
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A teacher covered the exterior of a rectangular prism-shaped box that measured 8 inches by 9 inches by 10 inches using one sheet of rectangular-shaped wrapping paper that measured 2 feet by 3 feet. There were no gaps or overlapping paper. How many square inches of wrapping paper were left over?
The area of left over wrapping paper is 380 square inches
How to determine the amount left?The given dimensions are:
Box = 8 inches by 9 inches by 10 inchesWrapping paper = 2 feet by 3 feet.The surface area of the box is calculated as
Surface area = 2(lw + lh + wh)
This gives
Box = 2 * (8 * 9 + 8 * 10 + 9 * 10) = 484 square inches
The surface area of the wrapping paper is calculated as
Wrapper = lw
This gives
Wrapper = 2 * 3 = 6 square feet
Express the area in square inches
Wrapper = 864 square inches
The area left is the difference between the areas calculated above
i.e. Amount left = Wrapper - Box
So, we have
Amount left = 864 square inches - 484 square inches
= 380 square inches
Hence, the amount left is 380 square inches
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The temperature went from 13o C at 3PM to -5o C at midnight that evening.
Which statement best describes the rate of change of the temperature
during this period of time?
The rate of change of the temperature on the time interval is -2°C. This means that, in average, for each hour that passes the temperature decreases by 2 degrees Celcius.
What is the rate of change on the temperature?A rate of change is defined as the quotient between the difference in some measure (in this case it will be the difference between the final temperature and the initial temperature) and the time interval in which it happens.
Here we know that:
final temperature = -5°C
Initial temperature = 13°C
And this change goes from 3 P.M. to midnight, so the change happens on an interval of 9 hours.
Then the rate of change of the temperature is:
r = (-5°C - 13°C)/9h = -2°C/h
So for each hour, the temperature decreases by 2°C.
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In an election for a corporation seat, there were two candidates. A total of 9,791 votes were polled. 116 votes were declared invalid. The successul candidate got 5 votes for every 4 votes his opponent had. By margin did the successful candidate win?
Margin did the successful candidate win is 5375 - 4300 = 1075.
Given:
In an election for a corporation seat, there were two candidates. A total of 9,791 votes were polled.
116 votes were declared invalid. The successful candidate got 5 votes for every 4 votes his opponent had.
Number of valid votes = 9791 - 116 = 9675.
Let the number of votes of successful candidate = 5x
Let the number of votes of opponent = 4x
5x + 4x = 9675
9x = 9675
divide by 9 on both sides
x = 9675/9
x = 1075
Hence the votes for successful candidate = 5*1075 = 5375.
votes for opponent = 4*1075 = 4300.
Margin by which the successful candidate wins = 5375 - 4300 = 1075.
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If X = 32 yards, Y = 60 yards, and Z = 68 yards, what is the sine of ZA?
The sin(x) = 0.88 and sin(y) = 32/68=0.47 in the Trigonometric Functions
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
The given triangle is a right-angled triangle
As Z² = X²+Y²
So sin (x) = 60/68=0.88
and sin(y) = 32/68=0.47
Hence the sin(x) = 0.88 and sin(y) = 32/68=0.47.
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The table below shows a proportional relationship between h and j.
h
18
27
48
j
6
9
16
Find the constant of proportionality from h to j. Express
your answer as a fraction in reduced terms.
As per the proportional relationship, the constant of the proportionality is 1/3
Proportional relationship
A relationship is said to be proportional if each pair of data values are related in the same way, by multiplying by a factor.
The standard form of proportional relationship is written as.
y = k x
where k refers the constant of proportionality.
Given,
The table shows the proportional relationship between h and j.
Now, we need to find the constant of proportionality from h to j and we have to express the answer as a fraction in reduced terms.
We know that the standard form of the proportionality is written as,
y = k x
So, here y takes the value of j and x takes the values of h.
Then we have to take the points as (18, 6) and apply t on the standard form to get the value of k,
=> 6 = k (18)
Here we need the value of k, so move the number to the other side then we get,
=> k = 6/18
When we reduce this, then we get,
=> k = 1/3
Therefore, the constant of proportionality is 1/3.
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