We can start solving the problem by using algebra. Let's call the first number x and the second number y. From the problem statement, we know that:
y = 4x + 6 (because the second number is 6 more than 4 times the first number)
x + y = 71 (because the sum of the two numbers is 71)
We can substitute the first equation into the second equation:
x + (4x + 6) = 71
5x + 6 = 71
5x = 65
x = 13
Now that we know the value of x, we can substitute it back into the first equation to find the value of y:
y = 4(13) + 6
y = 54
So the two numbers are 13 and 54.
Jaime está a 10 metros de un edificio y lanza su balón en línea recta ascendente y alcanza el segundo piso del edificio a 5 metros de altura). ¿Cuánto mide la trayectoria del balón (desde que lanza hasta que impacta)?
-25 POINTS-
Y=-X+[?]
Don’t need to explain. guessers will be reported
Answer:
the first one is 16=-4+12
from here you can solve
Step-by-step explanation:
Answer:
the answer is 20
Step-by-step explanation:
y= –x+z
1. 16= –4+z
16+4=z
20=z
z=20
2. 15= –5+z
15+5=z
20=z
z=20
z=20 is true
A group of researchers establish a p-value of 0.05 for their hypothesis test. What does this mean?
a. The probability of getting a significant result for the test is 5%.
b. There is 5% probability that a true null hypothesis will be rejected.
C. The chi-square critical value for their dataset is 0.05
d. Only measured values of 0.05 or greater will be included in the test.
Answer:
b
Step-by-step explanation:
b. There is 5% probability that a true null hypothesis will be rejected.
A p-value of 0.05 represents the probability of obtaining a test statistic as extreme or more extreme than the one observed under the assumption that the null hypothesis is true. In other words, it is the probability of observing the data or more extreme data assuming the null hypothesis is true. It is also the threshold level of significance beyond which the null hypothesis is rejected in favor of the alternative hypothesis. A p-value of 0.05 means that there is a 5% probability that the observed results occurred by chance under the null hypothesis and that there is a 95% probability that the observed results occurred due to a real effect.
which choice is equivalent to the product below? √6/8 x √6/18
Answer: √6/8 x √6/18
Step-by-step explanation: The square root of A over B is the same as the squared of A, so it's important to know that before I start with this product. To go over the square.
I can do that if I combine the two square roots under the exact square root. This is only for multiplication.
I could take the square root of the term separately
Since I'm using fractions, I'll add the tops and bottoms to the equation.
The square root is eight times 18 and the squared root is six times six. It is the square to 36 over. It's eight times 18. There are 44 items.
The square to 36 is a question. I don't know what time it gives me. There were 36. 36 times six is 6. Six Over would be this. What time gives me 1 44?
Twelve times. 6/12 would be the day. It doesn't want me to reduce that, but I could.
The answer would be 6/12.
URGENT!!!
Consider the graph of the polynomial function y=f(x) given below. The graph continues forever at both ends. Determine the following features (make sure you write all intervals in interval notation and all intercepts as points):
(A) State the domain and range.
(B) State the x-intercepts.
(C) State the y-intercept.
(D) State the interval(s) for which the function is increasing.
(E) State the interval(s) for which the function is decreasing.
(F) State the interval(s) for which the function is constant.
(G) State any symmetry about any axis and/or the origin.
(H) Determine whether the function is even, odd, or neither.
The features of the given polynomial graph are;
A) Domain: (-∞, ∞)
Range: (-∞, 16)
B) The x-intercepts are; (-2√2, 0), (0, 0), (2√2, 0)
C) The y-intercept is; (0, 0)
D) The interval(s) for which the function is increasing is; (-∞, -2) and (0, 2)
E) The interval(s) for which the function is decreasing. is; (-2, 0) and (2, ∞)
F) The graph has no constant interval.
G) It is symmetrical about the y-axis
H) Even function
How to find the domain and range of a polynomial graph?The domain of a function is defined as the set of all possible input values for which the function holds. The range of a function is defined as the set of all possible output values for all possible input values.
A) The x-values intervals we reckon will be positive and negative infinity as the graph extends till infinity. However, the maximum value of the y-values will be 16 while the minimum is negative infinity.
B) The x-intercepts are the points where the graph crosses the x-axis and they are; (-2√2, 0), (0, 0), (2√2, 0)
C) The y-intercepts are the points where the graph crosses the y-axis and it has the coordinate; (0, 0)
D) Looking at the given graph, it is increasing when the curve rises and in this case it is; (-∞, -2) and (0, 2)
E) Looking at the given graph, it is decreasing when the curve descends and in this case it is; (-2, 0) and (2, ∞)
F) The graph has no constant interval.
G) It is symmetrical about the y-axis
H) The function is an even function
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A test plane flies in a straight line with positive velocity v(t), in miles per minute, at time t minutes, where v is a differentiable function of t. Selected values of v(t) are shown in the table below. t (minutes) 0 5 10 15 20 25 30 35 40
v (t) (miles per minute) 7.0 9.2 9.5 7.0 4.5 2.4 2.4 4.3 7.3 Based on the values in the table, what is the smallest number of instances at which the acceleration of the plane could equal zero on the open interval 0
our function v(t) is differentiable in the interval 0 to 40, by mean value theorem a(t)=0 at least two value of t. it can be t=0 and t=5, which is smallest.
A test plane files in a straight line with positive velocity v(t), v is a differentiable function of t.
selected value of v(t) for 0≤ t≤ 40are shown in the table.
We have to justify that what is that smallest number of instances at which the acceleration of plane could equal to zero on the interval (0,40).
We are aware about mean value theorem.
somewhere between t=0 , t=5, v'(t) =0
because v(t) is a differentiable function.
also, t=25 and t=30
v'(t)=0 because
[tex]\frac{v(30)-v(25)}{30-25} =0[/tex],
this means a(t) =0 for at least two value of t.
So, our function is differentiable in the interval 0 to 40, by mean value theorem a(t)=0 at least two value of t. it can be t=0 and t=5.
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A bottle of liquid laundry detergent priced at $16.99 for a 52-load bottle has been changed to $16.49 for a 48-load bottle. By what percentage has the price per load changed?
Answer:
5.1% increase
Step-by-step explanation:
You want the percentage change in price per load when the price of detergent went from $16.99 for 52 loads to $16.49 for 48 loads.
Percentage changeThe percentage change is given by the formula ...
((new price)/(old price) -1) × 100%
Price per loadThe price per load is found by dividing the price of the bottle of detergent by the number of loads it will wash.
old price per load = $16.99/52 ≈ $0.32673
new price per load = $16.49/48 ≈ $0.34354
ApplicationThen the percentage change is ...
(0.34354/0.32673 -1) × 100% ≈ 0.05145 × 100% ≈ 5.1%
The price per load has increased by about 5.1%.
The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y-intercept.
Shawn should use the point-slope formula ⇒ y - y₁ = m(x - x₁) and the y-intercept is -12.
We already know that the point-slope formula goes as such -
⇒ y - y₁ = m(x - x₁)
We have also been told that the slope of the line is 4 and the line passes through the point (1,-8). So, point (1,-8) = (x₁ , y₁) and the slope, m = 4.
Using the given values and the formula of point-slope, we get -
⇒ y - (-8) = 4(x - 1)
⇒ y + 8 = 4x - 4
⇒ 4x - y = -12
⇒ y = 4x - 12
This is the equation of the line.
From this, we get the y-intercept = -12
The complete question that you might be looking for is given below -
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. If Shawn knows that the slope of the line is 4 and the line passes through the point (1,-8), which equation should he use to find the y-intercept, and what is the y-intercept of the line?
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A flute has a length of 49.0 cm. If the speed of sound in air is 343 m/s, what is the fundamental frequency of the flute, assuming it is a tube closed at one end and open at the other?
The fundamental frequency of the flute of length 49.0 cm and with its one end closed is 175 hertz.
Given,
Length of flute = 49.0 cm
Speed of sound in air = 343 m/s
The flute closed from one end and is open from the other exhibits a standing wave pattern.
We know that,
[tex]f =\frac{v}{4L}[/tex]
Now substituting values in the above equation:
[tex]f = \frac{343}{4* (0.49)}[/tex]
[tex]f = 175 hz[/tex]
Thus, the fundamental frequency of the flute is 175 hertz.
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Help with homework please!
The exponential depreciation rate to the nearest tenth of a percent is -0.2%.
How to calculate the exponential depreciation rate?we need to use the exponential decay formula to find exponential rate.
A = A0 * e^(-rt)
where:
A0 = initial value of car (52,000)
A = final price of the car (45,000)
t = elapsed time (32 months)
r = exponential depreciation rate
Rearrange the formula to solve for the exponential depreciation rate "r".
r = -ln(A/A0) / t
Insert value:
r= -ln(45,000 / 52,000) / 32
r = -0.067115074/32
r = -0.002097288
The exponential depreciation rate, expressed as a percentage to the nearest tenth of a percent, is obtained by multiplying by 100.
r = -0.002097288 * 100
r = -0.21D
44 Therefore, the exponential depreciation rate to the nearest tenth of a percent is -0.2%.
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Suppose that a sample of size 100 is selected from a population with unknown variance. If this information is used to construct a confidence interval for the population mean, which of the following statements is true?O The sample standard deviation cannot be used to estimate the population standard deviation because the sample size is too small, O The 2-score must be used in computing the limits for the confidence interval O The sample must be normally distributed O The population is assumed to be normally distributed
In the given case, the population is assumed to have a normal distribution.
When creating a confidence interval for the population mean with a sample size of 100, the population is taken to have a normal distribution. This is due to the Central Limit Theorem, which asserts that regardless of the population distribution's form, the distribution of the sample means approaches a normal distribution as the sample size increases.
Therefore, it is safe to infer that the population mean is normally distributed when the sample size is large enough, for instance, n>30. Additionally, it is also ideal to conclude that the population mean has a normal distribution since a sample size of 100 is greater than 30.
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A grocery supplier believes that the mean number of broken eggs per dozen is 0.6, with a standard deviation of 0.5. Olaf buys 3 dozen eggs without checking them.
a. How many broken eggs does Olaf expect to get?
b. What's the standard deviation?
c. Is it necessary to assume the cartons of eggs are independent? Why?
Olaf expects to get 1.8 broken eggs when he buys 3 dozen eggs, with a standard deviation of 0.5. It is necessary to assume the cartons of eggs are independent because each carton has its own probability of containing broken eggs.
Olaf expects to get 1.8 broken eggs when he buys 3 dozen eggs, with a standard deviation of 0.5. It is necessary to assume the cartons of eggs are independent because each carton has its own probability of containing broken eggs.
a. Olaf expects to get 1.8 broken eggs.
b. The standard deviation is 0.5.
c. Yes, it is necessary to assume the cartons of eggs are independent because each carton has its own probability of containing broken eggs, and if they are not independent, the probability of one carton containing broken eggs will influence the other cartons.
Olaf expects to get 1.8 broken eggs when he buys 3 dozen eggs, with a standard deviation of 0.5. It is necessary to assume the cartons of eggs are independent because each carton has its own probability of containing broken eggs.
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it would be greatly appreciated if someone could help me.
Here x = 5, The two angles are ∠B = 41° and ∠C= 63°.
What is a pentagon?A pentagon is a 2D polygon with five sides and five angles.
Pentagon is formed from three triangles, so the sum of angles in a pentagon = 3 × 180° = 540°.
We are given in the figure , following information about a pentagon:
3 angles are 90 degrees, one angle is (6x+1) degrees, and the other angle is (8x-11) degrees.
To solve for x, we need to add all of the angles together.
The sum of the angles in any polygon is always equal to (n-2)*180, where n is the number of sides in the polygon.
In this case, n=5, so the sum of the angles is (5-2)*180 = 540 degrees.
We can now solve for x by substituting our known values into the equation.
540 = 90 + (6x + 1) + (8x - 11)
540 = 14x
x = 540/14
x = 5
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An artist wants to paint a canvas based on a photograph that measures 4 inches by 5 inches. based on the canvas prices listed in the table, the artist could use canvases at which prices to make a painting that is proportional to the photograph? click on the canvas prices you want to select. $6.43, $11.65,$18.47, $22.80.
The artist wants to paint a canvas that is proportional to the photograph, which measures 4 inches by 5 inches.
To calculate the proportionality, we will use the formula for converting inches to centimeters. 1 inch is equal to 2.54 centimeters. Therefore, 4 inches is equal to 10.16 centimeters and 5 inches is equal to 12.7 centimeters. Therefore, the artist should purchase canvases that are 10.16 centimeters by 12.7 centimeters in size. This will correspond to the following canvas prices: $6.43, $11.65, $18.47, and $22.80. By purchasing these canvases, the artist will ensure that the painting is proportional to the photograph.
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9. Hachi uses 2 tablespoons of peanut butter on each slice of toast she prepares. Let s represent the number of slices of toast, and let t represent the number of tablespoons of peanut butter she needs. Write an equation to represent this relationship, and use it to determine how many tablespoons of peanut butter she would need for 5 slices of toast.
The following vitamins, minerals, and nutrients are particularly notable in each 2-tablespoon (tbsp) portion of smooth peanut butter: Protein. Protein content per 2-tbsp portion of peanut butter is 7.02 grammes (g).
How much protein is in 2 spoons of peanut butter?Although peanut butter is high in protein, vitamins, and minerals, it may also be quite calorie-dense, salty, and high in unsaturated fat. Given that many commercial brands include sugar and oil additives, low-sugar homemade peanut butter can be a decent alternative.Nutrients included in peanuts and peanut butter could help people with their blood sugar levels and heart health.Depending on how peanut butter is incorporated into a person's diet, it may aid in weight loss or weight gain during bodybuilding or weightlifting.The high calorie and fat content of peanut butter, however, means that it should only be consumed in moderation.In this piece, we examine the advantages of consuming peanut butter and outline its hazards.The Complete Question.
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Find the average rate of change if the function f(x)=7x from x1=0 to x2 =4
The average rate of change of the function f(x) = 7x from x1 = 0 to x2 = 4 is solved to be 7
How to solve for the rate of changeThe rate of change is solved using the formula
= change in y / change in x
In the problem, the function is f(x) = 7x from x1 = 0 to x2 = 4
hence y = f(x) =
For x = 0, y = 7 * 0 = 0
For x = 4, y = 7 * 4 = 28
rate of change
= 28 - 0 / 4 - 0
= 28 / 4
= 7
the rate of change is 7
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Which values of x make the following equation true?
3x = -x^2
A) x= -3
B) x= 0,-3
C) x= 0,3
D) x= 3
The correct option B) x= 0,-3, are the values of x make the given quadratic equation true 3x = -x^2.
Define the term roots of the quadratic equation?f(x) = ax² + bx + c, where a, b, as well as c are constants and just a = 0 represents a quadratic function.The roots of a quadratic equation are the values of the variables that fulfil the equation. In other words, if f() = 0, then x = is a root of a quadratic equation f(x). The x-coordinates of the sites in which the curve y = f(x) intersects the x-axis are the real roots of the an equation f(x) = 0.The stated quadratic equation is-
3x = -x^2
x^2 + 3x = 0
Taking x common.
x(x + 3) = 0
x = 0, -3
Thus, the values of x that makes the equation true are 0, -3.
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the present age of neha is 4 times the age of her 4 year old son.if her son is presently 14years old, find neha's present age.
Answer: 40
Step-by-step explanation:
Which is a certain event?
A) pulling a blue sock from a drawer that has 4 blue socks and 2 pink socks
B) pulling a pink sock from a drawer that has 4 blue socks and 2 pink socks
C) pulling a blue sock from a drawer that has only 5 blue socks
D) pulling a pink sock from a drawer that has only 5 blue socks
Answer:
C. Pulling a blue sock from a drawer of only blue socks
Step-by-step explanation:
If there is no other color in the drawer, only that color can be pulled certainly.
factorise the following:
4p + 10
Answer:
2(2p+5)
Step-by-step explanation:
4p + 10
taking common values
2(2p+5)
The expression 4p + 10 can be factored by grouping the like terms together.
4p + 10 can be factored as:
2(2p + 5)
This is the prime factorization of the given expression. Here we have factored out the common factor 2 from 4p and 10. This is the most simplified form of the expression.
The electric potential as a function of position y in a region of space is given by the equation V(y)=4y2 - 3y. Which of the following is correct for the magnitude of the electric field at position (2,6)?
The electric field is the derivative of the electric potential with respect to position. So we can find the electric field by finding the derivative of V(y) with respect to y.
What does a math function mean?
a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variablevariable).
dV/dy = 8y - 3
So, at position y=6, the electric field is E = dV/dy = 8*6 - 3 = 45
Therefore, the magnitude of the electric field at position (2,6) is 45 N/C.
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Jan had 1/4 pound of chocolate and shared it among her eight friends. How much
did each person get?
Zach had eight candy bars and gave each friend 1/4 of a candy bar. How many
people did he share with?
2 and 1/4 chocolate and shared it among her eight friends.
24 people did he share with candy bar.
What is meant by chocolate ?
The cacao tree's seeds are extremely bitter and must be fermented in order to produce a flavorful product.The seeds are dried, washed, and roasted after fermentation. The shell is taken off to create cocoa nibs, which are then ground to create cocoa mass, a kind of pure chocolate.Chocolate liquor is the result of boiling the cocoa material to a liquid state.It is also possible to chill the liquor and separate it into the two ingredients cocoa solids and cocoa butter.Baking chocolate, often known as bitter chocolate, is made only of cocoa butter and solids in different ratios.Dutch cocoa can be made by alkalizing powdered baking cocoa, which has more fiber than cocoa butter.To learn more about chocolate refer to
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Solar panel position
For locations between 20° and 60° north latitude a solar collector panel should be mounted so that its angle with the horizontal is 20°
greater than the local latitude. Consequently, the solar panel mounted on a roof forms a 54° angle with the horizontal. The bottom edge of the 12-ft long panel is resting on the roof and the high edge is 5 feet above the roof. What is the total area of the rectangular solar collector panel?
The rectangular solar collector panel has a total area of 74.164 feet2 since the solar panel put on a roof makes a 54° angle with the horizontal.
what is rectangle ?A quadrilateral having four right angles, or rectangle, in Euclidean plane geometry. A quadrilateral that is equiangular, or one in which all of the angles are equal, is another way to describe it. Also possible is a straight angle in the parallelogram. With four sides that are of the same size, a square is a rectangle. Four 90-degree vertices and equal parallel sides make up a quadrilateral with a rectangle-like shape. Its equirectangular rectangle moniker derives from this. The term "parallelogram" also refers to a rectangle, which has equal and parallel opposite sides.
given
A=12h
sin54°= h/5
ℎ= 5 / sin54°
h= sin54° / 5
Therefore: A=12 * sin54° / 5
74.164 feet2
The rectangular solar collector panel has a total area of 74.164 feet2 since the solar panel put on a roof makes a 54° angle with the horizontal.
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Tickey and Sixpence collected money for charity in the ratio of 5:2 respectively. Sixpence collected R600 less than Tickey. Determine the total amount collected by Tickey and Sixpence.
Answer:
2100
Step-by-step explanation:
let the unknown be x
5 : 2
x. 600
cross multiply
2x=3000
x= 3000
2
x=. 1500 .
Total amount collected= 1500+600
=2100
During _____________, the cell uses information from messenger RNA to produce proteins. Responses A respirationrespiration B transcriptiontranscription C amino acid sequencingamino acid sequencing D translationtranslation
Answer:
D) During translation, the cell uses information from messenger RNA to produce proteins.
Step-by-step explanation:
Hope it helps! =D
Consider the triangle A B C with C = 90 ∘ . Compute the following trigonometric values when a = 8 and b = 8 .
Sin A=
Cos A=
Sin B=
Cos B=
The values of the following are:
Sin A = 0.71
Cos A = 0.71
Sin B = 0.71
Cos B = 0.71
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
Right triangle ABC.
∠C = 90
The other two sides are a = 8 and b = 8
This means,
The angle opposite to the side a = 8 and b = 8 are equal.
Now,
∠A = ∠C
∠C + ∠A + ∠B = 180
90 + ∠A + ∠B = 180
2∠A = 180 - 90
∠A = 90/2
∠A = 45
∠B = 45
Now,
c² = a² + b²
c² = 64 + 64
c² = 128
c = √128
c = 11.31
Thus,
Sin A = a/c = 8/11.31 = 0.71
Cos A = b/c = 8/11.31 = 0.71
Sin B = b/c = 8/11.31 = 0.71
Cos B = a/c = 8/11.31 = 0.71
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Assume that for dry rice and beans:
1 basin =20 cups
40 basins ≈ 1 sack
(a) A sack contains 100 kg of rice.
Estimate the number of kilograms of rice in 1 başin.
Estimate the number of grams of rice in 1 cup.
(b) A trader buys a sack of rice for 6 000 and sells it at 200 per basin.
Estimate the profit on a sack of rice.
(c) A trader charges #5 000 for a sack and 140 for a basin for beans.
Four women buy a sack of beans between them. They share the beans equally.
How many basins does each woman get?
How much does each woman save by buying the beans in this way?
(a) 1 sack of rice contains 100 kg of rice. If 1 basin of rice is equal to 20 cups, then 1 sack is equal to 40*20 = 800 cups.
Therefore, 1 basin of rice contains 100/40 = 2.5 kg of rice.
1 cup of rice contains 2.5/20 = 0.125 kg of rice.
(b) A trader buys a sack of rice for 6 000 and sells it at 200 per basin. If 1 sack contains 800 cups of rice, then the total revenue from a sack of rice is 800*200 = 160,000.
Therefore, the profit on a sack of rice is 160,000-6,000 = 154,000
(c) A trader charges #5 000 for a sack of beans and 140 for a basin. If four women buy a sack of beans between them, they share the beans equally, so each woman gets 1/4 of a sack of beans, which is equal to 1/440 = 10 basins of beans.
Each woman gets 10 basins of beans which cost 14010 = 1,400. If they had bought the beans individually at 140 per basin, they would have spent 140*10 = 1,400.
So each woman saves 5,000/4 = 1,250 by buying the beans in this way.
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12 divied by 1 1/5 help me please
Answer:
10
Step-by-step explanation:
Determine a definite integral that represents the area. region in the first quadrant within the limacon r = 5 + sin(o)
The area of the region in the first quadrant within the limacon r = 5 + sin(o) is 25π/2 + 5π - 2.
The definite integral that represents the area of the region in the first quadrant within the limacon r = 5 + sin(o) is given by:
∫0π/2 (5 + sin(o))2 do
This integral can be evaluated by using the formula for the area of a circle, A = πr2, and converting it to polar coordinates. Since the radius of the limacon is given by r = 5 + sin(o), the area of the region within the limacon is calculated by:
A = ∫0π/2 (5 + sin(o))2 do
= ∫0π/2 (25 + 10 sin(o) + sin2(o)) do
= 25π/2 + 5π - (cos(π/2) - cos(0))
= 25π/2 + 5π - 2
Therefore, the area of the region in the first quadrant within the limacon r = 5 + sin(o) is 25π/2 + 5π - 2.
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Departmental allocation of overheadThe firm is considering a switch to departmental rates for MOH.XYZ will use machine hours (MH) to allocate Assembly Dept. costs. Of the $2,430,000 of MOH, the firm determined that $1,620,000 is related to the Assembly Dept. and $810,000 is related to the Packaging Dept.• Basic units6,000 MH in Assembly• Deluxe units 30,000 MH in Assembly• Total 36,000 MH in Assemblya) Assembly dept. allocation rate = Assembly dept. MOH allocated to Basic = Assembly dept. MOH allocated to Deluxe= XYZ will use labor dollars (DL$) to allocate Packaging Dept. costs• Basic units $990,000 DL$ in Packaging• Deluxe units $360,000 DL$ in Packaging• Total$1,350,000 DL$ in Packagingb) Packaging dept. allocation rate = Packaging dept. MOH allocated to Basic = Packaging dept. MOH allocated to Deluxe = c) Total cost for Basic = Total cost for Deluxe = d) Cost/unit for Basic = Cost/unit for Deluxe =
Assembly dept. allocation rate = $45 per MH; Packaging dept. allocation rate = $0.60/DL$; Total cost for Basic = $864,000; Total cost for Deluxe = $1,566,000; Cost/unit for Basic = $144/unit; Cost/unit for Deluxe = $52/unit.
a) Assembly dept. allocation rate = $1,620,000 MOH / 36,000 MH = $45 per MH
Assembly dept. MOH allocated to Basic = 6,000 MH * $45/MH = $270,000
Assembly dept. MOH allocated to Deluxe = 30,000 MH * $45/MH = $1,350,000
b) Packaging dept. allocation rate = $810,000 MOH / $1,350,000 DL$ = $0.60/DL$
Packaging dept. MOH allocated to Basic = $990,000 DL$ * $0.60/DL$ = $594,000
Packaging dept. MOH allocated to Deluxe = $360,000 DL$ * $0.60/DL$ = $216,000
c) Total cost for Basic = $270,000 + $594,000 = $864,000
Total cost for Deluxe = $1,350,000 + $216,000 = $1,566,000
d) Cost/unit for Basic = $864,000 / 6,000 units = $144/unit
Cost/unit for Deluxe = $1,566,000 / 30,000 units = $52/unit
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