The percentage of U.S. college freshmen claiming no religious affiliation has risen in recent decades. The bar graph shows the percentage of first-year college students claiming no religious affiliation for four selected years from 1980 through 2012.
a. Estimate the average yearly increase in the percentage of first-year college males claiming no religious affiliation. Round the percentage to the nearest tenth.
b. Estimate the percentage of first-year college males who will claim no religious affiliation in .
Answers
a) The estimated average yearly increase in the percentage of first-year college males claiming no religious affiliation is 0.5%.
b) Based on the above average, the percentage of first-year college males who will claim no religious affiliation in 2020 is 22.7%
How the average yearly increase and percentage are determined:Year Male
1980 6.6%
1990 10.6%
2000 13.5%
2012 21.8%
Percentage of first-year college males claiming no religious affiliation in 2012 = 21.8%
Percentage of first-year college males claiming no religious affiliation in 1980 = 6.6%
The number of years between 2012 and 1980 = 32 years
The percentage increase from 1980 to 2012 = 15.2% (21.8% - 6.6%)
a. Average yearly increase = 0.475% (15.2% ÷ 32)
= 0.5%
b. The number of years between 2020 and 2012 = 8 years
In 2020, the percentage of first-year college males who will claim no religious affiliation based on the average yearly increase above =
Percentage in 2012 x (1 + Yearly Average)^8
21.8% = 0.218 (21.8 ÷ 100)
0.5% = 0.005 (0.5 ÷ 100)
= 0.218(1.005)⁸.
= 0.2269
= 22.69%
= 22.7%
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.
Which two of the following are not characteristics of surveys?
A. The study involves one or more treatment groups and a control
group.
B. The study compares two or more treatments.
C. Statistical analysis is applied to the results of the study.
D. Data are gathered during the course of the study.
Answers
Answer: A and B are not characteristics of surveys.
Step-by-step explanation: A survey is a type of research method that involves collecting data from a sample of individuals or groups, usually by asking them questions or observing their behavior. Surveys can be used to describe, compare, or explain various aspects of a population or phenomenon of interest.
Some of the common characteristics of surveys are:
They use a predefined set of questions or items that are standardized and consistent for all respondents or participants.They use a sampling technique to select a representative subset of the population or target group that is relevant to the research question or objective.They use a mode of data collection that is suitable for the type and format of the questions or items, such as face-to-face interviews, telephone interviews, mail questionnaires, online surveys, etc.They use statistical analysis to summarize, describe, compare, or infer the results of the data collected from the sample to the population or target group.Some of the types of research methods that involve one or more treatment groups and a control group, and that compare two or more treatments, are:
Experiments: Experiments are research methods that involve manipulating one or more independent variables (the treatments) and measuring their effects on one or more dependent variables (the outcomes). Experiments aim to establish causal relationships between variables by controlling for other factors that may influence the results. Experiments usually involve random assignment of participants to different treatment groups and a control group that receives no treatment or a placebo.Quasi-experiments: Quasi-experiments are research methods that resemble experiments but lack some of the features of true experiments, such as random assignment or manipulation of variables. Quasi-experiments aim to estimate causal relationships between variables by using natural or existing variations in the independent variables (the treatments) and comparing their effects on the dependent variables (the outcomes). Quasi-experiments usually involve non-equivalent groups that differ in their exposure to the treatments or in other characteristics that may affect the results.Observational Studies: Observational studies are research methods that involve observing and measuring existing phenomena without manipulating any variables. Observational studies aim to describe, compare, or correlate variables by using natural or existing data sources. Observational studies usually involve different groups that are selected based on their exposure to the variables of interest or based on other criteria that may affect the results.Hope this helps, and have a great day! =)
I Need fast!!! 20 POINTS
Answers
Answer:
(x + 3)(5x + 2) , (2x - 1)(3x + 5)
Step-by-step explanation:
given
A = 5x² + 12x + 6
consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term
product = 5 × 6 = 30 and sum = 17
the factors are + 15 and + 2
use these factors to split the x- term
5x² + 15x + 2x + 6 ( factor the first/second and third/fourth terms )
= 5x(x + 3) + 2(x + 3) ← factor out (x + 3) from each term
= (x + 3)(5x + 2)
then
length = x + 3 , breadth = 5x + 2 or indeed the other way round
-------------------------------------------------------------------------------
given
A = 6x² + 7x - 5
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 6 × - 5 = - 30 and sum = + 7
the factors are - 3 and + 10
use these factors to split the x- term
6x² - 3x + 10x - 5 ( factor the first/second and third/fourth terms )
= 3x(2x - 1) + 5(2x - 1) ← factor out (2x - 1) from each term
= (2x - 1()3x + 5)
then
length = 2x - 1 , breadth = 3x + 5 or the other way round
Mr. John recently bought 2 cords of wood from a local contractor
(delivered in a dump truck). After the pile was dropped off, he stacked
the wood and wondered if he really received the 2 standard cords of
wood (see diagram) or if the company sold him less wood than he
ordered.
Note: a cord of wood if defined as 4ft X 4ft’ X 8ft stack
Mr. John ended up stacking to piles of wood this past week.
Mr. John ended up with two piles of wood with the following sizes
PILE #1: 72” X 167” X 16”
PILE #2: 65” X 266” X 16”
QUESTIONS:
1. Did Mr. John get more or less than 2 cords of wood (as defined in
the diagram above)?
2. If a standard piece of wood is 5” X 5” X 12”. How pieces of actual
wood did he receive based on his stacked piles?
3. If the cost for both cords of wood was actually $250/cord,
What was the cost per a standard piece of wood?
Answers
1. Mr. John received more than 2 cords of wood based on the sizes of the stacked piles.
2. Based on the stacked piles, Mr. John received approximately 11,974 pieces of actual wood.
3. The cost per standard piece of wood is approximately $0.0417.
1. To determine if Mr. John received more or less than 2 cords of wood, we need to calculate the volume of each pile and compare it to the volume of a standard cord of wood.
Calculating the volume of each pile:
PILE #1:
Volume = 72 inches * 167 inches * 16 inches = 1,523,584 cubic inches
PILE #2:
Volume = 65 inches * 266 inches * 16 inches = 2,068,480 cubic inches
Calculating the volume of a standard cord of wood:
Volume of a standard cord = 4 feet * 4 feet * 8 feet = 128 cubic feet
Since 1 foot = 12 inches, the volume in cubic inches is 128 * 12 * 12 * 12 = 221,184 cubic inches.
Comparing the volumes:
Pile #1: 1,523,584 cubic inches
Pile #2: 2,068,480 cubic inches
Standard cord: 221,184 cubic inches
It is evident that both piles have significantly more volume than a standard cord of wood. Therefore, Mr. John received more than 2 cords of wood.
2. To determine the number of standard pieces of wood received, we need to calculate the number of pieces that can be obtained from the total volume of the piles.
Total volume of the piles = Volume of Pile #1 + Volume of Pile #2
Total volume = 1,523,584 cubic inches + 2,068,480 cubic inches = 3,592,064 cubic inches
Volume of a standard piece of wood = 5 inches * 5 inches * 12 inches = 300 cubic inches
Number of standard pieces of wood received = Total volume of the piles / Volume of a standard piece of wood
Number of pieces = 3,592,064 cubic inches / 300 cubic inches = 11,973.55 pieces (rounded to the nearest whole number)
Therefore, Mr. John received approximately 11,974 pieces of actual wood based on his stacked piles.
3. To calculate the cost per standard piece of wood, we need to divide the total cost of the two cords by the number of standard pieces received.
Total cost for both cords of wood = 2 cords * $250/cord = $500
Cost per standard piece of wood = Total cost / Number of standard pieces
Cost per piece = $500 / 11,974 = $0.0417 (rounded to four decimal places)
Therefore, the cost per standard piece of wood is approximately $0.0417.
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Is the following infinite sum defined?
0.69+1.38+2.76+5.52+…
Select the correct answer below:
Answers
The given infinite sum 0.16 + 0.4 + 0.1 + 0.25 + ... is defined as it converges to a finite value. Option A is the correct answer.
To determine whether the given infinite sum is defined, let's examine its pattern.
If we observe the terms in the sum, we can see that each term is obtained by dividing the previous term by 4. Specifically, each term is one-fourth the value of the previous term.
Let's verify this pattern:
Term 1: 0.16
Term 2: Term 1 / 4 = 0.16 / 4 = 0.04
Term 3: Term 2 / 4 = 0.04 / 4 = 0.01
Term 4: Term 3 / 4 = 0.01 / 4 = 0.0025
It appears that each term is one-fourth the value of the previous term. If this pattern continues, we can write the nth term as:
Term n = (1/4)^(n-1) * 0.16
To determine whether the sum is defined, we need to check whether the terms approach a finite value or converge to a specific value.
As n approaches infinity, the term (1/4)^(n-1) * 0.16 will approach zero since (1/4)^(n-1) approaches zero exponentially. Therefore, the sum of the infinite terms in this sequence will converge to a finite value. Hence, Option A is the correct answer.
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An experiment was conducted in which a six-sided die was rolled 20 times. The outcomes of the experiment are listed
in the table below. Use the table to answer the questions.
Value of Die Frequency
1
5
2
3
4
5
6
Your answers should be exact decimal values.
The probability that a die will land on 5 is
The probability that a die will land on 1 is
If a probability is unlikely, then the probability is less than
4
1
2
4
4
Answers
The probability that a die will land on 5 is 0.1.
The statement "If a probability is unlikely, then the probability is less than 1/2" is true in this context.
To determine the probabilities, we need to calculate the relative frequency of each outcome by dividing the frequency of that outcome by the total number of rolls (20 in this case).
The frequency table provided is as follows:
Value of Die | Frequency
1 | 5
2 | 3
3 | 4
4 | 5
5 | 2
6 | 1
To find the probability that a die will land on 5, we divide the frequency of 5 by the total number of rolls:
Probability of landing on 5 = Frequency of 5 / Total number of rolls
= 2 / 20
= 0.1
Therefore, the probability that a die will land on 5 is 0.1.
Similarly, to find the probability of landing on 1:
Probability of landing on 1 = Frequency of 1 / Total number of rolls
= 5 / 20
= 0.25
Thus, the probability that a die will land on 1 is 0.25.
Now, if a probability is unlikely, it means the probability is less than 1/2. In this case, we need to compare the probabilities to 0.5.
Since the probability of landing on 1 is 0.25, which is less than 0.5, we can conclude that the probability of landing on 1 is unlikely.
Therefore, the statement "If a probability is unlikely, then the probability is less than 1/2" is true in this context.
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Which description is paired with its correct expression?
four less than the quotient of a number cubed and seven, increased by three; 4-2+3
five times the difference of a number squared and six; 5(6-n²)
nine more than the quotient of six and a number cubed, decreased by four; 8+²-4
9+
O twice the difference of nine and a number squared; 2(9-n²)
Answers
The correct pairings are:
a) Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3
b) Five times the difference of a number squared and six: 5(n² - 6)
c) Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4
d) O twice the difference of nine and a number squared: 2(9 - n²)
The correct pairings of descriptions and expressions are as follows:
Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3
This expression represents taking a number, cubing it, dividing the result by seven, subtracting four, and then adding three.
Five times the difference of a number squared and six: 5(n² - 6)
This expression represents taking a number, squaring it, subtracting six, and then multiplying the result by five.
Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4
This expression represents taking the cube of a number, dividing six by the cube, adding nine, and then subtracting four.
O twice the difference of nine and a number squared: 2(9 - n²)
This expression represents taking a number, squaring it, subtracting it from nine, and then multiplying the result by two.
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John's four brothers each have names that begin with the letter J, but none of the other
members of his family has a name that begins with J. If a person in John's family is randomly
selected, there is a 25% chance that the person's name will start with J. How many people are
in John's family?
Answers
Answer:16
Step-by-step explanation:
25/100 × x = 4
x = 4 × 4
x = 16
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
∠ G = 73° , ∠ H = 98°
Step-by-step explanation:
EFGH is a cyclic quadrilateral, its 4 vertices lie on the circle.
the opposite angles sum to 180°
A
∠ E + ∠ G = 180° , that is
11x + 8 + 8x + 1 = 180
19x + 9 = 180 ( subtract 9 from both sides )
19x = 171 ( divide both sides by 19 )
x = 9
Then
∠ G = 8x + 1 = 8(9) + 1 = 72 + 1 = 73°
B
∠ H + ∠ F = 180° , that is
6y - 4 + 5y - 3 = 180
11y - 7 = 180 ( add 7 to both sides )
11y = 187 ( divide both sides by 11 )
y = 17
Then
∠ H = 6y - 4 = 6(17) - 4 = 102 - 4 = 98°
Answer:
A) m∠G = 73°
B) m∠H = 98°
Step-by-step explanation:
The diagram shows a cyclic quadrilateral.
A cyclic quadrilateral is a four-sided shape drawn inside a circle, where every vertex touches the circle's circumference.
As the opposite angles in a cyclic quadrilateral add up to 180°, then:
m∠E + m∠G = 180°m∠H + m∠F = 180°We can use these equations to find the values of x and y.
m∠E + m∠G = 180°
(11x + 8)° + (8x + 1)° = 180°
11x + 8 + 8x + 1 = 180
19x + 9 = 180
19x + 9 - 9 = 180 - 9
19x = 171
19x ÷ 19 = 171 ÷ 19
x = 9
m∠H + m∠F = 180°
(6y - 4)° + (5y - 3)° = 180°
6y - 4 + 5y - 3 = 180
11y - 7 = 180
11y - 7 + 7 = 180 + 7
11y = 187
11y ÷ 11 = 187 ÷ 11
y = 17
Now we have found the values of x and y, substitute them back into the angle expressions to find m∠G and m∠H.
m∠G = (8x + 1)°
m∠G = (8(9) + 1)°
m∠G = (72 + 1)°
m∠G = 73°
m∠H = (6y - 4)°
m∠H = (6(17) - 4)°
m∠H = (102 - 4)°
m∠H = 98°
What is the area, measured in square centimeters, of the triangle below? Do
not include units in your answer.
Answer here
Answers
Answer:
The area of this triangle is (1/2)(9)(8) = 36.
What are 2 equations/ratios you could write to sovle for a? Do NOT SOLVE just write the equations
you would use to solve.
AN
Answers
The two equations to solve for angle α are sinα = u/t and sinα = r/s using the trigonometric ratio of sine
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
The bigger triangle with sides t, u, v and the smaller triangle with sides q, r , s are both right triangle so we can use the ratio of sine for their angle α to get the two equations as:
sin α = u/t {opposite/hypotenuse} for the bigger triangle.
sin α = r/s {opposite/hypotenuse} for the smaller triangle.
Therefore, the two equations to solve for angle α are sinα = u/t and sinα = r/s using the trigonometric ratio of sine
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Markshisand
Which steps should be used to compare the fractions and
O Find a common numerator.
O Add the numerators and denominators to determine which sum is larger.
O Use the "greater than" symbol to show which denominator is larger.
O Multiply the first fraction by 2 and the second fraction by 3
Answers
1. Find a common denominator: Make sure both fractions have the same denominator by finding a common multiple of the two denominators.
2. Compare the numerators: Once the fractions have a common denominator, compare the numerators to determine which numerator is larger.
3. Use the "greater than" or "less than" symbol: Based on the comparison of the numerators, use the appropriate symbol (> or <) to indicate which fraction is larger.
4. Simplify or convert: If necessary, simplify the fractions or convert them to mixed numbers for a clearer comparison.
Therefore, the steps mentioned in the given options are not entirely accurate. The correct steps to compare fractions are as described above.
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
The volume of the pyramid is 357.7 inches³.
The volume of the cone is 1230.9 yard³.
How to find the volume of a cone/pyramid?The volume of a pyramid can be represented as follows;
volume of the pyramid = 1 / 3 Bh
where
B =base areah = heightTherefore,
B = 10 × 8 = 80 inches²
Hence,
h² = 14² - 4²
h = √196 - 16
h = √180
h = √180 inches
volume of the pyramid = 1 / 3 × 80 × √180
volume of the pyramid = 357.7 inches³
Therefore, let's find the volume of the cone.
volume of the cone = 1 / 3 πr²h
h = √25² - 7²
h = √576
h = 24 yards
volume of the cone = 1 / 3 × 3.14 × 7² × 24
volume of the cone = 1230.9 yard³
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Two cars start moving from the same point. One travels south at 50 mi/h and the other travels west at 20 mi/h. At what rate is the distance between the cars increasing 2 hours later? Round the result to the nearest hundredth.
Answers
The rate at which the distance between the cars is increasing 2 hours later is 0 mi/h, by using the Pythagorean theorem.
To find the rate at which the distance between the cars is increasing, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
Let's assume that after 2 hours, the distance traveled by the southbound car is d_south and the distance traveled by the westbound car is d_west.
Since the southbound car travels at a speed of 50 mi/h for 2 hours, we have d_south = 50 mi/h [tex]\times[/tex] 2 h = 100 mi.
Similarly, the westbound car travels at a speed of 20 mi/h for 2 hours, so d_west = 20 mi/h [tex]\times[/tex] 2 h = 40 mi.
Now, we can use the Pythagorean theorem to find the distance between the two cars:
[tex]distance^2 = d_south^2 + d_west^2distance^2 = 100^2 + 40^2distance^2 = 10000 + 1600distance^2 = 11600[/tex]
distance ≈ sqrt(11600) ≈ 107.68 mi
To find the rate at which the distance between the cars is increasing, we differentiate the equation with respect to time:
2 [tex]\times[/tex] distance [tex]\times[/tex] [tex]\(\frac{{d(\text{{distance}})}}{{dt}}\)[/tex] = 2 [tex]\times[/tex] d_south [tex]\times[/tex] [tex]\(\frac{{d(d_{\text{{south}}})}}{{dt}}\)[/tex] + 2 [tex]\times[/tex] d_west [tex]\times[/tex] (d(d_west)/dt)
Since d_south and d_west are constant (no mention of their rates of change), we can simplify the equation to:
2 [tex]\times[/tex] distance [tex]\times[/tex] [tex]\(\frac{{d(\text{{distance}})}}{{dt}}\)[/tex] = 0
Therefore, the rate at which the distance between the cars is increasing 2 hours later is 0 mi/h.
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What did Amy do wrong
Answers
What Amy did wrong was not moving the pointer to the arc intersection with the horizontal side
What is an angle bisector?An angle bisector is defined in geometry as a line that splits an angle into two equal angles.
The steps involved in constructing an angle bisector are;
Draw an angle on your paper. Make sure one side is horizontal.Place the pointer on the vertex. Draw an arc that intersects both sides.Move the pointer to the arc intersection with the horizontal side.Connect the arc intersections from with the vertex of the angle.Learn more about angle bisectors at: https://brainly.com/question/24334771
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Sparx 4: Item A
Bookwork code: C20
Find the size of the angle marked n. Give your answer in degrees (°).
n
Watch video
52
1,326 XP
Not drawn accurately
Answer >
13 Jun
19:04 GB
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Answers
The size of angle marked n is ≈26.67 degrees.
Sparx 4:
Item A, bookwork code C20 requires us to determine the size of angle marked n in degrees.
We can solve the given question by using the angles sum rule that states that the sum of the angles of a triangle equals to 180 degrees.
The given figure represents an isosceles triangle since the two base angles are equal in length.
Also, the top line is parallel to the bottom line.
Using the angles sum rule for a triangle, we get:angle ABC + angle BCA + angle CAB = 180 degreesx + 2n + 50 = 180 degreesx = 180 - 2n - 50x = 130 - 2nWe know that angles that are opposite to equal sides of an isosceles triangle are equal.
Therefore, angle ABC = angle CAB = n
Thus, the above equation becomes:130 - 2n = n + 50.
Simplifying the equation, we get:3n = 80n = 80 / 3n ≈ 26.67 degrees.
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Question 5 of 5
How does the diagram illustrate why the sum of the lengths of two sides of a
triangle cannot be less than the length of the third side of the triangle?
4221
12
OA. by showing the two sides with lengths 4 and 3 can always meet to
form a vertex
B. by showing the two sides with lengths 4 and 3 will only meet when
the angle between them is large
OC. by showing the two sides with lengths 4 and 3 can never meet to
form a vertex
D. by showing the two sides with lengths 4 and 3 will only meet when
they lie on the third side
SUBMIT
Answers
Answer:
The diagram illustrates that the two sides with lengths 4 and 3 can never meet to form a vertex, therefore the correct answer is C.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Answer:
[tex]\textsf{(C)} \quad \dfrac{1}{4}[/tex]
Step-by-step explanation:
To find the probability of a point chosen at random being in the shaded area of the given diagram, we first need to calculate the areas of the larger circle and the shaded circle.
The formula for the area of a circle is A = πr², where r is the radius.
Given the radius of the larger circle is 8 units:
[tex]\begin{aligned}\sf Area\;of\;the\;larger\;circle&=\pi (8)^2\\&=64 \pi \end{aligned}[/tex]
Given the radius of the shaded circle is 4 units:
[tex]\begin{aligned}\sf Area\;of\;the\;shaded\;circle&=\pi (4)^2\\&=16 \pi \end{aligned}[/tex]
Probability formula[tex]\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}[/tex]
To find the probability that a point chosen at random is in the shaded area, divide the area of the shaded circle by the area of the larger circle:
[tex]\sf Probability= \dfrac{16 \pi}{64 \pi}=\dfrac{1}{4}[/tex]
Therefore, the probability of a point chosen at random being in the shaded area is 1/4.
Answer:
[tex]\frac{x}{y}[/tex] 1 over 4 (one-fourth)
Step-by-step explanation:
Sunita performed a transformation on trapezoid LMNQ to create L'M'N'Q', as shown
in the figure below:
What transformation did Sunita perform to create LMMQ?
1 rotation of 90 counterclockwise of the origin
2rotation of 270 counterclockwise of the origin
3 reflection across the xaxis
4reflection across the line of symmetry of the figure
Answers
Answer: rotation of 90 counter clockwise about the origin
Step-by-step explanation:
Kubin Company's relevant range of production is 13,000 to 18,000 units. When it produces and sells 15,500 units, its average costs per
unit are as follows:
Direct materials
Direct labor
Variable manufacturing overhead
Fixed manufacturing overhead
Fixed selling expense
Fixed administrative expense
Sales commissions
Variable administrative expense
Average
Cost per
Unit
$7.40
$ 4.40
$ 1.90
$ 5.40
$ 3.90
$ 2.90
$ 1.40
$0.90
Required:
1 Assume the cost object is units of production:
a. What is the total direct manufacturing cost incurred to make 15,500 units?
b. What is the total indirect manufacturing cost incurred to make 15,500 units?
2. Assume the cost object is the Manufacturing Department and that its total output is 15,500 units.
a. How much total manufacturing cost is directly traceable to the Manufacturing Department?
b. How much total manufacturing cost is an indirect cost that cannot be easily traced to the Manufacturing Department?
3. Assume the cost object is the company's various sales representatives. Furthermore, assume that the company spent $44,950 of
its total fixed selling expense on advertising and the remainder of the total fixed selling expense comprised the fixed portion of the
company's sales representatives' compensation.
a. When the company sells 15,500 units, what is the total direct selling expense that can be readily traced to individual sales
representatives?
b. When the company sells 15,500 units, what is the total indirect selling expense that cannot be readily traced to individual sales
representatives?
Answers
1. a. The Total direct manufacturing cost is $212,350. b. The Total indirect manufacturing cost is -$128,650. 2. a. the total manufacturing cost directly traceable to the Manufacturing Department is $212,350. b. the total manufacturing cost that is an indirect cost is $83,700. 3. a. the total direct selling expense that can be readily traced to individual sales representatives is $21,700. b. the total indirect selling expense that cannot be readily traced to individual sales representatives is $38,750.
1. Assume the cost object is units of production:
a. The total direct manufacturing cost incurred to make 15,500 units can be calculated by multiplying the average cost per unit for each cost component by the number of units produced:
Total direct manufacturing cost = (Direct materials cost + Direct labor cost + Variable manufacturing overhead cost) × Number of units produced
Direct materials cost = $7.40/unit × 15,500 units = $114,700
Direct labor cost = $4.40/unit × 15,500 units = $68,200
Variable manufacturing overhead cost = $1.90/unit × 15,500 units = $29,450
Total direct manufacturing cost = ($114,700 + $68,200 + $29,450) = $212,350
b. The total indirect manufacturing cost incurred to make 15,500 units can be calculated by subtracting the total direct manufacturing cost from the average cost per unit for fixed manufacturing overhead:
Total indirect manufacturing cost = Fixed manufacturing overhead cost × Number of units produced
Fixed manufacturing overhead cost = $5.40/unit × 15,500 units = $83,700
Total indirect manufacturing cost = $83,700 - $212,350 = -$128,650
Note: The negative value indicates that the fixed manufacturing overhead cost is not fully utilized within the relevant range of production. It suggests that there may be unused capacity or fixed costs that are not being allocated to the production of 15,500 units.
2. Assume the cost object is the Manufacturing Department and that its total output is 15,500 units:
a. The total manufacturing cost directly traceable to the Manufacturing Department is the sum of the direct manufacturing costs:
Total manufacturing cost directly traceable to the Manufacturing Department = Total direct manufacturing cost
Using the values calculated in part 1a, the total manufacturing cost directly traceable to the Manufacturing Department is $212,350.
b. The total manufacturing cost that is an indirect cost and cannot be easily traced to the Manufacturing Department is the fixed manufacturing overhead cost:
Total manufacturing cost that is an indirect cost = Fixed manufacturing overhead cost
Using the value calculated in part 1b, the total manufacturing cost that is an indirect cost is $83,700.
3. Assume the cost object is the company's various sales representatives. Furthermore, assume that the company spent $44,950 of its total fixed selling expense on advertising, and the remainder of the total fixed selling expense comprised the fixed portion of the company's sales representatives' compensation:
a. When the company sells 15,500 units, the total direct selling expense that can be readily traced to individual sales representatives is the sales commissions:
Total direct selling expense = Sales commissions × Number of units sold
Sales commissions = $1.40/unit × 15,500 units = $21,700
Therefore, the total direct selling expense that can be readily traced to individual sales representatives is $21,700.
b. When the company sells 15,500 units, the total indirect selling expense that cannot be readily traced to individual sales representatives is the fixed portion of the company's sales representatives' compensation:
Total indirect selling expense = Total fixed selling expense - Total direct selling expense
Total fixed selling expense = $3.90/unit × 15,500 units = $60,450
Total indirect selling expense = $60,450 - $21,700 = $38,750
Therefore, the total indirect selling expense that cannot be readily traced to individual sales representatives is $38,750.
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State if the pair of triangles are similar. If so, state how you know they are similar and complete the similarity statement.
Answers
The triangles ∆UTS and ∆UBA are similar, hence we can write the similarity statement as:"Triangle ∆UTS is similar to triangle ∆UBA."
How to determine if triangles ∆UTS and ∆UBA are similarTo determine if triangles ∆UTS and ∆UBA are similar, we need to check if their corresponding angles are congruent and if their corresponding sides are proportional.
If ∆UTS is similar to ∆UBA, the following conditions must be true, then each angle in ∆UTS must have a corresponding congruent angle in ∆UBA. Also, the ratio of the lengths of corresponding sides in ∆UTS and ∆UBA must be equal.
AB/ST = 984/1271 = 0.7742
UB/UT = 768/994 = 0.7742
UA/US = 648/837 = 0.7742
AB/ST = UB/UT = UA/US
Therefore triangles ∆UTS and ∆UBA are similar, hence we can write the similarity statement as:"Triangle ∆UTS is similar to triangle ∆UBA."
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What is the solution to this system of equations? 10 y = x - 2; y = - 0.5x + 7 10 (3, 2); (6, 4); (4, 6); (2, 3)
Answers
Answer:x=bx2 is the answer
Step-by-step explanation:
16. Taylor uses 2 sticks that are 13 feet long to make the slanted sides of
a tent. From the bottom poles, the opening is 10 feet long.
13 ft.
10 ft.
What is the height of the tent in feet?
Write the answer in the box.
feet
Answers
We may apply the Pythagorean theorem to calculate the height of the tent, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the total of the squares on the other two sides. So, the height of the tent is 8.3077 feet.
In this case, the two sticks form the slanted sides of the tent, and the opening at the bottom forms the base of the triangle. We can consider the height of the tent as the missing side, which is perpendicular to the base.
Let's denote the height of the tent as 'h.' Using the Pythagorean theorem, we have:
(10 ft.)² + (h)² = (13 ft.)²
Simplifying the equation:
100 + h² = 169
Now, subtracting 100 from both sides:
h² = 169 - 100
h² = 69
Taking the square root of both sides:
h = sqrt(69)
Therefore, the height of the tent is approximately 8.3077 feet (rounded to four decimal places).
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What are the important variables in the problem below?
A test is worth 80 points. Multiple-choice questions are worth 2 points, and
short-answer questions are worth 4 points. If the test has 25 questions, how
many multiple-choice questions are there?
OA. p for points, m for multiple choice
OB. s for short answer, t for test
OC. m for multiple choice, s for short answer
OD. t for test, q for questions
Answers
The important variables are the two types of test questions which can be represented as :
m for multiple choice, s for short answerVariables are used to represent unknown values which could be worked out in a mathematical expression or problem.
The variables or unknown in this case are the type of test questions. which are : m for multiple choice, s for short answer
Therefore, the correct option is C. m for multiple choice, s for short answer
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What is the area of this rectangle? Rectangle with width 5.1 cm and height 11.2 cm. Responses 16.3 cm2 16.3 cm, 2 32.6 cm2 32.6 cm, 2 57.12 cm2 57.12 cm, 2 571.2 cm2
Answers
The area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².
To find the area of a rectangle, we multiply its length by its width. In this case, the width is given as 5.1 cm and the height (or length) is given as 11.2 cm.
Area = length × width
Area = 11.2 cm × 5.1 cm
Calculating the product, we get:
Area = 57.12 cm²
Therefore, the area of the rectangle is 57.12 cm².
The correct answer is: 57.12 cm².
It is important to note that when calculating the area of a rectangle, we should always include the appropriate unit of measurement (in this case, cm²) to indicate that we are dealing with a two-dimensional measurement. The area represents the amount of space covered by the rectangle's surface.
So, the area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².
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16
Find X.
25
X
Pythagorean Theorem
Answers
Answer:
3√41
Step-by-step explanation:
a^2+b^2=c^2
rearrange this to make x (a or b it doesn't matter) the subject
√b=c^2-a^2
now substitute this in:
√b=25^2-16^2
=369
then simple do the square root
√369
=3√41
Hope this helps!
Solve for x.
OA. 9
OB. 1
OC. 4
OD.7
Answers
The value of x in the secant intersection is 4.
How to find the length in a secant?If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.
Therefore, let's find the value of x using the secant intersection theorem as follows;
4(4+x + 2) = 5(5 + x - 1)
4(6 + x) = 5(4 + x)
24 + 4x = 20 + 5x
24 - 20 = 5x - 4x
x = 4
Therefore,
x = 4
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You can make $ when you activate a prepaid device with equipment
Answers
When you activate a prepaid device with equipment, you may have the opportunity to earn money through various means.
Firstly, as a retailer or reseller, you can make a profit by selling the prepaid device and associated equipment at a higher price than your purchase cost. This markup allows you to earn a margin on each sale.
Additionally, some service providers or retailers offer commission-based programs where you earn a commission or referral fee for each prepaid device activation. By promoting and selling these devices, you can earn a percentage of the total sale value or a fixed amount per activation.
Furthermore, you might have the chance to upsell customers on additional accessories or services during the activation process. By offering relevant accessories like cases, screen protectors, or headphones, you can increase the overall sale value and earn extra income.
It's worth noting that the specific earning potential can vary depending on factors such as the popularity of the device, the commission structure, and the competitiveness of the market. It's advisable to research and understand the terms and conditions of any commission or referral programs before engaging in such activities.
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The slope of a parabola
�
=
3
�
2
−
11
�
+
10
y=3x
2
−11x+10 at a point
�
P is 7. Find the
�
−
y− coordinate of the point
�
P
Answers
The y-coordinate of point P is 1.To find the y-coordinate of the point P on the parabola y = 3x^2 - 11x + 10 where the slope is 7, we can differentiate the equation to find the derivative. The derivative of y = 3x^2 - 11x + 10 is y' = 6x - 11.
To find the x-coordinate of point P, we can set the derivative equal to the given slope: 6x - 11 = 7. Solving for x, we get x = 3.
To find the y-coordinate of point P, we substitute the x-coordinate back into the original equation: y = 3(3^2) - 11(3) + 10. Simplifying, we find y = 1.
Therefore, the y-coordinate of point P is 1.
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what is the solution to the system of equations graphed below
Answers
The solutions to the system of equations is (a) (1, 5)
Selecting the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
The graph
This point of intersection of the lines of the graph represent the solution to the system graphed
From the graph, we have the intersection point to be
(x, y) = (1, 5)
Hence, the solutions to the system is (1, 5)
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