First of all, we would calculate the predetermined overhead rate by using this formula:
Predetermined overhead rate = Manufacturing overhead/Direct material costs
Predetermined overhead rate = $2,342,400/$1,464,000
Predetermined overhead rate = 1.6 per DM $.
Next, we would calculate the overhead applied by using this formula:
Overhead applied = Job × DM cost
For job 0701, we have:
Overhead applied = 76,000 × 1.6
Overhead applied = $121,600.
For job 0702, we have:
Overhead applied = 104,000 × 1.6
Overhead applied = $166,400.
For job 0703, we have:
Overhead applied = 135,000 × 1.6
Overhead applied = $216,000.
For job 0704, we have:
Overhead applied = 67,000 × 1.6
Overhead applied = $107,200.
Part B.For the overapplied manufacturing overhead for year 1:
Less applied overhead = $1,630,000 × 1.6
Less applied overhead = $2,608,000.
Overapplied manufacturing overhead = Actual overhead cost - Less applied overhead
Overapplied manufacturing overhead = $2,480,000 - $2,608,000
Overapplied manufacturing overhead = $128,000.
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Select the common ratio and the 4th term of the geometric series: 9, -6,4...
The given geometric sequence has the common ratio, r = -2/3, and the value of the 4th term, a₄ = -8/3.
A geometric sequence is a special series where every term is the product of the previous term and a common ratio.
The first term of a geometric sequence is represented as a, the common ratio as r, and the n-th term as aₙ, which is calculated as, aₙ = a.rⁿ⁻¹.
In the question, we are asked to find the common ratio and the 4th term of the geometric sequence, 9, -6, 4, ........
The first term of the sequence, a = 9.
The second term of the sequence, a₂ = -6.
By the formula of the n-th term, aₙ = a.rⁿ⁻¹, we can show that:
a₂ = a.r²⁻¹.
Substituting the values, we get:
-6 = 9(r²⁻¹),
or, r²⁻¹ = -6/9,
or, r = -2/3.
Thus, the common ratio of the given geometric sequence is -2/3.
The 4th term can be calculated using the formula of the n-th term, aₙ = a.rⁿ⁻¹ as:
a₄ = a.r⁴⁻¹ = a.r³.
Substituting the values, we get:
a₄ = 9(-2/3)³,
or, a₄ = 9.(-8/27),
or, a₄ = -8/3.
Thus, the 4th term of the given geometric sequence is -8/3.
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Find X:
J:58
K:70
L:111
M:121
Answer:
L
Step-by-step explanation:
interior angle formula so
(number of sides - 2)*180
2*180 = 360
you can also just take an example from a square 4*90 = 360
360-121-58-70 = 111
PLEASE HELP AS SOON AS POSSIBLE
A quadrilateral PQRS is a parallelogram. PQ and RS are opposite sides then the answer of this particular question is , x = 4, the parallelogram PQRS is a rhombus, QR = 31, The opposite angles are congruent. Thus, more than one answer is correct.
According to the question,
PQ = 7x+12; RS = 5x -20 and QR = 31
Solving PQ and RS we get x = 4. Thus, PQ = 40 and RS = 40.
A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and congruent. A quadrilateral that has all sides equal and opposite sides parallel is called Rhombus.
Thus, the parallelogram PQRS is a rhombus.
Hence, a quadrilateral PQRS is a parallelogram. PQ and RS are opposite sides then the answer of this particular question is , x = 4, the parallelogram PQRS is a rhombus, QR = 31, The opposite angles are congruent. Thus, more than one answer is correct.
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if x varies directly as y, and
X = 24 when y= 21, Find x when
Y=6
Answer:
x = 48/7
Step-by-step explanation:
There's two good ways to do this problem.
Option 1:
Translate "x varies directly as y" into the equation y=kx
Then you have to find k. After you "reset" your y=kx equation, fill in k and then solve for x. See image.
Option 2:
Translate "varies directly" into a proportion, which is two fractions equal to each other:
x/y = x/y
Fill in the three numbers given and cross multiply and solve to find the fourth number. See image.
A COUPLE PLAN TO HAVE SIX CHILDREN. HOW MANY POSSIBLE OUTCOMES ARE IN
THE SAMPLE SPACE?
emily is standing 150 feet from a circular target with radius 3 inches. will she hit the target if her aim is off by 0.2 degrees?
Answer:
no
Step-by-step explanation:
The angle subtended by the radius of the target at Emily's distance can be found using the tangent relation.
Applicationtan(α) = opposite/adjacent = (1/4 ft)/(150 ft) = 1/600
The angle is found using the inverse relation:
α = arctan(1/600) ≈ 0.095°
If Emily's aim is off by 0.2°, she will miss the target by several inches.
__
Additional comment
Emily's projectile will miss her aiming point by ...
(150 ft)tan(0.2°) ≈ 0.524 ft ≈ 6.28 in
One company estimates same-day delivery as more than three less than half the total number of miles. Which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)? Note that the graphs have miles for the independent variable on the x-axis, and the y-axis is a unit of time dependent on the number of miles.
By using an online graphing calculator, the overall equation represented by this scenario is plotted in the image attached below.
How to determine the graph?Based on the information provided about this company with respect to its delivery and total number of miles to be covered, we would assign variables as follows:
Let y represent same-day delivery.Let x be the total number of miles.Next, we would translate the word problem into an algebraic equation by using an inequality:
y > x/2 - 3
Also, we would determine the intercepts as follows:
When x = 0, we have;
y = 0/2 - 3
y = -3.
y-intercept = (0, -3).
For the x-intercept, we have:
When y = 0, we have;
0 = x/2 - 3
x/2 = 3
x = 6.
x-intercept = (6, 0).
By using an online graphing calculator, the overall equation represented by this scenario is plotted in the image attached below.
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Answer:
c
Step-by-step explanation:
c is the answer
Suppose that the base salary of a salesperson is $30,000 per year. The salesperson gets an additional $50 for every sale. Let x represents the number of sales. How can we model the scenario with a linear function? How many items does the salesperson need to sell to earn $50,000
Answer:
See below
Step-by-step explanation:
Salary (y) = 30 000 + 50 x
y = 30 000 + 50x where x is the number of sales
How many sales for 50 000 ?
50 000 = 30 000 + 50 x
20 000 = 50 x
x = 400 sales
I. Model Problems
A linear model is a linear equation that represents a real-world
scenario. You can write the equation for a linear model in the same way
you would write the slope-intercept equation of a line. The y-intercept
of a linear model is the quantity that does not depend on x. The slope is
the quantity that changes at a constant rate as x changes. The change
must be at a constant rate in order for the equation to be a linear model.
Example 1 A machine salesperson earns a base salary of $40,000 plus
a commission of $300 for every machine he sells. Write an equation
that shows the total amount of income the salesperson earns, if he sells
x machines in a year.
The y-intercept is $40,000; the salesperson earns a $40,000 salary in a
year and that amount does not depend on x.
The slope is $300 because the salesperson’s income increases by $300
for each machine he sells.
Answer: The linear model representing the salesperson’s total income
is y = $300x + $40,000.
Linear models can be used to solve problems.
Example 2 The linear model that shows the total income for the
salesperson in example 1 is y = 300x + 40,000. (a) What would be the
salesperson’s income if he sold 150 machines? (b) How many
machines would the salesperson need to sell to earn a $100,000
income?
(a) If the salesperson were to sell 150 machines, let x = 150 in the linear
model; 300(150) + 40,000 = 85,000.
Answer: His income would be $85,000.
(b) To find the number of machines he needs to sell to earn a $100,000
income, let y = 100,000 and solve for x:
A certain cellular phone plan charges $31.00 per month plus $0.14 for each minute of usage. The monthly charge is given by the formula monthly charge=0.14x+31, where x represents the number of minutes of usage per month. What is the charge for a month with 340 minutes of usage? Write your answer to two decimal places as money is traditionally written.
Answer:
$78.60
Step-by-step explanation:
0.14x + 31 = 0.14*340 + 31 = 78.6
what is 7/8 - 1/2 as a fraction
Answer: 3/8
Step-by-step explanation:
1/2 is also 4/8 so you subtract 4/8 from 7/8 to get 3/8
please help :,)
(geometry involving arc lengths)
Answer:
bx/a (3rd choice)
Step-by-step explanation:
The length of an arc, s, in a circle of radius r, and central angle Θ given in radians is
s = rΘ
Circle M has radius a. The central angle in radians of the sector is Θ. The length of the arc is x.
x = aΘ
Solve for Θ:
Θ = x/a Eq. 1
Circle N has radius b. The central angle in radians of the sector is Θ. The length of the arc is s.
s = bΘ
Solve for Θ:
Θ = s/b Eq. 2
Since Θ = Θ, then equate the right sides of Equations 1 and 2 above.
x/a = s/b
Multiply both sides by ab.
abx/a = abs/b
bx = as
as = bx
s = bx/a
Answer: bx/a
a box with a square base has length plus girth of 108 in. What is the length of the box if its volume is 2200 in^3?
The missing length of the box with square base is 20.370 inches.
What is the missing length of the box?
This box can be represented by a right prism, whose volume (V), in cubic inches, is the product of the area of the base (A), in square inches, and the height of the box (h), in inches. The area of the base is equal to the square of the side length (l):
V = l² · h (1)
If we know that V = 2 200 in³ and l = 108 in, then the height of the box is:
h = V / l²
h = (2 200 in³) / (108 in)
h = 20.370 in
The missing length of the box with square base is 20.370 inches.
Remark
The statement presents typing mistakes, correct form is shown below:
A box with a square base has a side length of 108 in. What is the length of the box if its volume is 2 200 in³?
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7x+28=7(x+4) how many solutions
The equation 7x + 28 = 7(x + 4) has infinite many solutions
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the number of solutions?A system of linear equations is a collection of at least two linear equations.
In this case, the equation is given as
7x + 28 = 7(x + 4)
Open the bracket
7x + 28 = 7x + 28
Subtract 7x from both sides of the equation
28 = 28
Subtract 28 from both sides of the equation
0 = 0
The above equation is true, because both sides of the equation are the same
This means that the equation has infinite many solutions
Hence, the equation 7x + 28 = 7(x + 4) has infinite many solutions
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An unknown radioactive element decays into non-radioactive substances. In 340
days the radioactivity of a sample decreases by 61 percent.
(a) What is the half-life of the element?
half-life: ? (days)
(b) How long will it take for a sample of 100 mg to decay to 81 mg?
time needed: ? (days)
(a) The half-life of the unknown radioactive element is 250.28 days.
(b) The time taken for a sample of 100 mg to decay to 81 mg is 76.1 days.
Half life of the unknown radioactive elementN(t) = N₀(0.5)^t/h
where;
t is time of decayh is half lifeN₀ is initial massN(t) remaining mass at time, tin 340 days; N(340) = N₀(0.39);
1 - 0.61 = 0.39
N(340) = N₀(0.5)^340/h
N(340)/N₀ = 0.5^340/h
0.39 = 0.5^340/h
log(0.39) = 340/h x log(0.5)
log(0.39) /log(0.5) = 340/h
1.358 = 340/h
h = 340/1.358
h = 250.28 days
Time taken for the sample to decay 81 mg81 = 100(0.5)^t/250.28
81/100 = (0.5)^t/250.28
0.81 = (0.5)^t/250.28
log(0.81) = t/250.28 x log(0.5)
log(0.81) / log(0.5) = t/250.28
0.304 = t/250.28
0.304(250.28) = t
76.1 days = t
Thus, the half-life of the unknown radioactive element is 250.28 days and the time taken for a sample of 100 mg to decay to 81 mg is 76.1 days.
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Add: 5/7 + 9/11 + 21/77
Answer:
Step-by-step explanation:
You want to begin by making each fraction have the same common denominator. The LCF (least common factor) is 77. So, knowing this, we can now multiply the fractions that need to have a denominator of 77.
1. 5/7*11/11=55/77
2. 9/11 * 7/7 =63/77
Now we can add
55/77 + 63/77 + 21/77 = 139/77 or 1.805194805
What is the length of S?
Answer:
S = √( 1009)
Step-by-step explanation:
S = √( h² + 1/2)²)
S = √(28² + 15²)
S = √( 1009)
Hope this helps u!
[tex] \: \: \: \: \: \: \: \: \: \: \: n\\ evaluate \: \: \: \: \: Σ \: (nCi)\\ \: \: \: \: \: \: \: \: \: \: \: \: i = 0[/tex]
Evaluate the summation
Assuming you mean
[tex]\displaystyle \sum_{i=0}^n {}_nC_{i}[/tex]
where
[tex]{}_n C_i = \dbinom ni = \dfrac{n!}{i! (n-i)!}[/tex]
we have by the binomial theorem
[tex]\displaystyle (1 + 1)^n = \sum_{i=0}^n {}_nC_{i} \cdot 1^i \cdot 1^{n-i}[/tex]
so that the given sum has a value of [tex]\boxed{2^n}[/tex].
Two jets leave an air base at the same time and travel in opposite directions. One jet travels 80 mi/h faster than the other. If the two jets are 11392 miles apart after 8 hours, what is the rate of each jet?
Jet 1 moves with a speed of 672 mi/h, while jet 2 moves with a speed of 672 mi/h + 80mi = 752 mi/h.
How to get the rate of each jet?
Let's say that the rate (or speed) of the slower jet is R, then the rate of the faster jet is:
R + 80mi/h
Now, if we step on any of the two jets (such that we view it as if it doesn't move) the other jet will move with a speed equal to:
S = R + R + 80mi/h
We know that after 8 hours, the to jets are 11,392 mi apart, then we know that:
(R + R + 80mi/h)*8h = 11,392 mi
Now we can solve that for R:
2*R + 80mi/h = 11,392 mi/8h = 1,424 mi/h
R = 1,424 mi/h - 80mi/h)/2 = 672 mi/h
So Jet 1 moves with a speed of 672 mi/h, while jet 2 moves with a speed of 672 mi/h + 80mi = 752 mi/h.
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An object is launched directly in the air at a speed of 64 feet per second from a platform located 16 feet above the ground. The position of the object can be modeled using the function f(t)=−16t2+64t+16, where t is the time in seconds and f(t) is the height, in feet, of the object. What is the maximum height, in feet, that the object will reach?
Considering the vertex of the quadratic equation, the maximum height that the object will reach is of 80 feet.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex][tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the equation is:
f(t) = -16t² + 64t + 16.
Hence the coefficients are:
a = -16, b = 64, c = 16.
The maximum value is found as follows:
[tex]y_v = -\frac{64^2 - 4(-16)(16)}{4(-16)} = 80[/tex]
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\left(a-b\right)\sqrt{\frac{2}{a^2-b^2}}
Answer:
[tex]\left(a-b\right)\sqrt{\frac{2}{a^2-b^2}}[/tex]
=
[tex]\frac{ \sqrt{2} }{a + b} [/tex]
Step-by-step explanation:
[tex]\left(a-b\right)\sqrt{\frac{2}{a^2-b^2}}[/tex]
[tex](a - b)( \frac{ {2}^{ \frac{1}{2} } }{(a + b)(a - b)} )[/tex]
[tex] \frac{(a - b)( {2}^{ \frac{1}{2} }) }{(a - b)(a + b)} = \frac{ \sqrt{2} }{a + b} [/tex]
Melissa is putting money into a checking account. Let y represent the total amount of money in the account (in dollars). Let x represent the number of weeks Melissa has been adding money. Suppose that x and y are related by the equation y = 550+20x.
Answer the questions below. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.
What is the change per week in the amount of money in the account?
What was the starting amount of money in the account?
Check the picture below.
In 2016, the city of Rio de Janeiro had a population density of 5377 people/km2
What was the population density of Rio de Janeiro in people per square meter
As part of a summer internship, five people -- Cindy, Damaris, Eugenio, Fareed, and Guzal -- are to be assigned to floors 1-5 in a dormitory. Each person will occupy his or her own entire floor and no other people will be in the dormitory. The assignment of people to floors must follow the following rules: Eugenio lives immediately above Damaris. Cindy is not on the first floor. Fareed does not live immediately below Damaris. Guzal lives either on the first floor or the fifth floor. Which one of the five people could be assigned to live on any of the five floors in the dormitory?
Based on the information, it is expected Fareed can be assigned to live on any of the floors.
What condition limits Fareed's assignment?The only condition that limits the floor Fareed can be assigned to is that he cannot be immediately below Damaris. This means that as long as Damaris is not immediately above him, he can be assigned to all floors. Here are two possible arrangements:
Eugenio (5th floor)DamarisCindyFareedGuzal (1st floor)Guzal (5th floor)EugenioDamarisCindyFareed (1st floor)Learn more about arragements in: https://brainly.com/question/27909921
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So confused please help me thank u
Choose the equation that
matches the graph.
a. (1/2)x-4
b. y = 4x-1
C.
y = (1/1)
(¹²) ² − 4
-
d.
e.
x-4
y = (1/1)
y = 4x + 1
y = 4x+1
Answer: d
Step-by-step explanation:
The graph is increasing, so the base must be more than 1.
Eliminate a and c.Also, the y-intercept is 2.
Eliminate b and e.This leaves d.
Can I just get the answer for this I feel like it’s wrong.
The initial membership fee for Club A is; $2.5.
The initial membership fee for Club B is; $3.
Hence, Club A has a lower initial membership fee.
What is the initial membership fee for each Club?It follows from the concepts of linear graphs that the interpretation of the initial membership fee is the y-intercept of the graphs given.
This is so because, it corresponds to the total cost at a point when the number of movies watched is; 0. That is, before any movie is watched.
Consequently, the graph calibrations (including the missing Club A graph) allow the determination of the initial membership fee (y-intercept) as declared above.
Ultimately, Club A has a lower initial membership fee.
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From the diagram below, if the tree is 34 ft. tall, and the angle of elevation from point B to the top of the tree is 26 °, find the distance that the tree is from point B. (Round to the nearest whole foot.)
Given the height of the tree and the angle of elevation from point B, the distance between the tree is from point B is approximately 70ft.
What is the distance between the tree and point B?
Given the data in the question;
Height of tree opposite angle of elevation = 34ftAngle of elevation θ = 26°Distance between tree and point B| Adjacent = ?Since the scenario form a right angle triangle, we use trig ratio.
tanθ = Opposite / Adjacent
tan( 26° ) = 34ft / x
We solve for x
x = 34ft / tan( 26° )
x = 34ft / 0.4877
x = 70ft
Given the height of the tree and the angle of elevation from point B, the distance between the tree is from point B is approximately 70ft.
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Identify the coefficient -7x2 y4
The answer is -7.
The coefficient is the part of the variable that does not change with respect to the variable.
Hence, in the monomial -7x²y⁴, the coefficient is -7.
please help with the first one
Answer:
y = x +5
Step-by-step explanation:
The equation of a parallel line will have the same x- and y-coefficients, but a different constant. You need to find the constant that makes the line go through the given point.
ApplicationThe given line is y = x +1. The equation you're looking for is
y = x +c . . . . . . for some new constant c
We want this equation to be true for (x, y) = (-2, 3). Putting these values into the equation, we can solve for c.
3 = -2 +c
5 = c . . . . . . add 2
The desired equation is y = x +5.
So,some please help me with this question !
=============================================================
Explanation:
Angles EBA and DBC are congruent because of the similar arc marking. Both are x each.
Those angles, along with EBD, combine to form a straight angle of 180 degrees. We consider those angles to be supplementary.
So,
(angleEBA) + (angleEBD) + (angleDBC) = 180
( x ) + (4x+12) + (x) = 180
(x+4x+x) + 12 = 180
6x+12 = 180
6x = 180-12
6x = 168
x = 168/6
x = 28
Angles EBA and DBC are 28 degrees each.
This means angle D = 3x+5 = 3*28+5 = 89
-----------
Then we have one last set of steps to finish things off.
Focus entirely on triangle DBC. The three interior angles add to 180. This is true of any triangle.
D+B+C = 180
89 + 28 + C = 180
117+C = 180
C = 180 - 117
C = 63 degrees
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:x + 4x + 12 + x=180°[/tex]
( Angle EBA= Angle DBC, and the three angles sum upto 180° due to linear pair property )
[tex]\qquad❖ \: \sf \:6x + 12 = 180[/tex]
[tex]\qquad❖ \: \sf \:6x = 180 - 12[/tex]
[tex]\qquad❖ \: \sf \:6x = 168[/tex]
[tex]\qquad❖ \: \sf \:x = 28 \degree[/tex]
Next,
[tex]\qquad❖ \: \sf \: \angle C + \angle D + x = 180°[/tex]
[tex]\qquad❖ \: \sf \: \angle C +3x + 5 + x = 180°[/tex]
[tex]\qquad❖ \: \sf \: \angle C +4x = 180 - 5[/tex]
[tex]\qquad❖ \: \sf \: \angle C +4(28) = 175[/tex]
( x = 28° )
[tex]\qquad❖ \: \sf \: \angle C +112 = 175[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 175 - 112[/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \: \angle C = 63 \degree[/tex]
