The Laplace transform of the function f on (0,0) defined by f(t) = i Se^4t is L(f)(s) = i S / (2s-4).
Given function is f(t) = i Se^4t
Here, Laplace transform of the function f is given by:
L(f)(s) = ∫[0,∞) e^(-st) f(t) dt
On substituting the given function in the above equation, we get:
L(f)(s) = ∫[0,∞) e^(-st) i Se^(4t) dt
L(f)(s) = i S ∫[0,∞) e^(t(4-s)) dt
We know that the Laplace transform of e^(at) is 1/(s-a).
Therefore, Laplace transform of e^(t(4-s)) = 1/(s - (4-s)) = 1/(2s - 4).
Therefore,L(f)(s) = i S * ∫[0,∞) e^(t(4-s)) dt
L(f)(s) = i S * 1/(2s-4) * [-e^(-(4-s)t)]_0^∞
L(f)(s) = i S * 1/(2s-4) * [0 - (-1)] (since the exponentials evaluated at ∞ is zero)
L(f)(s) = i S * 1/(2s-4) * 1
L(f)(s) = i S / (2s-4)
Therefore, the Laplace transform of the function f on (0,0) defined by f(t) = i Se^4t is L(f)(s) = i S / (2s-4).
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6) You are shooting the puck along the path
seen in the picture of the air hockey table.
Find the mZxº and the mzmº.
Answer:
m = 58°
x = 64°
Step-by-step explanation:
When a puck touches one side of the air hockey table,
All the angles formed are located at a point on a straight line.
Therefore, sum of angles formed is 180°.
m° + m° + 64° = 180°
2m + 64 = 180
2m = 180 - 64
2m = 116
m = 58°
m∠y = m = 58° [Alternate interior angles]
Similarly, on the other side of the table,
58° + y° + x° = 180°
58° + 58° + x° = 180°
x + 116° = 180°
x = 180 - 116
x = 64°
Let 21, a2, a3 be a sequence defined by a1 = 1 and ak = 2ak-1 . Find a formula for an and prove it is correct using induction.
The formula for the sequence is an = [tex]2^n[/tex], where n is a positive integer. This formula is proven correct using mathematical induction.
To find a formula for the sequence defined by a1 = 1 and ak = 2ak-1, we can use mathematical induction to establish a pattern and then derive the formula. Here's how we can solve it step by step:
Step 1: Base case:
For k = 1, we have a1 = 1.
Step 2: Assume the formula holds for some positive integer n, where n ≥ 1.
Assume that an = [tex]2^{n-1[/tex] for some positive integer n.
Step 3: Use the assumption to prove the formula for the next term.
Now, let's prove that an+1 = [tex]2^n[/tex] holds.
Using the recursive formula ak = 2ak-1, we have:
an+1 = 2an
Substituting the assumed formula an = [tex]2^{n-1[/tex], we get:
an+1 = 2([tex]2^{n-1[/tex])
To simplify, we have:
an+1 = [tex]2^n[/tex]
Step 4: Conclusion:
Based on the assumption and the proof for the next term, we can conclude that the formula an = [tex]2^n[/tex] holds for all positive integers n ≥ 1.
Therefore, the formula for the sequence defined by a1 = 1 and ak = 2ak-1 is an = [tex]2^n[/tex].
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Simplify the problem.
Answer:
Option 4: 4¹¹
Step-by-step explanation:
Looking at the problem, I need to work out 4⁴ squared first, which is the same as 4⁸. Then multiply that by 4³ to get 4¹¹. What I did was simply add 3 + (4 * 2), which is 11.
Let In be the number of n-digit quinary (0, 1, 2, 3, 4) sequences with (i) at least one 3 and (ii) the first 3 occurs before the first 0 (possibly no 0's). (Examples of 4-digit legal quinary sequences: 3120, 3000, 4123) (a) Show 91 = 1,92 = 8. = (b) Show a recurrence for an is qn = 39n-1 +5n-1 (91 = 1). = = 5" - 35 (c) A closed form for en is In = (n > 1). Finish the induction proof of this fact 2 (began below) by completing the induction step: 57 - 31 Base case (n = 1): LHS = q1 = 1. RHS 1 2 5k - 3k Induction Hypothesis: Assume true for n=k, i.e., Pk Induction Step: = II 2 N (d) Show how to derive this closed form, i.e., show how one can arrive at this closed form if they only knew the recurrence and the initial values.
Part a:Here, In be the number of n-digit quinary (0, 1, 2, 3, 4) sequences with(i) at least one 3 and (ii) the first 3 occurs before the first 0 (possibly no 0's).Since there is at least one 3 in the n-digit sequence, we start the sequence by selecting one of the 5 digits. There are five ways to do this.The next digits are chosen according to one of the three cases shown below:1) A string of (n-1) digits where no 0's are included in the string.2) A string of (n-1) digits where at least one 0 appears in the string before the first 3.3) A string of (n-1) digits where 3 appears before the first 0 in the string.The first string in case 1 can be formed in 4 different ways because no 0's can appear in the string and there are 4 digits to choose from (0, 1, 2, 4). There are 5 choices for the first digit and thus 5*4 quinary sequences of length n with at least one 3 and no 0's that start with the selected digit.The first string in case 2 can be formed in 5 different ways because the first 3 can appear in any position before the first 0. The remaining digits are chosen in n-2 positions because the first digit is already chosen (which is 3) and n-1 digits are left. There are 4 choices for each of the remaining n-2 positions because no 0's can appear in the string and there are 4 digits to choose from (0, 1, 2, 4). Thus, there are 5*5*4^(n-2) quinary sequences of length n with at least one 3 and at least one 0 that start with the selected digit.The first string in case 3 can be formed in n-1 different ways because the first 3 can appear in any position before the first 0. The remaining digits are chosen in n-2 positions because the first digit is already chosen (which is 3) and n-1 digits are left. There are 4 choices for each of the remaining n-2 positions because no 0's can appear in the string and there are 4 digits to choose from (0, 1, 2, 4). Thus, there are 5*(n-1)*4^(n-2) quinary sequences of length n with at least one 3 and at least one 0 that start with the selected digit.Therefore, the number of n-digit quinary sequences with (i) at least one 3 and (ii) the first 3 occurs before the first 0 (possibly no 0's) is the sum of the number of sequences in each of the three cases above, i.e.In = 5*4^(n-1) + 5*5*4^(n-2) + 5*(n-1)*4^(n-2)Part b:Recurrence: qn = 3q(n-1) + 4^(n-1) + 2. q1 = 1. Let's see if qn = 39(n-1) + 5(n-1) satisfies this recurrence.q1 = 1 = 3(1-1) + 4^(1-1) + 2 = 0 + 1 + 2 = 3(0) + 5(1-1) + 1 = 0 + 0 + 1Thus, q1 = 1 satisfies the recurrence.qn+1 = 3qn + 4^n + 2 = 3(39n-1 + 5n-1) + 4^n + 2= 117(n-1) + 15(n-1) + 4^n + 2= 132(n-1) + 4^n + 3Using this formula, we can see that q2 = 91.Part c:Here, we need to finish the induction proof of this fact 2 that In = (n > 1).Induction Hypothesis: Assume true for n = k, i.e., Pk = Ik = 5*4^(k-1) + 5*5*4^(k-2) + 5*(k-1)*4^(k-2)Induction Step: To show that it is true for n = k+1, we need to show that the formula given above holds. The first digit can be any of the 5 digits (0, 1, 2, 3, 4) and the remaining digits can be selected in one of the three ways discussed in part (a).Case 1: n-1 digits with no 0'sThere are 4 choices for each of the n-1 digits, since 0 cannot be used. Therefore, there are 4^(n-1) such sequences with no 0's.Case 2: n-1 digits with at least one 0 before the first 3The first 3 can be in any of the n-1 positions, and the digits before it must be chosen from the set {0,1,2,4}. The remaining digits can be chosen in any of the 4 choices. Therefore, there are 5*(n-1)*4^(n-2) such sequences.Case 3: n-1 digits with 3 before 0We start by selecting one of the n-1 positions for the 3, then the remaining digits are chosen from the set {0,1,2,4}. There are (n-2) positions left for the remaining digits. There are 4 choices for each position, since 0 cannot be used. Therefore, there are 5*(n-1)*4^(n-2) such sequences.Thus, the total number of n-digit quinary sequences with at least one 3 and with the first 3 before the first 0 isIn = 5*4^(n-1) + 5*5*4^(n-2) + 5*(n-1)*4^(n-2) = qn+1 - qn = 132(n-1) + 4^n + 3 - (39(n-1) + 5(n-1)) = 93(n-1) + 4^n + 3which completes the induction proof.Part d:Since qn = 39n-1 + 5n-1, we haveqn+1 - qn = 132n - 39n - 5n = 88nTherefore, qn+1 = qn + 88nSubstituting qn = 39n-1 + 5n-1, we getqn+1 = qn + 88n = 39n-1 + 5n-1 + 88n = 39n + 5n + 88(n-1)Simplifying, we getqn+1 = 132(n-1) + 4^n + 3Therefore, en = In - In-1 = 93(n-1) + 4^n + 3 - 93(n-2) - 4^(n-1) - 3= 93n - 93(n-1) - 4^(n-1)= 93 - 4^(n-1)Thus, the closed form for en is en = 93 - 4^(n-1).
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question is on the picture
Answer:
12/5
Step-by-step explanation:
Pythagorean theorem=> adjacent side=5
tanx=oppx/adjx
tanx=12/5
HELP MEEEEEE i dont get it my teaher didnt teach me dis??
Answer:
6
Step-by-step explanation:
because i had the same question and the departments where 6
Answer:
Hey! I can teach you this.
The range is the distance between the highest and lowest numbers.
In this case, the lowest number is 3, and the highest is 54, making the range 54 - 3, which is 51.
Because 3 is 51 away from 54. I hope this helps you!
Your class is planning a breakfast bake sale and you have been tasked to bake the donuts and bagels. The system below represents the total amount of flour, in pounds, needed to replicate a batch-of-six bagel recipe and a batch-of-twelve donut recipe. You will be replicating the donut recipe d number of times and the bagel recipe b number of times. 3d + 5b = 21 d + b = 5
Answer:
3 bagel recipe and 2 doughnut recipes are needed
Step-by-step explanation:
Given the expression
3d + 5b = 21 .. 1
d + b = 5 .... 2
We can use the expression to look for the amount of doughnut recipe and bagel recipe needed by solving the equations simultaneously
Multiply equation 1 by 1 and 2 by 3 to have;
3d + 5b = 21 .. 3
3d + 3b = 15 .... 4
Subtract 3 from 4
5b - 3b = 21 - 15
2b = 6
b = 6/2
b = 3
Substitute b = 3 into equation 2;
From 2,
d = b = 5
d + 3 = 5
d = 5 - 3
d = 2
Hence 3 bagel recipe and 2 doughnut recipes are needed
Which of the following indicate that the result from a simple linear regression model could be potentially misleading? a. The error terms follow a normal distribution b. The error terms exhibit homoscedasticity c. Then n th error term (e_n) can be predicted with e_n = 0.91 * e_n - 1 d. The dependent and the independent variable show a linear pattern
The correct answer is: c. The n-th error term (e_n) can be predicted with e_n = 0.91 * e_n - 1.
This statement indicates that there is a correlation or relationship between consecutive error terms, where the n-th error term can be predicted based on the previous error term. In a simple linear regression model, the error terms are assumed to be independent and have no correlation with each other.
However, if there is a correlation between the error terms, it violates the assumption of independence, which can lead to biased and unreliable regression results. Therefore, this condition suggests that the result from the simple linear regression model could be potentially misleading.
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The green house is made completely of glass, except for the door. The entire building is 15 feet tall. The height of the vertical walls is 10 ft. The green house is 20 ft long (on side with door) and 16 feet wide. The triangles that make up the roof are isosceles triangles (both sides are equal and height is measured at the middle of the base). The door is 8 feet wide and 7 feet tall. Answer each of the following questions about your greenhouse.
Hose for watering the plants will be run along the entire outer edge of the floor, and up, around
the door. How much hose will be needed for this task?
A hose will be needed vertical walls to run along the entire outer edge of the floor and up around the door of the greenhouse 88 feet .
To calculate the length of the hose needed to run along the entire outer edge of the floor and up around the door of the greenhouse, we need to consider the perimeter of the floor and the additional distance around the door.
The perimeter of the floor is the sum of the lengths of all four sides of the rectangle. Since the greenhouse is 20 ft long and 16 ft wide, the perimeter of the floor is:
Perimeter of floor = 2(length + width) = 2(20 ft + 16 ft) = 2(36 ft) = 72 ft
In addition to the floor perimeter, to account for the distance around the door. The door is 8 ft wide, so the additional distance around the door is:
Distance around door = 2(width of door) = 2(8 ft) = 16 ft
calculate the total length of the hose needed by adding the perimeter of the floor and the distance around the door:
Total length of hose = Perimeter of floor + Distance around door = 72 ft + 16 ft = 88 ft
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Write an expression that is equivalent to -4(3x – 7).
-4(3x – 7) =
– D
2 +
?
What is the complement of an angle of 41°?
(A) 41°
(B) 49°
(C) 139°
(D) 90°
(E) 180°
Race) The longest racial grouping of respondents to the 2012 GSS was______, with ______%. The second-largest grouping was _____, with ______%.
The longest racial grouping of respondents to the 2012 GSS was non-Hispanic white, with 78.7%. The second-largest grouping was Black or African American, with 15.6%.
The General Social Survey (GSS) is a nationally representative survey of American adults that has been conducted annually since 1972. The GSS collects data on a wide range of topics, including race and ethnicity. In 2012, the GSS asked respondents to identify their race and ethnicity. The results showed that the largest racial grouping in the United States was non-Hispanic white, followed by Black or African American. in the 2012 GSS or any other related information, it is recommended to refer to the official documentation or reports from the General Social Survey (GSS).
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If the coordinate of A is (0,-2) and the coordinate of B is (10,-6), then the midpoint of AB is (______).
Answer:
5, -4
Step-by-step explanation:
midpoint = x1 + x2/2 ,y1 + y2/2
= 0 + 10 /2 , -2 + -6/2
= 10/2 , -8/2
midpoint = 5, -4
The scale on a map is 1 in: 55 miles. What is the distance on the map between two cities that are 99 miles apart?
Answer:
1.8 inches
Step-by-step explanation:
Create a proportion where x is the distance on the map
[tex]\frac{1}{55}[/tex] = [tex]\frac{x}{99\\}[/tex]
Cross multiply and solve for x
55x = 99
x = 1.8
So, the distance on the map is 1.8 inches
Answer:
1.8 inches
Step-by-step explanation:
Scales on a map always represent the direct proportion.
Compare the distances as fractions:
Inches on the map
________________ = [tex]\frac{1}{55} = \frac{x}{99}[/tex]
Miles on the ground
[tex]x = \frac{1x99}{55}[/tex]
[tex]x = \frac{99}{55}[/tex]
[tex]x = \frac{9}{5} = 1\frac{4}{5}[/tex]
x = 1.8 inches
50 points
The frequency table below shows the length of selected movies shown in a local
theater over the past six months.
Answer:
Lol its in total of 34
Step-by-step explanation:
Susan found the equation of the best fit line for the data shown in the scatterplot. The slope of the line of best fit is
Answer:
Negative
Step-by-step explanation:
From the scatter plot displayed, we could clearly observe the direction of the trend line as it produces a negative slope. For high values of y, the values of x are low and similarly, high values of x have low y values. Therefore, this kind of relationship between the two variables is considered negative.
which of the following functions are solutions of the differential equation y′′−9y′ 18y=0? a. y(x)=e6x b. y(x)=e−x c. y(x)=e3x d. y(x)=0 e. y(x)=6x f. y(x)=3x g. y(x)=ex
Only one of the following functions is a solution of the differential equation y′′−9y′+18y=0.
The second-order homogeneous linear differential equation is given as:y'' - 9y' + 18y = 0This differential equation is a linear homogeneous equation. We will have two roots of the characteristic equation: r1 = 3, r2 = 6So, the general solution to the differential equation is given as:y = c1e3x + c2e6xwhere c1 and c2 are arbitrary constants.a. y(x) = e6x is a solution because it is a part of the general solution of the differential equation.y(x) = e−x, y(x) = 0, y(x) = 6x, y(x) = 3x, y(x) = ex are not solutions because they don't satisfy the differential equation. Hence, the correct options are:a. y(x) = e6xTherefore, only one of the following functions is a solution of the differential equation y′′−9y′+18y=0.
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Is 7n+6 equal to 13n?
Answer:
No
Step-by-step explanation:
Say n was equal to 2
7(2) + 6 =20
13(2) = 26
5x + 2 = x – 10 help
Answer:-3/4
Step-by-step explanation:
5x+2=x-1
5x-x=-1-2
4x=-3
X=-3/4
A student selects three marbles of different color-One is red, the second blue and the third is green. He picks the marbles one at a time without replacement. What is the probability he selects a blue. followed by a red, and then green?
Here's an Overleaf PDF I created with an explanation for your question:
find the measure of each interior angle of a regular polygon with the following number of sides 4
Answer:
90°
Step-by-step explanation:
Formula to find EACH interior angle:
[tex]\frac{(n-2) *180}{n}[/tex]
Given:
n (number of sides) = 4
Work:
[tex]\frac{(n-2) *180}{n} \\\\\frac{(4-2) *180}{4} \\\\\frac{(2) *180}{4} \\\\\frac{360}{4} \\\\90[/tex]
The function h defined by h(t)=(-4.9t + 29.4)(t+2) models the height in meters, of an object t seconds after it is launched. When will the object hit the ground?
Answer:
The time the object will hit the ground is 2 s.
Step-by-step explanation:
Given;
h(t) = (-4.9t + 29.4)(t + 2)
Open the bracket;
h(t) = -4.9t² + 29.4t -9.8t + 58.8
h(t) = -4.9t² + 19.6t + 58.8
When the object hit the ground, the final velocity will be zero;
[tex]v = \frac{dh}{dt} = 0 \\\\\frac{dh}{dt} = -9.8t + 19.6 = 0\\\\9.8t = 19.6\\\\t = \frac{19.6}{9.8} \\\\t = 2 \ s[/tex]
Therefore, the time the object will hit the ground is 2 s.
A bag contains 4 blue coins and 7 red coins. A coin is removed at random and placed by three of the other color.
What is the probability that the removed coin is blue?
Answer:
The probability is 7/11
Step-by-step explanation:
This is because there are 7 blue coins that you can grab out of 11 coins in total.
Find the lateral surface area.
Answer:
Step-by-step explanation:
Cool-down Melanie and Kala each started solving equation 2 for x. 1 (7x – 6) = 6x – 10 The result of Melanie's first step was: 3.5x = 6 = 6x - 10 The result of Kala's first step was: 7x - 6= 12x - 20 One of them made an error. Who was it, and what was the error?
I need to find who made the error and what was the error
Answer:
Kala's first step.
Step-by-step explanation:
Solving linear equations.
Step 1: Simplify each side, if needed. Step 2: Use Add./Sub. Properties to move the variable term to one side and all other terms to the other side. Step 3: Use Mult./Div. Step 4: Check your answer. I find this is the quickest and easiest way to approach linear equations. Example 6: Solve for the variable.But Kala did not do that. Instead, she skipped the first stages and moved on ahead, making her equation invalid.
A business student conducts an OLS regression analysis in excel (with usual defaults) with demand for strawberries (in 1000 units) as the dependent and price (in dollars) as an independent variable. The OLS regression line is given by y= 9 − 3x. If the pvalue of the intercept coefficient is 0 and the pvalue of the slope coefficient is 2% & If the standard error of the intercept coefficient is 6 and the standard error of the slope coefficient is 1; the true slope will be ______ to/from the estimated slope and the true intercept will be ________ to/from the estimated intercept.
Group of answer choices
equal, equal
different, equal
equal, different
different, different
The true intercept and slope are both different from the estimated values based on statistical significance.
The p-value of the intercept coefficient and that of the slope coefficients are 0 and 0.02(2%) respectively. This means that they are statistically significant. Thus we can infer that the true intercept and slope is not equal to 0.
The standard error of the intercept coefficient is 6, which means that the true intercept is likely to be within 6 units of the estimated intercept. The standard error of the slope coefficient is 1, which means that the true slope is likely to be within 1 unit of the estimated slope.
Therefore, the true slope and intercept will be different from the estimated slope and intercept.
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HELP PLEASE AND ASAP!! look at screenshot (10 pts)
Answer:
C
Step-by-step explanation:
Add like terms to get
4.5a + 4b + 3.5c
Can someone please help me on this
Answer:
the 1 one
Step-by-step explanation:
Answer:
113.4=x(18)
x=6.3
Step-by-step explanation:
It says the product of a number, x, and 18 is 113.4. Since it says product there will be multiplication. The word "is" tells us that x and 18 equals 113.4. Is x= 6.3, 6.3 times 18 equals 113.4. This is a true equation.
The cutting department of Pharoah Manufacturing has the following production and cost data for July.
Production
Costs
1.
Completed and transferred out 12,500 units.
Beginning work in process
$-0-
2.
2,850 units in ending work in process inventory are 60% complete
Direct materials
42,980
in terms of conversion costs and 100% complete
Direct labour
15,700
in terms of materials at July 31.
Manufacturing overhead
18,404
Materials are entered at the beginning of the process. Conversion costs are incurred uniformly throughout the process.
(a)
Correct answer icon
Your answer is correct.
Determine the equivalent units of production for materials and conversion costs.
Direct Materials
Conversion Costs
Total equivalent units
enter a number of units enter a number of units
eTextbook and Media
Attempts: unlimited
(b)
Calculate unit costs and prepare a cost reconciliation schedule. (Round unit costs to 2 decimal places, e.g. 15.25.)
Unit costs
Direct materials
$enter a dollar amount rounded to 2 decimal places
Conversion costs
$enter a dollar amount rounded to 2 decimal places
Cost Reconciliation Schedule
Costs accounted for
Completed and transferred out
$enter a dollar amount
Work in process inventory, July 31
Direct materials
$enter a dollar amount
Conversion costs
enter a dollar amount enter a subtotal of the two previous amounts
Total costs
a) The determination of the equivalent units of production for materials and conversion costs is as follows:
Equivalent units of production:Units Materials Conversion
Completed and transferred out 12,500 12,500 12,500
Ending work in process 2,850 2,850 1,710
Total equivalent units 15,350 15,350 14,210
b) The calculation of the unit costs is as follows:
Unit costs:
Direct Materials Conversion Costs
Production costs $42,980 $34,104
Total equivalent units 15,350 14,210
Unit costs $2.80 $2.40
c) The preparation of the cost reconciliation schedule is as follows:
Cost Reconciliation Schedule:Direct Materials Conversion Costs Total Costs
Beginning work in process $0 $0 $0
Cost to be accounted for $42,980 $34,104 $77,084
Total production costs $42,980 $34,104 $77,084
Costs accounted for units:
Completed / transferred out $35,000 $30,000 $65,000
Ending work in process $7,980 $4,104 $12,084
Total costs accounted for $42,980 $34,104 $77,084
What are equivalent units?Equivalent units are the multiplication of the number of physical (or actual) units on hand by the percentage of completion of the units.
1. Completed and transferred out 12,500 units.
2. Beginning work in process = $0
Ending work in process = 2,850 units 60% complete
Production Costs
Direct materials costs = $42,980 100% complete in terms of materials at July 31.
Direct labour = $15,700
Manufacturing overhead = $18,404
Total conversion costs = $34,104 ($15,700 + $18,404)
Equivalent units of production:
Units Materials Conversion
Completed and transferred out 12,500 12,500 12,500
Ending work in process 2,850 2,850 (100%) 1,710 (60%)
Total equivalent units 15,350 15,350 14,210
Unit costs:
Direct Materials Conversion Costs
Production costs $42,980 $34,104
Total equivalent units 15,350 14,210
Unit costs $2.80 $2.40
($42,980 ÷ 15,350) ($34,104 ÷ 14,210)
Cost Reconciliation Schedule:
Direct Materials Conversion Costs Total Costs
Beginning work in process $0 $0 $0
Cost to be accounted for $42,980 $34,104 $77,084
Total production costs $42,980 $34,104 $77,084
Costs accounted for units:
Completed / transferred out $35,000 $30,000 $65,000
(12,500 x $2.80) (12,500 x $2.40)
Ending work in process $7,980 $4,104 $12,084
(2,850 x $2.80) (1,710 x $2.40)
Total costs accounted for $42,980 $34,104 $77,084
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Last year the highest temperature in a city was recorded as 23C and the lowest temperature was recorded as -10C how many degree warmer was the highest temperature than the lowest temperature
Answer:
The highest temperature was 33C warmer than the lowest temperature.
Step-by-step explanation:
In order to find how many degrees warmer was the highest temperature, you have to calculate the difference between both temperatures:
23-(-10)
According to the sign rule, you have to change the subtraction sign to addition and then, change the sign on the umber after that and add the numbers, which is:
23+10=33
According to this, the answer is that the highest temperature was 33C warmer than the lowest temperature.