Answer:
you answer is 7 1/25
Step-by-step explanation:
0.04 ---> 1/25
7 ---> 7
7 + 1/25 = 7 1/25
I can’t find the answer
Answer:
C. 225m^2
Step-by-step explanation:
Let's find the area of the shaded region. There are 5 whole squares shaded. There are 8 half squares shaded. (Each pair of triangles makes a whole square.) We have 4 more whole squares.
There are a total of 9 whole squares shaded.
The length of the side of the entire shape is 25m. The entire shape is divided into 25 squares. 25/5 = 5.
Each small square has an area:
A_smallsquare
= 5×5
= 25m^2
A_shaded
= 25 × 9
= 225m^2
What is the vertex of the graph of g(x)=|x-8|+6
The vertex of the function g(x) = |x - 8| + 6 is (8, 6)
How to determine the vertex of the function?From the question, we have the following parameters that can be used in our computation:
g(x) = |x - 8| + 6
The above equation is an absolute value function
An absolute value function represented as
y = a|x - h| + k
Where
Vertex = (h, k)
This means that the vertex is
Vertex = (8, 6)
Remove the x value
y = 6
Because the leading coefficient is positive, then the vertex is a minimum
i.e.
y ≥ 6
So, the range is y ≥ 6
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What are whole numbers integers and rational numbers are the set of whole numbers and their opposites?; What are whole numbers integers and rational numbers?; What are whole numbers and their opposites?; What is a whole number ?
Whole numbers range in size from 0 to infinity.
The collection of rational numbers is p/q, q ≠0.
Integers have no decimal portion and range from -infinity to infinity.
Given that,
We have to finding whole numbers, integers, and rational numbers is necessary.
the collection of whole numbers and their opposites,
The group of numbers that can be expressed as fractions is called ______.
The group of counting numbers and zero is known as ______.
We know that,
What is number system?All of the numbers that are there can be defined or represented using a number system.
Complex numbers (a + ib)
Imaginary numbers
(0 + ib)
Real numbers
(a + i0)
Rational numbers
(perfect squares)
Irrational numbers
(non-perfects squares)
Fractions.
(p/q, q ≠ 0)
Integers
Negative integers is - ∞ to - 1
Positive integers is 1 to ∞
whole numbers is 0 to ∞
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plot the probability mass function of the sample mean of x1, ... , xn, when (a) n = 2; (a) n = 3. assume that the probability mass function of the xi is p{x = 0} = .2, p{x = 1} = .3, p{x = 3} = .5 in both cases, determine e[x ] and var(x ).
The probability mass function of the sample mean of x1, ... , xn, then the
Expectation [tex]E[X][/tex] = 1 and Variance [tex]Var[X][/tex] = 4.9
To find the expected value, E(X), or mean μ of a discrete random variable X, simply multiply each value of the random variable by its probability and add the products. The formula is given as E(X)=μ=∑xP(x).
var(X)=∑(x−μ)2pX(x), where the sum is taken over all values of x for which pX(x)>0. So the variance of X is the weighted average of the squared deviations from the mean μ, where the weights are given by the probability function PX(x) of X.
Given that,
The probability mass function of the sample mean of x1, ... , xn,
p{x = 0} = 0.2, p{x = 1} = 0.3, p{x = 3} = 0.5
when (a) n = 2; (a) n = 3
Expectation is defined as
[tex]E[X][/tex] = ∑ˣ [tex]x P(X =x)[/tex]
We have
[tex]E[X][/tex] = ∑ [tex]x P(X =x)[/tex]
[tex]x[/tex]∈(2,3)
[tex]E[X][/tex] = [tex]P(X =0)+2P(X=1)+3P(X=3)[/tex]
[tex]E[X][/tex] = 0.2 + 0.3 + 0.5
[tex]E[X][/tex] = 1
Variance is defined as
[tex]Var[X][/tex] = E[(X-[tex]E[X]^{2}[/tex]]
[tex]Var[X][/tex] = [tex]E[X^{2}][/tex] - [tex](E[X])^{2}[/tex]
We get
[tex]E[X]^{2}[/tex] = [tex]1^{2} P[X=0]+2^{2} P[X=1]+3^{2} P[X=2][/tex]
[tex]E[X]^{2}[/tex] = 0.2 + 4(0.3) + 9(0.5)
[tex]E[X]^{2}[/tex] = 0.2 + 1.2 + 4.5
[tex]E[X]^{2}[/tex] = 5.9
Variance is defined as
[tex]Var[X][/tex] = [tex]E[X^{2}][/tex] - [tex](E[X])^{2}[/tex]
[tex]Var[X][/tex] = 5.9 - [tex]1^{2}[/tex]
[tex]Var[X][/tex] = 5.9 - 1
[tex]Var[X][/tex] = 4.9
Therefore,
The probability mass function of the sample mean of x1, ... , xn, then the
Expectation [tex]E[X][/tex] = 1 and Variance [tex]Var[X][/tex] = 4.9
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farrow co. expects to sell 150,000 units of its product in the next period with the following results.
Farrow co has to accept the offer.
Given that,
In the upcoming time frame, Farrow Co. anticipates selling 150,000 pieces of its product, with the following outcomes.
The calculation of the total combined net income is displayed below:
Normal Volume Additional Volume Total
Sales $2,250,000 $180,000 $2,430,000
(15,000 × $12)
Costs and expenses:
Direct materials $300,000 $30,000 $330,000
Direct labor $600,000 $60,000 $660,000
Overhead $150,000 $22,500 $172,500
($150,000 × 15%)
Selling expenses $225,000 $225,000
Administrative expenses $385,500 $64,500 $450,000
Total costs and expenses $1,660,500 $177,000 $1,837,500
Incremental income (loss) from new business $589,500 $3,000 $592,500
Therefore, the company should accept the offer
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what ratio, a:b, is represented in the table?
a b
1.5 2.5
51 85
99 165
Answers
A 4:54:5
B 2:32:3
C 3:5
Answer:is c or 3:5
Step-by-step explanation:
wich of the following statements are true
Answer:
A
Step-by-step explanation:
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.
x = 1 + (y â 4)2, x = 2
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis.
y = x3, y = 8, x = 0; about x = 7
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis.
y = 6x â x2, y = 5; about x = 1
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the graphs of the given equations about the x-axis.
y = x3â2, y = 8, x = 0
The volume of the solid obtained by rotating the region bounded by the given curves about the X-axis is 340978 vu.
Given curve is,
y = [tex]x^{3}[/tex] , y = 8, x = 0 about x = 7
we know the formula for cylindrical shell is
V = πR²h
where R² = f(x)₂-f(x)₁ ,
h = dx
here f(x)₂ = 8 and f(x)₁ = x³
⇒ V = π(8 - x³)²h
V = π(64 - 16x³+x⁶)dx
integrating on both sides,
[tex]\int dV[/tex] =π [tex]\int ({64 - 16 x^{2} + x^{6} }) \, dx[/tex]
= [tex]64 \int dx - 16 \int {x^{3} } \, dx + \int\ {x^{6} } \, dx[/tex]
V = π(64x - 4x⁴+[tex]\frac{x^{7} }{7}[/tex])
V = π(64 × 7 - 4(7)⁴ + [tex]\frac{7^{7} }{7}[/tex])
= π(448 - 9604 + 117649 )
= [tex]\frac{22}{7}[/tex](108493)
V = 340978 vu
Therefore volume of the cylindrical shells to the region y = x³, y = 8, x = 0 about x = 7 is 340978 vu.
Cylindrical shells are essential structural elements in offshore structures, submarines, and airspace crafts. They are often subjected to combined compressive stress and external pressure, and therefore must be designed to meet strength requirements.
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Given the equation, proof it
Answer:
Step-by-step explanation:
I forgot to add the last reason is AAS (two angles one side are congruent = triangles are congruent)
S.
1.Given
2. AE = EC
3. <AEB = <CED
4. <CDE = <ABE
5. triangles congruent
R.
1. Given
2. Segment bisector theorem
3. Vertical angles theorem
4. PAI Theorem
Hope this helps!
which graph represents the function fx 2 x 12
On solving the provided question we go to know that - Graph with points- (2,1) (0,3) (4,3) (x,y).
What is function?In mathematics, a function is an expression, rule, or law that establishes the connection between two variables (the dependent variable).
What is function define with example?a unique connection where every input only has one output. Where x is the input value, it is frequently expressed as yields a single output [tex]"x/2,"[/tex]indicating that it is a function:[tex]* f(2) = 1.[/tex]
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What is the equation of the line that passes through the point (4,-2)(4,−2) and has a slope of \frac{5}{4}
4
5
The equation of the line that passes through the point (4, -2) and has a slope of 5/4, in point-slope form is: y + 2 = 5/4(x - 4).
How to Find the Equation of a Line? Goes through a Point?If we are given a point (a, b), that a line goes through and we also know the slope (m) of the line, the equation of the line can be written as y - b = m(x - a) in point-slope form
Given that the line has the following:
A point (a, b) = (4, -2)
The slope of the line (m) = 5/4
To write the equation of the line, substitute m = 5/4, a = 4, and b = -2 into y - b = m(x - a):
y - (-2) = 5/4(x - 4)
y + 2 = 5/4(x - 4)
The answer is: y + 2 = 5/4(x - 4).
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Answer this for 5 star! Need explanation
Answer: 6
Step-by-step explanation: To solve we first start by adding like terms in our equation which is 30 + 54 = x(5+9) which becomes 84=x(14). Now we need to isolate the x variable by dividing both sides by 14.
x(14) ÷ 14 = x, 84 ÷ 14 = 6
This leaves us with the answer x = 6
Help!
Para determinar el monto del interés de un depósito con cierta tasa de interés , capital inicial
y tiempo , se usa la siguiente expresión: =
∙ (1 +
100)
. Carlos depositó un capital de
$ 1.500.000 durante un año y medio a una tasa de interés mensual del 2,5 %, ¿cuál es el monto que
retirará Carlos después de este período?
The balance of Carlos account after this period, using simple interest, is of:
$2,339,488.08.
How to obtain the balance?This is a simple interest problem, hence the balance of the account can be obtained using an exponential function, defined as follows:
[tex]B(n) = B(0)(1 + r)^n[/tex]
In which the parameters of the exponential function are defined as follows:
B(0) is the initial deposit.r is the interest rate, as a decimal.n is the number of periods.In the context of this problem, the values of these parameters are given as follows:
B(0) = 1500000, r = 0.025, n = 18, as one and a half year = 18 months.
Then the balance of Carlos account is obtained as follows:
B(18) = 1500000(1.025)^18 = $2,339,488.08
TranslationCarlos deposited: $1,500,000.Time of 1.5 years.Interest rate of 2.5% montly.Asks for the balance.More can be learned about simple interest at
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what is the greatest and least quotient for 7,6,8 and 3
The greatest quotient is 292 and the least quotient will be equal to 45.8.
What is an arithmetic operation?
The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the given information in the question,
The greatest quotient will be,
3 ) 876 (
= 292 and,
The smallest quotient will be,
8) 367 (
= 45.8
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The equation s equals two fifths times f represents the proportional relationship between the amount of sugar (s) and flour (f) in a recipe. Which table represents the equation of the proportional relationship?
Sugar Flour
1 two fifths
2 four fifths
Sugar Flour
four fifths 1
two fifths 2
Sugar Flour
1 four fifths
2 two fifths
Sugar Flour
two fifths 1
four fifths 2
The table which represents the equation of the proportional relationship as described is;
Sugar Flour
two fifths 1
four fifths 2
Which table represents the equation of the proportional relationship?It follows from the task content that the table which represents the proportional relationship is to be identified among the given answer choices.
Since the given relationship is defined by the equation;
s = (2/5) f.
Hence, when f = 1; s = (2/5) • 1; s = 2/5.
Also, when f = 2; s = (2/5) • 2 = 4 / 5.
Therefore, the table which represents the equation of the proportional relationship is;
Sugar Flour
two fifths 1
four fifths 2
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△JKL∼△STU Which statements are true? more than one are right? ∠K≅∠T
JK≅ST
KL/TU=JK/ST
JL=SU
m∠J=m∠S
∠K≅∠T , KL/TU=JK/ST and m∠J=m∠S are true .
Given: △JKL∼△STU
When two triangles are similar , then their corresponding sides are proportional and Corresponding angles of one triangle is equal to corresponding angles of another Triangle.
The two Triangles can be similar by following Similarity axiom
1. AA
2. S A S
3. S S S
The Options are
→∠K≅∠T( True) Corresponding angles are equal.
→JK≅ST (False)
→KL/TU=JK/ST (True) Because sides are proportional.
→JL=SU (False)
→m∠J=m∠S (True) Corresponding angles are equal.
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(10, y) and (3,4) ;m = 2/7
The value of the y such that the slope associated with both points is 2/7 will be 6.
What is the slope?A slope is a tangent or angle at a point and a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
The slope could be positive or negative.
The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope = (y₂ - y₁)/(x₂ - x₁)
As per the given points,(10, y) and (3,4) and slope m = 2/7
2/7 = (4 - y)/(3 - 10)
4 - y = -7(2/7)
4 - y = -2
y = 4 + 2 = 6
Hence "The value of the y such that the slope associated with both points is 2/7 will be 6".
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What’s the value of y 3(13/2)+2y=9
Answer:
3(13/2)+2y=9 the answer is y=-21/4
Enter the ordered pair for the vertices for (Ry-axis o T(2,0))(QRST).
On solving the provided question, we got to know the vertices those are - Q' = (-3, 3), R' = (-5, -3), S' = (-2, -2), T' = (0, 1)
what is vertices?As kids learn about the characteristics of 3D forms, vertices, faces, and edges start to appear often in geometry. Here's what it means and how to figure out how many vertices, faces, and edges each form has. The most popular forms' edge, face, and vertex counts are also included.
[tex]The coordinates of the vertices of the quadrilateral are;[/tex]
[tex]T(-2, 1), Q(1, 3), S(0, -2), R(3, -3)[/tex]
T
The coordinates of the vertices of the quadrilateral are;
[tex]T(2, 0)QRST, gives;\\ T(2, 0)QRST→ T(-2 + 2, 1), Q(1 + 2, 3), S(0 + 2, -2), R(3 + 2, -3)\\ T(2, 0)QRST→ T(0, 1), Q(3, 3), S(2, -2), R(5, -3)\\[/tex]
For the next process R y-axis which is the reflection about the y-axis, the preimage (x, y) becomes the image (-x, y)
Therefore, we have;
[tex]R y-axis(T(0, 1), Q(3, 3), S(2, -2), R(5, -3)) = T'(0, 1), Q'(-3, 3), S'(-2, -2), R'(-5, -3)\\ From which we get (Ry-axis T(2, 0))(QRST = T'(0, 1), Q'(-3, 3), S'(-2, -2), R'(-5, -3).[/tex]
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how can you prove that these two triangles are congruent?
f(x) = 2x – 3x and g(x) = 1 – 2x find (f+g)(x)
The value of the composite function is (f + g)(x) = -3x + 1
How to evaluate the composite functions?From the question, we have the following parameters that can be used in our computation:
f(x) = 2x - 3x
g(x) = 1 - 2x
The composite function is given as
(f + g)(x)
Mathematically, this can be represented as
(f + g)(x) = f(x) + g(x)
Substitute the known values in the above equation, so, we have the following representation
(f + g)(x) = 2x- 3x + 1 - 2x
Evaluate the like terms
(f + g)(x) = -3x + 1
Hence, the composite function is (f + g)(x) = -3x + 1
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In a simple random sample of 144 households in a city in Kentucky, the average number of children in these households was 1.12 children. The standard deviation from this sample was
2.40 children. A 90 percent confidence interval for the mean number of children in all
households in this city is:
Select one:
O a. 1.12 ± 0.2.
O b. 2.40 ± 0.2.
c. It is impossible to tell without a census.
O d. 1.12 ± 2.40.
O e. 1.12 ± 0.328.
A 90% confidence interval for the mean number of children in all household in this city is 1.12 ± 0.328, using formula for confidence interval.
What are mean and standard deviation ?
The standard deviation is a summary measure of the differences of each observation from the mean.
Formula to calculate confidence interval using mean and deviation:
mean ± Z*(std deviation/√n)
where n = sample size,
Given that :
mean = 1.12
deviation = 2.40
n = 144
We know Z is fixed for 90% confidence i.e. 1.64
So, the confidence interval = 1.12 ± 1.64*(2.4/√144)
= 1.12 ± 1.64 * .2
= 1.12 ± .328
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please help i cant copy and paste it but yea ty
Answer:
a = 2
b = 4
c = 3
d = 4
e = 6
Step-by-step explanation:
When dividing fractions, you flip the fraction on the right; here, we have
1/2 / 3/4 so it is the same as 1/2 * 4/3. From there, we would assign our values, so a =2, b = 4, c =3, d is equal to 1*4, so 4, and e is equal to 2*3, so 6.[tex]1[/tex]
What type of function is odd?
Rotational symmetry about the origin is present in odd functions. By substituting x with -x and computing f, we can determine algebraically if a function is even, odd, or neither (-x). The function is odd if f(-x) = f(x).
Which one of the following functions is odd?If -f(x) = f(-x), then the function f is said to be odd for all values of x. When studying additive inverses, the functions even and odd are those that satisfy particular symmetry relations.
Is odd function continuous?Evenness or oddness in a function does not imply continuity or differentiability. For instance, the Dirichlet function is even but in no way continuous.
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Check all properties that the following relations on the set of positive integers have: The relations are defined by (x, Y) € R if and only if the indicated condition is satisfied x and Y have a common prime factor A. reflexive B. symmetric C. irreflexive D. transitive E: antisymmetric (b) x _ y is a multiple of 3 A. symmetric B. antisymmetric C: irreflexive D. reflexive E. transitive (c) x and y are both prime A. transitive B. irreflexive C. symmetric D. reflexive E: antisymmetric (d) x and y are twin primes (they are primes and their distance is 2) A. symmetric B. irreflexive C.antisymmetric D. reflexive E: transitive
If x and y have a common prime factor then y and x also have a common prime factor,so x and y are symmetric.
If x-y is divisible by 3 then y-x is also divisible by 3.so it is symmetric and x-y is reflexive as x ∈Z+ ,x-y is a multiple of 3.so it is reflexive.
If x,y and y,z are primes then x,z are also primes.So it is transitive and it is also symmetric If x,y are primes then y,x are also primes.
x and y are symmetric since (a,b)∈ R⇒ a,b are prime and their difference is 2⇒(b,a)∈ R
Step-by-step explanation:
Part a: x and y have a common prime factor
If x and y have a common prime factor then y and x also have a common prime factor, so x and y are symmetric.
Reflexive: x and y are not reflexive since {1,1}∉ R(1 has no prime factor)
Symmetric: If x and y have a common prime factor then y and x also have a common prime factor , so x and y are symmetric.
Irreflexive: refer point A(above)
Transitive: x and y are not transitive since {2,9}∉ R(has no common prime factor)
Anti symmetric: x and y are not anti symmetric [Refer point B(above)]
If x and y have a common prime factor then y and x also have a common prime factor, so x and y are symmetric.
b) x - y is a multiple of 3
If x-y is divisible by 3 then y-x is also divisible by 3.so it is symmetric and x-y is reflexive as x ∈Z+ ,x-y is a multiple of 3.so it is reflexive.
Symmetric: If x-y is divisible by 3 then y-x is also divisible by 3.so it is symmetric.
Antisymmetric x-y is not anti symmetric (refer above)
Irreflexive refer point D
Reflexive : x-y is reflexive as x ∈Z+ ,x-y is a multiple of 3.
Transitive: if x-y,y-z is multiples of 3 then x-z is also multiples of 3.so it is also transitive.
(c) x and y are both prime
If x,y and y,z are primes then x,z are also primes.So it is transitive and it is also symmetric If x,y are primes then y,x are also primes.
Transitive: If x,y and y,z are primes then x,z are also primes.So it is transitive.
irreflexive Refer It is not reflexive since {4,4}∉ R(4 is not a prime)
Symmetric: If x,y are primes then y,x are also primes.So it is symmetric..
Reflexive:It is not reflexive since {4,4}∉ R(4 is not a prime)
Antisymmetric: Refer point C
(d) x and y are twin primes (they are primes and their distance is 2)
x and y are symmetric since (a,b)∈ R⇒ a,b are prime and their difference is 2⇒(b,a)∈ R
Symmetric: x and y are symmetric since (a,b)∈ R⇒ a,b are prime and their difference is 2⇒(b,a)∈ R
Irreflexive Refer point D
Antisymmetric Refer point A
Reflexive: It is not reflexive since {4,4}∉ R
Transitive: It is not transitive because (3,5)∈R and (5,3)∈R but (3,7)∉ R
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given that l has been defined to refer to a list, write an expression whose value is a set containing all the elements of l.
For given that L has been defined to refer to a list , the expression whose value is a set containing all the elements of L is
set = { 1,2,3,4}
Writing List in Python :Lists are used to store multiple items in one variable. Lists are one of Python's four built-in data types used to store collections of data, the other three being tuples, sets and dictionaries, all of different qualities and uses.
A list is a container which holds comma-separated values (items or elements) between square brackets where items or elements need not all have the same type.
#Programme representation
Input:
#Python code
#A list L is initialised
L = [ 3,4,2,1 ]
#set L containing all elements of list L
print(str(set(L)))
Output:
{ 1, 2, 3, 4 }
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Find the measure of angle 0.
35°
83°
23°
23
Step-by-step explanation:
The answer is 23 because it is closer to the 0
Answer: the answer is 141
Step-by-step explanation:
bro its not that hard the guy up top is a bum just add all the angles together thats the answer and remember the formula is (n-2)180 for INTERIOR i wrote it in caps cuz some of yall goofy fr
brainly explain why we need to define the vector space p n as the set of all polynomials with degree up to and including n instead of the more obvious set of all polynomials of degree exactly n .
Any n-dimensional vector should be able to be represented in space.
The highest degree of terms is written first when writing a polynomial in its standard form, then the next highest degree, and so on.
If there are multiple variables in a single term, add the exponents of each term together and choose the largest sum or highest power of the variable to determine the polynomial's degree.
It should be possible to represent any n-dimensional vector in space. It can only express polynomials of degree n if it only has terms of degree n.
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Prepared building plans for Spangler Construction Company. Sent Spangler an invoice for $900 requesting payment within 30 days. (The appropriate revenue account is entitled Drafting Fees Earned.)
The appropriate sales journal entry for the building plans prepared for Spangler Construction Company is as follows:
Sales Journal Entry:Debit Accounts Receivable (Spangler Construction Company) $900
Credit Drafting Fees Earned $900
(To record the revenue from drafting fees.)
What are sales journals?Sales or service journals are used to record sales or service revenue transactions.
When the services are performed on credit, the Accounts Receivable account is debited while the Service Revenue account is credited.
Transaction Analysis:Accounts Receivable (Spangler Construction Company) $900 Drafting Fees Earned $900
Thus, the above demonstrates the appropriate recording of the service revenue transaction in the sales/service revenue journal.
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Question Completion:Prepare the appropriate journal entry.
cost per pound ($) ingredient beginning ending quantity (pounds) per 100 pounds of product a 2.50 3.95 25 b 8.75 9.90 15 c 0.99 0.95 50
The relative price of ingredient A is 158, ingredient B is 131.1 and ingredient C is 96.
In the given question we have to compute the price relatives for the three ingredients A, B and C.
Now finding the relative price using the formula.
Relative Price(RP) = Ending Cost(E)/Beginning Cost(B) *100
Now from the given table;
Ingredient Beginning(B) Ending(E) E/B E/B*100
A 2.50 3.95 1.58 158
B 8.75 9.90 1.131 131.1
C 0.99 0.95 0.96 96
Hence, the relative price of ingredient A is 158, ingredient B is 131.1 and ingredient C is 96.
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The right question is
A chemical company produces a special industrial chemical that is a blend of three chemical ingredients. The beginning-year cost per pound, the ending-year cost per pound, and the blend proportions follow. (Round your answers to the nearest integer.)
Cost per Pound ($)
Ingredient Beginning Ending Quantity (pounds) per 100
Pounds of Product
A 2.50 3.95 25
B 8.75 9.90 15
C 0.99 0.95 70
Compute the price relatives for the three ingredients.
Item Price Relative
A
B
C