Answers
We split a given vector by its magnitude to get a unit vector that has the same direction. Consider the vector v = (1, 4), which has a magnitude of |v|. The unit vector uv, which is in the same direction as v, is obtained by dividing each component of the vector v by |v|.
What is unit vector?The magnitude of a unit vector must be exactly one unit. They are quite helpful for a variety of reasons. The unit vectors [0,1] and [1,0] in particular can combine to generate any other vector. A vector of magnitude one is known as a unit vector. A vector's direction can be expressed using unit vectors regardless of the magnitude of the vector. Even though a unit vector must have a direction to be defined, even though it has a magnitude of 1, not all unit vectors will have the same direction. Now that we are aware that a unit vector is a vector whose magnitude is one, we will check to see whose magnitude is one and provide the response. [Right Arrow] Not a unit vector, it.To learn more about unit vector, refer to:
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Related Questions
A scientist studies a sample that weighs 1 ounce, which is about 28 grams. About how many grams would be in a 48-ounce sample?
Answers
Step-by-step explanation:
1 ounce = 28 grams
48 ounce = 1344 grams
So, 1344 grams would be in a 48-ounce sample.
the difference of two times a number and five is eight
Answers
2x - 5 = 8
2x = 8+5
2x = 13
X= 6.5
In a poker hand consisting of 5 cards, find the probability of holding a. 3 kings b. 4 hearts and 1 diamonds Expert's answer A poker hand consists of 5 cards. The sample space has (52/5) possible outcomes. a. Choose 3 kings from 4 kings. From the remaining 52−4=48cards choose 2 non-kings to make a five-card poker hand P(3 kings)=(43)(52−45−3)(525)=P(3 kings)=(552)(34)(5−352−4)= =4!3!(4−3)!⋅48!2!(48−2)!52!5!(52−5)!==5!(52−5)!52!3!(4−3)!4!⋅2!(48−2)!48!= =2(48)(47)(120)52(51)(50)(49)(48)=9454145≈0.001736=52(51)(50)(49)(48)2(48)(47)(120)=5414594≈0.001736 b. There are total 13 hearts and 13 diamonds. Choose 4 hearts from 13 hearts (134)(413) Choose 1 diamonds from 13 diamonds (131)(113) P(4 hearts and 1 diamonds)=(134)(131)(525)=P(4 hearts and 1 diamonds)=(552)(413)(113)= =13!4!(13−4)!⋅13!1!(13−1)!52!5!(52−5)!==5!(52−5)!52!4!(13−4)!13!⋅1!(13−1)!13!= =13(12)(11)(10)(5)(13)52(51)(50)(49)(48)=14339984≈0.003576=52(51)(50)(49)(48)13(12)(11)(10)(5)(13)=39984143≈0.003576
Answers
In a poker hand consisting of 5 cards, the probability of holding 3 kings is 0.0009 .
The probability of holding 3 kings in a poker hand of 5 cards can be calculated as follows:
The number of ways to choose 3 kings from a deck of 4 kings is= ⁴C₃ = 4.
The number of ways to choose 2 other cards from the remaining 48 cards is = ⁴⁸C₂ = 1128.
The total number of 5-card hands from a standard deck of 52 cards is = ⁵²C₅ = 2598960.
So , the probability of holding 3 kings in a 5 card hand is
⇒ (4 × 1128)/2598960
⇒ 4512/2598960 .
⇒ 0.00085148 .
Therefore , probability of holding 3 kings in a 5card hand is approximately 0.0009 .
The given question is incomplete , the complete question is
In a poker hand consisting of 5 cards, find the probability of holding 3 kings .
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i need to add this fraction i need to know the explantion and answer Add: 3 38
+ 7 34
Answers
The addition of the given fraction numbers 3(3/8) and 7(3/4) is, 89/8
What is a fraction?Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.
Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.
Given that,
Two fraction numbers,
3(3/8) and 7(3/4)
The addition of two fraction number is,
⇒ 3(3/8) + 7(3/4)
In simple form it can be written as,
⇒ 24+3/8 + 28+3/4
⇒ 27/8 + 31/4
LCM Of 8 & 4
= 8
⇒ 27/8 + 31×2/4×2
⇒ 27/8 + 62/8
⇒ (27 + 62)/8
⇒ 89/8
Hence, the result is 89/8
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Triangle ABC is defined in the coordinate plane by the points A(1, 2), B(4, 3), and C(4, 0).
Under which transformations will the image of triangle ABC be similar to the preimage?
select all that apply
Answers
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
What’s dilation?The dilation of the image means expanding the image or reducing the image. In this case, the two figures will be similar in shape but not necessarily in size. In dilation, the new shape remains the same even if the original is larger or smaller.
According to the figure AB=1. AC=4
A'B' = 3, A'C' = 12
FAB'=3AB [A'C' = BAC
So, the scale factor is 3
Dilation is a method for producing comparable numbers. By increasing distances by the scale factor, each point is extended outwards from the center point D. (If the scale factor is more than one, go outwards.)
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Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
What’s dilation?The dilation of the image means expanding the image or reducing the image. In this case, the two figures will be similar in shape but not necessarily in size. In dilation, the new shape remains the same even if the original is larger or smaller.
A. [tex]$T(x, y) \rightarrow(-x, -y)$[/tex]
This is a reflection to the origin that does not preserve angles or aspect proportions. Therefore, triangle ABC under this transformation does not resemble that image.
Example: [tex]$T(x, y) \rightarrow(x, x-y+1)$[/tex]
This is a shear transformation that does not preserve angles or aspect ratio. Therefore, triangle ABC under this transformation does not resemble that image.
C. [tex]$T(x, y) \rightarrow(x+3, y)$[/tex]
This is a translation that preserves angles and aspect ratio. So the triangle ABC under this transformation resembles that image.
D. [tex]$T(x, y) \rightarrow(0.2x, 4y)$[/tex]
This stretches by a factor of 0.2 in the x direction and 4 in the y direction, preserving angle and horizontal proportions. So the triangle ABC under this transformation resembles that image.
E. [tex]$T(x, y) \rightarrow(2x, 2y)$[/tex]
This is a stretch by a factor of 2 in both the x and y directions, preserving the proportions of the angles and sides. So the triangle ABC under this transformation resembles that image.
F. [tex]$T(x, y) \rightarrow(3x, 4y)$[/tex]
This stretches by a factor of 3 in the x direction and 4 times in the y direction, preserving the proportions of angles and sides. So the triangle ABC under this transformation resembles that image.
Therefore, the similarity-preserving transformations between triangle ABC and its image are C, D, E, and F.
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According to a recent article the average number of babies born with significant hearing loss (deafness) is approximately
two per 1,000 babies in a healthy baby nursery. The number climbs to an average of 30 per 1,000 babies in an intensive care
nursery.
Suppose that 1,000 babies from healthy baby nurseries were randomly surveyed. Find the probability that exactly two babies
were born deaf. Round answer to four decimal places
Answers
Answer:
Step-by-step explanation:
According to a recent article the average number of babies born with significant hearing loss (deafness) is approximately two per 1,000 babies in a healthy baby nursery. The number climbs to an average of 30 per 1,000 babies in an intensive care nursery.
None of the students taking literature are taking physics, but several of the students taking physics are taking art. In addition, none of the students taking rhetoric are taking physics.
Which one of the following statements follows logically from the statements above?
A. There are students who are taking art but not literature.
B. None of the students taking literature are taking art.
C. There are students who are taking rhetoric but not literature.
D. None of the students taking rhetoric are taking literature.
E. There are students who are taking both art and literature.
Answers
The correct option is (A).
The following statements follows logically from the statements is there are students who are taking art but not literature.
"None of the students taking literature are taking physics."
So: if you are student taking literature, then you are not taking physics.
⇒TL=Taking Literature
⇒TP=Taking Physics
⇒TA=Taking Art
⇒TR=Taking Rhetoric
P1: TL ==> not TP
TP ==> not TL
"but several of the students taking physics are taking art."
So: some of the students taking physics are also taking art.
Q1: TP-some-TA
TA-some-TP
"In addition, none of the students taking rhetoric are taking physics."
So: if you are a student taking rhetoric, then you are not taking physics.
P2: TR ==> not TP
TP ==> not TR
Answer choice (A) states: "There are students who are taking art but not literature."
So: some students who are taking art are not taking literature.
(A): TA-some-not TL
not TL-some-TA
Can we logically infer this from the statements above? Yes.
Remember we can combine a quantifier statement with a Sufficient & Necessary statement if the right-hand side variable of the quantifier statement is the same as the sufficient condition of the Sufficient & Necessary statement. We have that with P1 and Q1.
So, we can combine Q1 to P1 like so: TA-some-TP ==> not TL to infer: TA-some-not TL, so the correct option is (A).There are students who are taking art but not literature.
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Bally Manufacturing sent Intel Corporation an invoice for machinery with a $14,000 list price. Bally dated the invoice July 23 with 2/10 EOM terms. Intel receives a 40% trade discount. Intel pays the invoice on August 5. What does Intel pay Bally?
Answers
The amount of money Intel pay Bally is given by the equation A = $ 8,232
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the amount be represented as A
Now , the equation will be
The total invoice amount = $ 14,000
The trade discount given by Intel = 40 %
So , the amount of discount = trade discount x total invoice amount
Substituting the values in the equation , we get
The amount of discount = ( 40/100 ) x 14000
The amount of discount = 0.4 x 14000
The amount of discount = $ 5600
So , the amount after 40 % discount = total invoice amount - amount of discount
Substituting the values in the equation , we get
The amount after 40 % discount = 14,000 - 5,600
The amount after 40 % discount = $ 8,400
And , 2/10 means 2%discount if the amount received within 10 days
So , the amount after 2 % discount = amount after 40 % discount - ( 2/100 ) x amount after 40 % discount
Substituting the values in the equation , we get
The amount after 2 % discount A = 8400 - 0.02 x 8400
The amount after 2 % discount A = $ 8400 - $ 168
The amount after 2 % discount A = $ 8,232
Hence , the amount is $ 8,232
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Table bellow shows the number of cups of coffee people drink completely the table and work out the mean number of cups of coffee
Answers
The mean number of cups of coffee will be 4.
How to calculate the meanThe sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. It is known as the "average" and is the most widely used central tendency measure.
A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When a data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.
The mean number of cups of coffee will be:
= 140 / 35
= 4.
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Please help, I am trying to get this question answered.
Answers
They are similar by the property of SAS and the factor by which the triangle grows is 1.25
1. Explain the difference between a discrete variable and a continuous variable. Choose the correct answer below.
2. Give an example of each type. Choose the correct answer below.
1. A discrete variable has possible values that are separate numbers, while a continuous variable has possible values that form an interval.
2. The number of children in a family is a discrete variable, while the time it takes to run a marathon is a continuous variable.
Answers
what is a discrete variable and example?
Discretized variables require a certain amount of time to count. Consider counting the coins in your pocket as an example. Your bank account's funds can be counted. The balances in each person's bank accounts might also be added up. Even if it may take some time to count the last thing, it is still a countable item.
what is a Continuous Variable and example?
Counting continuous variables would literally take an eternity. In actuality, you would reach "forever" and never reach the end of the list. Consider age as an example. Age cannot be measured. why not Considering that it would take an eternity? For instance,
Twenty-five years, ten months, two days, five hours, four seconds, four milliseconds, eight nanoseconds, 99, and so on.
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The full question would be just part 1.
Explain the difference between a discrete variable and a continuous variable.
A monument is constructed by first laying a row of 60 bricks at ground level. A second row, with two fewer bricks, is centered on that; a third row, with two fewer bricks, is centered on the second; and so on. The top row contains 10 bricks. How many bricks are there in the monument?
Answers
Let's call the number of bricks in the ith row as B_i. Then, B_i = 60 - 2 * (i - 1) for i = 1, 2, ..., n, where n is the number of rows.
The number of bricks in the monument can be found by summing up the bricks in each row. So, the total number of bricks is:
T = B_1 + B_2 + … + B_n
= 60 + (60 - 2) + (60 - 4) + … + (60 - 2 * (n - 1))
= 60 * n + (-2) * (1 + 2 + … + (n - 1))
To find the sum of 1 to (n-1), we can use the formula for the sum of an arithmetic series: S_n = n * (a_1 + a_n) / 2, where a_1 = 1 and a_n = n - 1.
Substituting these values into the formula, we get: S_n = (n - 1) * (1 + (n - 1)) / 2 = (n - 1) * n / 2.
Therefore, T = 60 * n + (-2) * (n - 1) * n / 2 = 30 * n^2 + 30 * n.
Finally, to find the number of bricks for n = 10 rows, we substitute n = 10 into the equation:
T = 30 * 10^2 + 30 * 10 = 300 + 300 = 600
So, there are 600 bricks in the monument.
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Please any assistance
Answers
Answer: y=-4x+4
Step-by-step explanation: the "+4" represents the y intercept, so (0,4)
Answer:
Step-by-step explanation:
3) The following are the trial balance and other information related to Soft Tech, a
consulting engineer.
Soft Tech, Consulting Engineer
Trial Balance
December 31, 2022
Debit Credit
Cash Br. 59,000
Accounts Receivable 99,200
Allowance for Doubtful Accounts Br. 1,500
Supplies 3,920
Prepaid Insurance 2,200
Equipment 50,000
Accumulated Depreciation—Equipment 12,500
Notes Payable 14,400
Share, Capital 104,020
Dividend 34,000
Service Revenue 200,000
Rent Expense 19,500
Salaries and Wages Expense 61,000
Utilities Expense 2,160
Office Expense 1,440
Br. 332,420 Br. 332,420
Other data:
1. Fees received in advance from clients Br.12,000.
2. Services performed for clients that were not recorded by December 31,
Br.9,800.
3. Bad debt expense for the year is Br.2,860.
4. Insurance expired during the year Br.960.
5. Equipment is being depreciated at 10% per year.
6. Fine Tech gave the bank a 90-day, 10% note for Br.14,400 on December 1,
2022.
7. Rent of the building is Br.1,500 per month. The rent for 2022 has been
paid, as has that for January 2023.
8. Salaries and wages earned but unpaid December 31, 2022, Br.5,020.
Instructions
a. From the trial balance and other information given, prepare annual
adjusting entries as of December 31, 2022.
b. Prepare the worksheet
c. Prepare an income statement for 2022, a statement of owner’s equity,
and a classified statement of financial position.
d. Maintain the necessary closing entry.
find the area of the parallelogram with vertices p(3, 3, 2), q(5, 6, 4), r(9, 10, 12), and s(7, 7, 10).
Answers
The area of the parallelogram with vertices p(3, 3, 2), q(5, 6, 4), r(9, 10, 12), and s(7, 7, 10) is √336≈18.34 units.
A unique variety of quadrilateral made up of parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but it must have opposite sides that are parallel for it to be a parallelogram.
Calculate the length of PQ → Position vector of Q - Position vector P
PQ→ (5-3)i + (6-3)j + (4-2)k
PQ→ 2i + 3j + 2k
Calculate the length of PS →Position vector of S - Position vector P
PQ→ (7-3)i + (7-3)j + (10-2)k
PQ→ 4i + 4j + 8k
Area of parralelogram = [tex]\left[\begin{array}{ccc}i&j&k\\2&3&2\\4&4&8\end{array}\right][/tex]
= √16² + 8² + 4²
=√336
=18.34 units
The area of a parallelogram is the region bounded by the parallelogram's four sides. It is measured in square units like cm2, m2, and inch2 and can be computed if we know the size of the parallelogram's base and height.
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a high school sells students tickets for $5 as well as general admission tickets for $7 to attend thier football games. The school needs to bring in at least $1500 per game in order to maintain the costs of the football team
Answers
The cost of students ticket is $37.5and the cost of general admission is $187.5.
What is system of equations?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.
Assume s be the students tickets cost and g be the general admission cost.
From the given information,
⇒ s + g = 225 ..(1)
5s + 7g = 1500 ..(2)
From equation (1),
s = 225 - g
Plug the value of s in equation (2)
5(225 - g) + 7g = 1500
1125 - 5g + 7g = 1500
2g = 1500 - 1125
2g = 375
g = 187.5
Plug g = 125 in equation (1),
s + 187.5= 225
s = 225 - 187.5
s = 37.5
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I have added a screenshot.
Answers
The value for n(A ∩ [tex]B^c[/tex]) is {3}
Option D is the correct answer.
What is a Venn diagram?A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.
We have,
Set A = {1, 3}
Set B = {1, 7}
U = {1, 3, 5, 7}
[tex]B^c[/tex] = U - B = {3, 5}
A ∩ [tex]B^c[/tex].
= Numbers that are common to both A and [tex]B^c[/tex].
= {3}
Thus,
n(A ∩ [tex]B^c[/tex]) = {3}
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Victoria scored a total of 9 points
Answers
The expression that represents the total number of points Victoria scored in the basketball games for the whole season is,
5x + 9.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.
Given:
Victoria scored a total of 9 points in the first basketball game of the season.
She scored 5 points per game in each of the other x basketball games she played that season.
That means, 5x is the score.
The expression that represents the total number of points Victoria scored in the basketball games for the whole season is,
5x + 9.
Therefore, the expression is 5x + 9.
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The complete question:
Victoria scored a total of 9 points in the first basketball game of the season. She scored 5 points per game in
each of the other x basketball games she played that season.
Which of the following expressions represents the total number of points Victoria scored in the basketball games for the whole season?
a raised flower bed is 25 feet long 8 feet wide and 1.5 feet deep. find the volume of soil that it holds in cubic yards round to 1 decimal place. please explain
Answers
The volume of the soil that it holds in cubic yards is 11.1.
What is cuboid?A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.
Given:
A raised flower bed is 25 feet long 8 feet wide and 1.5 feet deep.
In yards,
a raised flower bed is 8.33 yards long, 2.67 yards wide, and 0.5 yards deep.
The volume of the soil that it holds,
= 8.33 x 2.67 x 0.5
= 11.10 cubic yards.
Therefore, the volume is 11.1 cubic yards.
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15. ______________________ a scientific procedure undertaken to make a discovery, test, a hypothesis or demonstrate a known or unknown fact
Answers
Experimentation is a scientific procedure undertaken to make a discovery, test, a hypothesis or demonstrate a known or unknown fact.
What is experimentation in scientific method?Experimentation in the scientific method is the process of testing a hypothesis or theory through the process of collecting data and making observations.
This involves designing and performing experiments to test the hypothesis or theory, and then analyzing the results to determine whether the hypothesis or theory is supported by the data or not.
Experimentation allows for the collection of direct evidence about the hypothesis or theory being tested, which can then be used to make informed decisions about the hypothesis or theory.
Experimentation is the ultimate test of a hypothesis or theory and is fundamental to the scientific method.
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esc Calculate the wavelength in meters of electromagnetic radiation that has a frequency of 1.82 x 10^8 s-1¹. (c = 3.00 X 10^8 m/s) k C #C [] CA 9 %
Answers
The wavelength in meters of electromagnetic radiation that has a frequency [tex]2.5[/tex] × [tex]10^{5}[/tex] .
How can you determine the electromagnetic radiation's wavelength at different frequencies?The wavelength in meters of electromagnetic radiation that has a frequency of [tex]1.82[/tex] ×[tex]10^{8}[/tex] s-1¹. (c = 3.00 X [tex]10^{8}[/tex] m/s) k C #C [] CA 9 %
The frequency f of electromagnetic waves, or, equivalently, the wavelength c/f, is used to classify them.
The characteristics of electromagnetic radiation include amplitude (brightness), wavelength, frequency, and period. We have shown that the frequency of a light wave is related to its energy by the equation E = h v E=hnu E=h.
v=1.210 3 Hz and
e=310 8 m/s equal v and e, respectively.
3×[tex]10^{8}[/tex]
λ = 2.5 ×[tex]10^{5}[/tex].
The wavelength in meters of electromagnetic radiation that has a frequency 2.5 × [tex]10^{5}[/tex].
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What is the Area of this Shape?
Answers
Answer:
38.5
Step-by-step explanation:
rectangle = (2.5x2)+1.5=6.5
6.5x5=32.5
both triangle = 4/2 = 2
(1.5x2)x2=6
total area = 32.5 + 6 = 38.5
bgrvfecdwxsafecdwxstcrefdxwsza
Answers
The value of x in the triangle is 23.83
How to determine the value of x in the triangleFrom the question, we have the following parameters that can be used in our computation:
A right triangle
The value of x can be calculated using the following tangent equation
tan(40) = 20/x
Make x the subject of the equation
x = 20/tan(40)
Evaluate
x = 23.83
Hence, the value of x is 23.83
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Finney & Associates is an interior decorating firm in Tucson. The following costs were incurred in a project to redecorate the mayor's offices. • Direct material: $29,000 • Direct professional labor: $42,000 The firm's budget for the year included the following estimates: • Budgeted overhead: $800,000 • Budgeted direct professional labor: $640,000 Overhead is applied to contracts by using a predetermined overhead rate that is based on direct professional labor cost. Actual professional labor during the year was $655,000 and actual overhead was $793,000. Question What is the total cost to redecorate the mayor's offices?
Answers
The total cost to redecorate the mayor's office by Finney & Associates is $123,500.
How to compute the total production cost:The total production cost consists of direct materials, direct labor, and overhead costs.
The overhead cost can be computed using a predetermined overhead rate or activity-based costing rates.
In this situation, the predetermined overhead rate is the quotient of the budgeted overhead cost and the budgeted direct professional labor cost.
Direct material: $29,000
Direct professional labor: $42,000
Allocated overhead cost: $52,500
Total cost = $123,500
Budgeted overhead: $800,000
Budgeted direct professional labor: $640,000
Predetermined overhead rate = Budgeted overhead/Budgeted direct professional labor cost
= $1.25 ($800,000/$640,000)
Allocated overhead cost = $52,500 ($1.25 x $42,000)
Thus, Finney & Associates can reliably claim that they incurred a total cost of $123,500 in redecorating the mayor's offices.
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Find the equation of the line that contains the given point and is perpendicular to the given line. Write the equation in slope-intercept form, if possible. (6,2); 3x−2y=7 please help me with this, it’s due tomorrow!!?
Answers
The equation of the line is passing through a point (6, 2) and is perpendicular to the line 3x-2y = 7 is y = -2x/3 + 8
What is slope-intercept form?The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point
Given that, a line is passing through a point (6, 2) and is perpendicular to the line 3x-2y = 7, we need to find the equation of the line,
The line is
3x-2y = 7
Converting into slope-intercept form,
3x-2y = 7
2y = 3x - 7
y = 3x/2 - 7/2
We know that, the slopes of two perpendicular lines are negative reciprocal of each other,
Therefore, the slope of the asked line = -2/3
Therefore, the equation of the asked line is, y = -2x/3 + c....(I)
Put x = 6 and y = 2 in equation to find c,
2 = -4 + c
c = 8
Therefore, put c = 8 in equation (i)
y = -2x/3 + 8
Hence, the equation of the line is passing through a point (6, 2) and is perpendicular to the line 3x-2y = 7 is y = -2x/3 + 8
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Derive an exact closed form bound in terms of n on the number of times function F called in each code segment. Use floor/ceilings as needed. Clearly explain your answer and show your work. (a) 1: function COUNT1 (n) 2: for i = 1 to 2n ^ 2 do for 1 to i do 3: k = 1 4: 5: while k <= n do 6: k = k + 8 7: F(i, j) (b) 1: function COUNT2(n) 23 for i = 1 ton do for j = 1 to i do 4: 6: for k = j ton do 5: 2966 F(i, j) F(j, k) 7: F(k, i) (c) The initial call is F(n ^ 2) 1: function F(i) 2: if i < 4 then 3: return 4: while i > 1 do 5: i leftarrow i / 4 6: F(i)
Answers
In order to calculate the exact closed form bound of the number of times function F is called in each code segment, we need to consider the number of times F is called in each line of code.
For COUNT1, line 3 calls F once, line 5 calls F n times, and line 7 calls F once more, for a total of n+2 calls.For COUNT2, line 4 calls F once, line 6 calls F n(n+1)/2 times, and line 7 calls F n(n-1)/2 times, for a total of n*(2n+1)/2 calls.For the initial call of F(n^2), the number of times F is called depends on the value of n. To calculate the exact number of calls for any value of n, we can use a recursive approach, starting from the top line of code and working our way down.
For example, for n=4, the initial call of F(16) will call F(4), which will then call F(1) four times, for a total of 5 calls. For n=8, the initial call of F(64) will call F(16), which will call F(4) four times and F(1) sixteen times, for a total of 20 calls.
Thus, for any value of n, the exact closed form bound of the number of times function F is called is given by the formula [1]:
F(n^2) + 4 * F(n/4) + 16 * F(n/16) + …Where the number of terms in the summation is equal to the number of times n is divided by 4 before it reaches 1.
For example, for n=16, the summation will have four terms (n=16, n=4, n=1), and for n=32, the summation will have five terms (n=32, n=8, n=2, n=1).
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Question in picture, pls help
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No, there do not exist nonzero constants a and b such that a p(x)+b.
What is nonzero constants?Nonzero constants are numerical values used in mathematical equations which cannot be reduced to zero. They are also referred to as non-zero numbers or constants. Non-zero constants can take on any real or complex number value that is not equal to zero. Non-zero constants are used in various areas of mathematics including linear algebra, calculus, statistics, geometry and trigonometry.
No, there do not exist nonzero constants a and b such that a p(x)+b. q(x) is a polynomial with degree 1. This is because the degree of the polynomial P(x) is 1 and the degree of the polynomial Q(x) is 2, so the degree of the sum of the two polynomials (a p(x)+b. q(x)) must be 2 or greater.
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Please help me with this question.
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The value of x is in the quadrilateral PQRS is 1.6
What are similar quadrilateral?Two quadrilaterals are similar if their corresponding angles are equal and also their corresponding sides must be proportional.
The ratio of the corresponding angle of a similar quadrilateral are equal.
This means that all quadrilateral are not similar if the ratio of their corresponding sides are not equal
Therefore AD/PS = DC/ SR
= 4/3.2 = 2/x
4x = 2× 3.2
4x = 6.4
divide both sides by 4
x = 6.4/4
x = 1.6
Therefore the value of x or line RS in the quadrilateral PQRS = 1.6
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The quotient of -20 and the sum of u and v
Answers
Answer:
-20 ÷ (u +v) or -20/(u +v)
Step-by-step explanation:
You want an expression that represents the quotient of -20 and the sum of u and v.
SumThe sum of two quantities is indicated with a plus (+) sign.
"The sum of u and v" is written in symbols as ...
u + v
QuotientThe wording "the quotient of a and b" means "a divided by b". It is written in symbols using a division sign or fraction bar:
a ÷ b or a/b
The desired quotient can be written as ...
-20 ÷ (u +v) or -20/(u +v)
__
Additional comment
The parentheses are needed so that the sum is computed before the quotient is computed. If the expression is typeset, the division bar does the grouping:
[tex]\dfrac{-20}{u+v}[/tex]
simplyfy
(2/x)/(1-4/x)
Answers
The result = 2/ (x-4) is obtained by simplifying the provided equation (2/x)/(1-4/x)
What is meant by fraction?A fraction represents a component of a whole or, more generally, any number of equal parts. As in one-half, eight-fifths, and three-quarters, a fraction in conversational English denotes the number of components of a specific size.A portion of something is called a fraction. When the numerator and denominator are split, a number is represented mathematically as a quotient. In a simple fraction, both are integers.A complicated fraction contains a fraction in either the numerator or denominator. Any fraction that is right has a numerator that is less than its denominator. In mathematics, there are three primary fraction types.There are three types of them: mixed fractions, improper fractions, and proper fractions. Fractions are terms with a numerator and a denominator.Given,
[tex]$\frac{\frac{2}{x}}{1-\frac{4}{x}}[/tex]
Use the fractional rule : [tex]$\frac{\frac{a}{b}}{c}=\frac{a}{b \cdot c}$[/tex]
[tex]$=\frac{2}{x\left(1-\frac{4}{x}\right)}[/tex]
Simplify [tex]$x\left(1-\frac{4}{x}\right): \quad x-4$[/tex]
Then we get,
[tex]$=\frac{2}{x-4}[/tex]
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A water tank is being filled with water. Before water is pumped in, the water level in the tank is 14 inches high. After 20 minutes, the water level is 52 inches high.If t represents the time in minutes and h represents the water level, which of the following equations can be used to model this situation?A. h= 39+13tB. h=1.95t-13C. h=1.95t+13
Answers
The equation which can be used to model this situation is equals to the h = 1.9t + 14 , where h represents the water level , t represents the time in minutes.
We have, A water tank which is filled with water. Before pumping the water,
The level i.e., high of water in water tank
= 14 inches
After 20 minutes, the level of water in tank = 52 inches
We have to determine the equation to model this situation in form of time "t" in minutes. Let "h" be level of water increases from initial point/ level in t minutes. As the change in water level from initial to after 20 minutes = 52 inches - 14 inches = 38 inches
That is, water level increased 38 inches in 20 minutes. Then rate of increase in level = 38/20 = 1.9 inches per minutes
Now, the for time 't' the equation is formed by multiplying the rate of chenge of water level with 't' and adding initial water level.
=> h = 1.9t + 14
which is linear equation in two variables,i.e., h and t . Hence,the required equation model is h = 1.9t + 14 .
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