Solve for k, the constant of variation, in a direct variation problem, where x = 2 and y = 12.k=1/24k=6k=24k=1/6
Answers
1) Typically, a direct variation is given as:
\(y=kx\)2) Since we were told that x=2 and y =12 we can plug those variables into the formula and find the constant of variation "k"
\(\begin{gathered} y=kx \\ 12=k2 \\ 12=2k \\ \frac{12}{2}=\frac{2k}{2} \\ k=6 \end{gathered}\)Thus, the answer is k=6
Related Questions
?/5 =8/10 type the missing number that makes this fraction equal
Answers
Answer:
4/5 = 8/10
Step-by-step explanation:
x/5 = 8/10
x = 8/10 × 5
x = 4
Carbon Company provides the following information about resources.
Unused Resources Capacity Cost Driver Volume
Resources used
Materials $ 2,300 9,000 pounds
Energy 2,210 380 machine-hours
Setups 0 87 setups
Purchasing 7,800 80 purchase orders
Customer service 9,700 70 returns
Long-term labor 4,650 330 labor-hours
Administrative 5,950 450 labor-hours
Resources supplied
Materials $ 101,300
Energy 21,590
Setups 24,360
Purchasing 26,200
Customer service 20,200
Long-term labor 29,400
Administrative 30,700
Sales revenue for Carbon Company is $600,000.
Required:
a. Prepare a traditional income statement.
b. Prepare an activity-based income statement.
Answers
a) The preparation of a traditional income statement for Carbon Company is as follows:
Carbon Company
Income Statement (Traditional)Sales revenue $600,000
Costs:
Materials $ 101,300
Energy 21,590
Setups 24,360
Purchasing 26,200
Customer service 20,200
Long-term labor 29,400
Administrative 30,700 $253,750
Operating Income $346,250
b) The preparation of an activity-based income statement for Carbon Company is as follows:
Carbon Company
Income Statement (Activity-based)Sales revenue $600,000
Resources supplied Unused Resources Used Resources
Materials $ 101,300 $ 2,300 $99,000
Energy 21,590 2,210 19,380
Setups 24,360 0 24,360
Purchasing 26,200 7,800 18,400
Customer service 20,200 9,700 10,500
Long-term labor 29,400 4,650 24,750
Administrative 30,700 5,950 24,750
Total $253,750 $32,610 $221,140
Operating Income $378,860
Data and Calculations:Unused Resources Capacity Cost Driver Volume
Resources used
Materials $ 2,300 9,000 pounds
Energy 2,210 380 machine-hours
Setups 0 87 setups
Purchasing 7,800 80 purchase orders
Customer service 9,700 70 returns
Long-term labor 4,650 330 labor-hours
Administrative 5,950 450 labor-hours
Resources suppliedMaterials $ 101,300
Energy 21,590
Setups 24,360
Purchasing 26,200
Customer service 20,200
Long-term labor 29,400
Administrative 30,700
Sales revenue $600,000
Activity-based Calculations:Resources supplied Unused Resources Used Resources
Materials $ 101,300 $ 2,300 $99,000
Energy 21,590 2,210 19,380
Setups 24,360 0 24,360
Purchasing 26,200 7,800 18,400
Customer service 20,200 9,700 10,500
Long-term labor 29,400 4,650 24,750
Administrative 30,700 5,950 24,750
Total $253,750 $32,610 $221,140
Thus, the traditional income statement for Carbon Company shows an operating income of $346,250, while the activity-based income statement shows an operating income of $378,860.
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The area of a rectangle is the product of its length and width. Both length and width are whole numbers. A rectangular poster has an area of 204 square inches. The width of the poster is greater than 10 inches and is prime. What is the width of the poster?
Answers
Answer:
17 inches.
Step-by-step explanation:
If the area of a rectangle is the product of its length and width, then;
Area of a rectangle = Length × Width
Given that the width of the poster is greater than 10 inches and is prime, this means and W>10
Area of the rectangle = 204in²
On substituting the values in the formula;
A = LW
204 = LW
Since W is greater than 10 and is prime, it can be between the prime numbers 11, 13 and 17. Note that L must be a whole number as well for any number to be the right answer we seek.
Let's test each values of the prime width that will give a length that is a whole number.
If W = 11
204 = 11×L
L = 204/11
L = 18.54
Since the length didn't give us a whole number, this means our width is not 11.
If W = 13
204 = L × 13
L = 204/13
L = 15.69
Also, we can see that the length is not also a whole number for the value of 13 as the prime width.
If W = 17
204 = L × 17
L = 204/17
L = 12
It can be seen that the length of the rectangle gave us a whole number when we used the prime width of 17, hence the width of the poster that is greater than 10 inches and is prime that makes both length and width to be a whole number is 17 inches.
Answer:17 inches
Step-by-step explanation:
Alice and Bob each have a certain amount of money. If Alice receives n dollars from Bob, then she will have 7 times as much money as Bob. If, on the other hand, she gives n dollars to Bob, then she will have 2 times as much money as Bob. If neither gives the other any money, what is the ratio of the amount of money Alice has to the amount Bob has?
Answers
The ratio of the amount of money Alice has to the amount Bob has is approximately 3.36 : 1.
How to find the ratio of money ?According to the problem, two equations can be set up:
If Alice receives n dollars from Bob, then she will have 7 times as much money as Bob. This gives us the equation:
A + n = 7(B - n)
If Alice gives n dollars to Bob, then she will have 2 times as much money as Bob. This gives us the second equation:
A - n = 2(B + n)
We can rearrange these equations to make them easier to solve:
8n = 7B - A
3n = A - 2B
Setting these equal to each other, since they are both equal to 24n, gives:
21B - 3A = 8A - 16B
37B = 11A
A / B = 37 / 11
= 3. 36
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The town of Winchester recently built an artificial body of Vater. This reservoir will store drinking water for the
town. Which of the following could cause contamination of the water and lead to human health-related problems
and loss of native species?
development of a water quality plan
B building a fence around the reservoir
C improvements to a water treatment facility
increased use of pesticides (chemicals) by farmers within the local watershed
Answers
Answer:
This reservoir, will store drinking water for the town. Which of the following could cause contamination of the water and lead to human health-related problems and loss of native species? ... Air pollution can affect human health and the health of other living things.
Step-by-step explanation:
what does it mean what does it meannnn AHHHHH
Answers
Answer:
31.125
Step-by-step explanation:
I think UF means Upper Fence, check your reference.
Number 22. The local toy store sells a package of 7 different shaped erasers for 4.20 $ what is the unit cost of each eraser in the package
Answers
Answer:
$4.20 / 7 erasers = $0.60 per eraser
So each eraser in the package costs $0.60.
It's possible to create a regular tessellation with a regular heptagon.
Answers
Answer:
False, No.
Step-by-step explanation:
No, it is not possible to create a regular tessellation with a regular heptagon. A regular tessellation, also known as a tiling, is a repeating pattern of identical regular polygonal shapes that cover a plane without any gaps or overlaps. The only regular polygonal shapes that can be used to form a regular tessellation are the equilateral triangle, square, and hexagon. These shapes have interior angles that are multiples of 60 degrees, which allows them to fit together seamlessly to form a repeating pattern. The interior angle of a regular heptagon is roughly 128.5714 degrees, which does not divide evenly into 360 degrees, so it cannot be used to form a regular tessellation.
Which of the following is a trigonometric identity?
cot 0 + tan 0 = 1
sec2 0 +csc2 0 = 1
tan2 0 = sin2 0 x sec2 0
cos2 = sec2 0 x tank 0
Answers
Answer:
it's the first one... I think
Answer:
third one
I'm assuming does 2's are squared symbols.
Step-by-step explanation:
It's the third one because
sin^2 x sec^2 x
sin^2 x (1/cos^2 x) by reciprocal identity
sin^2 x/cos^2 x by multiplicative identity prop
tan^2 x by quotient identity
The first one wouldn't work because plugging in pi/4 gives 1+1=1 which isn't true.
The second one doesn't work because plugging in pi/4 gives 2+2=1 which isn't true.
The last equation doesn't make sense at all. There is no variable on the left and on the right there is an extra variable.
Marty saved $200 this month. That is 50% of the money he earned mowing lawns. How much money did Marty earn mowing lawns? dollars.
Answers
Answer:
400
Step-by-step explanation:
half of 400 is 200? i need more letterssss
HELP PLEASE ! Due tonight! A pharmaceutical salesperson receives a monthly salary of $5000 plus a commission of
7% of sales. Write a linear equation for the salesperson's monthly wage W in terms of monthly sales S
Answers
Answer:
w=5000+0.7s
Step-by-step explanation:
if its possible give me 5 start I need it
Plz help me well mark brainliest if correct!....
Answers
Answer:
C
Step-by-step explanation:
B can immediately be eliminated because it has an area of 14.
A and C have an area of 10.
So add the sides.
C:
4 + 4 + 1 + 1 + 2 + 2 + 1 + 3
= 18
A: 3 + 3 + 2 + 2 + 1 + 1 + 1 + 1 =
10 + 4 =
14
please answer this!!!!! im begging !!! pleaseeeeeeee
Answers
Write down the coordinates of point B?
Answers
Answer:
The answer is 4,5.
Step-by-step explanation:
Go over 4 times and go up 5, and there is your answer.
please help will give Brainly!
Answers
Answer:
Range is 21
I believe
Step-by-step explanation:
pleaseeee help ill give brainliest
Answers
The graph of a linear relationship contains the points (1,10) and (3,16) write the equation of the line in slope
Answers
Answer:
Step-by-step explanation:
The equation of the line with the given points is y = 6x - 4. This can be derived by calculating the slope of the line, which is 6, and then using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the given points are (x1, y1) = (1, 10), so the equation of the line is y - 10 = 6(x - 1) or y = 6x - 4.
Answer y == 3
+7
Step-by-step explanation:
The graph of a linear relationship contains the points (1, 10) and (3, 16).
Write the equation of the line in slope-intercept fo
Step-by-step explanation:
the general slope-intercept form is
y = ax + b
a is the slope, which is the ratio of "y coordinate change / x coordinate change" when going from one point to another on the line.
b is the y-intercept - the y value when x = 0.
for the slope we see
x changes by +2 (from 1 to 3)
y changes by +6 (from 10 to 16)
so, the slope a is +6/+2 = 3
and the semi-ready equation is
y = 3x + b.
now we use one of the points in the equation to solve for b. I picked (1, 10) :
10 = 3×1 + b = 3 + b
b = 7
so, the full equation is
y = 3x + 7
What is the standard form of the following equation?
y= -3x+2
3x+y=2
y-2=-3x
y-3x=2
3x-y=2
Answers
Answer:
(a) 3x +y = 2
Step-by-step explanation:
You want the equation y = -3x +2 written in standard form.
Standard formThe standard form of a linear equation is ...
ax +by = c
where a, b, c are mutually prime integers with a ≥ 0. If a=0, then b > 0.
To put the given equation into that form, we can add 3x to both sides:
3x +y = 3x -3x +2
3x +y = 2
Determine whether the point (4,2) is in the solution set of the system of inequalities below. 4x + y < 2 y > –2
Answers
Answer:
False
Step-by-step explanation:
4x + y < 2
y > –2
Substitute the point into the inequalities and see if they are true
4(4) + 2 < 2
16+2 < 2
18 <2 False
2 > –2 True
Since one is false the point is not a solution
$600 invested at 5% compounded daily after a period of 3 years.
Answers
Answer:
$697.09
Step-by-step explanation:
The computation of the investment after 3 years is shown below:
As we know that
Amount = Present value × (1 + rate)^number of years
= $600 × (1 + 0.05 ÷ 365)^365× 3
= $697.09
Hence, the investment after 3 years is $697.09
We simply used the above formula to determine the investment
I will have to send a picture to show you
Answers
The volume of the box-shaped a cuboid is
\(V=l\times w\times h\)l is the length
w is the width
h is the height
From the given figure
The volume of the box is 93 1/2 ft^3
V = 93 1/2
The width is 2 ft
w = 2
The height is 5 1/2 ft
h = 5 1/2
Substitute them in the rule above
\(\begin{gathered} 93\frac{1}{2}=l\times2\times5\frac{1}{2} \\ \frac{93\times2+1}{2}=l\times2\times\frac{5\times2+1}{2} \\ \frac{187}{2}=l\times2\times\frac{11}{2} \\ \frac{187}{2}=l\times11 \end{gathered}\)Multiply both sides by 2 to remove the denominator
\(187=22l\)Divide both sides by 22 to find l
\(\begin{gathered} \frac{187}{22}=\frac{22l}{22} \\ 8\frac{1}{2}=l \end{gathered}\)The length of the box is 8 1/2 ft
The answer is B
15n+24-4(n-3)+6-2n=105
Answers
Answer:
n = 7
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Question: 15n+24-4(n-3)+6-2n=105
Answer: 3 • (3n + 14)
Explanation:
STEP 1: Restate
Equation at the end of step 1
(15n + 24) - 4 • (n - 3)) + 6) - 2n
STEP 2: Pulling out like terms
STEP 3: Pull out like factors :
9n + 42 = 3 • (3n + 14)
Final result :
3 • (3n + 14)
Hope this helps~
use deductive reasoning to show that the following procedure always produces the number 8. procedure: pick a number. add 5 to the number and multiply the sum by 3. subtract 7 and then decrease this difference by the triple of the original number.
Answers
After using the deductive reasoning the procedure always produces the number 8.
Procedure:
Let the number be x.
We have to add 5 to the number x.
So the expression is x + 5.
We have to multiply the sum by 3.
Now the expression is 3(x + 5).
Now we have to subtract 7.
Now the expression is 3(x + 5) - 7.
Then we have to decrease this difference by the triple of the original number.
The triple of original number is 3x.
Now the expression is {3(x + 5) - 7} - 3x.
Now solving this expression
= {3(x + 5) - 7} - 3x.
First simplify the bracket
= 3x + 15 - 7 - 3x.
= 8
Now we can se that the after following the whole procedure the answer is 8.
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Compute the monthly payments for an add-on interest loan of $ 2890, with an annual interest rate of 10% and a term of 3 years.
Answers
The principle is $2890 the rate is 10% and the term is 3 years so it follows:
\(P=2890,r=0.1,n=3\)The interest is given by:
\(I=p\times n\times r=2890\times0.1\times3=867\)The principle to be repaid is given by:
\(P^{\prime}=\frac{2890}{36}=80.28\)The monthly interest will be:
\(I=\frac{867}{36}\approx24.083\)The monthly payment is given by:
\(M=P^{\prime}+I=104.363\)The monthly payment is $104.363.
can someone please help
Answers
Answer:
The measure of CD is 46
Step-by-step explanation:
From the midpoint theorem, we have,
FG = (1/2)CD
so,
\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)
Now,
\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)
NO LINKS HELP PLEASE PLEASE EXPLAIN
Answers
Answer: 1,278
Step-by-step explanation: 2(18x18)+2 1/2(18x14)
p.e.m.d.a.s. 18x18= 324 18x14= 252
2x324= 648 2.5x252=630
648+630 =1,278
A soccer player has a large cylindrical water cooler that measures 3 feet in diameter and is 4 feet tall. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water are in the water cooler when it is completely full? Use π = 3.14 and round to the nearest hundredth. 28.26 gallons 113.04 gallons 211.38 gallons 845.54 gallons
Answers
The volume of the cylindrical water cooler is 211.38 gallons. Therefore, option C is the correct answer.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, a soccer player has a large cylindrical water cooler that measures 3 feet in diameter and is 4 feet tall.
Now, radius = 3/2 =1.5 feet
We know that, the formula to find the volume of a cylinder is πr²h.
Here, 3.14×1.5²×4
= 28.26 cubic feet
In gallons = 28.26×7.48
= 211.38 gallons
Therefore, option C is the correct answer.
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The correct option is C, 211.38. Hope this helps :)
Evaluate 12.3v+11.9w when v=7 and w=8.
please
Answers
Answer:
181.3
Step-by-step explanation:
I hope this helps!
Sunni is riding a raft down a stream that is moving at a rate of 75 feet per minute how far downstream does she travel in 5 minute?
Answers
Answer: 375 feet
Step-by-step explanation:
From the question, we are given the information that Sunni is riding a raft down a stream that is moving at a rate of 75 feet per minute.
To calculate how far downstream that she can travel in 5 minute, we have to multiply the distance covered per minute by 5. This will be:
= 75 feet × 5
= 375 feet
the area of a rectangle is 33.12cm². Given that one side of length is 4.6cm. Find the length of the other side
Answers
Answer:
7.2 cm----------------------------
Area of rectangle formula:
A = lwGiven:
A = 33.12 cm²,w = 4.6 cm.Find the missing side length:
l = A/wl = 33.12/4.6l = 7.2 cmAnswer:
7.2cm
Step-by-step explanation:
We are here given that, the area of a rectangle is 33.12cm² and one of the side is 4.6cm .
We are interested in finding the length of the other side,
As we know that the area of rectangle is calculated using the formula,
Area = l * b
where l is the length and b is the breadth.
Now substitute the respective values,
33.12cm² = l * 4.6cm
l = 33.12cm²/4.6cm
l = 7.2 cm
Hence the value of second side is 7.2cm