4 and 3.14 are the constant of proportionality .
What does the arithmetic word proportional mean?
In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.There is a correlation between the quantity of fuel we put in our car's tank and the price we will have to pay when we fill it up. In other words, we will pay more money the more gas we put in.2×4 = 8
2×3.14=6.28
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You and your friend were thinking about pairs of whole numbers that
have a sum of 12. How many pairs of whole numbers can you find that have a sum
of 12? (Note: A whole number is equal to or greater than 0 and does not include a
fraction. 2 is a whole number. 2 ½ is not a whole number.)
Answer:
0, 12 or 12, 0
1, 11 or 11, 1
2, 10 or 10, 2
3, 9 or 9, 3
4, 8 or 8, 4
5, 7 or 7, 5
6, 6
All these pairs add up to 12.
Hope this helps :)
There are 7 pairs of whole numbers that have a sum of 12.
Given that we need to determine the pairs of whole numbers can you find that have a sum of 12.
To find the pairs of whole numbers that have a sum of 12, we can simply list all the possible combinations and count them.
Let's consider two whole numbers, x and y, such that x + y = 12. Since the numbers should be whole numbers and greater than or equal to 0, we have the following options:
x = 0, y = 12
x = 1, y = 11
x = 2, y = 10
x = 3, y = 9
x = 4, y = 8
x = 5, y = 7
x = 6, y = 6
So, there are 7 pairs of whole numbers that have a sum of 12.
These pairs are (0, 12), (1, 11), (2, 10), (3, 9), (4, 8), (5, 7), and (6, 6). Each of these pairs satisfies the condition that both x and y are whole numbers and their sum is equal to 12.
Note: We only consider x and y values up to 6 since beyond that, the sum would exceed 12, and we are only looking for pairs with a sum of 12.
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Which of the following explains the relationship between angles C and D?
Lines JK and JM intersect at point J creating four angles identified as angle B, angle D, angle C, and angle A clockwise from the top right.
Adjacent angles
Corresponding angles
Complementary angles
Vertical angles
The term that explains the relationship between angles C and D is: A. Adjacent angles.
What are Adjacent Angles?When two angles share a common vertex and a common side, the two angles are referred to as adjacent angles.
In the diagram given, lines JK and JM intersect at point J to form 4 angles of which angles C and D share a common side and a common vertex (point J).
Therefore, the term that explains the relationship between angles C and D is: A. Adjacent angles.
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Answer:
A
i took the test and got it right
What is the area of this composition shape enter your answer in the box 7 inches and 3 inches in 5 inches in 12 inches blank inches square
The area of the composite shape that is given in the image below = 40 in.².
How to Find the Area of a Composite Shape?In the diagram given below, the shape can be decomposed into a triangle and a rectangle, since it is composed of both shapes.
Thus:
The area of the composite shape = area of rectangle + area of triangle.
Area of the triangle = 1/2(b)(h)
base = 12 - 7 = 5 in.
height = 5 - 3 = 2 in.
Area of the given triangle = 1/2(5)(2)
Area = 5 in.²
Area of the given rectangle = (l)(w)
length = 7 in.
width = 5 in.
Area of the given rectangle = (7)(5) = 35 in.²
The area of the composite shape given = 35 + 5 = 40 in.².
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Simplify
18/4 -36x/4
Please help me asap thanks
x = 1/2 is the simplify answer of linear equation .
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.18/4 - 36x/4 = 0
18 - 36x / 4 = 0
18 - 36x = 0
18 = 36x
x = 18/36
x = 1/2
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The average ocean depth is 3.7*10^(3)m, and the area of the oceans is 3.6*10^(14)m^(2). What is the total volume of the ocean in liters? (One cubic meter contains 1000 liters.)
The total volume of the ocean in litres is [tex]1.332\times10^{21}[/tex] litres.
Given that, the depth of an ocean =[tex]3.7\times 10^{3}[/tex] m and the area of the ocean = [tex]3.6\times10^{14}[/tex] m².
We need to find the total volume of the ocean in litres.
What is volume?Volume is defined as a capacity occupied by a three-dimensional solid shape. Any shape is hard to visualize but can be compared between shapes. The volume of any object is the product of the area of a base and the height of the object.
Now, the volume of the ocean=[tex]3.6\times10^{14}[/tex]×[tex]3.7\times 10^{3}[/tex]
=[tex]13.32\times10^{17}[/tex] m³
=[tex]13.32\times10^{17}\times1000[/tex]
=[tex]1.332\times10^{21}[/tex] litres
Therefore, the total volume of the ocean in litres is [tex]1.332\times10^{21}[/tex] litres.
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An item is regularly priced at $55. It is on sale for 45% off the regular price.
An item is $55 before sale, and bought for 45 percent off the regular price. therefore the sale price of item is $30.25.
What is Markup and Markdown?Markup is the amount that will be increased in the original price of the considered thing.
Markdown is the amount that will be decreased from the original price of the considered thing.
Think of "up" and "down" as increasing and decreasing prices respectively.
Given that item is $55 before sale, and bought for 45 percent off the regular price.
WE have to do that as; 45% off $55 implies subtract 45% from $55
= 45/100 × 55 = $24.75
therefore the item bought at $55 - $24.75= $30.25.
Hence, the sale price of item is $30.25.
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The complete question is
An item is regularly priced at $55. It is on sale for 45% off the regular price. What is the sale price?
Sandy collected 10 pounds of apples at an apple orchard. She is determined to
eat 20% of the apples remaining every day after the day she went to the orchard.
Write an exponential function to model this scenario and use it to estimate how
many pounds of apples she has left after 1 week.
The weight of apple that Sandy has left after one week is 2.1 pounds.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the number of apple remaining after x days. Sandy collected 10 pounds of apples at an apple orchard and eat 20% daily, hence:
y = 10(1 - 0.2)ˣ
y = 10(0.8)ˣ
After 1 week, x = 7:
y = 10(0.8)⁷ = 2.1 pounds
The weight of apple that Sandy has left after one week is 2.1 pounds.
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An object is launched from the top of a hill and travels in a parabolic path until it reaches the ground. Write a quadratic function
that models the path of the object with a maximum height of 200 feet, represented by a vertex of (25, 200) , landing at the point
(55.0)
Answer:
Bonjour,
Step-by-step explanation:
y=k*(x-25)²+200
0=k*(55-25)²+200 => k=-2/9
y=-2/9(x-25)²+200
The a quadratic function that models the parabolic path of the object is y = -2/9(x-25)²+ 200.
What is defined as the parabolic path?A projectile's trajectory angle is defined as a parabolic path. A parabola is just a curve that represents a quadratic equation graphically. The initial velocity of a projectile is either horizontal or upward at such an angle. If a projectile starts out straight up, it will end up straight down. It's not much of a parabola because it's squished into the a straight line.For the given question;
The maximum height of the object which is launched from the top of a hill is 200 m.
The equation of the parabola is -
y=a*(x-h)²+k
(h,k) = vertex = (25, 200)
y = a*(x-25)²+200
Put (x,y) = (55,0)
0=a*(55 - 25)²+200
=> a = -2/9
Now put the value of 'a' and form the equation.
y = -2/9(x-25)²+ 200
Thus, the a quadratic function that models the parabolic path of the object is y = -2/9(x-25)²+ 200.
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In baseball, a commonly used rate is earned run average (ERA). ERA is a rate of earned runs to a constant number n of innings. In 2020, the pitcher in Example 2 had an ERA of 2.70. Find the value of n.
The value of n which is a constant representing number of innings is equal to 50.
What is ERA or earned run average ?
Earned runs without the help of passed ball, are represented by the earned run average, which is the number of earned runs a pitcher allows per nine innings.
It is given that In 2020, the pitcher had an ERA of 2.70.
A rate of earned runs to a fixed number of innings, n, which is also known as ERA.
Let's check it.
To determine a pitcher's earned run average or (ERA), multiply the runs by nine, then divide it by the number of innings pitched.
The runs earned in 2020 is 15 , let's multiply it by 9.
So , we get 15 × 9 = 135.
Now , divide it by number of innings which is 50.
So , the value of ERA will be equal to : 135 ÷ 50 = 27 which is also given in the question.
Now we will calculate the value of n.
So ,
n = (9 × Earned runs) / ERA
or
n = ( 9 × 15 ) / 2.7
n = 135 / 2.7
n = 50 innings
Therefore , value of n which is a constant representing number of innings is 50.
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make rates equivalent.
16 points scored in 4 games.
48 points scored in 8 games.
The rates aren't equivalent based on the information given regarding the games.
How to illustrate the information?It should be noted that 16 points were scored in 4 games. Therefore, the points per game will be:
= 16 / 4
= 4 points.
Also, 48 points scored in 8 games. Therefore, the points per game will be:
= 48 / 8
= 6 points.
Therefore, the rates aren't equivalent.
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16 points scored in 4 games.
48 points scored in 8 games.
Are the rates equivalent?
A number is multiplied by 20, and that product is added to 10. The sum is equal to the product of 5 and 10. Find the number
Seven subtracted from seven times a number is 147. What is the number?
A) Translate the statement above into an equation that you can solve to answer this question. Do not solve it yet. Use
x
as your variable.
The equation is
B) Solve your equation in part [A] for
The translation of the statement is 7x - 7 = 147 and the numerical value of x is 22.
What is the numerical value of x?Given the statement in the question?
"Seven subtracted from seven times a number is 147"
Translate the statement into an equation;
Let x represent the unknown number.
Seven times a number ⇒ 7 × x = 7xSeven subtracted from ⇒ -7Is 147 ⇒ = 147Now, combine
7x - 7 = 147
Therefore the translation of the statement is 7x - 7 = 147.
Next, we solve for x
7x - 7 = 147
Add 7 to both sides
7x - 7 + 7 = 147 + 7
7x = 154
x = 154/7
x = 22
Therefore, the translation of the statement is 7x - 7 = 147 and the numerical value of x is 22.
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K
Assume that adults have IQ scores that are normally distributed with a mear
top 75%. (Hint: Draw a graph.)
The first quartile is
(Type an integer or decimal rounded to one decimal place as needed.)
am from India . Hi .
Please subscribe Stone Gamer
What are the specs of your pc
(2x-22)+(5x-8)=180
what is x
Answer:
x =30
Step-by-step explanation:
2x-22+5x-8=180 (st. line)
7x-30=180
7x=210
x=210/7
x=30
At the lakeside aquarium there are 7 freshwater fish on display for every 5 salt water fish
Based on the number of freshwater fish per s-a-l-t-water fish, the ratio for s-a-l-t-water fish to freshwater fish is 5 : 7.
What is the ratio?The ratio between the s-a-l-t-water fish and the freshwater fish putting both figures against each other as a ratio.
The ratio would be:
Number of s-a-l-t-water fish : Number of freshwater fish
Putting in the quantities gives:
5 s-a-l-t-water fish fish : 7 freshwater fish
5 : 7
In conclusion, the ratio is 5 : 7.
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Someone HELP ME PKS PLS PLS PLS S I BEG U PLS JUST HELP ME
Answer:
How about this: A bag of 8 oranges is $6.50 and you want to know the price per orange? Or how about this: You have a soda vending machine and each soda is $2.00. A case of soda (24 cans) costs you $15.00. You need to know how much the case costs per can to see if you will make a profit.
Step-by-step explanation:
A unit rate is a type of ratio that compares one unit of some quantity to a different number of units of a quantity.
5,323 ÷ 34
I need answers asap
Answer: 156.55882352941176470588235294118
Or 156.56 rounded to the nearest hundredth!
Hope this helps!
Answer: 156.558823529
Step-by-step explanation: You divide for example, 5,323 cookies to 34 people
If the price of a business math text rose to $220 and this was 7% more than the original price, what was the original selling price? (Round to the nearest cent.)
Answer:
235.4
Step-by-step explanation:
7% more than 220 would be 235.4
First you would turn 7% as a decimal which would be .07. Then, you would multiply .07 times 220 which would give you 15.4. Lastly, you would add 15.4 plus 220 which would equal 235.4.
7%=.07
.07×220=15.4
15.4+220=235.4
When Rahul moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 32 inches tall and Tree B was 20 inches tall. Each year thereafter, Tree A grew by 6 inches per year and Tree B grew by 9 inches per year. Let AA represent the height of Tree A tt years after being planted and let BB represent the height of Tree B tt years after being planted. Write an equation for each situation, in terms of t,t, and determine the number of years after the trees were planted when both trees have an equal height.
A= B=
Answer:
The equation to represent the growth of the trees is given by
AA=32+6t and BB=20+9t and both the trees will be of equal height after 3 years.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Equation is defined as the quality of being equal and is frequently represented by a mathematical statement with equal values on either side or by a problem requiring consideration of a number of factors.
Given that tree A is 32 inches tall and tree B is 20 inches tall.
Tree A grows 6 inches per year.
Length of the tree A after t years = 32 + 6t
Tree B grows 9 inches per year
Length of the tree B after t years = 20 + 9t
Now let us consider that both trees grows equal after a certain period of time.
If we equate both the expressions then we can form an equation to calculate the value of t.
∴ 32+6t = 20+9t
or, 6t - 9t = 20 - 32
or, -3t = -12
or, t = 4 years
The trees will be of equal length after 4 years.
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A machine costing $214,200 with a four-year life and an estimated $19,000 salvage value is installed in Luther Company’s factory on January 1. The factory manager estimates the machine will produce 488,000 units of product during its life. It actually produces the following units: 123,200 in Year 1, 123,600 in Year 2, 120,900 in Year 3, 130,300 in Year 4. The total number of units produced by the end of Year 4 exceeds the original estimate—this difference was not predicted. (The machine cannot be depreciated below its estimated salvage value.)
The appropriate journal entries for year 4 depreciation is:
Dr. depreciation $52,210
Cr. Accumulated depreciation $52,210
What is depreciation?
Depreciation is the gradual systematic allocation of the cost of asset over its useful years, the fact that the machine in this case would be used for 4 years means that its initial cost needs to be allocated over the 4 years.
Depreciation(straight-line method)=(cost-salvage value)/useful life
Depreciation(straight-line method)=( $214,200-$19,000)/4=$48,800 per year
Depreciation rate per unit=($214,200-$19,000)/488000
Depreciation rate per unit=$0.40
Depreciation in year 4=130,300*$0.40
Depreciation in year 4=$52,210
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Additional information provided by the student in the comment section:
How do I record the 4th year?
In a survey on internet usage , it was found that out of a total of 27 people, 16 use ADSL lines, 15 use wireless internet and 3 use neither of the two . what is the probability that a person chosen at random uses both internet connections
The probability that a person chosen at random uses both internet connections is 1/9
Total number of people = 27
Number of people who use ADSL lines = 16
Number of people who use wireless internet = 15
Number of people who use neither of the two = 3
Let the number of people who use only ADSL lines and wireless internet be denoted by A and B respectively.
Then A + B + A∩B + 3 must be equal to 27
A + B + A∩B = 24
further, we can see that
(A + A∩B) = 16
B + 16 = 24
B = 8
Also, (B + A∩B) = 15
8+ A∩B = 15
A∩B = 7
Thus, the number of people who use both internet connections = 7
Now, P(A∩B) = 7/27
= 1/9
Hence, probability that a person chosen at random uses both internet connections is 1/9.
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Maria bought 5 tickets for $20 each. Each ticket had a $2 fee. Write an expression that shows how much Maria paid for the tickets. plssss help will give 10 points :)
The expression to illustrate the information when Maria bought the tickets is C = (5 × $20) + ($2 × 5) and the total amount paid is $110.
How to illustrate the information?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. A mathematical expression shows the value of something by combining numbers, variables, and operators. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing. For instance, the mathematical equation for "4 added to 2" will be 2+4.
From the information, Maria bought 5 tickets for $20 each. Each ticket had a $2 fee.
The expression that can be used to illustrate this will be:
C = (5 × $20) + ($2 × 5)
where C = Total cost
C = $100 + $10
C = $110
Therefore the expression to illustrate the information when Maria bought the tickets is C = (5 × $20) + ($2 × 5) and the total amount paid is $110.
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5÷540 long divison with a grid
Answer:
0.00925925925.Step-by-step explanation:
I really don't have explanation on this.
Why, because it's too hard to explain.
The function f is graphed below.
determine the intervals on which f is increasing and decreasing
The function is decreasing on the interval [-5 < x < -1] (segment 1),
The function is increasing on the interval [-1 < x < 4] (segment 2),
The function is decreasing on the interval [4 < x < 9] (segment 3).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
As per the given graph,
The function is decreasing from the interval from -5 to -1 in its domain
The function is increasing from the interval from -1 to 4 in its domain
The function is decreasing from the interval from 4 to 9 in its domain
Therefore, the function is decreasing on the interval [-5 < x < -1] (segment 1), increasing on the interval [-1 < x < 4] (segment 2), and decreasing on the interval [4 < x < 9] (segment 3).
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SOMEONE HELP ME PLS!
Answer:
are u sure this is the question ⁉️
Answer:
x=10 or 4
Step-by-step explanation:
square root of x-7²=x-7
x=3+7 or -3+7=10 or4
Which equations have the same solution as the equation 4y - 3 = -2y + 1?
Choose all that apply.
A. 2y-3=1
B. 4y = -2y + 4
C. -3=-6y +1
D8y-3=-4y + 1
E. 8y-6=-4y+2
Answer:
B and C
Step-by-step explanation:
B = 4y - 3 + 3 = -2y + 1 + 3
= 4y = -2y + 4
C = 4y - 3 -4y = -2y + 1 -4y
= 3 = -6y +1
Oak Creek Furniture Factory (OCFF), a custom furniture manufacturer, uses job order costing to track the cost of each customer order. On March 1, OCFF had two jobs in process with the following costs:
Work in Process Balance on 3/1
Job 33 $ 7,500
Job 34 6,000
$ 13,500
Source documents revealed the following during March:
Materials Requisitions Forms Labor Time Tickets Status of Job at Month-End
Job 33 $ 3,500 $ 6,500 Completed and sold
Job 34 6,000 7,800 Completed, but not sold
Job 35 4,200 3,250 In process
Indirect 1,300 2,140
$ 15,000 $ 19,690
The company applies overhead to products at a rate of 150 percent of direct labor cost.
Required:
Prepare journal entries to record the materials requisitions, labor costs, and applied overhead.
The journal entries to record the materials requisitions, labor costs, and applied overhead is: Debit Work in process inventory $16,300, Credit Manufacturing overhead $1,300, Credit Raw materials inventory.
Journal entries1. Debit Work in process inventory $16,300
($15,000+$1,300)
Credit Manufacturing overhead $1,300
Credit Raw materials inventory $15,000
(To record material acquisition)
2. Debit Work in process inventory $17,550
($19,690-$2,140)
Debit Manufacturing overhead $2,140
Credit Factory payroll $19,690
(To record labor costs)
3. Debit Work in process inventory $26,325
Credit Manufacturing overhead $26,325
($17,550×150%)
(To record applied overhead)
Therefore the journal entries to record the materials requisitions, labor costs, and applied overhead is: Debit Work in process inventory $16,300, Credit Manufacturing overhead $1,300, Credit Raw materials inventory.
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The perimeter of the parallelogram below is 32.2. What equation would you set up to solve for x? What is the value of x?
The value of x from the given figure is 8/3
Perimeter of a parallelogramThe sum of all the ides of the parallelogram is perimeter. According to the given figure;
2(3x-8)+2(16) = 32.2
Expand to have:
6x-16 + 32 = 32.2
6x + 16 = 32.2
Subtract 16 from both sides
6x = 16
x = 16/6
x = 8/3
Hence the value of x from the given figure is 8/3
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Answer:
Step-by-step explanation:
A pail holds 634 gallons of water. How much is this in cups?
Answer: 10,144 cups
Step-by-step explanation:
Determine d in the equation.
12.6 = −1.8 − 4d
A. d = 2.7
B. d = −2.7
C. d = 3.6
D. d = −3.6
Answer:
D. d= -3.6
Step-by-step explanation:
12.6= -1.8 -4d
Add the negative 1.8 to the left side and then divide by -4
