The constant of proportionality is 5/3.
What is the constant of proportionality?In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one double, and both decrease in size when one drops to a tenth of its original value.
The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to by the terms constant ratio, constant rate, unit rate, constant variation, or even change rate.
Let the constant of proportionality is k.
Harry buys 3 granola bars for $ 5. So, we can write it as
3 × k = 5
k = 5/3
To Check:
Sidney buys 9 granola bars for $ 15, we can write it as
9 × k = 15
Put k= 5/3 in the equation
9 × 5/3 = 15
3 × 5 = 15
15 =15
The Left and right-hand sides are equal. Hence, the constant of proportionality is k=5/3.
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helpp me teacher said this is a quadratic formula 3x2+x+1
Answer: 0.434
Step-by-step explanation:
Answer:
3 (x + 16) 2 + 11 12
Step-by-step explanation:
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the store has a speaker equipment listed for a price of $100 per set of speakers there is a sale, the current selling price is 89.99 how much money does the customer save ?
The amount of money saved by the customer is $10.01
If the selling price is greater than the cost price, then the difference between the selling price and cost price is called profit or the money saved.
If the selling price is less than the cost price, then the difference between the cost price and the selling price is called loss or the money loss.
Profit/ Loss= Cost Price(CP)- Selling Price(SP)
When CP> SP, then we can say there is a profit.
When CP<SP, then we can say there is a loss.
When CP=SP, then we can say neither there is a loss nor profit.
Given data, CP= $100
SP= $89.99
Profit/Loss= CP- SP
= $100- $89.99
= $10.01
As we can see our result is positive, so there is a profit.
Final answer: The amount of money saved by the customer is $10.01
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Round 45.8 to the nearest whole number
Answer: 46
Step-by-step explanation: 8 is closer to 10, so 45.8 would round to 46
Which graph models function
The function g(x) models a downward facing parabola shape which is option A
The function g(x) have the solutions which are given in the form of coordinates
This can be solved on a sheet of graph using coordinate geometry
(-3,0), (-2,-4) , (-1, -6) , (0, -6 ), (1,-4),(2,0) and (3,6)
If we will plot all the given seven points given on the graph and join the points we would get a downward sloping parabola model which looks like reverse 'U' shaped whose highest point is between -1 and 0 that is -0.5
lies in second quadrant of the graph sheet.
Hence the given function g(x) models a parabola shape which is option A
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Solve negative four and one third ÷ two and one fifth.
Answer: -2/15 according to the calculator.
Answer:
-1.9681
the 81 is repeating
Step-by-step explanation:
A rectangular field is 15m longer than it is wide.
The area of the field is 800m²
Work out the length of the field.
Give your answer to 1 decimal place.
The length of rectangular field is 36.76 m.
What is a length?Distance is quantified by length. A quantity with the dimension of distance is called length in the International System of Quantities. Most measurement systems choose a length base unit from which all other units are derived. The fundamental unit for length in the International System of Units is the metre.
The term "length" refers to the measurement or size of something from end to end. In other terms, it is the greater of the upper two or third dimension of a geometric shape or object.
Area of rectangle is L × W = 800
given L = 15 + W
W × ( 15+ W) = 800
15W + [tex]W^{2}[/tex] = 800
[tex]W^{2}[/tex] + 15W - 800 = 0
by solving the above quadratic equation W= 21.76 m.
L = 15 + W
L = 36.76 m
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in jeff’s sample, the number of siblings each person has is as follows: one, two, three, four, and ten. what is the median number of siblings in his sample?
If the number of siblings each person has is one, two, three, four and ten, then the median of number of siblings is 3
Given,
The number of siblings each person has = 1,2,3,4 and 10
Arrange them in ascending order =1,2,3,4 and 10
We know the median is the middle term of the ordered pair
The number of terms n= 5
Middle term is = [tex]\frac{n+1}{2}[/tex]
=[tex]\frac{5+1}{2}[/tex]
=3
The 3rd term is 3.
The median = 3
Hence, If the number of siblings each person has is one, two, three, four and ten, then the median of number of siblings is 3
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What is the quotient of 81/(-9)/(-3)
Answer:
3
Step-by-step explanation:
81/(-9)/(-3)=3
The number 3 is prime number.
A(n) ____ turns a figure a certain number of degrees around a point.
Rashon needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 4.25 hours and charged him $141 for parts. The total was $332.25. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.
Answer:
Step-by-step explanation:
The cost of labor per hour is $45.
The total cost of the parts is $141.The total time for which the technician worked is 4.25 hours.The total cost of repair is $332.25.Let the cost of labor per hour be "x".The total cost of labor is the product of the total time for which the technician worked and the cost of labor per hour.The cost of labor is 4.25*x.The total cost of repairing the computer is the sum of the cost of the parts and the cost of labor.The total cost of repairing the computer is $141 + 4.25*x.The equation is as follows:332.25 = 141 + 4.25*x191.25 = 4.25xx = 191.25/4.25x = 45Thus, the cost of labor per hour is $45.To learn more about equation, visit :
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NEED HELP IMMEDIATELY!
Simplify 10√2y + 5√2y + 3√2y.
A. 18√6y
B. 18√2y
C. 12√2y
D. 18√6y^3
(ANSWER IS NOT A)
18 root
2
Step-by-step explanation:
In this question imagine there is no y
It will be 10 root2 +5 root2 +3 root 2 it will be 18 root 2
What does the symbol bc represent
Answer:
ray BC
Step-by-step explanation:
What is -33.44/-1.9 in division?
The division of the number -33.44/-1.9 is 17.6.
What is referred as division?Division is one of four fundamental mathematical operations, along with addition, subtraction, as well as multiplication.
Division is defined as the separating of a large group in to other smaller groups so that each group has an equal amount of items.Division is a process of repeated subtraction. It is the inverse operation of multiplication.It is characterized by the creation of equal groups. When we divide numbers, we break them down into smaller numbers so that the multiplication of the those smaller numbers equals the larger number taken.For the given expression;
= -33.44/-1.9
as, both numerator and denominator is negative values, both negative signs will be cancelled.
Now, divide numerator 33.44 by denominator by 1.9, we get 17.6.
Thus, the division of the number -33.44/-1.9 gives quotient 17.6.
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State the property that justifies the statement.
If m∠ 1=25 and m∠2=25 , then m∠1=m∠2.
The equality property that justifies the statement "If m∠ 1=25 and m∠2=25 , then m∠1=m∠2" is; Substitution Property
What is the property of equality used?The substitution property of equality states that 'If a variable C is equal to another variable D, then C can be substituted in place of D in any equation/expression and D can be substituted in place of C in any equation/expression.
Now, we are given the expressions;
If m∠ 1 = 25 and m∠2 = 25 , then m∠1 = m∠2.
Thus, we can also say that the property used here is called substitution property because the parameters were interchanged and still equal.
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What is 96,902,123 in expanded form
Answer: 90,000,000 + 6,000,000 + 900,000 + 2,000 + 100 + 20 + 3
Step-by-step explanation: you add each one and get 96,902,123
are the ratios 1:4 and 3:5 equivalent
Answer:no
Step-by-step explanation:1:4 is not equivalent to 3:5
3 is subtracted from three times a number
“a number” is x
Answer:
3x - 3
The answer above matches with the statement:
"Three is subtracted from three times a number."
Hope this helps :)
Simplify the expression
Answer:
A
Step-by-step explanation:
Answer:
your answer will be A the first one
Step-by-step explanation:
q equals 4 l plus 2 k with l on the horizontal axis and k on the vertical axis, draw an isoquant. the slope of this isoquant equals
The slope of this isoquant equals -2.
What is an isoquant?A contour line formed across a set of locations where the same quantity of output is produced while changing the quantities of two or more inputs is called an isoquant (derived from quantity and the Greek word iso, meaning equal). A factor of production, like as labor, money, land, or organization, is typically represented by the x and y axes on an isoquant. Another name for an isoquant is a "Iso-Product Curve" or a "Equal Product Curve."
The isoquant mapping deals with the cost-minimization, profit, and output maximization problems of producers, whereas an indifference curve mapping helps consumers address the utility-maximizing problem. Indifference curves and isoquants diverge much more.
Calculations:
q=4L+2K
So, MPL=dq/dL =4
MPK=dq/dK =2
So,Slope=-MPL/MPK
=-4/2=-2
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3
5
Dan reads chapters in
56
hours.
What is the unit rate in chapters per hour?
Write your answer in simplest form.
Answer:
How many chapters does Dan read in 56 hours?
Step-by-step explanation:
A salesclerk is creating a display of 12 polo shirts and 48 team shirts. Only one type of shirt can be in each row. What is the maximum number of shirts in each row so that all the rows are equal in length? 12 4 3 2
The maximum number of shirts in each row so that all the rows are equal in length is 12.
How to illustrate the information?From the information, the salesclerk is creating a display of 12 polo shirts and 48 team shirts and only one type of shirt can be in each row.
It should be noted that the value van be found by knowing the highest common factor for the numbers.
The highest common factor for 12 and 48 is 12.
Therefore, the correct option is A.
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6. Select all the expressions that result in the same value as
40 + 120.
A. 4 (10
+30)
B. 2 (20 + 120)
C. 40 (1 + 3)
D. 40 (1 +30)
E. 10 (4+12)
Answer:
A, C, E
Step-by-step explanation:
40 + 120 = 160
Remember the correct order of operations, and do the operation inside parentheses first.
A. 4(10 + 30) = 4(40) = 160
B. 2(20 + 120) = 2(140) = 280
C. 40(1 + 3) = 40(4) = 160
D. 40(1 + 30) = 40(31) = 1240
E. 10(4 + 12) = 10(16) = 160
Answer: A, C, E
Taylor makes $13 per hour at the grocery store. she always works between 10-15 hours per week to leave time for her homework and band practice. her gross wages can be modeled as w(h) = 13h, where h is the number of hours worked per week.
1. how much will her gross wages be if she works 12 hours this week?
2. what is the domain of this function?
3. what is the range of this function?
a) Her gross pay will be $156
b) The domain is D: [10, 15]
c) The range is R: [$130, $195]
What will be her gross wage if she works 12 hours this week?
We know that Taylor earns 13 dollars per hour on her job at the grocery store.
Then, if she works x hours in the week, her gross wage will be given by the linear equation:
g(x) = $13*x
So, if she works 12 hours, her gross pay will be:
g(12) = $13*12 = $156
what is the domain of this function?
we know that she works between 10 and 15 hours peer week, so the domain (set of the possible inputs of the function) is:
10 ≤ x ≤ 15 or [10, 15] in interval notation.
what is the range of this function?The range is the set of the outputs, the minimum of the rane is:
g(10) = $13*10 = $130
The maximum of the range is:
g(15) = $13*15 = $195
The range of the linear function is: [$130, $195]
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A town's population is 42,975. About 125 people move out of the town each month. Each month, 150 people on average move into town. A nearby town has a population of 45,225. It has no one moving in and an average of 200 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation. Then solve the equation and answer the question.
It would take 10 months to equate the population of both the towns
Let the number of months required to equate the population of both the town( Town A and Town B) be x
This question can be solved using linear equations
So, town A's population would be current population adjusted with migration of people which is 42975-125x+150x
And town B's population would be current population adjusted with migration of people which is 45225 -200x
As at the end of x months the population of the two towns is equal, so equating both the linear equations
42975 -125x +150x = 45225-200x
Now solving the equation for x
150x-125x+200x= 45225-42975
225x=2250
Therefore x= 2250/225= 10
Hence it would take 10 months to equate the population of both the towns
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9. What is the slope of the graph of y= 12 x - 19?
12
Explanation:
Slope Intercept form is: y=mx+b
m would be the slope
So in y=12x-19, 12 would be the slope in this case.
The sum of all proportions in a frequency distribution should be______.
Oliver and his friends like to collect and trade cards from a certain combat card game. Oliver used his allowance to purchase 5 booster packs and 4 premade decks, which included a total of 178 cards. For his birthday, he received 4 booster packs and 7 premade decks, which included a total of 264 cards. How many cards come in every booster pack and every premade deck?
Solving system of equations in two variable gives that the number of cards in every booster pack are 10 and number of cards in every premade deck are 32
What is system of equations in two variables and how to find its solution by substitution?
Let x and y be two variables and
a₁x+b₁y =c₁
a₂x+b₂y =c₂
Where a₁, a₂, b₁, b₂, c₁, c₂ are constants then we can solve these simultaneous equations by substitution take value of x from equation (1) and then put it in (2) to get an equation for y only and then solve for y. put value of y in equation (1) to get value of x.
Let the number of cards in every booster pack are x and the number of cards in every premade deck be y
Number of cards in 5 booster packs will be 5x and Number of cards in 4 premade deck will be 4y
As Oliver purchases 5 booster packs and 4 premade decks, which included a total of 178 cards.
Thus we get 5x + 4y = 178 .....(1)
Number of cards in 4 booster packs will be 4x and Number of cards in 7 premade deck will be 7y
As Oliver received 4 booster packs and 7 premade decks, which included a total of 178 cards.
Thus we get 4x +7y = 264 ...(2)
System of equations to be solved is
5x + 4y = 178 .....(1)
4x +7y = 264 ...(2)
From (1) , we get x = [tex]\frac{178-4y}{5}[/tex]
Put this value in (2)
[tex]4(\frac{178-4y}{5}) +7y= 264\\\frac{712}{5} -\frac{16y}{5} +7y = 264\\\frac{712}{5}-264=\frac{16y}{5} -7y\\ y= 32\\x= \frac{178-4(32)}{5 }\\ x=50/5\\x=10[/tex]
Therefore x=10 and y= 32
The number of cards in every booster pack are 10 and number of cards in every premade deck are 32
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What is the equation of the slant asymptote of the rational function f(x) = 4x^2+6x-1 / x+2?
Answer:
Hello,
y=4x-2
Step-by-step explanation:
1: slope.
[tex]\displaystyle \lim_{n \to \infty} \dfrac{f(x)}{x}\\\\= \lim_{n \to \infty} \dfrac{4x^2+6x-1)}{x(x+2)}\\\\= \lim_{n \to \infty} \dfrac{4x^2}{x^2}\\\\=\boxed{4}\\[/tex]
2:
[tex]\displaystyle \lim_{n \to \infty} (f(x)-4x)\\\\= \lim_{n \to \infty} (\dfrac{4x^2+6x-1}{x+2}-4x)\\\\= \lim_{n \to \infty} (\dfrac{4x^2+6x-1-4x^2-8x}{x+2})\\\\= \lim_{n \to \infty} (\dfrac{-2x-2}{x+2})\\\\= \lim_{n \to \infty} (\dfrac{-2x}{x})\\\\=\boxed{-2}\\[/tex]
Slant asymptote is y=4x-2
What can you say about the 3s in 43,862 and 75,398?
Answer:
Step-by-step explanation:
43,862 - place value - 3,000
75,398 - place value - 300
they are also numbers
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What is the standard notation for the following expression?
4.62 × 10⁻³
Answer:
Step-by-step explanation:
Calculate 10 to the power of −3 and get 1 over 1000
4.62(1/1000)
the answer is 231 over 50000 or 0.00462