Proportionality denotes a linear relationship between two quantities or variables.
A. Table is mentioned below.
B. Yes, it is a proportional relation.
C. y = 1/24 x
What is meant by proportional?A linear relationship between two quantities or variables is referred to as proportionality. If one quantity doubles in size, the other does as well; if one variable decreases to one-tenth of its previous value, the other does as well.If the ratio or relationship between y and x is the same or constant, the quantities are proportional: y/x = k, where k is the proportionality constant.When two quantities are proportional, it means that as one increases, so does the other, and the ratio of the quantities remains constant across all values.Consider a circle's circumference and diameter; the ratio of the two values equals pi.Therefore,
Part C : We know that,
1 day = 24 hours,
⇒ 1 hour = 1/24 day
As a result, the number of days in x hours (say y) = hours number of days in each hour
⇒ y = 1/24 x
Which is an equation of line.
Part A :
Hours 1 2 3 4 5
Days 1/24 1/12 1/8 1/6 5/24
Part B :
∵ a line passes through the origin always shows a proportional relation,
Since, for (0, 0),
0 = 1/24 (0) ( True )
i.e. there is a proportional relation between number of days and number of hours.
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Select all rational numbers.
√75
-√25
2*√7
√100
√0.36
√0.0144
√3/7
-√36/49
The rational numbers are -√25, -√25, √100, √0.36, √0.0144 and -√36/49. Select them
How to identify rational numbers?A rational number is a number that can be expressed as a fraction where both the numerator and the denominator in the fraction are integers e.g 2/3, 7/1, √100 = 10/1, etc.
An irrational number is any real number that cannot be expressed as the quotient of two integers. This is the opposite of rational numbers. They are usually of roots that cannot give integers e.g 3√5, √8, etc.
√75 = √(25 x 3) = √25 x √3 = 5 x √3 = 5√3 (This is not rational)
-√25 = -5 = -5/1 (This is rational)
2*√7 = 2√7 (This is not rational)
√100 = 10 = 10/1 (This is rational)
√0.36 = √(36/100) = 6/10 (This is rational)
√0.0144 = √(144/10000) = 12/100 (This is rational)
√3/7 = √3/7 (This is not rational)
-√36/49 = -6/7 (This is rational)
Therefore, -√25, -√25, √100, √0.36, √0.0144 and -√36/49 are rational numbers. They should be selected
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please help!!
the function shown in the graph is f(x)= ???
Answer:
The answer is x^{3}-2x^{2}-5x+6
Step-by-step explanation:
This is because only a Cubic Function would have such a shape. That leaves x^3 functions from there just substitute points and check
Make X
the subject of m=n+x/p
Answer:
m+n=x/p
p×(m+n)=(x/p)×p
x=pm+pn
Plot these points of graph f(x)= -(x-5)^2+5 that correspond to x-values 3 and 4. Plot the vertex and reflections of these points in axis
Answer:
On the attached graph
Step-by-step explanation:
See attached graph
Which of these strategies would eliminate a variable in the system of equations?
The strategy which would eliminate a variable in the system of equations is to multiply the top equation by 3 ,multiply the bottom equation by -2 then add the equation and is denoted as option B.
What is Equation?This is a mathematical term which is made up of two expressions and is connected by an equal sign.
In the example given below:
2x + 8y = -3
3x + 6y = -4
We can multiply the top by 3 and the bottom by -2 which will result in:
6x + 24y = -9
-6x - 12y = 8
They are then added to each other to give:
6x - 6x + 24y - 12y = -9+8
12y = -1
y = -1/12
From this we can notice that the variable x was eliminated which is why option B is the correct choice.
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What is the value of the product 2/3 x 9/5?
Answer:
[tex]\frac{6}{5}[/tex]
Step-by-step explanation:
[tex]\frac{2}{3} *\frac{9}{5} =\frac{18}{15} =\frac{6}{5}[/tex]
The value of the product of 2/3 × 9/5 is 6/5.
In the given question, we have to attempt fraction multiplication.
For fraction multiplication, we simply multiply the respective numerators and denominators with each other.
Here, in 2/3 × 9/5 ⇒ 18/15 (since 2×9=18) (since 3×5=15)
Now, since we can see that both the numerator and denominator in the solution can get divided by 3, we can simplify the fraction by dividing both the numerator and denominator by 3.
On dividing by 3, we get ⇒ 6/5
So, on multiplying 2/3 and 9/5, we get 18/15 which we later simplify into 6/5.
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can you help me in graph
i came back home now....
Can someone help me with this please?
The volume of the rectangular prism is the 75 ft cube.
How to find the volume of a prism?The prism below is a rectangular prism.
A rectangular prism is a three-dimensional shape, having six faces, where all the faces (top, bottom, and lateral faces) of the prism are rectangles such that all the pairs of the opposite faces are congruent.
The volume of a rectangular prism can be express as follows:
Volume of a rectangular prism = base area × height
Therefore,
base area of the prism = 25 ft²
height of the prism = 3 ft.
Hence,
Volume of the rectangular prism = 25 × 3
Volume of the rectangular prism = 75 ft³
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Peter, Bridget and Caroline share some sweets in the ratio 4:3:1. Peter gets 20 sweets. How many sweets are there altogether?
Sasha sells t-shirts. Each day she earns a set amount, plus a commission. What kinds of numbers make sense for the domain of this function? Explain your reasoning.
The domain of the given function is {1, 2, 3, 4, 5} which represents she sells t-shirts.
What are the domain and the range of a set of ordered pairs?The domain of a set of ordered pairs includes all possible x values of a function, and the range includes all possible y values of a set of ordered pairs.
We have been given that Sasha sells t-shirts. Each day she earns a set amount, plus a commission.
The domain of the given function represents she sells t-shirts.
According to the given table, the required domain will be as:
The domain of the given function = {1, 2, 3, 4, 5}.
Therefore, the domain of the given function is {1, 2, 3, 4, 5}.
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victoria deposited $5000 into a savings account that earns an annual simple interest rate of 0.3%. To the nearest tenth of a year, how long will it take for the account to reach $5500?
It will take 33.33 years for the account to reach $5500
What is simple interest?
Simple interest is defined as the direct crediting of cash flows related to an investment or deposit.
We know,
Victoria deposited into a savings account $5000
Annual simple interest rate of 0.3%.
Formula of Simple Interest
A = P(1 + rt)
5500 = 5000(1 + 0.003t)
5500 = 5000 + 15t
15t = 500
[tex]t = \frac{500}{15} = 33.33[/tex]
It will take 33.33 years for the account to reach $5500
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A palindrome is a word or number that is the same when read forwards or backwards. For example, DAD is a palindrome, and so is
RACECAR. 484 is a palindrome number, and so is 9229.
What is the sum of a three digit palindrome number that ends in 71 and a four digit palindrome number that ends in 83?
Answer:
4054
Explanation:
171 is the three-digit palindrome that ends with 71
3883 is the four-digit palindrome that ends with 83
171 + 3883 = 4054
Solve the equation:
3/2=4x
x= ____________
Answer:
x = [tex]\frac{3}{8}[/tex]
Step-by-step explanation:
[tex]\frac{3}{2}[/tex] = 4x ( multiply both sides by 2 to clear the fraction )
3 = 8x ( divide both sides by 8 )
[tex]\frac{3}{8}[/tex] = x
Solve 15+ax/5= 10 for x.assume that a=0
The solution for x in the expression given as 15 + ax/5 = 10 is x = -25/a
How to determine the solution to the variable x in the expression?From the question, the algebraic expression is given as
15 + ax/5 = 10
There is a constant to add to or subtract from the expression
So, the we subtract 15 from both sides
- 15 + 15 + ax/5 = 10 - 15
Evaluate
ax/5 = -5
Multiply both sides of the equation by 5
This gives
5 * ax/5 = -5 * 5
Evaluate the products
So, we have the following equation
ax = -25
Multiply both sides of the equation by 1/a
This gives
1/a * ax = -25 * 1/a
Evaluate the products in the above expression
x = -25/a
Hence, the solution is x = -25/a
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A painter work 7 3/4 hours per hour. How.
many hours does this painter work in 5
days a week
Answer: 38.75 hours
Step-by-step explanation: so one thing real quick, you said “A painter worked 7 3/4 hours per hour” that’s not possible so instead I’m guessing you meant 7 3/4 hours per day.
Turn 7 3/4 hours into 7.75 hours then it’s simple, you multiply 7.75x5! You get 38.75 hours!
Answer:
38 3/4
Step-by-step explanation:
7 3/4 times 5 =
7 3/4 = 31/4
31/4 times 5 = 155/4
= 38 3/4
12. 15-2x) ≤ 11 What is the solution set to the inequality above?
its 4 cause i have done this
First, we isolate the variable on one side of the inequality by subtracting 15 from both sides:
15 - 2x - 15 ≤ 11 - 15
Simplifying the left side, we get:
-2x ≤ -4
Next, we divide both sides by -2. Since we are dividing by a negative number, we need to flip the inequality sign:
-2x/-2 ≥ -4/-2
Simplifying, we get:
x ≥ 2
Therefore, the solution to the inequality 15-2x ≤ 11 is x ≥ 2.
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wilma can mow a lawn in 40 minutes. vanessa can mow the same lawn in 120 minutes. how long does it take for both wilma and vanessa to mow the lawn if they are working together?
It takes 13 minutes 20 seconds for both wilma and vanessa to mow the lawn if they are working together.
A lawn can be mowed by Wilma in 40 minutes. In one hour, Vanessa can cut the same lawn in 120 minutes.
1/120 + 1/40 = 1/T
multiply by 40T;
3T = 40
T = 40/3
= 13 1/3 minutes
= 13 minutes 20 seconds
It takes 13 minutes 20 seconds for both wilma and vanessa to mow the lawn if they are working together.
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a rectangular field measures 90 meters by 162 meters. what will it cost to cover the field with pallets of grass each covering 90 squard yards and costing $213 per pallet
The cost of covering the field with grass pallets is $40996.58.
Given that the rectangular field measures 90 m and 162 m.
Hence, the area of the field is 90 X 162 m²
The grass pallets are sure in shape with an area covering 90 square yards.
1 m = 1.09 yards
Hence,
1 m² = 1.09² square yards
Hence,
90 X 162 m² = 90 X 162 X 1.09² square yards
Hence the number of pallets to be used is
(90 X 162 X 1.09²) / 90
= 162 X 1.09² pallets.
= 192.4722 pallets.
1 pallet costs $213
Hence,
192.4722 pallets cost
192.4722 X 213
= $40996.58
Therefore we get the cost of covering the field with grass is $40996.58.
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A television antenna is 10 feet tall. It has three wires that attach to its top and are anchored 8 feet
from its base. How long is each wire?
The length of each wire is 12.8 feet
The television antenna makes an angle 90 with the ground
The height of the antenna is 10 feet
The wires are anchored to the base which is 8 feet
We need to calculate the length of the wires
The height of the wire can be calculated by using pythagoras theorem
h² = b² + p²
h² = 8² + 10²
h² = 64 + 100
h = √164
h = 12.8
Therefore, the length of each wire is 12.8 feet
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Isabel got a prepaid debit card with $20 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 7
cents per yard. If after that purchase there was $17.13 left on the card, how many yards of ribbon did Isabel buy?
The number of yards of ribbon Isabel bought is 41 yards.
It is given in the question that:-
Money in prepaid debit card = $ 20
Price of ribbon = 7 cents per yard
Money left on the card after buying the ribbon = $ 17.13
We have to find the number of cards of ribbon Isabel bought.
Money used in buying the ribbon = 20 - 17.13 = $ 2.87
We know that,
$ 1 = 100 cents
Hence, according to the data given in the question, we can write,
$ 2.87 = 287 cents
Yards of ribbon bought = 287/7 = 41 yards.
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Decide whether events A and B are overlapping or non-overlapping, you roll a red die and a blue die. event a is that you get a sum of 9. event b is that you get a double.() overlapping ()non-overlapping
Events A and B are non-overlapping. Option(2) is correct.
When two sets A and B have at least one element in common, they are said to be overlapping.
The sets of photographs that don't overlap are the sets where no two pictures (correctly) don't overlap. They are the expansion of the cross-bifix-free sets of strings to two dimensions is called non-overlapping.
A red die and a blue die are rolled.
Assume that Event A is receiving the number 9.
Event B: You receive a double.
Whether events A and B overlap or not is what we want to determine.
When two red dice and two blue dice are thrown, a sample space is then provided by,
S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5),(3,6), (4,1), (4,2), (4,3), (4,4),(4,5),(4,6) (5,1), (5,2), (5,3), (5,4),(5,5),(5,6),(6,1), (6,2),(6,3)(6,4),(6,5),(6,6)}
The two dice are rolled, and there are a total of 36 outcomes.
n(S)=36
Assume that Event A is receiving the number 9.
The probable results for A = (3,6), (4,5), (5,5), (5,6), (6,3)
And let's say that you receive a double in Event B.
The events that may occur if B=(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)
We can observe that the two events are distinct from one another since there is no overlap in the potential outcomes of the two events.
Therefore events A and B are non-overlapping
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You and 3 buddies take a job cleaning up your neighbor's garage and he pays you $220. How will you divvy it up so everyone gets an equal share? What percentage is that?
Answer:73.33
Step-by-step explanation:
The answer is 73.33 because 73.33 multiplied by 3 = 219.99
Write a linear function f with f(-10) = 4.5 and f(-2)=4.5.
Answer:
plsssssssssssssssssssssssssssssssssss
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Our school flag is a rectangle. We are changing to a new rectangular flag design. The length of the new flag is 20% greater than the length of the old flag, and the width of the new flag is 10% less than the width of the old flag, The old school flag is 25 square feet. What is the area of the new flag?
Answer:
27 square feet-------------------------------
Let the sides of the old rectangle are l and w.
Its area isA = lw = 25New flag has dimensionsLength is 20% greater = 1.2lWidth is 10% less = 0.9wArea of new flagA = 1.2l × 0.9w = 1.08 lwA = 1.08×25 = 27Answer: Hence the answer is 27 square feet.
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Two parallel lines are cut by a transversal as shown below.
Suppose m2 = 46°. Find m5 and m 27.
Marsha deposited $5500 into a savings account 4 years ago. The simple interest rate is 5% How much money did Marsha earn earn in interest?
Marsha deposited $5500 into savings with 5% interest rate
1st year, Marsha will earn : [tex]0.05 \times 5500 = 275[/tex]
2nd year, Marsha will earn: [tex]0.05 \times 5775 = 288.75[/tex]
3rd year, Marsha will earn: [tex]0.05 \times 6063.75 = 303.19[/tex]
4th year, Marsha will earn: [tex]0.05 \times 6366.94 = 318.35[/tex]
A restaurant has a 33,500 gallon aquarium and a 500 gallon aquarium. About how many times is the capacity of the smaller aquarium?
Answer:
67 times
Step-by-step explanation:
33,500 divided by 500 is equivalent to 67
Vivian and Kyle each want to run for president of their school's student body council. In order to do so, they must collect a certain number of signatures and get a nomination. So far, Vivian has 18 signatures, and Kyle has 14. Vivian is collecting signatures at an average rate of 1 per day, whereas Kyle is averaging 3 signatures every day. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How long will that take? How many signatures will they both have?
The number of days it take the same number of signature will be 2 days.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Vivian has 18 signatures, and Kyle has 14.
Vivian is collecting signatures at an average rate of 1 per day, whereas Kyle is averaging 3 signatures every day.
Now,
Since, Vivian has 18 signatures, and Kyle has 14.
And, Vivian is collecting signatures at an average rate of 1 per day, whereas Kyle is averaging 3 signatures every day.
Let number of days it take the same number of signature = x
So, We can formulate;
⇒ 18 + x = 14 + 3x
Solve for x as;
⇒ 18 + x = 14 + 3x
⇒ 18 - 14 = 3x - x
⇒ 4 = 2x
⇒ 2x = 4
⇒ x = 2
Thus, The number of days it take the same number of signature will be 2 days.
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18. a rectangular page is to contain 42 square inches of printable area. the margins at the top and bottom of the page are each 1 inch, one side margin is 1 inch, and the other side margin is . what should the dimensions of the page be so that the least amount of paper is used?
The page is in landscape mode with a width : height is 3: 2
Given that,
The printable area is should be 42 square inches on a rectangular page. The margins at the top and bottom of the page are each one inch, while the margins on one side are one inch and two inches, respectively.
x = length of the horizontal side of the printable area
y = length of the vertical side of the printable area
XY = 42 inch²
y = 42/x
page height = y + 1 + 1
page width = x + 1 + 2
A = area of an entire sheet of paper
= (x+3)(y+2)
= (x+3)(42/x+2)
= x(42/x+2)+3(42/x+2)
= 42+2x+126/x+6
A = 2x+126/x+48
Extremes occur when A' = 0:
A' = 0 = 2 – 126/x²
1 = 63/x²
x² = 9*7
x = 3√(7), x has to be positive
y = 42/x = 42/(3√(7)) = 14√(7)/7 = 2√(7)
What should the dimensions of the page be so that the least amount of paper is used?
page width = x + 3 = 3√(7) + 3 = 3(√(7) + 1)
page height = y + 2 = 2√(7) + 2 = 2(√(7) + 1)
So, the page is in landscape mode with width: height is 3: 2.
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