The expression 11⁹ / 15⁶ to the fourth power is equivalent to 11³⁶ / 15²⁴
How to solve an equationAn equation shows the relationship between two or more numbers and variables.
Giving the exponents:
11⁹ / 15⁶ to the fourth power
Representing this equation in exponent form:
(11⁹ / 15⁶)⁴
Applying the law of exponents:
(11⁹)⁴ / (15⁶)⁴
= 11³⁶ / 15²⁴
The equation (11⁹ / 15⁶)⁴ gives 11³⁶ / 15²⁴
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Suppose you have a monthly entertainment budget that you use to rent movies and purchase cds. You currently use your income to rent 5 movies per month at a cost of 5.00 per movie and to purchase 5 cds per month at a cost of 10 per cd. Your marginal utility from the fifth movie is 30 and your marginal utility from the fifth cd is 70
Total utility of movies and cds will be $160
What is Budget?
A spending plan based on income and costs is called a budget. In other words, it's a projection of your income and expenses for a specific time frame, like a month or a year. (Or, if you're keeping track of the money coming in and going out of your home as a whole, that's a family budget.)
The cost of 1 movie = $5
The cost of 1 CDS = $10
The marginal utility from fifth movie = 30
The marginal utility from fifth CDS = 70
Total cost spent in month for movies = 5+5+5+5+30
= $50
Total cost spent in month for CDS = 10+10+10+10+70
= $110
The total monthly entertainment budget will be
= 50 + 110
= $160
Hence, The total monthly entertainment budget is $160
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A bicycle has a listed price of $522.95 before tax. If the sales tax rate is 7.75%, find the total cost of the bicycle with sales tax included. Round your answer to the nearest cent, as necessary.
$_____
If a bicycle has a listed price of $522.95 before tax and the sales tax is 7.75%, then the total cost of the bicycle with sales tax included is $563.47
The listed price of bicycle = $522.95
The sales tax percentage = 7.75%
We know
C = p(t×p)
Where C is the total cost
p is the listed price
t is the sales tax percentage
Substitute the values in the equation
C = 522.95+((7.75/100)×522.95)
= 522.95+40.53
= $563.47
Hence, if a bicycle has a listed price of $522.95 before tax and the sales tax is 7.75%, then the total cost of the bicycle with sales tax included is $563.47
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assume a pool measuring 26 meters by 12 meters is surrounded by a path of uniform width as shown in the figure Express the area in the past A in Square meters as a function of its width X in meters
We know that
• The dimensions of the pool are 26 meters by 12 meters.
,• The uniform surrounding path has a width of ,x, meters.
To find a function of x to express the whole area, we have to define the width and length including the path.
The width would be-
[tex]w=26-2x[/tex]The length is
[tex]l=12+2x[/tex]The total area is
[tex]\begin{gathered} A=w\cdot l \\ A(x)=(26-2x)(12+2x) \end{gathered}[/tex]We use the distributive property to show the function in the simplest form.
[tex]A(x)=312+52x-24x-4x^2[/tex]Then, we reduce like terms. So, the function is
[tex]A(x)=-4x^2+28x+312[/tex]An auto mechanic charges $55 for a house call plus $40 per hour for any work done. The client can spend no more than $250 for the call to the mechanic. Write ✍️ the inequality that represents this scenario.
Solution
Houe Call = $55
Workdone call per hour = $40
Let h denotes the number of hours used
Total charges on the call
[tex]55+40h[/tex]The client can spend no more than $250 for the call to the mechanic
[tex]55+40h\leq250_{}[/tex]The inequality is
[tex]55+40h\leq250_{}[/tex]pls be quick or is do Friday
Consider the following functions.f = {(-5, 2), (2, -5), (-1, -3)}and g = {(-1, 1), (-5,3)}Step 1 of 4: Find (f + g)(-1)
To calculate (f g)(-1), we use the definition:
[tex](f+g)(x)=f(x)+g(x)[/tex]This is true if x is defined for f and g. Now, for our problem:
[tex](f+g)(-1)=f(-1)+g(-1)=-3+1=-2[/tex][tex]undefined[/tex]What are the solutions of the equation (x + 2)2-2(x + 2)-15 = 0? Use u substitution to solve.
O x=-7 and x = 1
O x = -5 and x = 3
O x=-3 and x = 5
O x= -1 and x = 7
The solution for the given equation is x = -5 and x = 3.
How to solve a quadratic equation by substitution?
The equation is first transformed into a more familiar form. Replace the substitutions with the original variables after factoring the problem. The difference of squares equation is used to finish the factorization and locate the answers for x.
Given, the equation for solving is: (x + 2)² - 2(x + 2) - 15 = 0 --(i)
Let in the equation, y = x + 2 --(ii)
Equating (i) and (ii), we get:
y² - 2y - 15 = 0 ⇒ y² - 5y + 3y - 15 = 0 ⇒ y(y - 5) + 3(y - 5) = 0
⇒ (y + 3)(y - 5) = 0 ⇒ y = -3, 5 (by solving the equations)
Thus, from (ii) and value of y obtained above, we get,
x + 2 = -3 ⇒ x = -3 -2 = -5 and x + 2 = 5 ⇒ x = 5 - 2 = 3
Thus, (b) x = -5 and x = 3 is the correct answer.
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Describe a series of transformations Matt can perform to device if the two windows are congruent
We can generate congruent shapes by combining the three types of transformations: rotations, reflections, and translations. Actually, using a combination of one or more of these three transformations, any pairs of congruent shapes can be matched to one another.
What are transformations?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
Given Data
We now understand that the size and shape of the figures are preserved during stiff transformations (reflections, translations, and rotations). Pre-image and image are always congruent with one another.
Series of transformation Matt can perform:
Reflection (Flip)
Because the equivalent points from the pre-image to the image remain at the same distance from the line of reflection, a reflection maintains its original shape.
Rotations as a Transformation of Congruence
A rotation is when a figure turns. Although the figure is the same size and shape, it appears to have fallen over. A clock is a fantastic example of a rotation in the real world. Every hour or every day, the connecting arms of a clock revolve around its central point. The degree of rotation is used to characterize a rotation; popular rotations include 90 degrees, 180 degrees, and 270 degrees. The figure returns to its original position after a full 360-degree spin. A rotation must additionally include the direction, either clockwise or counterclockwise. A rotation's degree amount and direction can be computed using this information.
Congruence transformation through translation
When we move an object or shape from one location to another without changing its size, shape, or orientation, we call that movement a translation. A translation, often known as a slide, involves moving each point on an object or shape by the same amount and in the same direction.
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write equations for total edge length E, total surface area A, and volume V of a cube with side lengths of s.
side length--volume
3. 9
5. 25
9.5. 90.25
s. s*3^2
If the length of a side of cube is "s", then total edge length (E = 12s), total surface area (A = 6s²) and Volume (V = s³).
As per the question statement, the length of a side of cube is "s".
We are required to write down the equations for total edge length "E", total surface area "A" and Volume "V" of the cube with respect to "s".
To solve this question, we need to know a couple of basic structural properties of a cube, that is,
There are 12 edges in a cube, all of equal length,
And, there are 6 faces in a cube, all of equal surface area.
[A reference image is attached hereby for better understanding;
The 12 edges of the cube are: AB, BC, CD, AD, CG, DH, BF, AE, EF, FG, GH and EH,
And, the 6 Faces of the cube are: ABCD, ABEF, CDGH, BCFG, ADEH and EFGH]
Therefore, total edge length (E) = (12 * s) = 12s,
Or, (E = 12s)
Total surface area (A) = [6 * (s)²] = 6s²,
Or, (A = 6s²)
[Since, area of a square of edge length "s" = s², and every face of a cube is a square]
Finally, Volume (V) of the cube = [s * s * s] = s³,
Or, (V = s³).
Cube: In Mathematics, particularly in Geometry, a Cube is a three-dimensional figure, which has 6 square faces, each having equal edge length and surface area, 8 vertices and 12 equal edges.To learn more about Cubes, click on the link below.
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What two numbers are located 5/8 of a unit from 1/6 on a number line?Show your work.
ANSWER
[tex]\frac{19}{24}\text{ and }\frac{-11}{24}[/tex]EXPLANATION
To find the two numbers that are located 5/8 of a unit from 1/6 on the number line, we have to first understand that for a number on a number line, there are numbers both ahead and behind the number.
So, the numbers that are 5/8 from 1/6 on the number line will be:
=> one number that is +5/8 from 1/6
=> one number that is -5/8 from 1/6
Therefore, the two numbers are:
[tex]\begin{gathered} \frac{1}{6}\text{ + }\frac{5}{8}\text{ and }\frac{1}{6}\text{ - }\frac{5}{8} \\ \Rightarrow\text{ }\frac{19}{24}\text{ and }\frac{-11}{24} \end{gathered}[/tex]Those are the two numbers.
i need help asap!!! im bad at graphing
Answer:
Step-by-step explanation:
eq. of any line with slope -1/2 and through (-1,-5) is
y+5=-1/2(x+1)
2y+10=-x-1
2y=-x-11
x+2y=-11
y=0
x=-11
point is (-11,0)
draw a line through (-11,0) and (-1,-5)
Let g(x)=x^2-64 and h(x)=root(8x+512). Find each combination and state its domain. 1. (h/g)(x)(Number one has a fraction) 2. (h・g)(x)3. (g・h)(x)Show work please!
Given the functions:
[tex]\begin{gathered} g(x)=x^2-64 \\ h(x)=\sqrt[]{8x+512} \end{gathered}[/tex]1. (h/g)(x)
[tex](\frac{h}{g})(x)=\frac{h(x)}{g(x)},\text{ g(x)}\ne0[/tex]We substitute the functions and solve:
[tex](\frac{h}{g})(x)=\frac{\sqrt[]{8x+512}}{x^2-64}[/tex]Factor the common term 8:
[tex]=\frac{\sqrt[]{8(x+64)}}{x^2-64}[/tex]And we have:
[tex]\begin{gathered} x^2-64\ne0 \\ x^2-64+64\ne0+64 \\ x^2\ne64 \\ x\ne8\text{ and x}\ne-8 \end{gathered}[/tex]Assume that when human resource managers are randomly selected, 43% say job applicants should follow up within two weeks. If 6 human resource managers are randomly selected, find the probability that exactly 3 of them say job applicants should follow up within two weeks.
The probability is 0.9204 that exactly 3 of them say job applicants should follow up within two weeks.
Binomial probability distribution
P(X = x) = [tex]C_{n,x}[/tex] . [tex]p^{x}[/tex] .[tex](1-p)^{n-x}[/tex]
[tex]C_{n,x}[/tex]= n!/ x!(n - x)!
The parameters are:
n is the number of trails.
x is the number of successes.
p is the probability of success on a single trial.
In this problem:
43% say job applicants should follow up within two weeks, thus p = 0.43
6 managers are selected, thus n= 6.
The probability that at least 3 of them say job applicants should follow up within two weeks is P(X≥ 3), which is given by:
P(X ≥3) = 1 -P(X < 3)
In which:
P(X < 3 ) = P(X = 0) + P(X = 1) + P(X = 2)
Then:
P(X = x) = [tex]C_{n,x}[/tex]. [tex]p^{x}[/tex]. [tex](1-p)^{n-x}[/tex]
P(X = 0) = [tex]C_{6,0}[/tex] [tex](0.43)^{0}[/tex]. [tex](0.57)^{6}[/tex] = 0.0342
P(X = 1) = [tex]C_{6,1}[/tex](0.43) . [tex](0.57)^{5}[/tex] = 0.0259
P(X = 2) = [tex]C_{6,2}[/tex](0.43)² [tex](0.57)^{4}[/tex] =0.0195
P(X<3) = P(X = 0) + P(X = 1) + P(X =2) = 0.0342 + 0.0259 + 0.0195
= 0.0796
P(X≥3) = 1 - P(X<3) = 1- 0.0796 = 0.9204
0.9204 is the probability that at least 3 of them say job applications should follow up within two weeks.
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Find the length of the side labeled x. Step by step.
Answer: 72.4
Step-by-step explanation:
soh-cah-toa
cos(25)= adjacent/hypotenuse
cos(25)= adjacent/48
adjacent= 48 * cos(25)
tan(59) = opposite/adjacent
tan(59) = x / 48 * cos(25)
x = 72.4
Find the perimeter of the rectangle. Then, Find area of the rectangle. Round your answer to the nearest tenth
Answer:
To find the perimeter of the rectangle, simply add all sides of the rectangle together to get the answer. For finding the area, you have to multiply the length and width together.
Step-by-step explanation:
math.
A cookie factory uses 1 1/3 bags of flour in each batch of cookies. The factory used 6 2/3 bags of flour yesterday. How many batches of cookies did the factory make
Answer: you can get the full fraction by multiplying 6x3 which is 18 so then you add 18 and 2 and you get 20 so now the fraction is 20/3
and you need 11/3 for a batch so now you have 1 whole batch and 9/3 so you just make the 11 a percentage which is 81%
so the answer is 1 whole batch and 81% of another
or 1 9/3
Alexandria a car dealer, earns 1/25 commission of her luxury vehicle sales. Last year, her sales were $480,000. What was the total dollar amount of her commission last year?
The total dollar amount of her commission last year equals to $19,200.
What is a sales commission?This refers to the percentage of the value of a sale that a sales associate or representative may earn.
To start, we must analyze the data we have. Given that Alexandria's total sales were $ 480000, and the commission received is 1/25 of that sales.
The commission earned from the sales:
= 1/25 * $480000
= $19,200
Therefore, the total dollar amount of her commission last year equals to $19,200.
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E Homework: HW 9.3Question 7, 9.3.17HWотFind the area of the shaded regionInside the square and between thetwo circles. Use x 3.1410 m10 mThe area of the shaded region is approximatelym?(Type an integer or decimal)
Area of shaded region = 168.56 [tex]m^2[/tex]
What is area of square and semicircle?
Area of square is the total space taken by the square.
If the side of square is a units, then area of square is calculated by
Area of square = [tex]a \times a[/tex] sq units
Area of semicircle is the total space taken by the semicircle
If the radius of semicircle is r units, then area of semicircle is calculated by
Area of semicircle = [tex]\frac{1}{2}\times \pi \times r^2[/tex] sq units
Here,
Side of square = 28 m
Area of square = [tex]28 \times 28 = 784 m^2[/tex]
Radius of circle = [tex]\frac{28}{2} = 14 m[/tex]
Area of two semicircles =
[tex]2 \times \pi \times r^2 \times \frac{1}{2}\\3.14 \times 14 \times 14\\615.44 m^2[/tex]
Area of shaded region = [tex](784 - 615.44) m^2[/tex]
= 168.56 [tex]m^2[/tex]
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Complete Question
The figure has been attached here.
At store A, 3 pounds of apples cost $12. At store B, the cost is given by y = 2x where y is the cost in dollars and x is the number of pounds of apples. The cost of apples at store C is shown in the graph. Answer the questions to find out which store's apples are the least expensive. 1. What is the unit price of apples at store A? Explain how you found this unit price. (2 points) 2. What is the unit price of apples at store B? How did you use the equation to find the unit price? (2 points) 3. What is the unit price of apples at store C? How did you use the graph to find the unit price? (3 points) 4. Which store has the lowest unit price for apples? (3 points)
1. Store A's unit price = $4 per pound
2. Store B's unit price = $2 per pound.
3. Store C's unit price = $3 per pound.
4. Store B's unit price is the lowest.
How to Find the Unit Rate of a Relationship?The unit rate of the relationship between variables x and y, is given as:
Unit rate, m = y/x.
In a given equation, y = mx, the value of m represents the unit rate of the relationship.
In the scenario given, y represents cost in dollars while x represents the number of pounds of apples.
1. The unit rate = unit price of apples. For store A, we are given 3 pounds of apples will cost $12, therefore:
Unit price = y/x = 12/3
Unit price = $4 per pound
2. For store B, the "2" in the equation, y = 2x, represents the unit price.
Unit price for store B = $2 per pound.
3. Using one point on the graph for Store C, say, (2, 6):
Unit price = y/x = 6/2
Unit price = $3 per pound.
4. The lowest unit price is $2 per pound, therefore, Store B has the lowest unit price for apples.
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Write the correct inequality for the following statement and then solve for the given number of
yards.
You have found a used car and your parents have agreed to pay the first
$750 for you. You have a summer job mowing yards for $25 per yard.
Write and inequality that will calculate the number of yards (y) you will
have to mow to get to at least the cost (C) of the car.
If the car cost a total of $4500 how many yards will you have to mow?
Step-by-step explanation:
You have found a used car and your parents have agreed to pay the first $750 for you. You have a summer job mowing yards for $25 per yard. Write and inequality that will calculate the number of yards (y) you will have to mow to get to at least the cost (C) of the car.
25y + 750 = C
If the car cost a total of $4500 how many yards will you have to mow?
25y + 750 = 4,500
subtract 750 from both sides:
25y + 750 - 750 = 4,500 - 750
25y = 3,750
divide both sides by 25:
25y/25 = 3,750/25
y = 150
Must mow 150 yards.
check:
25(150) + 750 = 4,500
3,750 + 750 = 4,500
4,500 = 4,500
3(x+4) -4 = 2(x+4) + x
Answer: Infinite Solution
Step-by-step explanation:
3x+12-4=2x+8+x
3x+8=3x+8
Answer:
All real numbers
The answer to this equation is 0=0
Step-by-step explanation:
3(x+4)-4= 2(x+4)+x
3x+12-4= 2x+8+x
3x+8=3x+8
3x-3x=8-8
0=0 Answer
What is the answer to this or is the answer right
Answer:
(c) corresponding angles
Step-by-step explanation:
You want to know the description of the marked angles in the given diagram.
Interior anglesInterior angles are between the "parallel" lines. Angle 5 is interior, but angle 1 is not, so they cannot be described as interior angles.
Exterior anglesExterior angles are both outside the "parallel" lines. Angle 1 is exterior, but angle 5 is not, so they cannot be described as exterior angles.
Corresponding anglesCorresponding angles are both in the same direction from the point of intersection of the "parallel" lines with the transversal. Here, both angles 1 and 5 are "northwest" of the intersection point, so are corresponding angles.
Alternate anglesAlternate angles are on opposite sides of the transversal. Consecutive, or same-side, angles are on the same side of the transversal. Angles 1 and 5 are not alternate angles, as they are both on the same side of the transversal.
A personal trainer offers two different plans. Plan A costs $25 per session and Plan
B costs $50 per session. If the trainer coaches 18 sessions this week and earns $625
dollars, how many sessions of each type did he coach?
The personal trainer took 11 plan A and 7 plan B classes.
Let the number of sessions of plan A be x. So, the number of sessions of plan B be (18 - x). Now forming the equation as per the mentioned information.
25×x + 50 (18 - x) = 625
Performing multiplication on Left Hand Side of the equation
25x + 900 - 50x = 625
Rearranging the equation
900 - 625 = 50x - 25x
Performing subtraction on both the sides of the equation
275 = 25x
Shifting 25 to other side of equation
x = 275/25
Performing division to find the value of x
x = 11
Number of plan A classes = 11
Number of plan B classes = 18 - 11
Number of plan B classes = 7
Thus, the number of plan A classes is 11 and plan B classes is 7.
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Find the average rate of change of the function f(x) = x² + 8x from x₁ = 1 to x₂ = 2.
The average rate of change of the function f(x) = x² + 8x from x₁ = 1 to x₂ = 2. is 16
what is average rate of change ?The average rate of change expresses how frequently one quantity changes in relation to another. It provides an idea of the amount the function changed per unit throughout the specified time period. In order to calculate the rate of change, one simply divides the amount of change in one thing by the comparable amount of change in another.
The average rate of change of a continuous function,
f(x) , on a closed interval [a,b] is given by
F(x)=[tex]\frac{F(b)-F(a)}{b-a}[/tex]
[tex]\frac{25 -9}{1}\\ \frac{16}{1}\\ =16[/tex]
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Pythagorean Theorem
Find the length of the third side, write in simplest radical form if needed.
Using Pythagoras's theorem, the length of the third side of the right triangle is 3 units.
How to find the side of a right triangle using Pythagoras's theorem?The length of the third side of the right triangle can be found using Pythagoras's theorem.
The Pythagoras's theorem can be represented as follows:
c² = a² + b²
where
a and b are the legsc is the hypotenuse of the right triangleTherefore, the missing side of the right triangle is the other legs.
b² = (3√5)² - 6²
b² = 45 - 36
b = √9
b = 3
Therefore,
third side of the right triangle = 3 units
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By using Pythagoras' theorem the length of the third side is 3 units
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
Given, the hypotenuse is 3√5 units and one of the legs is 6 units and assuming the length is x units.
∴ x² = (3√5)² - 6².
x² = 9×5 - 36.
x² = 45 - 36.
x² = 9.
x = ± 3.
As length can not be negative the appropriate value for x is + 3.
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thirty-thousandths in decimal
Thirty thousandths in decimal is written as ;
[tex]0.3000[/tex]Note that numbers after the decimal point begin from tenths, hundredths, thousandths, tens of thousandths, and so on.
Thirty-thousandths therefore is four digits after the decimal point, starting from the digit 3.
What is the length of segment SR?
____ units
The value of the length of the segment SR is; 12 units.
What is a line segment?A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
According to the diagram at point it makes the angle of 90° with both triangles, thus;
SR = SQ
2x + 8 = 8x - 4
And to find the value of x, we will find the value of line segment SR
8x -2x = 8+4
6x = 12
x = 12/6
x = 2
Then we will put the value of x in SR ;
SR = 2x + 8 = 2(2) + 8 = 4 + 8 = 12
SR = 12
Hence, The value of the length of the segment SR is; 12 units.
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A smiley face (orange) and its image (open) are graphed on the coordinate plane below. Which sequence of transformations maps the solid smiley face onto the open smiley face?A. reflect over x-axis, rotate 270° counterclockwiseB. rotate 270° counterclockwise, translate right 8 unitsC. translate up 8 units, reflect over y-axisD. reflect over y-axis, rotate 90° counterclockwise
The only way to check which one is the correct answer is to perform each set of transformations and check which one is the correct one. First, note that the initial position of the smiley face is the third quadrant. So, we will first apply vaguely the transformations to check to which one is the smiley face located in the first quadrant once we are done with the transformations.
So, let us analyze each set of transformations separately.
Option A
After reflexing over the x axis, the smiley face position would be
so, once rotated 270° counterclockwise, the position of the smiley face would be
so option A is not the correct answer
Option B
if we rotate 270° counterclockwise, the smiley face's position would be
and by translating 8 units to the right, it would be
so option B is the correct answer
. A line is parallel to the line y = -x +9 and passes through the point of intersection of
x+y = 10 and 3x - 4y + 12 = 0. Determine the equation of the line.
Answer:
Step-by-step explanation:
point of intersection of the equations: (4,6)
The line parallel to the given line would be y = -x + k
the line passes through (4,6)
putting the values, we get, 6 = -4 + k ⇒ k = 10
Required equation⇒ y = -x + 10
Can you help me understand the steps to solve this?
a)36 is 75 % of 48
b)18 is 25% of 72
Explanation
when we have the percentage and the number , the easiest way to find the value is by applying this formula:
[tex]\text{value}=origial\text{ value}\frac{\text{ \% percentage}}{100}[/tex]hence
Step 1
a)
what percet of 72 is 18?
let
100 % = 72, ( the number)
x %, = 18
so
replace
[tex]\begin{gathered} \text{18}=72\frac{\text{ x\% percentage}}{100} \\ 18=\frac{72}{100}x \\ \text{Multiply both sides by 100/72} \\ 18\cdot\frac{100}{72}=\frac{72}{100}x\cdot\frac{1}{0072} \\ 25=x \end{gathered}[/tex]therefeore,
18 is 25% of 72
Step 2
b) 36 is 75 % of what,so
let
100%= x=original value
75%=36
so
[tex]\begin{gathered} \text{value}=origial\text{ value}\frac{\text{ \% percentage}}{100} \\ 36=x\frac{75}{100} \\ \text{Multiply both sides by 100/75} \\ 36\cdot\frac{100}{75}=x\frac{75}{100}\cdot\frac{100}{75} \\ 48=x \end{gathered}[/tex]therefore, 36 is 75 % of 48
I hope this helps you