''By taking log'' on both side Mike solve this equation.
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;
The expression is,
⇒ 37ˣ = 12
Now,
Since, The expression is,
⇒ 37ˣ = 12
Solve this expression as;
⇒ 37ˣ = 12
Taking log both side, we get;
⇒ log 37ˣ = log 12
⇒ x log 37 = log 12
⇒ x = log 12 / log 37
⇒ x = 1.08 / 1.57
⇒ x = 0.69
Thus, The value of x = 0.69
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Given: AAED ≈ ABEC and
AC BD.
Prove: AABD≈ ABAC.
Note: quadrilateral properties are not permitted in this
proof.
The solving in the below shows similarity in triangles ΔAED ≈ΔBEC By SSS criteria.
What are the four traits of triangles that are similar?The sizes of similar triangles vary while having the same shape. The comparable angles in identical triangles are equal. The ratio of the corresponding sides of comparable triangles is the same. The ratio of any pair of corresponding sides' squares to any similar triangle's area is the same.
According to given information:Two triangles are comparable if they fall under one of the headings below: Angles in two comparable pairs are equal. Three pairs of corresponding sides make up the ratio. The comparable angles amongst two pairs of adjacent sides are proportional and equal.
Given that ΔAED ≈ΔBEC & AC = BD.
as ΔAED ≈ΔBEC, AD = BC .................(1)
Now in ΔABD and ΔBAC,
AD = BC
(corresponding sides of similar triangles) [from (1)]
AB = AB
(common side)
AC = BD
(given)
∴ ΔABD ≈ΔBAC (By SSS criteria)
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You decide you want to go snowboarding for the day and you have to figure out your budget. Tickets are $75.00 per day and there is a 5% convenience charge when you order your ticket. You also have to pay for a bus ticket that is $12 for the day. You mom gives you a 15% off coupon that applies to the lift ticket only (not the bus). What is the total cost for your fun day out? (round to the nearest hundredth)
The total cost for your fun day out is $23.82.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".Given is that you decided to go snowboarding for the day and you have to figure out your budget. Tickets are $75.00 per day and there is a 5% convenience charge when you order your ticket. You also have to pay for a bus ticket that is $12 for the day. You mom gives you a 15% off coupon that applies to the lift ticket only.
Assume that the total cost for your fun day out is ${x}. Then, we can write the equation as -
{x} = 15% of (75 + {5% of 75}) + 12
{x} = 15% of (75 + {5/100 x 75}) + 12
{x} = 15% of (75 + {1/20 x 75}) + 12
{x} = (15/100) x (75 + 75/20) + 12
{x} = (3/20 x 78.75) + 12
{x} = 11.82 + 12
{x} = 23.82
Therefore, the total cost for your fun day out is $23.82.
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What is a coordinate plane example?
A coordinate plane is a two-dimensional surface formed by two number lines
What is coordinate system?In a plane, a Cartesian coordinate system is a system of coordinates that designates each point uniquely by a pair of numerical coordinates, which are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length. Two number lines combine to produce the coordinate plane, a two-dimensional surface. The x-axis is the name given to one horizontal number line. The y-axis is the name given to the other number line, which is vertical. At a place known as the origin, the two axes collide. The coordinate plane allows us to graph points, lines, and more. The plane that houses the x- and y-axes is known as the xy-plane, while the y- and z-axes are housed in the yz-plane and the x- and z-axes are housed in the xz-plane.To learn more about coordinate system refer to:
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Mrs. Hanover borrows $1,413 at a
rate of 5% per year. How much
Simple Interest will she owe if it
takes her 9 months to repay the
loan? Round your answer to the
nearest cent
well, let's recall that a year has 12 months, so 9 months is really 9/12 of a year
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1413\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases} \\\\\\ I = (1413)(0.05)(\frac{3}{4}) \implies I = 1413(\frac{3}{80})\implies I\approx 52.99[/tex]
50PTS 50PTS don’t explain just answer.
Answer:
[tex] \sf \: x = 7[/tex]
Step-by-step explanation:
Now we have to,
→ find the required value of x.
Forming the equation,
→ 2x + 5 = 3x - 2
Then the value of x will be,
→ 2x + 5 = 3x - 2
→ 2x - 3x = -2 - 5
→ -x = -7
→ [ x = 7 ]
Hence, the value of x is 7.
Which mixed number is equal to 35
Answer:
35 [tex]\frac{0}{1}[/tex]
Step-by-step explanation:
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A measurement which could be the side lengths of a right triangle include the following: C. √24 in, √6 in, √30 in.
How to determine the side lengths?In order to determine which measurements could be the side lengths of a right triangle, we would have to apply Pythagorean's theorem.
Mathematically, Pythagorean's theorem is given by this formula:
x² + y² = z²
From the side lengths of the first triangle, we have the following:
(√6)² + (√30)² = (√33)²
6 + 30 = 33
36 = 33 (False).
From the side lengths of the first triangle, we have the following:
(√27)² + (√18)² = (√48)²
27 + 18 = 48
45 = 48 (False).
From the side lengths of the first triangle, we have the following:
(√6)² + (√24)² = (√30)²
6 + 24 = 30
30 = 30 (True).
From the side lengths of the first triangle, we have the following:
(√18)² + (√21)² = (√48)²
18 + 21 = 48
39 = 48 (False).
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The moon orbits earth at 384400km. The distance from earth to the sun is 149600000km. The diamiter of the sun is 1391000km. What would the diamiter of earth have to be to appear the same size as the sun from the moon if the celestial objects are in the order shown here : Sun, earth, moon.
Answer:
The diameter of Earth that would appear the same size as the Sun from the Moon is approximately 54304839.858 kilometers
Step-by-step explanation:
To find the diameter of Earth that would appear the same size as the Sun from the Moon, we need to know the distance from the Moon to the Sun and the distance from the Moon to Earth.
Since the distance from the Moon to the Sun is much greater than the distance from the Moon to Earth, the angle subtended by the Sun at the Moon will be much smaller than the angle subtended by Earth at the Moon.
Therefore, the size of Earth as seen from the Moon will be much larger than the size of the Sun as seen from the Moon.
To find the ratio of the size of Earth to the size of the Sun as seen from the Moon, we can use the formula:
size ratio = (distance to Earth / distance to Sun) x (Sun's diameter / Earth's diameter)
Substituting in the given values, we get:
size ratio = (384400km / 149600000km) x (1391000km / Earth's diameter)
Simplifying, we get:
size ratio = 0.00257 x (1391000km / Earth's diameter)
To find the diameter of Earth that would appear the same size as the Sun from the Moon, we need to solve for Earth's diameter. Dividing both sides of the equation by 0.00257, we get:
Earth's diameter = (1391000km / 0.00257) = 54304839.858km
Therefore, the diameter of Earth that would appear the same size as the Sun from the Moon is approximately 54304839.858 kilometers.
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Enter your answer and show all the steps that you use to solve this problem in the space provided in the triangle there is a 72° c113° write a list of steps that are needed to find the measure of b
The steps for measuring the angle b is shown below, <b= 41.
What is Exterior angle Property?If a triangle side is created, the outside angle that results is equal to the sum of the two opposite internal angles.
If an equivalent angle is measured at each triangle vertex, the exterior angles always add up to 360 degrees.
Given:
exterior angle = 113
and, opposite interior angle =72
Using Exterior angle property we have
72 + b = 113
Subtract 72 from both side
72 + b -72 = 113 -72
b = 113- 72
b = 41
Hence, the measure of b is 41 degree.
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6x + y = 20
x - 4y = -5
The value of [tex]x[/tex] is [tex]3[/tex] and [tex]y[/tex] is [tex]2[/tex]
The given equations are
[tex]6x+y=20\\x-4y=-5[/tex]
We need to find the value of [tex]x[/tex] and [tex]y[/tex]
First let's take equation [tex]2[/tex] and we can simplify it
[tex]x-4y=-5\\x=-5+4y[/tex]
Now, let's substitute the value of [tex]x[/tex] in equation [tex]1[/tex], that is
[tex]6x+y=20\\6(-5+4y)+y=20[/tex]
We can open the bracket and simplify
[tex]=-30+24y+y=20\\=-30+25y=20\\=25y=20+30\\=25y=50\\=y=\frac{50}{25} \\y=2[/tex]
Now we can substitute the value of [tex]y[/tex] in equation [tex]x-4y=-5[/tex]
[tex]x-4(2)=-5\\x-8=-5\\x=-5+8\\x=3[/tex]
The complete question is find the value of [tex]x[/tex] and [tex]y[/tex] from the given equations.
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For m(x)=
-3/4x+6, find the value of x for which m(x) = 0.
The value of x when m(x) = 0 is 8.
What is Linear Function?A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables but does not have exponents to the variables or the exponent of the variable is 1.
The given function is,
m(x) = -3/4 x + 6
Here the value of m(x) depends on the value of x.
m(x) = 0
-3/4 x + 6 = 0
-3/4 x = -6
x = -6 ÷ -3/4
x = 6 × 4/3
x = 8
Hence when m(x) = 0, the value of x is 8.
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As a 11 1/3 inch candle burns down, its height decreases 1/6 inch each hour. How many hours does it take for the candle to burn completely?
SHOW YOUR WORK
The number of hours after which the candle is burned completely is
68 hours.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Candle height = 11(1/3) inches
Each hour the height decreases by 1/6 inch.
Now,
The equation to find the number of hours x after which the candle is burnout is 11(1/3) - (1/6)x = 0
Solve for x.
11(1/3) - (1/6)x = 0
11(1/3) = (1/6)x
34/3 = (1/6)x
x = (34 x 6) / 3
x = 34 x 2
x = 68
Thus,
After 68 hours the candle is completely burnt.
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A frozen yogurt shop charges $4. 00 for a bowl of yogurt and $0. 25 for each topping.
If the total charge for yogurt is dependent on the base price of the bowl of yogurt plus the number of toppings added, what is the value of y at the y-intercept of the line representing this situation?
A $4. 25
B $0. 25
C $4. 00
D $3. 75
If the total charge for yogurt is dependent on the base price of the bowl of yogurt plus the number of toppings added, the value of y at the y-intercept of the line representing this situation is C $4.00
The y-intercept of a line is the point where the line crosses the y-axis. In this case, the y-intercept is the cost of the bowl of yogurt without any toppings. The base price of the bowl of yogurt is $4.00, so the y-intercept of the line representing this situation would have a value of $4.00.
This means that the cost of a bowl of yogurt without any toppings is $4.00. The cost of the bowl of yogurt with toppings is determined by adding the cost of the bowl of yogurt plus the cost of the toppings. Therefore, the y-intercept of the line representing this situation would have a value of $4.00.
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The Fudd family is attending a family reunion. They plan to rent a
car from the ABC Car Rental Company. Let m represent the number
of miles the family will drive. Let c represent the cost for renting a
car. Complete problems
The complete problem equation will be c = k*m + b
The cost equation for renting a car from the ABC Car Rental Company in terms of the number of miles driven, m, and the cost, c, would likely take the form of:
c = k*m + b where k is the rate of cost per mile and b is the fixed cost for renting the car independent of the miles driven.
It is important to note that this is a general equation and the specific cost equation of the ABC Car Rental Company is not provided. Also, this equation assumes that the cost of renting a car is linear to the miles driven, which may not be the case in practice. Other factors such as the type of car and duration of the rental period could also be included in the cost equation.
Therefore, the problem equation will be c = k*m + b
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please help asap. i need help.
The slope of the linear equation that passes through the two given points is 1/7.
How to find the slope of the line?A general linear equation can be written in the slope-intercept form as:
y = a*x + b
Where the coefficients are:
a: the slope.
b: the y-intercept.
If a line passes through two known points (x₁, y₁) and (x₂, y₂), then the slope is equal to:
a = (y₂ - y₁)/(x₂ - x₁)
In this case, we know that the line passes through (-10, -9) and (-3, -8), then the slope of this linear equation will be:
a = (-8 + 9)/(-3 + 10) = 1/7
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(i) Six horses are each given 5 ml spoons of medicine three times each day.
Calculate the number of whole days a 2 L bottle of medicine will last.
Answer:22 days
Step-by-step explanation: since 6days are each given 5ml spoons of medicine three times a day,
Therefore consumption of each day is 90 ml and we have 2000 ml(2litre=2000 ml)
so, 2000/90 = we will get number of days
therefore 22.22 days
Which emplies 22 days.
Fill in the blanks
Complete the sentence
Answer: There are 30 cubes in each layer and 3 layers. (Up to down.)
Explanation: You can multiply the x and y axis for one layer, and then count how many layers there are. There are 90 cubes in all.
I hope this helps, have a good day!
A family visits a car show to research information on vehicles they might consider purchasing. Brochures for each vehicle provide helpful information for the vehicle. Which of the following is an example of a continuous quantitative variable that might be included in the brochure?
number of seats
type of transmission
presence of a sunroof
fuel efficiency (in mpg)
answer is fuel efficiency
Since the family visits a car show to research information on vehicles they might consider purchasing. The option that is an example of a continuous quantitative variable that might be included in the brochure is option D: fuel efficiency (in mpg).
What is continuous quantitative variable?A continuous quantitative variable is a type of variable that can take on any value within a certain range, such as fuel efficiency which can take on any value between a certain range of miles per gallon (mpg). In contrast, a categorical variable can only take on a discrete set of values.
"Number of seats" is also a continuous quantitative variable, but it is a bit different in the sense that it only can take on a certain values, for example the possible values for number of seats in a car can only be 2,4,5,6, etc.
Type of transmission is not a continuous quantitative variable, but it's a categorical variable, it can only take certain values such as Automatic, manual, etc.
Note also that presence of a sunroof also not a continuous quantitative variable, but it's a binary categorical variable which has only two possible values: true (presence) and false (absence)
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CPM 6-18
AP statistics
Consider a random variable X with μx = 40 and σx = 5. Let Z = X + X + X + X.
a. Find μz and σz.
d. Find μ1/4z and σ1/4z.
Consequently, the solution of the given question of probability comes out to be P(x<5.67 = 0.63
What is probability?Probability fundamentals. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Here,
we use the z-score algorithm to answer this query.
Score Z = x - 40/5
x = the raw score
population mean= μ
Population standard deviation is σ
Hence,
x = 40 μ = 5.67, σ =5
Z = 5.67 - 40/5
z=0.37
Probability based on the Z-Table:
P(x<5.67 = 0.63
Consequently, the solution of the given question of probability comes out to be P(x<5.67 = 0.63 .
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Please help I have a learning disablity and need help with this.
Use Distribute Property to rewrite the algebraic expression.
Please answer both parts
8(x + 7)
Answer here _____________
Use Distribute Property to rewrite the algebraic expression.
6(11 + x)
Answer here ____________
The value of 8(x + 7) is 8x + 56.
The value of 6(11 + x) is 66 + 6x.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The distributive property of multiplication over addition states that,
a x (b + c) = a x b + a x c
Now,
8 x (x + 7)
= 8 x (x) + 8 x 7
= 8x + 56
6 (11 + x)
= 6 x 11 + 6 x (x)
= 66 + 6x
Thus,
The value is 8x + 56 and 66 + 6x.
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What is the coefficient of X²Y in the product 7x² 5y X² 3y )? *?
The coefficient of the expression X²Y in the product 7x² 5y X² 3y is 35.
7x² 5y X² 3y
= 7x² X² (5y 3y)
= 7x² X² (2y)
= 7x² X² 2y
= 14x² 2y
= 28xy
= 35
The given expression is 7x² 5y X² 3y. This can be rearranged as 7x² X² (5y 3y). This is equal to 7x² X² (2y). This can further be rearranged as 7x² X² 2y. This is equal to 14x² 2y. This can be further rearranged as 28xy. This is equal to 35. Therefore, the coefficient of X²Y in the product 7x² 5y X² 3y is 35.
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How do you check if an inverse is a function?
If a value of y relates only to one value of x, then the function does have an inverse function.
Define the term function and its inverse?A relation between such a collection of inputs and outputs is known as a function.
A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is just the input.If and only if the outcome of reflecting a function's graph about the line y = x is the function's graph, then the function f does have an inverse (passing from the vertical line test).Thus, if a value of y relates only to one value of x, then the function does have an inverse function.
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HELP!! Find the value of…
Answer:
It C man.
Step-by-step explanation:
You don't need this
Colorado State Flag (7. 4. A. 1. 4)
Illustrative Mathematics
1. 4: Colorado State Flag
The side lengths of the state flag of Colorado are in the ratio 2:3. If a flag is 12 feet long, what is its height?
The height of the flag is 18 feets.
What is a rectangle?Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.
Length is equal to 2 (2 + 3) the sum of the side lengths.
The sum of side length divided by (12) equals (2/5)
12 = 0.4(sum of side length) (sum of side length)
divide both sides by 0.4.
The height of the flag is calculated as side lengths plus length.
Height of flag: (30 – 12) = 18 feet
Therefore, the height of the flag is 18 feets.
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At a fancy dinner party, the number of courses that will be served determines how many forks will be set out by the hostess.
c = the number of courses served during dinner
f = the number of forks set out by the hostess
Which of the variables is independent and which is dependent?
Answer:
c is the independent variable and f is the dependent variable
Step-by-step explanation:
A gardener has 400 feet of fencing t0 fence in a bordered rectangular garden: One side of the garden Is river and so it does not need any fencing: river garden What dimensions would guarantee that the garden has the greatest possible area? shorter side: ft (feet) longer side: (feet) greatest possible area: (square-feet) Submit Question
The shorter side should be 200 ft and the longer side should be 200 ft. This would give the garden the greatest possible area of 40,000 square-feet.
1. The area of a rectangle can be calculated by multiplying the length and width together.
A = L * W
2. We know that the total amount of fencing is 400 ft.
3. We also know that one side of the garden is a river and so it doesn't require fencing.
4. Therefore, the remaining fencing must be divided equally between the two other sides of the garden (200 ft per side).
5. We now know that the length and width of the garden are both 200 ft.
6. Plugging these values into the area equation, we get:
A = 200 ft * 200 ft = 40,000 sqft
7. Therefore, the greatest possible area of the garden is 40,000 square-feet..
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The population of Smallville in the year 1890 was 6250. Assume the population increased at a rate of 2.75% each year. a) Estimate the population in 1915 and 1940. b) Predict when the population reached 50,000
If the population grew 2.75% each year then each year the population was multiplied by 1+2.75%=1+0.0275=1.0275
What is the population of Smallville in 1890 was 6250?Population in the year 1890 = 6250. Population increased at the rate of 2.75% per year or increased by 11400 , which will become 411400 after the increaseif you were to do it a step at a time it would mean multiplying 6250 by 0.0275(2.75%), and adding the result to 6250, then repeating the operation with the new number for each year until you reached the amount of years required (25 and 50 years).Now an easier way to do that first step would be multiplying by 1.0275, which already takes care of adding the original number. Now just do that for each of the intervals (25 and 50) required.
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Find the slope between (3,-2) (-4,1)
Answer:
- [tex]\frac{3}{7}[/tex]
Step-by-step explanation:
Change in y over the change in x.
(3,2)(-4,1)
The y values are 1 and 2.
The x values are -4 and 3.
You find the change by subtracting.
[tex]\frac{1--2}{-4-3}[/tex] = [tex]\frac{1+2}{-7}[/tex] = [tex]\frac{3}{-7}[/tex]
Can be written - [tex]\frac{3}{7}[/tex]
How many solutions does y 2x 5 and 8x 4y =- 20 have?
A system of linear equations: y + 2x = -5 and 8x + 4y = -20 has infinitely many solutions.
The 3 possible solutions of a linear system are:
- Unique or one solution
- Infinite solutions
- No solution
If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.
The given linear system is:
y + 2x = -5 ....... (equation 1)
8x + 4y = -20 ..........(equation 2)
Rearrange equation 1 to:
2x + y = -5
Multiply both sides by 4:
8x + y4 = -20
Hence, equation 1 is equivalent to equation 2. Hence, the given linear system has infinitely many solutions.
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The double number line shows that a traffic signal allows traffic through the intersection for 363636 seconds. A double number line with 2 tick marks. The line labeled Time, seconds, reads from left to right: 0, 36. The line labeled Percentage, reads from left to right: 0 percent, 100 percent. A double number line with 2 tick marks. The line labeled Time, seconds, reads from left to right: 0, 36. The line labeled Percentage, reads from left to right: 0 percent, 100 percent. Complete the table to show different percentages of the time the signal allows. Time (\text{s}sstart text, s, end text) Percentage 100\%100%100, percent of 36\,\text{s}36s36, start text, s, end text 25\%25%25, percent of 36\,\text{s}36s36, start text, s, end text 125\%125%125, percent of 36\,\text{s}36s36, start text, s, end text Report a problem
The percentages for this problem are calculated as follows:
100% of 36 seconds: 36 seconds.25% of 36 seconds: 9 seconds.125% of 36 seconds: 45 seconds.How to obtain the percentages?The percentages in this problem are obtained applying proportions, multiplying the total amount by the decimal equivalent of the percentage.
Hence the amount that represents 100% of 36 seconds is obtained as follows:
1 x 36 = 36 seconds.
(as a percentage of 100% has a decimal equivalent of 1).
The amount that represents 25% of 36 seconds is obtained as follows:
0.25 x 36 = 9 seconds.
(as a percentage of 25% has a decimal equivalent of 1).
The percentage of 125% of 36 students can be obtained combining the two previous expressions as follows:
1.25 x 36 = 1 x 36 + 0.25 x 36 = 36 + 9 = 45 seconds.
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