What is the end behavior of the graph of f(x) = x5 - 8x4 + 16x³?
O
O f(x)→→∞ as x→∞; f(x) →→∞ as x→ +∞
f(x)→∞ as x→-∞0; f(x) → +∞o as x→ +∞
O f(x) +∞o as x→-∞; f(x) →→→∞as x→ +∞
+∞o as x→∞0; f(x)→ +∞ as x→→ +00
O
f(x)
DONE
The end behaviour of the graph of f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³ is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞ , the correct option is (a) .
In the question ,
it is given that ,
the function is f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³ ,
In the function as x approaches -∞ , x⁵ will also approach -∞ , because negative number raised to the odd power , gives a negative result .
In the function as x approaches ∞ , x⁵ will also approach ∞ , because positive number raised to the odd power , gives a positive result .
that is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞
let us find the roots of the function ,
f(x) [tex]=[/tex] 0
x⁵ - 8x⁴ [tex]+[/tex] 16x³ = 0
taking x³ common ,
x³(x² - 8x [tex]+[/tex] 16) = 0
x³(x² - 4x - 4x + 16) = 0 .... by using splitting the middle term method
x³(x(x - 4) - 4(x - 4)) = 0
x³(x - 4)(x - 4) = 0
which means x³ [tex]=[/tex] 0 and x-4 = 0
that is x=0 and x = 4 .
So , the roots of the function f(x) are x=0 and x=4 .
This means that the graph has a repeated root and so it will touch the x-axis but not at the repeated root of x [tex]=[/tex] 4.
Therefore , The end behaviour of the graph of f(x) [tex]=[/tex] x⁵ - 8x⁴ [tex]+[/tex] 16x³ is f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞ , the correct option is (a) .
The given question is incomplete , the complete question is
What is the end behavior of the graph of f(x) = x⁵ - 8x⁴ + 16x³ ?
(a) f(x)→∞ as x→∞; f(x) →-∞ as x→ -∞
(b) f(x)→∞ as x→-∞0; f(x) → +∞ as x→ +∞
(c) f(x)→∞ as x→ -∞; f(x) →-∞ as x→ +∞
(d) f(x)→-∞ as x→∞ ; f(x)→ -∞ as x→∞
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Monica’s dose from the fluoroscopy tower, at a distance of 9 feet, is 100 mR/hr. What is the radiation intensity, in Roentgens, at 1 foot from the fluoroscopy tower?
The radiation intensity, in Roentgens at a distance of 1 foot is 8.1 R/hr
How to the radiation intensity, in Roentgens?
Radiation intensity is defined as the radiation energy that strikes in one second upon a surface of 1 square unit perpendicular to the direction of the ray
The equation below relates the radiation intensity and distance:
I₁/I₂ = D₂²/D₁²
where: I₁ = intensity at distance 1, I₂ = intensity at distance 2, D₁ = distance 1 from source and D₂ = distance 2 from source
Given: D₁ = 9 feet, I₁ = 100 mR/hr and D₂ = 1 foot
Using the formula:
100/I₂ = 1²/9²
100/I₂ = 1/81
I₂ = 100 × 81
I₂ = 8100 mR/hr
I₂ = 8100×10⁻³ R/hr (1 mR/hr = 1×10⁻³ R/hr)
I₂ = 8.1 R/hr
Therefore, the radiation intensity in Roentgens is 8.1 R/hr
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if I make 11 dollars an hour and i worked 20 hours for 4 days, how much would I earn?
Answer: I think you would earn $8.35 per hour
Step-by-step explanation:
Answer: $880
Step-by-step explanation:
As I understand you are working 20 hours a day for 4 days.
[tex]\frac{11 dollars}{hour} * \frac{20 hours}{day} * 4 days[/tex] = $880
Critique Reasoning An office manager has $10,000 to spend on new equipment. He planned to purchase 300 lamps for $72 each. He completed the calculations at the right and concluded that there would be plenty of money left to buy additional equipment. 4. What does the office manager do to support his thinking?
The probability that the sum of the two die rolls is 9 is 4 / 11.
What is the probability?Probability determines the chances that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Probability that the sum of the two die roll is 9 = number of sides that roll a sum of 9 / total number of sides that at least one of them is a 5
number of sides that roll a sum of 9 =(4,5) (6 , 3), (3 , 6), ( ,4) = 4
total number of sides that at least one of them is a 5 = (1, 5), (2, 5), (3, 5), (4, 5) , (5, 5), (6, 5), (5, 1), (5, 2) , (5, 3), (5, 4), (5, 6) = 11
Probability that the sum of the two die roll is 9 = 4/11
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The office manager will either put up a clearer calculation and model the equation to ascertain money remaining at each quaintly bought or a graph to present his calculations
What is a graph ?A graph is a representation of data, it helps to analyze data clearly with lesser time
The calculation the office manager will do is to multiply the number of lamps with the unit price then subtract from the amount set aside to spend on new equipment
The calculation
let the money left be z
10000 = 300 * 72 + z
10000 = 21600 + z
subtraction
z = 10 000 - 21600
z = - 16000
The calculation shows that the money will not be enough
The equation is modeled as
y = 10000 - 300x
where x is the number of bulbs
y is amount left
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2*8/3 give me answer
Answer:
Exact Form: 16/3
Decimal Form: 5.3
Mixed Number Form: 5 1/3
Step-by-step explanation:
A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2 + 2 = 4 .
Which integer makes the following sentence true? -10 < ? < -1
Answer:
Below
Step-by-step explanation:
Any of the following
-9 -8 -7 -6 -5 -4 -3 -2
4. A local video store has seen good linear growth in rentals since 2005. In 2009, the store had
23,500 rentals. In 2015, the store had 28,540 rentals.
a. Find the average rate of change of the store's rentals in rentals per year.
b. Using the average rate of change, determine the number of rentals in 2005.
The average rate of change of the store's rentals in rentals per year is 840 rentals per year and the number of rentals in 2005 is 20,140.
According to the question,
We have the following information:
A local video store has seen good linear growth in rentals since 2005. In 2009, the store had 23,500 rentals. In 2015, the store had 28,540 rentals.
a) Average rate of change of store's rentals =(Rentals in 2015-rentals in 2009)/Number of years
Now, the number of years passed between 2009 and 2015 is 6 years.
So, we have:
Average rate of change = (28540-23500)/6
Average rate of change = 5040/6
Average rate of change = 840 rentals per year
b) Now, the number of rentals in 2005:
(Number of rentals in 2009-number of rentals in 2005)/4 = 840
Let's take the number of rentals in 2005 to be x.
(23500-x)/4 = 840
23500-x = 3360
-x = 3360-23500
-x = -20140
x = 20,140
Hence, the average rate of change of the store's rentals in rentals per year is 840 rentals per year and the number of rentals in 2005 is 20,140.
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I need help with this please help me
The measurement of angles ∠1 is 126° and ∠2 is 154°.
According to the question,
We have the following information:
We have a figure of two triangles and some of the measurements of the angles are given.
We know that the sum of three angles of a triangle is 180°.
So, for the larger triangle, we have the following expression:
96+30+third angle = 180
Third angle = 180-126
Third angle = 54°
We know that sum of angles on a straight line is 180°.
So, we have:
∠1+54 = 180
∠1 = 180-54
∠1 = 126°
Now, finding the sum of angles in smaller triangle:
126+28+third angle = 180
Third angle = 180-154
Third angle = 26°
Now, angle 2 and this angle will make a straight line.
∠2+26 = 180
∠2 = 180-26
∠2 = 154°
Hence, the measurement of angles ∠1 is 126° and ∠2 is 154°.
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Write an equation and solve:
Sandy has $60 and saves $10 a month. Randy has
$45 and saves $20 per month. After how many
months will they have the same amount of
money?
Answer:
3/2 month
Step-by-step explanation:
Write an equation and solve: Sandy has $60 and saves $10 a month. Randy has $45 and saves $20 per month. After how many months will they have the same amount of money?
When x = months:
Sandy: 10x + 60
Randy: 20x + 45
You are looking for x when:
Sandy = Randy
10x + 60 = 20x + 45
subtract 45 from both sides:
10x + 60 - 45 = 20x + 45 - 45
10x + 15 = 20x
subtract 10x from both sides:
10x + 15 - 10x = 20x - 10x
15 = 10x
divide both sides by 10:
15/10 = 10x/10
x = 15/10
reduce:
x = 3/2
It will take 3/2 months of Sandy and Randy to have the same amount of money.
[3/2 month also equals 1.5 months, depending on the format of the answer you need]
Question 6(Multiple Choice Worth 2 points)
(Pythagorean Theorem MC)
Determine which set of side measurements could be used to form a right triangle.
O 4, 8, 11
O 6, 8, 13
O√3, √5,8
O√3, √13, 4
K
The set of side that could be used to form a right triangle is {√3 , √13 , 4} , the correct option is (d) .
In the question ,
four set of sides is given ,
we need to find the set of side that forms a right triangle ,
we know that for right triangle , By Pythagoras Theorem , the sum of square of two shorter side is equal to the square of the longest side .
Option(a)
the sides are 4 , 8 , 11.
4 + 8 = 11
16 + 64 = 121
80 = 121
we know that 80 121 ,
So , the sides do not form a right triangle
Option(b)
the sides are 6 , 8 , 13
6 + 8 = 13
36 + 64 = 169
100 169
we know that 100 169 ,
So , the sides do not form a right triangle .
Option(c)
the sides are √3, √5 , 8
√3 + √5 = 8
3 + 5 = 64
8 = 64
we know that 8 64 ,
So , the sides do not form a right triangle .
Option(d)
the sides are √3, √13 , 4
√3 + √13 = 4
3 + 13 = 16
16 = 16
Yes , the sides form a right triangle .
Therefore , The sides {√3 , √13 , 4} forms a right triangle .
The given question is incomplete , the complete question is
Determine which set of side measurements could be used to form a right triangle ?
(a) 4, 8, 11
(b) 6, 8, 13
(c)√3, √5,8
(d)√3, √13, 4
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(18x³ - x² + 9x - 3) and (5x³ + 6x² - 14x +11) Add the polynomials (Provide only the coefficients. If a coefficient is negative, include the negative sign on the left side of the number. Do not type 'plus' sign)
Answer: put it in a caculator
Step-by-step explanation:
Combine 18x^3 and 5x^3.
23x³ - x² + 9x-3 + 6x² - 14x+11Combine x^2 and 6x^2.
23x³ + 5x² + 9x -3 - 14x + 11Combine 9x and −14x.
23x³ + 5x² + -5x -3 + 11Add −3 and 11.
23x³ + 5x² -5x + 8For the following, based on the information given which would you use to find the missing variable?
The missing variables are b, x, x and y are 3.73m, 7.88 units, 41.06 units and 8.94 units respectively
How to find the missing variables?We will use trigonometrical ratios to solve this problem. Below are the definitions of the trigonometrical ratios:
sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent or tan = sin/cos
The opposite is the side the angle of consideration is facing
The hypotenuse is the side the right angle is facing
The adjacent is the side left after determining the opposite and hypotenuse
1st triangle
tan 25° = b/8 (tan = opp/adj)
b = 8 tan 25° = 3.73m
2nd triangle
sin 21° = x/22 (sin = opp/hyp)
x = 22 sin 21° = 7.88 units
3rd triangle
cos 47° = 28/x (cos = adj/hyp)
x = 28/cos 47° = 41.06 units
4th triangle
Use Pythagoras' theorem:
12² = 8² + y²
y² = 12² - 8²
y² = 144 - 64
y² = 80
y = √80 = 8.94 units
Therefore, the missing variables are b = 3.73m, x = 7.88 units, x = 41.06 units and y = 8.94 units
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NO LINKS! Please help me with this problem #3
Answer:
b) f(x) = -16x² + 8x + 30
Step-by-step explanation:
When a ball is thrown, its path of motion can be modelled as a parabola that opens downwards.
The graph of a quadratic equation f(x) = ax² + bx + c is a parabola.
If a > 0, the parabola opens upwards.If a < 0, the parabola opens downwards.Therefore, f(x) = -16x² + 8x + 30 could potentially model the time (in seconds) it takes a ball tossed from a window to touch the ground, as its graph is a parabola that opens downwards.
If this function was used to model the scenario, the height of the window above the ground would be the y-intercept (30 feet), and the time when the ball touched the ground would be the positive x-intercept (approx 1.64 s).
QUATIONS
Use the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to make true equations of
the following. Use each digit once
The true equations are :
2 + 7 = 9
8 × 5 = 4 0
6 ÷ 3 = 2
2 - 1 = 1
We are given a total of ten digits. The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. We are given four equations with blanks. An equation is a mathematical statement that proves the equality of two mathematical expressions. The first equation involves addition. The second equation involves multiplication. The third equation involves division. The fourth equation involves subtraction. We need to use every digit only once.
The first true equation is 2 + 7 = 9.
The second true equation is 8 × 5 = 4 0.
The third true equation is 6 ÷ 3 = 2.
The fourth true equation is 2 - 1 = 1.
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a sponsor of one person walking in a charity walkathon will donate 7 plus an additional .25 for each mile a person walks. which of the following functions , d, models the total amount , in dollars that the sponsor will donate to teh charity when the person walks m miles?
The function that models the total amount, in dollars, that the sponsor will donate to the charity when the person walks m miles is F(d) = 7 + 0.25m.
What is a function?Mathematically, a function is an expression involving two or more variables (independent and dependent) showing that a mathematical relationship exists between the expressions.
Functions use the equation symbol to show that the expressions are equal when the variables are substituted with integers.
Every function has a domain (input variable) and a range (output variable) or codomain.
Constant donation = $7
Variable donation per mile = $0.25
Function, F(d) = 7 + 0.25m
where d = the total amount donated
m = the total miles the person walks
Thus, the total donation made by the sponsor is represented by the function, F(d) = 7 + 0.25m.
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The temperature in the United States last night was -9℃. It is now -3℃. What was the change in temperature?
The change in temperature in United States since last night is -6 degree centigrade.
Given the temperature in United States last night is = -9 degree C
Now the temperature is = -3 degree C
So the change in temperature is given by,
= Final Temperature - Initial Temperature
= -9 - (-3)
= -9 + 3
= -6 degree C
Hence the change in temperature in United States since last night is -6 degree centigrade.
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At his most recent medical checkup, a boy was 40 inches tall. Currently, he is 46 inches tall. What percent taller is the boy now?
im not smart at this lol
Answer:
15%
Step-by-step explanation:
15%*40=46
Answer:
15%
Step-by-step explanation:
[tex]Percent of change =\frac{new -old}{ old} *100\\[/tex]
The boy was 40 inches tall so that means 40 inches is the old value
The boy is currently 46 inches tall now, so 46 is the new value
Plug these values into the equation:
[tex]Percent of change =\frac{46 -40}{ 40} *100\\[/tex]
Simplify:
[tex]Percent of change =\frac{6}{ 40} *100\\[/tex]
[tex]Percent of change =\frac{600}{ 40} \\[/tex]
[tex]Percent of change =15[/tex]
I hope this answers your question :)
can you help me use compatible numbers to find two estimates of 478/12 i will give you 100000 points
Answer:
48
Step-by-step explanation:
Help i need it fast!
write 28 plus 24 as a product of two factors
Answer:
4(13)
Step-by-step explanation:
[tex]28+24=7(4)+6(4)=\boxed{4(13)}[/tex]
Kathleen’s grandfather has a very old pet tortoise. He told Kathleen that the tortoise was 61 years old when she was born 10 years ago. Kathleen is amazed and wants to know how old the tortoise is now. Write an equation Kathleen can use to find the tortoise’s age t and solve.
Answer:
t - 10 = 61
Step-by-step explanation:
We are given that the tortoise was 61 years old 10 years ago. Let's suppose that t is the tortoise's current age. We can then write the equation t - 10 = 61
so t = 71.
Solve the system of equations by graphing. List the coordinates.
u=v
4u=2v-12
By using the graphing method, an ordered pair which represent a solution to the given system of equations is (-6, -6).
What is a graph?A graph simply refers to a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.
In order to plot the system of equations on a graph, we would simplify the second equation as follows:
4u = 2v - 12
Dividing both sides of the equation by 4, we have the following:
4u/4 = 2v/4 - 12/4
u = v/2 - 3
Note: The values of v would be plotted on the y-axis of a graph while the values of u would be plotted on the y-axis of a graph.
By critically observing the graph (see attachment) of the given system of equations, we can logically deduce that its solution occur at this point of intersection (-6, -6).
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Nicole charges a flat fee of $3, plus $5 per hour. Write an equation for the cost, after h hours
The equation when Nicole charges a flat fee of $3, plus $5 per hour is c = 3 + 5h.
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario
Let the number of hours be given as h.
Since Nicole charges a flat fee of $3, plus $5 per hour, this will be:
c = 3 + (5 × h)
c = 3 + 5h
where c = total cost
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4. Using the Place Value Method, order the following from least to greatest.
.134
.2
.051
.46
Answer: 0.051, 0.134, 0.2, 0.46
Step-by-step explanation:
Complete the table representing a linear function.
hint:Use the rate of change to find the missing values.
hint:Find the rate of change using change in y divided by change in x.
After finding the rate of change, this table representing a linear function can be completed as follows:
x y
1 0
2 10
5 40
10 90
What is the rate of change?Mathematically, the rate of change can be calculated by using this formula;
Rate of change, k = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change, k = (y₂ - y₁)/(x₂ - x₁)
Next, we would determine the rate of change of the value of y with respect to the value of x as follows:
Rate of change, k = (40 - 0)/(5 - 1)
Rate of change, k = 40/4
Rate of change, k = 10.
For the first blank, we have:
10 = (40 - y)/(5 - 2)
10 = (40 - y)/3
30 = 40 - y
y = 40 - 30
y = 10.
For the second blank, we have:
10 = (90 - 40)/(x - 5)
10 = (50)/(x - 5)
10x - 50 = 50
10x = 50 + 50
10x = 100
x = 10.
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Find the perimeter and area of the polygon shown below 15 8 17 16
The perimeter and area of the polygon is B. Perimeter = 72 feet; Area = 308 square feet.
How to calculate the perimeter?It is important to note that the perimeter is the addition of all the sides. Therefore, the perimeter will:
= 16 + 15 + 16 + 8 + 17
= 72 feet
The area will be:
= Area of triangle + Area of rectangle
= (1/2 × base × height) + (length × width)
= (1/2 × 8 × 17) + (15 × 16)
= 68 + 240
= 308ft²
Therefore, the correct option is B.
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Why does completing the square always result in a perfect square trinomial?
Answer: Adding will make a perfect square trinomial. It is always positive because it is the square of the number.
When a binomial is squared, the result is the square of the first term added to twice the product of the two terms and the square of the last term. a2+2ab+b2=(a+b)2anda2−2ab+b2=(a−b)2.
Hope this helps.
Step-by-step explanation:
Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ = 1.1 kg and a standard deviation of o= 4.6 kg.
Complete parts (a) through (c) below.
b. If 25 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg.
The probability is
(Round to four decimal places as needed.)
The probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
Amounts of weight that male college students gain during their freshman year are normally distributed
mean of μ = 1.1 kg and
Standard deviation of o= 4.6 kg.
Z score=x-μ/o
=25-1.1/4.6
=23.9/4.6
=5.196
Z score=x-μ/o
=25-1.1/0
=0
Z score=25-1.1/3
=23.9/3
=7.966
By observing the z table the probability that their mean weight gain during freshman year is between 0 kg and 3 kg is 70%
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In hypothesis testing,the assumption(s) for the Z test for a Mean when the σ is known The sample is a random sample Either n > or = 25 or the population is normally distributed if n < 25 both a) and b) none of the above
In hypothesis testing, the assumption for the Ztest for a mean when the σ is known then n > 30. Hence the answer is : None of the above
What is hypothesis?Using sample data, hypothesis testing is used to assess the plausibility of a hypothesis. Given the data, the test provides evidence for the hypothesis's plausibility.
Statistical analysts put a hypothesis to the test by measuring and examining a random sample of the population under consideration. Because the distributions of small samples are not normal, a t-test is required. If the sample size is large (n> 30), statistical theory predicts that the sample mean is normally distributed and that a z test for a single mean can be used.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each set of prices with the correct percent of increase or decrease.
11% decrease
11% increase
8.7% decrease
7.4% increase
8% decrease
12.4% decrease
9.9% increase
8% increase
original price: $63.00
new price: $56.07
arrowRight
original price: $98.00
new price: $108.78
arrowRight
original price: $37.50
new price: $34.50
arrowRight
original price: $12.25
new price: $13.23
arrowRight
Each set of prices should be matched with the correct percentage of increase or decrease as follows:
12.4% decrease = original price: $63.00 and new price: $56.07.11% increase = original price: $98.00 and new price: $108.78.8.7% decrease = original price: $37.50 and new price: $34.50.8% increase = original price: $12.25 and new price: $13.23.How to calculate percentage change?Mathematically, percentage increase can be calculated by using this formula:
Percentage increase = [original price - new price]/new price × 100
At original price: $63.00 and new price: $56.07, we have:
Percentage decrease = [63.00 - 56.07]/56.07 × 100
Percentage decrease = 6.93/56.07 × 100
Percentage decrease = 0.124 × 100
Percentage decrease = 12.4%.
At original price: $98.00 and new price: $108.78, we have:
Percentage increase = [108.78 - 98.00]/98.00 × 100
Percentage increase = 10.78/98.00 × 100
Percentage increase = 0.11 × 100
Percentage increase = 11%.
At original price: $37.50 and new price: $34.50, we have:
Percentage decrease = [37.50 - 34.50]/34.50 × 100
Percentage decrease = 3/34.50 × 100
Percentage decrease = 0.087 × 100
Percentage decrease = 8.7%.
At original price: $12.25 and new price: $13.23, we have:
Percentage increase = [13.23 - 12.25]/12.25 × 100
Percentage increase = 0.98/12.25 × 100
Percentage increase = 0.08 × 100
Percentage increase = 8%.
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