Therefore , the mean time until the one-hundredth call is 4.35 ,the mean time between call numbers 50 and 80 is 1.30 and s the probability that three or more calls occur withing 15 seconds is 0.754
What is poisson distribution?The Poisson distribution, used in probability theory and statistics, is a discrete probability distribution that expresses the likelihood that a specific number of events will take place within a predetermined window of time or space, provided that they do so at a known constant mean rate and regardless of the interval since the last event.
Here,
Thus, calls occur according to a poisson process with λ=23 calls per minute
a)X is the time until the one-hundredth call , X has Erlang distribution with rate of 23 and r =100
E(X)=r/ λ = 100/23 =4.35
b)The expected time between call numbers 50 and 80 is the same as the expected time until the 30th call this is Erlang distribution with rate of 23 and r =30
E(X)=r/ λ =30/23=1.30
c)P(N≥3) λ=23, x=1/4 ,λx=5
1-P(N≤2) = 1- ∑ [tex]\frac{e^{-5}-5^{k}}{k!}[/tex](from k=0 to 2 )=0.754
Therefore , the mean time until the one-hundredth call is 4.35 ,the mean time between call numbers 50 and 80 is 1.30 and s the probability that three or more calls occur withing 15 seconds is 0.754
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-3 1/2 x -5 2/3=?
Please help me with this problem.
Answer: 119/6
Step-by-step explanation:
-3 1/2 can be written as -7/2
-5 2/3 can be written as -17/3
-7/2 times -17/3 = 119/ 6
Point slope form (-8,2) m=-3/4
Answer:
y - 2 = - [tex]\frac{3}{4}[/tex] (x + 8)
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = - [tex]\frac{3}{4}[/tex] and (a, b ) = (- 8, 2 ) , then
y - 2 = - [tex]\frac{3}{4}[/tex] (x - (- 8) ) , that is
y - 2 = - [tex]\frac{3}{4}[/tex] (x + 8)
2. sophia is considering buying a dress and a necklace. the probability she will buy a red dress is 0.2, and similarly, it is 0.4 for a blue dress. there is a 10% chance she will buy a necklace. she wants to buy at most one dress, and buying a necklace is independent of buying a dress find the probability she buys at least one of the previous items. assume event a: she buys a red dress; event b: she buys a blue dress; event c: she buys a necklace.
Therefore the probability that she buys at least one of the previous items is 0.1333
What is probability ?The area of mathematics known as probability deals with numerical descriptions of the likelihood that an event will occur or that a statement is true .A number between 0 and 1 is the likelihood of an event, where, broadly speaking, 0 signifies the event's impossibility and 1 denotes its certainty.
Given:
event A: she buys red dress.
event B: she buys a blue dress.
event C: she buys a necklace.
the probability she will buy a red dress is 0.2,
the probability she will buy a blue dress is 0.4
there is 10% chance she will buy a necklace =0.10
The probability she wants to buy at most one dress,
P(A or B or C) =0.2 +0.4 +0.1 -(0.08 -0.04 -0.02 +0.08)
P(A or B or C) =0.568
the probability she buys at least one of the previous items is
[tex]\frac{P(A or B or C)}{P(AorB andC)}[/tex] = [tex]\frac{0.2 * 0.1 * 0.4}{(0.2 * 0.1)+(0.1 *0.4)}[/tex]
[tex]\frac{P(A or B or C)}{P(AorB andC)}[/tex]= 2/15 =0.133
Therefore the probability that she buys at least one of the previous items is 0.1333
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please please help me
Answer:
I'm pretty sure its 3500
Answer:
3,500 meters above the ground.
Step-by-step explanation:
The working is in the picture I attached to this response.
⭐ if this response helped you, please mark it the "brainliest"!⭐
a doctor claims that people are more than 11 pounds overweight. to test the claim, 25 randomly selected people were weighed and the difference between their actual weight and their ideal weight was calculated. the sample mean and sample standard deviation of that difference were12 and 4 pounds, respectively. assuming a paired t-test is appropriate, can we conclude at the 1% level of significance that the claim is true? group of answer choices yes, conclude the claim is true by accepting h0.
There is enough evidence to conclude that the doctor's claim is true.
We have given that,
population mean μ = 11 pounds
sample size n = 25
sample mean x = 12 ponds
standard deviation σ = 4 pounds
so the null hypothesis is H₀ : μ = 11 pounds
and the alternative hypothesis is Hₐ : μ > 11 pounds
now we will calculate test statistics,
t = (x-μ)/(σ/√n)
= (12 - 11)/(4/√25)
= 1/(4/5)
t = 1.25
p-value from the z-table is 0.10565
the result is non significant at p < 0.01.
Hence the null hypothesis rejected .
Therefore there is enough evidence to conclude that the doctor's claim is true.
The level of significance is the measurement of the statistical significance. It defines whether the null hypothesis is assumed to be accepted or rejected. It is expected to identify if the result is statistically significant for the null hypothesis to be false or rejected.
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Here is a data set (n = 117) that has been sorted. 58.5 59.4 60.5 62.1 65.9 65.9 66.2 66.3 66.5 67.4 67.8 68 68.1 68.2 68.2 68.7 69.3 69. 469. 469.8 70. 270.5 70. 771.2 71.5 71.6 71. 9 72. 1 72.6 72.8 73.1 73.4 74.6 | 74.8 74.9 74.9 74.9 75 75.4 75.4 76. 2 76. 4 76. 5 76. 7 76.8 76.9 77.1 . 77.2 77.7 77.9 78 78. 1 78. 2 78. 9 79.4 79.5 79. 8 79.9 80.2 80.5 80. 6 80.7 81.2 81.5 81.7 81. 8 81.8 82.4 82.6 83.183. 1 83.5 83.9 83.9 84.1 | 84.2 84.3 84.3 84.6 85.2 85.6 86 86.1 | 86.1 86.5 86. 6 86. 7 87.1 87.8 88.6 89.1 90. 2 90. 6 90.7 91.4 922 93 93.3 93. 3 94.1 94. 3 95.3 95.5 | 96.1 66.4 69 71.4 74.5 76.2 77.4 79.5 81.6 83.5 85.3 87.3 92.7 101.8 Find the 33rd-Percentile: P. = Preview
The 33rd percentile is 75.4.
Percentile is defined as the value below which a given percentage falls under. The percentile formula is used when we need to compare the exact values or numbers over the other numbers from the given data i.e. the accuracy of the number.
To find the percentile, here are a few steps to use the percentile formula. If q is any number between zero and hundred, the qth percentile is a value that divides the data into two parts i.e the lowest part contains the q percent of the data and the rest of the data is the upper part.
We find the rank.
Rank = Percentile ÷ 100
Rank = 33 ÷ 100 = 0.33
So, the rank is 0.33.
Using the percentile formula,
Percentile = Rank × Total number of the data set
Percentile = 0.33 × 117
Percentile = 38.61 ≅ 39
Now, counting 39 values from left to right we reach 75.4, and we can say that all the values below 75.4 will come under the 33rd percentile. In other words, 33% of the values are below 75.4.
Therefore, the 33rd percentile is 75.4.
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Triangle ABC is similar to triangle XYZ. What is the length of YZ?
28 in.
32 in.
AA
C
20 in.
B
А
26 in.
15 in.
30 in.
24 in.
The length of the YZ for the two similar triangles will be 9 inches.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
Given that triangle, ABC is similar to triangle XYZ. The value of the side YZ will be calculated by the similarity property,
YZ / BC = XZ / AC
x / 3 = 15 / 5
x = ( 15 x 3 ) / 5
x = 3 x 3
x = 9 inch
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a ______________ is a distribution of scores where a straight line can be visualized in the middle of a maze of cases running from one corner to another.
A linear relationship is a distribution of scores where a straight line can be visualized in the middle of a maze of cases running from one corner to another.
What does the term "linear relationship " mean?
A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association).
Graphs and mathematical equations of the form y = mx + b can both be used to represent linear relationships.
Why are relationships linear and nonlinear?
Plotting a linear relationship on a graph results in a straight line, whereas plotting a nonlinear relationship results in a curve.
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How do you solve 3(x−5)=12?
Answer:
9
Step-by-step explanation:
3(x-5)=12
Use distributive property on with the 3 and parenthesis (3 times x and 3 times -5)
3x-15=12
Add fifteen to both sides (15 on the left side cancels out)
3x=27
Divide both sides by 3 (3 on the left side cancels out)
x=9
How do you use demoivre's theorem to simplify (1−i)^12?
The correct answer is 64
Demoivre's theorem states that for all complex numbers z and all positive integers n:
z^n = (r^n) × (cos(n∅) + isin(n×∅))
where r is the magnitude of z and theta is the argument of z.
To use Demoivre's theorem to simplify (1−i)^12, we can first write (1−i) in polar form as r × cis(∅). where r is the magnitude and cis(∅) is the size complex number. is 1, the argument ∅. In this case the size of (1−i) is √(1^2 + (-1)^2) = √(2) and the argument of (1−i) can be found using the arctangent function.
∅ = arctan(-1÷1) = -45 degrees.
So (1−i) can be written as sqrt(2) × cis(-45 degrees). Applying this to Demoivre's theorem, we get:
(1−i)^12 = (√(2)^12) × (cos(-540°) + i×sin(-540°))
We can simplify this to:
(1−i)^12 = 2^6 × cis(-180°)
This can be further simplified as follows.
(1−i)^12 = 64 × (-1)
the final answer is -64.
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Write the equation in standard form for the circle that has a diameter with endpoints (-2,10) and (-2,8)
The equation in standard form for the circle will be;
⇒ (x + 2)² + (y - 9)² = 1
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The circle that has a diameter with endpoints (-2,10) and (-2,8).
Now,
Since, The circle that has a diameter with endpoints (-2,10) and (-2,8).
Hence, The radius of circle is the half of the distance between two points of the diameter.
So, Radius = 1/2 (√ (8 - 10)² + (- 2 - (-2))²
= 1/2 √4
= 1/2 × 2
= 1
Thus, Radius (r) of circle = 1
And, The center of circle is midpoint of the endpoints of the diameter.
Hence, Centre = (- 2 + (-2))/2, (10 + 8)/2
= - 4/2 , 18/2
= (- 2, 9)
Hence, The equation of circle with center (-2, 9) and radius 1 is;
⇒ (x - (-2))² + (y - 9) = 1²
⇒ (x + 2)² + (y - 9)² = 1
Thus, The equation in standard form for the circle will be;
⇒ (x + 2)² + (y - 9)² = 1
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(2,-2) and (0,-1) in linear equation
Answer:
Step-by-step explanation:
(2,-2) to draw it the y-intercept is -2 and the x-intercept is 2.(0,-1) to draw it the y-intercept is -1 and the x-intercept is 0.a wodden plnk 15
[tex] \sqrt{3} [/tex]
m long rests on a wall in such a way that it mskes an angel with ground at 15m away from the foot of the wall. find the angle made by the plank with the ground
Step-by-step explanation:
when you look at that right-angled triangle that is created by the plank as Hypotenuse (the side opposite of the 90° angle), and the distance on the ground from the wall and the height on the wall (from ground to the plank) as the legs, we know that the Hypotenuse (the plank) is the radius of the trigonometric circle we can draw there, and the 15 m ground distance from the wall is
cos(our angle) × radius
15×sqrt(3) × cos(our angle) = 15
cos(our angle) = 1/ sqrt(3) = 0.577350269...
our angle = 54.73561032...°
about 10% of the population has a particular genetic mutation. 800 people are randomly selected. find the mean for the number of people with the genetic mutation in such groups of 800.
The mean number of people with the genetic mutation in these groups is 80 as this follows a Binomial Distribution.
It is given that 10% of the population has a genetic mutation. We have a sample of 800 here.
Let X be the random variable that defines the number of people with the mutation in the sample.
Since every person can or can't have the mutation, this is a Binomial distribution.
Here,
n = 800
p = 0.1
According to the formula for a Binomial Distribution,
the mean = np
Therefore, the mean for the above distribution will be
800 X 0.1
= 80.
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can someone pls help me with this one?
Answer:
y = x + 2
Step-by-step explanation:
Use the slope-intercept form:
y=mx+b
M represents the slope of the line
B represents the y-intercept
How do you find the derivative of 1/(1+x^2) ?
The answer is:
- 2x/(1+x^2)^2
Given rhombus ABCD, find mLADC.
The measure of the required angle of the given rhombus ABCD is m∠ADC = 64°.
Properties of a rhombus:In a rhombus, the opposite angles are equal in measure.The diagonals in a rhombus are the angle bisectors.The two diagonals bisect each other.The adjacents angles of a rhombus are supplementary.Calculation:The given rhombus has four angles as
∠ADC, ∠DCB, ∠CBA, and ∠BAD
It has two diagonals that bisect each other at point E.
And we have ∠ABD = 32° and ∠ACD = 58°
Here, the angles ∠ABD and ∠BDC are alternate angles. Since we know that, the alternate angles are equal in measure, we can write
∠ABD = ∠BDC
⇒ 32° = ∠BDC
Since we know that the diagonals of a rhombus bisect the angles, we get
∠ADC = 2∠BDC
⇒ ∠ADC = 2 × 32° = 64°
Therefore, the required angle of the rhombus is ∠ADC = 64°.
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A ball of mass of 6kg rolls with a velocity of 10m/s and creates 300 Jules of kinetic energy.how much kinetic energy would a ball with a mass of 3kg and a velocity of 5m/s create
The value of kinetic energy will be 37.5 Jules.
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;
A ball of mass of 6kg rolls with a velocity of 10m/s and creates 300 Jules of kinetic energy.
Now,
Since, A ball of mass of 6kg rolls with a velocity of 10m/s and creates 300 Jules of kinetic energy.
Hence, The value of kinetic energy with a mass of 3kg and a velocity of 5m/s create will be;
⇒ Kinetic energy = 1/2 mv²
⇒ Kinetic energy = 1/2 × 3 × 5²
= 1/2 × 3 × 25
= 37.5 Jules
Thus, The value of kinetic energy will be 37.5 Jules.
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(3a2 – 5ab + b2) + (–3a2 + 2b2 + 8ab)
Which of the following shows the sum of the polynomials rewritten with like terms grouped together?
[3a2 + (–3a2)] + (–5ab + 8ab) + (b2 + 2b2)
[3a2 + (–3a2)] + (–5ab + 2b2) + (b2 + 8ab)
[3a2 + 3a2] + (5ab + 8ab) + (b2 + 2b2)
[3a2 + 3a2] + (5ab + 2b2) + (b2 + 8ab)
Answer:
(3a2 – 5ab + b2) + (–3a2 + 2b2 + 8ab)
Which of the following shows the sum of the polynomials rewritten with like terms grouped together?
[3a2 + (–3a2)] + (–5ab + 8ab) + (b2 + 2b2)
[3a2 + (–3a2)] + (–5ab + 2b2) + (b2 + 8ab)
[3a2 + 3a2] + (5ab + 8ab) + (b2 + 2b2)
[3a2 + 3a2] + (5ab + 2b2) + (b2 + 8ab)
The answer is A.
Step-by-step explanation:
How do you write 0.0045 in scientific notation?
Answer:
[tex]4.5 x 10^{-3} \\[/tex]Step-by-step explanation:
in the capgemini iot industry 4.0 case, what dimension focuses on the way that smart products are equipped with computing power that enables autonomous decision-making and self-learning processes based on algorithms?
The capgemini iot industry 4.0 case provide an entire end-to-end transformation, we encourage human-centered design and ground-breaking innovation.
The new era of digitization, known as smart industry, includes industry 4.0 but expands well beyond it. Disruptive technologies and data enable use cases that were not previously possible, such as multi-physics modelling, remote operations, digitization of products and processes, driver less cars, linked products, reinvented consumer experiences, and novel as-a-service business models.
We work with customers to uncover new business model options, address industry obstacles, and navigate complicated ecosystems so they can gain and maintain a competitive edge. Using our expertise in engineering, technology, IT, data, and consulting, we inject intelligence into our operations, products, and services. To provide an entire end-to-end transformation, we encourage human-centered design and ground-breaking innovation.
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How do you simplify (1/1+i)?
Answer:
1+i
Step-by-step explanation:
Divide by 1
(1/1+i)
(1+i)
Identify the components of the numbers and add the real and imaginary parts separately
=(1)+(1)i
=(1)+(1)i
=(1+i)
Construct the simplest polynomial with integer coefficients with the given roots:
3i, -2,2,0
The simplest polynomial with the given roots will be equal to x⁴ + 5x² - 36.
What is a Polynomial?
A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and raising non-negative integers to power, together with uncertainty and coefficients. x² + 4x + 7 is an illustration of a single indeterminate x polynomial.
The total of terms with the pattern [tex]kx^n[/tex] forms a polynomial. Where n is indeed a positive number and k is any number. For instance, the polynomial 3x + 2x - 5 exists.
As per the given information in the question,
The given roots are 3i, -2, 2
As we know that if 3i is a root then -3i is also a root.
Then, the factored form of this polynomial will be:
p(x) = (x - 3i)(x + 3i)(x + 2)(x - 2)
= (x - (3i)²) (x² -2x + 2x - 4)
It will become: (x² + 9)(x² - 4)
It can be further expanded,
x⁴ - 4x² + 9x² - 36
x⁴ + 5x² - 36
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BRAINLIEST TO BEST SOLUTION! The question is attached. THANK YOU FOR YOUR HELP!
Answer: not sure on this problem too
Step-by-step explanation:
sorry, can't really help!
The area of the circle is 66.50cm²
How to calculate the area of the circle?A circle is an object in which all distances are equal from the center.
In a circle, the length of the two tangents are equal.
From the figure, BP=CP
Also, the angles between a tangent and a radius is = 90⁰
⇒<OCP=90⁰
<PCB=<PBC=(180-60)/2 = 120/2 = 60⁰
Using cosine rule,
p²=b²+c²-2bccosP
p²=8²+8²-2*8*8*cos60
p²=64+64-128*0.5
p²=128-64
p²=64
Take the square root of both sides to get
p=√64=8
Note that CB=8 .....................(given)
Cx=8/2=4cm
Using trigonometric ratio
CosC = Adjacent/Hypotenuse
Cos30 = 4/CO
CO = 4/cos30
CO = 4/0.8660
CO = 4.6cm
CO = radius (r)
Area of circle = пr²
Area = 22/7 * 4.6 * 4.6
Area = 66.50 cm²
In conclusion, the area of the circle is 66.50cm²
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How do I find 2/3 of a whole number?
To find [tex]\frac{2}{3}[/tex] of a whole number, you can divide the number by 3 and then multiply the result by 2.
For example, if you want to find [tex]\frac{2}{3}[/tex] of the number 15, you can perform the following calculation:
[tex]\frac{2}{3}[/tex] × 15 = 10
This means that [tex]\frac{2}{3}[/tex] of the number 15 is equal to 10.
You can also find [tex]\frac{2}{3}[/tex] of a whole number by dividing the number by 3 and then multiplying the result by 2.
For example:
[tex]\frac{15}{3}[/tex] = 5
2 × 5 = 10
So, [tex]\frac{2}{3}[/tex] of the number 15 is also equal to 10.
Alternatively, you can find [tex]\frac{2}{3}[/tex] of a number by expressing it as a decimal. [tex]\frac{2}{3}[/tex] can be expressed as 0.6666666667, so you can multiply the whole number by 0.6666666667 to find [tex]\frac{2}{3}[/tex] of it. For example:
0.6666666667 × 15 = 10
So [tex]\frac{2}{3}[/tex] of the number 15 is equal to 10.
A whole number is a positive integer that is greater than 0, such as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc. Whole numbers do not include fractions, decimals, or negatives.
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at a store, 4% of the eggs are cracked. if you buy a dozen (12 eggs), what is the probability that at least 1 is cracked?
If at a store 4% of the eggs are cracked and you buy a dozen, then the probability that at least 1 is cracked is 0.916
The probability that the egg is cracked = 4%
= 0.04
The probability that the egg is not cracked = 1 - 0.04
= 0.96
Total number of eggs = 12 eggs
The probability that the one egg is cracked = 12 × 0.04 × (0.96)^11
= 0.306
The probability that 0 eggs are cracked = 1 × 0.04^0 × 0.96^12
= 0.61
The probability that at least 1 egg is cracked = 0.306 + 0.61
= 0.916
Therefore, the probability that at least 1 egg is cracked is 0.916
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HELP MEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!
In Diagram 2. find the value of x 119
The value of angle x that extends from the given polygon is 61°.
How to find the value of x?
If a line is divided into two angles, we can always find the other angle if we know the first, many angles on one side of a straight line can be handled with this method.Angles in a straight line are the total of all the angles that can be arranged in a straight line.Standing with your back to the North and turning to face East equals a 90° clockwise turn. If you turn 90 degrees more clockwise, you'll find yourself looking south. If you were to make two more turns like this, you would first face West and then North (the full turn). Therefore, a half turn is two lots of 90 degrees, or 180 degrees.A straight line's angles add up to 180 degrees.The angle of straight line will be 180°
119° + x = 180°
x = 180° - 119°
x = 61°
Hence, the value of x that extends from the given polygon is 61°.
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the volume of a room is 235 sq base area is 47 sq m find the hieght of room
Answer:
height = 5 m
Step-by-step explanation:
the volume (V) of a cuboid ( shape of room ) is calculated as
V = A h ( A is the area of the base and h the height )
here V = 235 and A = 47 , then
47h = 235 ( divide both sides by 47 )
h = 5 m
Answer:
volume= height * length * breadth = 235
area= length * breadth = 47
Step-by-step explanation:
47*height= 235
height=5sq
Find the vertex of the following function. Write your answer in the form (x, y).
Use the slash mark (/) as a fraction bar if necessary, but do not enter
decimals.
y = x² - 8x+12
Answer here
SUBMIT
The parabola's vertex has the equation y = x² - 8x + 12 is (4, -4).
Define parabola.A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line. A plane curve created by a point moving so that its distance from a fixed point equals its distance from a fixed line is known as a parabola. A normal parabola's standard equation is y 2 = 4 an x, where an is the distance from the vertex to the focus.
Given,
Function,
y = x² - 8x + 12
The supplied equation's vertex must be located.
The equation is a parabolic equation when we look at it.
We are aware that a parabolic equation's generic form is
y = x² - 8x + 12
where the parabola's vertex's x and y coordinates are denoted by h and k.
We can determine the following by comparing the aforementioned equation with the parabola's general form:
x = 4, y = 4 and h = -8
The parabola's vertex has the equation y = x² - 8x + 12 is (4, -4).
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