The greatest number of elements that s can have is 2002, and the set s = {1,2,3,4,5,...,2002}
The property of the set s states that for every element x in s, the arithmetic mean of the set obtained by deleting x from s is an integer.
To understand this property, we can start by considering the case when the set s has only two elements, say x and y. In this case, the arithmetic mean of the set obtained by deleting x from s is y, and the arithmetic mean of the set obtained by deleting y from s is x. As both x and y are integers, this property holds true.
When the set s has three elements, say x, y, and z. The arithmetic mean of the set obtained by deleting x from s is (y+z)/2. as y and z are integers, (y+z) is always even, thus (y+z)/2 is always an integer. The same applies to the arithmetic mean of the set obtained by deleting y and z.
As we can see, this property holds true for any set of distinct positive integers, no matter the number of elements.
Given that 1 belongs to s and that 2002 is the largest element of s, we can use the property of the set to find the greatest number of elements that s can have.
The arithmetic mean of the set obtained by deleting 1 from s is (x+y+z+...+2002)/(n-1) = (x+y+z+...+2002)/n + 1/n. as x, y, z... 2002 are integers, (x+y+z+...+2002) is always an integer, thus (x+y+z+...+2002)/n is always an integer. Then, as 1/n is always an integer, (x+y+z+...+2002)/n + 1/n is always an integer.
Therefore, the greatest number of elements that s can have is 2002, and the set s = {1,2,3,4,5,...,2002}
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For 2011, if foreign students comprise exactly 1/8 of the number of out-of-state undergraduates, indicate which could be the number of in-state undergraduates.
200
330
1320
The number of in-state undergraduates could not be 200.
What is foreign students comprise?International or foreign students are students who migrate to another country to pursue their studies and complete all or a portion of their postsecondary education there.
Each nation has its unique national educational system, which affects how "foreign students" and "international students" are defined.
If foreign students comprise exactly 1/8 of the number of out-of-state undergraduates, then the number of in-state undergraduates would have to be a value that yields an integer value for the number of foreign students.
In-state undergraduates are 55% of 60% of the total, or (.55)(.6) = (.33) of the total.
If 330 is the number of in-state undergraduates, which comprise 33% of the total, then you can calculate the total number of admitted students:
(0.33) (total) = 200
⇒ total = 200/0.33
⇒ total = 200*100/33
⇒ total = 606.06
So that The number of in-state undergraduates could not be 200.
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The correct question is with graph
For 2011, if foreign students comprise exactly 1/8 of the number of out-of-state undergraduates, indicate which could not be the number of in-state undergraduates.
200
330
1320
Help Solve the system of equations 2x+3y=02x+3y=0 and -4x-y=30−4x−y=30 by combining the equations. Look at screen shot im 14 thanks
The solution for the system of equations:
2x + 3y = 0
-4x - y = 30
is y = 7 and x = -10.5
How to solve the system of equations?
Here we want to solve the following system of equations:
2x + 3y = 0
-4x - y = 30
By combining the equations.
If we add two times the first equation and the second equation, we will get:
2*(2x + 3y) + (-4x - y) = 0 + 30
We can simplify that to get:
4x + 6y - 4x - y = 30
5y = 30
Now we can solve that for y.
y = 30/5
y = 7
Now to find the value of x, we can replace y by 7 in one of the equations of the system.
2x + 3*7 = 0
2x = -21
x = -21/2
x = -10.5
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converting 1,000 mg to 1 gram would require moving the decimal place ________ places to the left.
Converting 1,000 mg to 1 gram would require moving the decimal place zero places to the left.
Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters. By definition conversion of units means the conversion between different units and measurements of the same quantity done by the process of multiplication or division. In maths, conversion is the process of changing the value of one form to another for example inches to millimeters, or liters to gallons. Units are used for measuring length, measuring weight, measuring capacity, measuring temperature, and measuring speed.
If we want to calculate how many Grams are 1000 Milligrams we have to multiply 1000 by 1 and divide the product by 1000. So for 1000, we have (1000 × 1) ÷ 1000 = 1000 ÷ 1000 = 1 Gram.
So finally 1000 mg = 1 g
Thus, converting 1,000 mg to 1 gram would require moving the decimal place zero places to the left.
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is there end behavior for square root function? like for example: [tex]\sqrt{6x}[/tex] or [tex]\sqrt{x-5}-6[/tex]
Answer:
Step-by-step explanation:
Yes, there is an end behavior for a square root function. The end behavior of a square root function is determined by the sign of the leading coefficient of the equation. For example, if the leading coefficient is positive, then the end behavior will be asymptotic to the positive x-axis as x increases, and asymptotic to the negative x-axis as x decreases. Conversely, if the leading coefficient is negative, then the end behavior will be asymptotic to the negative x-axis as x increases, and asymptotic to the positive x-axis as x decreases.
calculer la longueur dun cercle de diametre 78mm
Answer:
La circunferencia es 245.044 mm
After Susanna parked her car she paid for 3/5 of an hour of parking. How many minutes did she pay for?
Answer:
To find out how many minutes Susanna paid for, we need to convert the fraction of an hour to minutes.
There are 60 minutes in an hour. So, to find out how many minutes 3/5 of an hour is, we can multiply 3/5 by 60:
3/5 * 60 = 36
Therefore, Susanna paid for 36 minutes of parking.
Answer:
36 minutes
Step-by-step explanation:
We need to convert hours to minutes and then multiply by a fraction.
1 hour = 60 minutes
3/5 of 60 minutes
3/5 * 60
180/5
36 minutes
8 hr 18min Divided by 5
Answer: 99.6 min
Step-by-step explanation:
Drina wrote the system of linear equations below : 3x - 2y +-2 | 7x+3y + 26 | -x - 11y +-46. Which type of matrix can be formed using this system of equations? A)a diagonal matrix B)a square matric C)a matrix with 3 rows and 4 columns D) a matrix with 4 rows and 3 columns
The square matrix can be formed using this system of equations option second is correct.
Matrix:
A matrix is a rectangular array of numbers, variables, symbols, or expressions defined for operations such as subtraction, addition, and multiplication. The size of a matrix (called matrix order) is determined by the number of rows and columns in the matrix. The order of a matrix with 6 rows and 4 columns is expressed as 6×4 and read as 6×4.
We have three linear equations:
3x - 2y = -2
7x + 3y = 26
-x -11y = 46
To solve the above equations we can use the matrix concept:
The matrix will be:
[tex]\left[\begin{array}{ccc}3&-2&-2\\7&3&26\\-1&-11&-46\end{array}\right][/tex]
The above matrix is a square matrix.
Square Matrix:
A square matrix is a matrix that has the same number of rows and columns. Its order is of the form n x n. The product of these rows and columns also gives the number of elements in a square matrix, so the number of elements in it is always a perfect square.
Thus, the square matrix can be formed using this system of equations option second is correct.
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5. If 1 tonne of coal cost $2000, what is the cost of 250kg of the same coal?
The cost of 250 kg of coal is 500 dollars.
How to find the cost of the coal?One tonne of coal cost $2000. The cost of 250kg of the same coal can be found as follows:
Let's convert the mass of the coal in kilograms to tonnes.
Hence,
1 kilogram = 0.001 tonnes
250 kilogram = ?
cross multiply
mass of the coal in tonnes = 0.001 × 250
mass of the coal in tonnes = 0.25 tonnes
Hence,
1 tonne = 2000 dollars
0.25 tones = ?
cross multiply
mass of 250 kg of coal = 0.25 × 2000
Therefore,
mass of 250 kg of coal = 500 dollars
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7 pengiuns for $188.88
Answer:
1 penguin = $26.97
Step-by-step explanation:
188.88/7=
26.971429 which approximately equals 26.97
Solve the following equation for m.
Show all work.
5m + 2 - 3.9m = 2.1(m — 3)
-
m=
A. - 4.2
B. -8.3
C. 8.3
D. no solution
The solution for "m" for the equation is 8.3.
What is an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
Expression: (Math Operator, Number/Variable, Math Operator)
Given expression
5m + 2 - 3.9m = 2.1(m — 3)
5m + 2 -3.9m = 2.1m - 3(2.1)
1.1m + 2 = 2.1m - 6.3
compare variables on one side and constant other,
2 + 6.3 = 2.1m - 1.1m
8.3 = m
Hence the value of m is 8.3.
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8 multilpy (3y mulitply 0.5)
Answer:
Step-by-step explanation:
8(3y + 0.5) so first we do 8 * 3 = 24y and 8 * 0.5 = 4. Then that becomes 24y = 4. so now we do 24y / 24 = y bc 24 cancels out, 4 / 24 = 0.166. So y = 0.166. HOPE THIS HELPS!!!
Simplity
√75
OA. 3√5
OB. 15√5
O c.
25√3
OD. 5√3
Simplifying √75 the answer is option D. 5√3.
Surd of numbers.An expression of a number which has a square root is termed surd. Some procedures are required to solve any given question on surd, especially when the given expression involves numbers that do not have a whole root.
To simplify √75 as required in the question, we have to look for a two numbers. One of these numbers must have a whole square root.
So that we can use 3 and 25.
Thus,
√75 = √(3 x 25)
= √3 * √25
= √3 * 5
= 5√3
√75 = 5√3
The answer is option D. 5√3
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four turns flipping a fair coin until a head appears. what is the probability that the first girl is the first to flip a head
The probability that the first girl is the first to flip a head is; 1/2.
What is the probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
We are given that if the number of toss required is odd as in one attempt represent odd number , we have following sequence of events
H, TTH, TTTTH.....
The required probability P will be as;
P = 1/2 + (1/2)³ + (1/2)⁵..........
As she flipped it in first go the probability is 1/2.
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Questions 2-5. Simplify each of the following.
2. (-1/3)(12)(-3/4)
3. 1/4(-8a + 4b)
4. (24x - 12y)(-1/6)
5. 1/2(4c - 6d) - 1/3(6c-9d)
there are 24 juice boxes in a pack, and 6 of them are fruit punch. what percent of the juice boxes are fruit punch?
a $300 trampoline is 25% off . what is the sale price of the trampoline ?
Answer: The sale price would be 225.00
The selling price of the trampoline will be $225.
The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that there is a 25% discount on the price $300. The discounted price will be calculated as:-
Discounted price = 300 x 0.75
Discounted price = $225
Therefore, the selling price of the trampoline will be $225.
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Jamie is an analyst at an education technology company. she gathered data on the results of a certain type of question. of the 2,000 re
she looked at, 1,092 responded correctly.
what equation could jamie use to calculate the margin of error at a 90% confidence interval?
0.454
2.58
1,092
1.96
2,000
0.546
1.65
(1-1
me=
reset
next
next
The 90% confidence interval's margin of error is 0.0183, and its success probability is 0.546.
What is margin of error?
The term "margin of error" refers to the probability or "chances of error" when selecting or computing a sample in a survey.
Jamie works as an analyst for a provider of educational technologies. She gathered information on the outcomes of a particular kind of query. 1,092 of the 2,000 replies she examined were accurate.
Here,
Number of samples, N=2000
Probability of responding correctly,
=1092/2000
=0.546
Z-score at 90% confidence level,
=1.645
Margin of Error ME,
=z*√(p*(1-p)/N)
=1.645*√(0.546*(1-0.546)/2000)
=1.645*√(0.546*0.454)/2000
=1.645*√(0.248/2000)
=1.645*√0.000124
=1.645*0.011
=0.0180
With a success rate of 0.546 percent, the margin of error for the 90% confidence interval is 0.0183.
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given the summary statistics below for the size of a sample of automobile engines, show how we can tell there are no outliers in the data set.?
There are a few ways to tell if a dataset contains outliers, one of which is by using summary statistics.
Outliers are data points that fall far outside of the main body of a dataset. They can have a significant impact on the overall summary statistics of a dataset, such as the mean and standard deviation.
Given the summary statistics below for the size of a sample of automobile engines:
Mean: 2.5
Median: 2.5
Mode: 2.5
Standard deviation: 0.5
We can tell that there are no outliers in the data set because the mean, median, and mode are all equal. This indicates that the values in the dataset are tightly clustered around a central value, which is a good indication that there are no outliers. Additionally, the standard deviation is relatively small, which also suggests that the values in the dataset are not spread out very much, again indicating that there are no outliers.
Another approach is using the interquartile range (IQR). This can be calculated by subtracting the 25th percentile (Q1) from the 75th percentile (Q3) of a dataset. Values that fall outside of the range of 1.5*IQR below the first quartile (Q1) or above the 3rd quartile (Q3) are considered outliers.
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how did the chapter 6 test go? ody, we will be taking a sample from a ppulation. we will use teh average from teh sample to estimate the avrage for the poulation
(a) Mean of given sample = 75
(b) Mean (60, 80) = 70
(c) All possible samples of size two are 6 (60,70), (60,80), (60,90), (70, 80), (70,90), (80,90) and means are 65, 70, 75, 75, 80, and 85 respectively.
The given sample is (60, 70, 80, 90)
(a) Mean of sample = (60+70+80+90)/4 = 300/4 = 75
(b) Mean of any 2 of scores
let's take (60,80)
mean(60,80) = (60+80)/2 = 70
(c) All possible samples of size 2 are
(60,70), mean(60,70) = 65
(60,80), mean(60,80) = 70
(60,90), mean(60,90) = 75
(70,80), mean(70,80) = 75
(70,90), mean(70,90) = 80
(80,90), mean(80,90) = 85
Therefore, for the given sample (a) Mean of the sample = 75, (b) Mean (60, 80) = 70, (c) All possible samples of size two are 6 (60,70), (60,80), (60,90), (70, 80), (70,90), (80,90) and means are 65, 70, 75, 75, 80, and 85 respectively.
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The complete question is:
How did the Chapter 6 test go? Today, we will be taking a sample from a population. We will use the average from the sample to estimate the average for the population. Let's start with a very simple example. My 5th period is very small. There were only 4 students who took the chapter 6 test. Their scores were: 60, 70, 80, and 90. Answer the following questions:
(a) Find the mean of the sample
(b) Take a sample of any 2 of the scores. Find the mean of your sample.
(c) Figure out all of the possible samples of size two. Calculate a sample mean for each sample of 2.
Coins are placed into a treasure chest, and each coin has a radius of 1.4 inches and a height of 0.0625 inches. If there are 230 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? Round to the nearest hundredth and approximate using π = 3.14.
0.38 in3
126.39 in3
353.88 in3
88.47 in3
Answer:
D. 88.47 in3
Step-by-step explanation:
The volume of a single coin would be the volume of a cylinder with a radius of 1.4 inches and a height of 0.0625 inches. The formula for the volume of a cylinder is V = πr^2h. So, V = 3.14 * (1.4^2) * 0.0625 = 0.38 in^3
Since there are 230 coins, the total volume of the coins would be 230* 0.38 = 87.40 in^3
So, the answer would be 87.40, which is closest to D. 88.47 in3
Answer: D: 88.47 in³
Step-by-step explanation:
So what you want to do is first find the individual volume of the coins. Use the volume formula: V = πr^2h
Take 1.4 and times it by itself
1.4 x 1.4 = 1.96
Now multiply 1.96 by 0.0625
1.96 x 0.0625 = 0.1225
And times 0.1225 by pi, or in this case, 3.14
0.1225 x 3.14 = 0.38465
Now you have found the individual volume of each coin. You are trying to find how much space all of the coins take up together. The question says that there is 230 coins in total. So times 0.38465 by 230 to find how much space all the coins take up.
0.38465 x 230 = 88.4695 in³
Now round it to the nearest hundredth: 88.47 in³
That is your answer.
Also I took the same test and I picked 88.47 inches cubed and got it right.
Proof:
Have a good day :)))
(2x-3y)(x+5y)=0 where x>0 and y>0
Find the ratio x:y
Give your answer in its simplest form.
Answer: [tex]3:2[/tex]
Step-by-step explanation:
Using the zero-product property, we know that [tex]2x-3y=0[/tex] or [tex]x+5y=0[/tex]. We can rearrange these cases to yield [tex]x=\frac{3}{2}y[/tex] and [tex]x=-5y[/tex].
However, since [tex]x[/tex] and [tex]y[/tex] have the same sign, we neglect the case [tex]x=-5y[/tex]. This means [tex]x=\frac{3}{2}y[/tex].
[tex]x=\frac{3}{2}y \implies \frac{x}{y}=\frac{3}{2} \implies x:y=3:2[/tex]
Answer: We can use the distributive property to expand the left side of the equation:
2xx + 2x5y - 3yx - 3y5y = 0
Then, combine like terms:
2x^2 + 10xy - 3xy - 15y^2 = 0
Now we can add 3xy + 15y^2 on both sides of the equation to get:
2x^2 + 10xy = 0
We know that x and y are positive, so we can divide both sides by 2:
x^2 + 5xy = 0
and since x>0, we can divide both sides by x:
x + 5y = 0
So the ratio x:y = x/(-5y) = -x/5y.
To simplify we can divide x by -x and 5y by 5y and get the final answer as
x:y = -1:
Step-by-step explanation:
a fair six-sided die with sides labeled 1 through 6 is rolled. quantity a quantity b the probability that the number rolled is closer to 4 than it is to 2 the probability that the number rolled is closer to 5 than it is to 3
On solving the provided question, we can say that probability that a four or higher number will first emerge on the third or fourth roll.= 4/27 + 8/81 = 20/21
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
On a dice, the numbers 5 and 6 are the ones above 4. The likelihood of receiving a number higher than 4 (i.e., 5 or 6) is = 2/6 = 1/3
and as a result, the likelihood of receiving 4 or less is= 1-1/3 = 2/3
The likelihood that a number larger than 4 will show up on the third roll is equal to
2/3* 2/3 * 1/3 = 4/27
The likelihood that a number larger than 4 will emerge on the fourth roll is equal to =2/3*2/3* 2/3 * 1/3 = 8/81
probability that a four or higher number will first emerge on the third or fourth roll.= 4/27 + 8/81 = 20/21
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which of the following expressions is equivalent to -4x^3-12x^3+9x^2
The expression that is equivalent to -4x³ -12x³ + 9x² will be -16x³ + 9x²
How to calculate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. The expression that is equivalent to -4x³ -12x³ + 9x² will be:
= -4x³ -12x³ + 9x²
= -16x³ + 9x²
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Find the value of fx) = 3x + 7 for x = 8.
Answer:
the value of f(8) is 31
Step-by-step explanation:
To find the value of f(x) = 3x + 7 for x = 8, we need to substitute 8 in for x in the equation and perform the arithmetic.
f(x) = 3x + 7
f(8) = 3(8) + 7
f(8) = 24 + 7
f(8) = 31
[tex]f(x)=3x+7[/tex] x = 8
Substitute 8 with x:
[tex]f(8)=3(8)+7[/tex]
[tex]f(8)=24+7[/tex]
[tex]\fbox{f(8) = 31}[/tex]
if we repeatedly toss a balanced coin, then, in the long run, it will come up heads about half the time. but what is the probability that such a coin will come up heads exactly half the time in 16 tosses
if we repeatedly toss a balanced coin, then, in the long run, it will come up heads about half the time. but the probability that such a coin will come up heads exactly half the time in 16 tosses is 1 in 65536 (2^16).
This can be calculated using the binomial probability formula which states that the probability of getting a certain number of heads in a certain number of tosses is given by (Number of ways to get the desired number of heads) / (Total number of possible outcomes). In this case, the number of ways to get 8 heads in 16 tosses is equal to 16C8, or 120.
The total number of possible outcomes is equal to 2^16, or 65536. Thus, the probability of getting 8 heads in 16 tosses is 120/65536, which is approximately equal to 1/65536.
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Seven times the first number plus six times the second number equals 31. Three times the first number minus ten times the second number is 29.
Answer:
1st number = 5.5
2nd number = -1.25
Step-by-step explanation:
1) 7x + 6y = 31 (multiply entire equation by 3) → 21x + 18y = 93
2) 3x - 10y + 29 (multiply entire equation by 7) → 21x - 70y = 203
3) 21x + 18y = 93
4) -(21x - 70y = 203) now subtract equation (4) from equation (3) to make the x terms drop out
0 + 88y = -110
y = -110/88 = -1.25 now plug this into equation (1) and solve for x
7x + 6(-1.25) = 31
7x = 38.5
x = 38.5/7 = 5.5
Elliot adds 15 ml of creamer to 240 ml of coffee. His creamer is 20%
milk fat.
How much pure milk fat has Elliot added to his coffee?
Answer:
▪ 20% of 15 ml
(20/100) × 15 ml = 3% pure milk fat
you choose a number with 3 digits from 0 to 9; the state chooses a three-digit winning number at random and pays you $500 if your number is chosen. Because there are 1000 numbers with three digits, you have probability 1/1000 of winning. Taking X to be the amount your ticket pays you, the probability distribution of X is
The probability distribution of X is given as follows:
P(X = 500) = 1/1000.P(X = 0) = 999/1000.How to define a probability distribution?A probability is defined as the division of the number of desired outcomes by the number of total outcomes.
A probability distribution gives the probability of all the possible outcomes in the context of a problem.
There are two outcomes for this problem, listed as follows:
Winning $500.Winning nothing = losing the game.Only one of the 1000 combinations are a winning combination, hence the probability distribution of X is given as follows:
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Please help with this one
The vertex of the quadratic equation:
f(x) = 2x^2 - 8
is (0, -8)
How to find the vertex of the quadratic equation?For a general quadratic equation:
a*x^2 + b*x + c
The vertex is located at the x-value:
x = -b/2a
Here we have the quadratic equation:
f(x) = 2x^2 - 8
Then the values are:
a = 2
b = 0
c = -8
Then the vertex is at:
x = 0/2*2 = 0
To get the y-value of the vertex, we need to evaluate on x = 0.
f(0) = 2*0^2 - 8 = -8
So the vertex is (0, -8).
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