Answer:
If the probability of getting a two on a biased dice is 0.1, then the probability of not getting a two is 0.9.
To find the expected number of times a two is rolled in 250 rolls:
Expected value = (probability of an event occurring) x (number of trials)
Expected number of twos = 0.1 x 250 = 25
To find the expected number of times a number other than two is rolled in 250 rolls:
Expected number of non-twos = 0.9 x 250 = 225
Therefore, we would expect to roll a two 25 times and a number other than two 225 times in 250 rolls of this biased dice.
Answer:
0.790, or 79%.
Step-by-step explanation:
If the probability of getting a two on a biased dice is 0.1, then the probability of not getting a two is 0.9.
We can use the binomial distribution to calculate the probability of getting a certain number of twos in 250 rolls of the dice. The formula for the binomial distribution is:
P(X = k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
P(X = k) is the probability of getting exactly k twos
n is the number of trials (250 rolls)
k is the number of successes (getting a two)
p is the probability of success (0.1)
(1-p) is the probability of failure (0.9)
C(n, k) is the number of ways to choose k successes from n trials (n choose k)
To calculate the probability of getting exactly k twos in 250 rolls, we plug in the values for n, k, p, and (1-p) into the formula:
P(X = k) = C(250, k) * 0.1^k * 0.9^(250-k)
We can use a calculator or a software program to find the probabilities for different values of k. Here are some examples:
The probability of getting no twos (k = 0) is P(X = 0) = C(250, 0) * 0.1^0 * 0.9^250 = 0.057
The probability of getting exactly one two (k = 1) is P(X = 1) = C(250, 1) * 0.1^1 * 0.9^249 = 0.153
The probability of getting at least two twos (k >= 2) is the complement of the probability of getting zero or one two:
P(X >= 2) = 1 - P(X = 0) - P(X = 1)
= 1 - 0.057 - 0.153
= 0.790
Therefore, the probability of getting at least two twos in 250 rolls of the biased dice is approximately 0.790, or 79%.
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If the lengths of the legs of a right triangle are 5 and 12, what is the length of the hypotenuse?
Select the correct answer.
A graph with a y-axis and an x-axis in positive and negative planes. A figure is formed M F G H I J K L is made by connecting points (-3,5), (8,5), (8,2), (3,2), (3,-5), (-8,-5), (-8,-2), and(-3,-2).
Eleanor is participating in a game show in which she has to complete a lap with seven different obstacles. The lap starts and ends at F. The obstacles are placed at points G, H, I, J, K, L, and M. What is the total length of the lap?
A.
52 units
B.
54 units
C.
56 units
D.
58 units
Thus, the total length of lap covered to get the seven different obstacles is found as: 52 units.
Define about the distance formula?the Pythagorean theorem is used to calculate the distance between two locations using the distance formula. The Pythagorean theorem can be rewritten as d = √((x2 - x1)²+(y2 - y1)²) to calculate the separation between any two locations.
Given data:
Points on y-axis and an x-axis are given,
M(-3,5), F(8,5), G(8,2), H(3,2), I(3,-5), J(-8,-5), K(-8,-2), and L(-3,-2).
Starting and ending point is F.
Points lies between the starting and ending are-
F ,G, H, I, J, K, L, M, F
Total length = sum of all length
d = √((x2 - x1)²+(y2 - y1)²)
FG = √((8 - 8)²+(2 - 5)²)
FG = √9
FG = 3
GH = √((8 - 3)²+(2 - 2)²)
GH = √25
GH = 5
HI = √((3 - 3)²+(2 + 5)²)
HI = √49
HI = 7
IJ = √((3 + 8)²+(-5 + 5)²)
IJ = √121
IJ = 11
JK = √((-8 + 8)²+(-2 - 5)²)
JK = √9
JK = 3
KL = √((-8 + 3)²+(-2 + 2)²)
KL = √25
KL = 5
LM = √((-3 + 3)²+(-2 - 5)²)
LM = √49
LM = 7
MF = √((8 + 3)²+(+5 - 5)²)
MF = √121
MF = 11
Total length = 3 + 5 + 7 + 11 + 3 + 5 + 7 + 11
Total length = 52 units
Thus, the total length of the lap covered to get the seven different obstacles is found as: 52 units.
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true/false: let a be an n \times n matrix. a is diagonalizable if it has n eigenvalues, counting multiplicities.
The given statement " let a be an n \times n matrix. a is diagonalizable if it has n eigenvalues, counting multiplicities." is False. Because Matrix has only one linearly independent eigenvector.
Having n eigenvalues, counting multiplicities, only guarantees that A is diagonalizable over the field of complex numbers, but not necessarily over other fields such as the real numbers. The correct statement is Let A be an n × n matrix. A is diagonalizable if and only if it has n linearly independent eigenvectors.
For example, the matrix:
A = [0 1; -1 0] hhggjjjhjhjhj
has eigenvalues i and -i, but it is not diagonalizable over the field of real numbers, since it has only one eigenvector which is also linearly independent. However, it is diagonalizable over the field of complex numbers. So, the given statement is false.
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0.
Ryan checked out 3 books from the library: one mystery (M), one history book (H), and one biography (B). Which tree diagram shows all the possible orders in which Ryan can read the 3 books?
...
This tree diagram shows all possible orders in which Ryan can read the 3 books, including reading the mystery book (M) first, the history book (H) second, and the biography (B) last, as well as reading the biography first, the mystery second, and the history last.
What is mystery?Mystery is an intriguing and often baffling phenomenon or situation. It is something that is not easily explained or understood and often involves a puzzle or secret that needs to be solved. It can be an event, an entity, or a situation that evokes curiosity, suspense, and a desire to uncover the truth. Mystery can be found in everyday life, literature, films, and other forms of entertainment. It is often used to create a sense of anticipation and wonder, and can be a powerful tool in storytelling. Mystery can also be used to explore deeper truths and to connect with our own inner mysteries.
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Complete Question is attached below:
the sides of a square are growing at a rate of 3 inches per minute. how fast is the area increasing when each side is 5 inches long?
24 centimeters. Hope this helped!
What is the probability that a random sample of 52 pregnancies has a mean gestation period of 222 days or less?The probability that the mean of a random sample of 52 pregnancies is less than 222 days is approximately ____. (Round to four decimal places as needed.)
The probability that the mean of a random sample of 52 pregnancies is less than or equal to 222 days is approximately 0.0005 (rounded to four decimal places).
Let's discuss it further below.
To solve the problem, we use the z-score formula, which is as follows:
z=(X−μ)/σX = sample mean = 222 days
μ = population mean = 226 days
σ = standard deviation of the population = 15 days
n = sample size = 52
To find the probability, we need to convert the sample mean to a z-score, which is calculated as follows:
z=(X−μ)/σ=(222−226)/(15/√52)=−4/2.096=−1.91
Now we need to find the probability that a random sample of 52 pregnancies has a mean gestation period of 222 days or less, which is equivalent to finding the probability that a z-score is less than or equal to −1.91.
Using a z-table or calculator, we find that the probability of a z-score being less than or equal to −1.91 is approximately 0.0005 (rounded to four decimal places).
Therefore, the answer is 0.0005.
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Need help
With this answer
The value of x in the given triangle is 2.44 units.
What are similar triangles?If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable.
Similar figures are described as items with the same shape but varying sizes, such as two or more figures. While both have the same form, the sizes may vary. Each pair of comparable angles are equal. Similar equivalent side ratios exist.
Given that, LM bisects angle JLK.
Thus, angle JLM = angle MLK.
The two triangles triangle JKL and triangle MLK are similar using AA criteria.
Since, the two triangles are equal the ratio of their sides are equal.
Using Pythagoras theorem in triangle MLK we have:
LM² = 4² + 8²
LM = 8.9
Now, using the ratio:
x + 3 / 8.9 = x / 4
4x + 12 = 8.9x
12 = 4.9x
x = 2.44
Hence, the value of x in the given triangle is 2.44 units.
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pls help Mariah sells her paintings which she frames using pieces of wood that are 1 inch wide . Her paintings come in difference sizes , but the width is always 1.5 times the height Write an equation to represent the total area of her paintings and their frames .
if u can pls draw the height and width :)
Step-by-step explanation:
Lets use A for area, W for width, and H for height (sorry in advance for bad handwriting, I am writing using a mouse)
Since area is equal to width times height, lets make an equation given what we already know.
A = W * H
Now lets use the given parameters to create a proper area equation, partially answering the question.
A = (H*1.5) * H, H*1.5 being the width
Now we have the frames to add to this equation
Since these frames are 1 inch thick, this adds one inch to the width and the height.
You use order of operations to assume that we are calculating this by multiplying the height by 1.5 first, then adding the one inch to the width and height.
So our final equation is:
A = ((h*1.5)+1) * (h+1)
Lets give some example values
Height is 6, width is 6*1.5, meaning width is 9
After, we add one to the height and the width, meaning the height is 7 and the width is 10.
Lets multiply these together, and the total square area is 70 inches squared.
a nation had a birth rate of 20 in 1990. the rate fell to 13 in 2000. what was the percentage change?
The percentage change in the birth rate of a nation from 1990 to 2000 is -35%.
Percentage change is the relative difference between two values expressed as a percentage of one of the values, where the value of the latter is used as the reference point.
It can be calculated by using the following formula:
Percentage change = ((new value - old value) / old value) x 100
Given the birth rate of a nation in 1990 as 20 and the birth rate in 2000 as 13, the percentage change can be calculated as follows: Percentage change = ((13 - 20) / 20) x 100= (-7 / 20) x 100= -0.35 x 100= -35%
Hence, the percentage change is -35%.
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license plates are made using 2 letters followed by 2 digits. how many plates can be made if repetition of letters and digits is allowed?
The number of license plates that can be made if repetition of letters and digits is allowed is:
67,600
How to determine the number of plates when repeating the letters and numbers?Can be found by multiplying the number of possibilities for each position.
License plates are made using 2 letters followed by 2 digits. In this case, repetition is allowed, which means that each of the 2 letters can be any of the 26 letters of the English alphabet, and each of the 2 digits can be any of the 10 digits from 0 to 9. Thus, the total number of possible license plates can be found by multiplying the number of possibilities for each position.
There are 26 choices for each of the two letter positions, and 10 choices for each of the two digit positions, so the total number of possible license plates is:
26 x 26 x 10 x 10 = 67,600
Therefore, there are 67,600 plates that can be made if repetition of letters and digits is allowed.
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Use the right triangle below to answer the following question. What is the value of x? Enter the answer in the box. degrees
The value of the angle x is 30 degrees
What are trigonometric identities?Trigonometric identities are identified as those equalities of a function holding that all of the values in the given function, equation or expression are true.
There are distinct trigonometric identities. They are enumerated thus;
sinetangentcotangentsecantcosecantcosineNote that the sine identity is represented as;
sin θ = opposite/ hypotenuse
Opposite of angle x = 48cm
Hypotenuse = 96cm
Substitute the values
sinx =48/96
sin x = 0. 5000
Take sine inverse
x = 30 degrees
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one side of a triangle is 5 and the altitude to that side is 12. another side of the triangle is 13. can you tell what the length of the altitude to that side of the triangle is? if not, why not? if so, show what it is.
12
Yes, it is possible to calculate the length of the altitude to the other side of the triangle. To do so, use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this triangle, the hypotenuse is the side of length 13 and the other two sides are the side of length 5 and the altitude to it. So, the equation to use is:
132 = 52 + altitude2
Solving for altitude gives:
altitude2 = 132 - 52
altitude2 = 169 - 25
altitude2 = 144
altitude = √144 = 12
Therefore, the length of the altitude to the side of the triangle with length 13 is 12.
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Graph the line passing through (−4,−1) whose slope is m=−45
Step-by-step explanation:
y=mx+b
let(-4,-1)
x. y
then lets fill it with the formula
-4=-45(-1)+b
-4=45+b
-b=45+4
-b=49
b=-49
for each model, choose categorical or numeric for the explanatory and response variables. for simple linear regression, the explanatory variable is
For simple linear regression, the explanatory variable is numeric.
What is simple linear regression?Simple linear regression is a statistical method that allows researchers to understand the relationship between two continuous variables. A simple linear regression model is used to represent the relationship between a dependent variable (Y) and an independent variable (X) by making a linear equation of the form
Y = a + bX, where a is the constant, and b is the regression coefficient.
In simple linear regression, the explanatory variable is of numeric type. This statistical method involves the use of two numeric variables, namely the explanatory (independent) variable and the response (dependent) variable, which are analyzed to establish a linear relationship between them.
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housing costs: a government report on housing costs says that single-family home prices nationwide are skewed to the right, with a mean of $235,700. a. we collect price data from a random sample of 50 homes in orange county, california. why is it okay to use these data for inference even though the population is skewed?
It is fine to use these data because the price sample is random so bias will not interfere with the results.
Why is it okay to use this data?Based on the information, we can infer that it is correct to use the data from this sample because it is random, that is, it does not have a defined order. Therefore, it is not necessary to take bias into account because it will not have any influence on the results.
In accordance with the above, it would be incorrect to take the data from a non-random sample because information would be prioritizing and this would cause the results to be blinded.
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Suppose a medical researcher constructs a mathematical model describing the size of a lesion. The model that describes the diameter of a lesion in cm as function of time(days) is given by D(t)= (t-10)^2 ; 0
The graph of the equation is a parabola with its vertex at (10, 0), and it can also be used to calculate the diameter of the lesion for any given time.
Suppose a medical researcher constructs a mathematical model describing the size of a lesion. The model that describes the diameter of a lesion in cm as function of time(days) is given by [tex]D(t)= (t-10)^2[/tex]; 0. We will solve this problem by finding the answer step by step. FunctionThe function of the lesion's size over time is provided by the equation D(t)= (t-10)2, where t is the time in days and D(t) is the diameter of the lesion at the time t.
The origin of this equation is given by D(t) = f(t), where the variable t represents the independent variable, and the variable D(t) represents the dependent variable. To calculate the diameter of the lesion over time, substitute values of t into the equation D(t) = (t-10)2. When t = 0, for instance, D(0) = (0-10)2 = 100. This means that the lesion's diameter at time zero is 100cm.
The model's interpretation The mathematical model that describes the diameter of a lesion as a function of time was created by a medical researcher. The equation D(t) = (t-10)2 represents this model. The researcher's model indicates that the diameter of the lesion is equal to the square of the difference between the time and ten. The difference between the time and ten is squared, which means that the model represents a parabolic curve.
The question is, "Suppose a medical researcher constructs a mathematical model describing the size of a lesion. The model that describes the diameter of a lesion in cm as a function of time (days) is given by D(t)= (t-10)^2; answer in 200 words."
The given equation is a quadratic function, which is expressed as[tex]D(t)= (t-10)^2.[/tex]This means that the diameter (D) of the lesion is dependent upon the time (t) that has passed since the lesion's onset. Specifically, the diameter of the lesion will increase as the time since onset increases.
The graph of this equation will be a parabola with its vertex at (10, 0). This is because, when t=10, the diameter of the lesion (D) will be zero. As t increases, the graph will move up and to the right, forming a parabola with a positive slope.
In addition to describing the diameter of the lesion as a function of time, the equation also allows us to calculate the diameter of the lesion for any given time. To do this, we can plug in the desired time value for t, and calculate the resulting diameter.
For example, if the medical researcher wants to determine the diameter of the lesion when t=15 days, they can plug in 15 for t, and calculate that the diameter of the lesion at that time is 25 cm. This can be found by plugging in 15 for t and calculating [tex]D(15)=(15-10)^2[/tex]=25 cm.
In conclusion, the equation[tex]D(t)= (t-10)^2.[/tex]is a quadratic function that describes the diameter of a lesion in cm as a function of time (days). The graph of the equation is a parabola with its vertex at (10, 0), and it can also be used to calculate the diameter of the lesion for any given time.
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If you have 4 purple marbles and 8 yellow marbles in a bag, what is
the probability of getting a purple marble ?
Answer: 1/3
Step-by-step explanation:
4 + 8 = 12 so there's 12 marble in the bag and only 4 purple ones. so the probability is 4/12 which we can simplify to 1/3
what percentage of fat are in a 200 calorie peanut butter sandwich if the total amount of calories of fat are 80 calories?
The percentage of fat in a 200 calorie peanut butter sandwich is 40%.
To find the percentage of fat in a 200 calorie peanut butter sandwich if the total amount of calories of fat are 80 calories, we need to use the formula:
Percentage of fat = (Calories of fat / Total calories) x 100
Let's substitute the given values in the above formula:
Calories of fat = 80
Total calories = 200
Percentage of fat = (80/200) x 100 = 40%
Therefore, the percentage of fat in a 200 calorie peanut butter sandwich is 40%.
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Oliver practices the piano 448 minutes in 4 weeks. At what rate did she practice, in
minutes per day?
Answer:
16
Step-by-step explanation:
First you figure out how many days are in 4 weeks which is 28. Then you do 448 divided by 28 which equals 16. There's your answer.
The transformation shown is a translation.
IN
True
False
****
True, the image shows a transformation where the figure has been moved to a different position while maintaining its size and shape.
what is a triangle?
A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles. It is one of the most basic and fundamental shapes in geometry.
The image shows a transformation where the figure has been moved to a different position while maintaining its size and shape. This type of transformation is called a translation, which involves sliding an object in a particular direction without changing its size or shape.
To perform a translation, we need to know how far the object has been moved horizontally and vertically. In the image, we can see that the blue triangle has been moved 2 units to the right and 3 units up. We can represent this translation using vector notation, where the vector (2, 3) represents the horizontal and vertical distances that the triangle has been moved.
Therefore, true the image shows a transformation where the figure has been moved to a different position while maintaining its size and shape.
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What is the vertical distance between (2, 11/3)
and (2, - 4/3)?
The vertical distance between (2, 11/3) and (2, -4/3) is -5 units.
Define distance formulaThe distance formula is a mathematical equation used to find the distance between two points in a plane. It is derived from the Pythagorean theorem and is expressed as:
d = √((x₂- x₁)²+ (y₂ - y₁)²)
The distance formula can also be extended to three-dimensional space by adding an additional term to the equation.
The two points (2, 11/3) and (2, -4/3) have the same x-coordinate, which means they lie on a vertical line. To find the vertical distance between these two points, we simply subtract their y-coordinates:
Vertical distance = (y-coordinate of second point) - (y-coordinate of first point)
= (-4/3) - (11/3)
= -15/3
= -5
Therefore, the vertical distance between (2, 11/3) and (2, -4/3) is -5 units. Since this is a negative value, it means that the second point is located 5 units below the first point.
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Please help me on a math problem it’s for a grade
Thank You
Answer:
Angle 4 and angle 8 are corresponding angles because they are the same angle on the same side.
what is the probability that the person selected will be someone whose response is never and who is a woman?
The probability that the person selected will be someone whose response is never and who is a woman is 3/7.
The probability that the person selected will be someone whose response is never and who is a woman can be found by using conditional probability.What is conditional probability?Conditional probability is the likelihood of an event occurring given that another event has already occurred. The probability of event A happening given that event B has already occurred is known as conditional probability.Mathematically, the formula for conditional probability is:P(A|B) = P(A ∩ B) / P(B)Where,P(A|B) represents the probability of event A given that event B has already occurred.P(A ∩ B) represents the probability of both A and B occurring.P(B) represents the probability of event B occurring.The given scenario states that the person selected should have two attributes: the response never and the gender woman. Let A be the event that the person selected has a response never and B be the event that the person selected is a woman. Therefore, we need to find the probability of event A given event B.P(A|B) = P(A ∩ B) / P(B)Therefore, we need to find the probability of both A and B occurring and the probability of event B occurring.P(B) = 70/120P(B) = 7/12There are 50 women in the group. The number of women who have never responded is 30. Therefore,P(A ∩ B) = 30/120P(A ∩ B) = 1/4Therefore,P(A|B) = P(A ∩ B) / P(B)P(A|B) = 1/4 / 7/12P(A|B) = 3/7The probability that the person selected will be someone whose response is never and who is a woman is 3/7.
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Ashok gets an increase of 4% in his weekly salary. In addition to that, he gets ₹ 75 per week. If his present salary is ₹ 2,500 per week, what will be his new salary next week?
Answer:
Ashok's salary increases by 4%, which means his new salary will be:
New salary = Old salary + (4% of old salary)
New salary = 2500 + (4/100) * 2500
New salary = 2500 + 100
New salary = 2600
In addition to the increase, Ashok also gets an extra ₹75 per week, so his new salary will be:
New salary = Old salary + Increase + Extra amount
New salary = 2500 + 100 + 75
New salary = ₹ 2675 per week
Therefore, Ashok's new salary next week will be ₹ 2,675 per week.
Ranko bought two dozen eggs at the store. On the way home Ranko dropped the eggs and broke 3/4 of them. How many eggs broke
Answer:
Step-by-step explanation:
9 eggs broke
a small cube with side length 6y is placed inside a larger cube with side length . what is the difference in the volume of the cubes?
The difference in the volume of a small cube with a side length 6y is placed inside a larger cube with a side length is 5616y³
To find: the difference in the volume of the cubes.
Let the length of the larger cube be x.
So, the volume of the smaller cube is (6y)³ and the volume of the larger cube is x³.
As the smaller cube is placed inside the larger cube, it means that its side length is equal to the side length of the smaller cube plus twice the side length of the smaller cube.
So, x = 6y + 2(6y) = 18y.
The volume of the smaller cube = (6y)³ = 216y³
The volume of the larger cube = x³ = (18y)³ = 5832y³.
So, the difference in volume
= Volume of the larger cube - Volume of the smaller cube
= 5832y³ - 216y³
= 5616y³.
Therefore, the difference in the volume of the cubes is 5616y³.
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describe the difference between intersect and union, including the purposes for which they are used.
The intersection of two sets is the set of elements that are common to both sets, while the union of two sets is the set of elements that are in either of the two sets. Intersection and union are two of the most important operations in set theory and are used for a variety of purposes.
The purpose of the intersection operation is to find common elements between two sets, such as the common elements in two groups of people. The intersection operation produces a new set, which contains only the elements that are in both sets.
The purpose of the union operation is to join two sets together. The union operation produces a new set, which contains all the elements that are in either of the two sets. This is useful when you want to combine two different sets of data.
In summary, the intersection operation finds the common elements between two sets, while the union operation combines two sets of data into one. Both operations are important in set theory and are used for a variety of purposes.
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Identify all expressions below that are polynomials.
Answer:
All the expressions except d are polynomials.
Which equation of f(x) reveals the minimum or maximum value of f(x) without changing the form of the equation?
In option C, we can see that the equation is in vertex form.
What is parabola ?
A parabola is a symmetrical U-shaped curve formed by the graph of a quadratic function. It is a type of conic section that results from the intersection of a cone and a plane that is parallel to one of the sides of the cone. A parabola can also be defined as the set of points in a plane that are equidistant from a fixed point called the focus and a fixed line called the directrix. Parabolas have many applications in physics, engineering, and mathematics, including projectile motion, antenna design, and optimization problems.
According to the question:
The equation that reveals the minimum or maximum value of f(x) without changing the form of the equation is C f(x)=(x-2)²-16.
This equation is in vertex form, which is f(x) = a(x-h)² + k. In this form, the vertex of the parabola is at the point (h, k), and the value of "a" determines whether the parabola opens upwards or downwards.
In option C, we can see that the equation is in vertex form, where the vertex is (2, -16). Therefore, the minimum value of f(x) is -16, which occurs at x=2.
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What is the median for 5, 7, 24, 3, 6, 4, 4, 30, 19
There is only one middle number because the collection has an odd number of numbers. Since six is the midpoint, six represents the median.
what is median ?When a dataset is sorted from lowest to highest, the median, a measure of central tendency, reflects the midpoint value of the dataset. The values are first presented from lowest to greatest in order to get the median of a set of data. The median is the middle value when there are an odd number of values. Use the following data set as an example: 5, 7, 24, 3, 6, 4, 4, 30, 19. We first organise the data in order before calculating the median: 3, 4, 4, 5, 6, 7, 19, 24, 30
The dataset contains 9 values, which is strange. The middle value, which is six, is therefore the median.
given
We must first arrange the numbers in ascending order in order to determine the median of the group:
3, 4, 4, 5, 6, 7, 19, 24, 30
The median will be the middle number as there are nine numbers in this collection.
There is only one middle number because the collection has an odd number of numbers. Since six is the midpoint, six represents the median.
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