Answers
Answer:
g(y) = √(3/2 y)
Step-by-step explanation:
To find the inverse of a function, we need to solve for x in terms of y and interchange x and y. That is, we need to write the given function f(x) = 2/3x^2 in the form y = 2/3x^2 and then solve for x in terms of y.y = 2/3x^2
Multiplying both sides by 3/2, we get:
3/2 y = x^2
Taking the square root of both sides, we get:x = ± √(3/2 y)
Note that we have two possible values of x for each value of y, because the square root can be either positive or negative. However, for a function to have an inverse, it must pass the horizontal line test, which means that each value of y can only correspond to one value of x.Therefore, we need to restrict the domain of the original function to ensure that it is one-to-one. The simplest way to do this is to take the range of the function and use it as the domain of the inverse function.The range of f(x) = 2/3x^2 is all non-negative real numbers, or [0, ∞). Therefore, we can define the inverse function g(y) as:
g(y) = ± √(3/2 y)
where we choose the positive square root to ensure that the function is one-to-one.Thus, the inverse of the function f(x) = 2/3x^2 is:
g(y) = √(3/2 y)
with domain [0, ∞).
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Related Questions
find the following answer
Answers
The cardinality of set from the given vein diagram is found as 2.
Explain about the cardinality of set?Think about set A. The set A is said to be finite and so its cardinality is same to the amount of elements n if it includes precisely n items, where n ≥ 0. |A| stands for the cardinality of such a set A.
It turns out that there are two kinds of infinite sets that we need to determine between since one form is much "bigger" than the other. Particularly, one type is referred to as countable and the other as uncountable.
From the given figure
Set A = {8 , 8, 3, 6}
Compliment of Set B (elements not present in set B):
Set [tex]B^{c}[/tex] = {8, 8, 6(pink), 3(white)}
Thus,
(A∩ [tex]B^{c}[/tex] ) = {8, 8} (present in both set)
n (A∩ [tex]B^{c}[/tex] ) = 2 (cardinal number)
Thus, the cardinality of the set from the given vein diagram is found as 2.
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Brianna Wallen lives in Denver, Colorado, where the rate of assessment is 29% of market value. The tax rate is 81.16 mills. The county tax assessor determined that the market value of her home is $438,300. What is the real estate tax on her home?
Step 1 Find the assessed value. Step 2 Express the tax rate as a decimal. Step 3 Find the real estate tax
Answers
The real estate tax on Brianna Wallen's home is $37,934.83.
What is property tax?Property owners, including homeowners, are subject to a tax based on the assessed value of their properties. It is often collected by local governments and used to pay for amenities like public transportation, roads, and security.
The assessed value of the property and the tax rate are used to determine the amount of property tax due. The assessed value of a property is its worth as established by a government assessor and may be based on a number of variables, including recent sales prices of nearby properties, the price to replace the property, and the property's condition.
The tax is calculated using the given formula:
Tax = (Assessment Rate x Market Value) x (Tax Rate / 1000)
Substituting the given values we have:
Tax = (0.29 x $438,300) x (81.16 / 1000)
Tax = $37,934.83
Hence, the real estate tax on Brianna Wallen's home is $37,934.83.
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label each example with the type of variable that best represents it. labels can be used more than once.
Answers
Answer:
Step-by-step explanation:
pseudoinverse [[1,1,0,1],[1.5,0.5,0,1],[2,1,0,1],[2.5,2,0,1],[0,0,0,1],[0,0,0,0.5],[0,0,2,1],[0,0,2.5,2]]
Answers
The pseudoinverse of the given matrix is:A+ = [tex][[-2.00, 0.50, 0.00, -1.00][/tex], [ [tex]0.00, -1.00, 0.00, 1.00], [ 1.00, -0.50, 0.00, 0.00], [ 0.50, -0.50, 0.00,[/tex][tex]0.00], [ 0.00, 0.00, 0.50, 0.00], [ 0.00, 0.00, -2.00, 1.00], [ 0.00, 0.00, 0.75, -0.50], [ 0.00, 0.00, -1.50, 1.00]].[/tex]
The Moore-Penrose pseudoinverse is a tool used to solve a system of linear equations when the rank of the matrix is less than the number of columns. When a matrix has a rank that is less than the number of columns, it is said to be "singular", meaning that it has no unique solution. To solve this problem, the Moore-Penrose pseudoinverse uses a combination of inverse matrix and transpose matrix operations to calculate a solution that is as close as possible to the true solution. The pseudoinverse is defined mathematically as[tex]A+ = (A*A)^-1A*,[/tex] where A is the original matrix and A* is its transpose. The pseudoinverse of the given matrix is:A+ = [[-2.00, 0.50, 0.00, -1.00], [ 0.00, -1.00, 0.00, 1.00], [ 1.00, -0.50, 0.00, 0.00], [ 0.50, -0.50, 0.00, 0.00], [ 0.00, 0.00, 0.50, 0.00], [ 0.00, 0.00, -2.00, 1.00], [ 0.00, 0.00, 0.75, -0.50], [ 0.00, 0.00, -1.50, 1.00]].It is calculated by taking the inverse of the matrix multiplication of the transpose of the matrix and the original matrix, and then multiplying that by the original matrix transpose. This process allows for the calculation of the closest solution possible to the original set of equations given by the matrix.
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Why is the following not a probability? model?
LOADING...
Click the icon to view the data table.
Determine why it is not a probability model. Choose the correct answer below.
A.
This is not a probability model because at least one probability is greater than 0.
B.
This is not a probability model because at least one probability is greater than 1.
C.
This is not a probability model because the sum of the probabilities is not 1.
D.
This is not a probability model because at least one probability is less than 0
Answers
The correct answer is C. This is not a probability model because the sum of the probabilities is not 1.Therefore, the sum of the probabilities must be equal to 1 for a set of probabilities to be considered a probability model.
What is probability?Probability is a measure of the probability of an event, expressed as a number between 0 and 1.
For example, the probability of rolling a 6 on a fair six-sided die is 1/6 or approximately 0.17.
In order for a set of probabilities to represent a probability model, the sum of all the probabilities must be equal to 1. This ensures that there is a 100% chance that one of the possible outcomes will occur.
If the sum of the probabilities is less than 1, then there is a possibility that none of the outcomes will occur.
If the sum of the probabilities is greater than 1, then there is a possibility that more than one outcome will occur, which is not possible in a probability model.
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the value of the given test statistic lies between the given cutoffs -2.58 and 2.58. it falls in acceptance region.
Answers
Here the values -0.94 and 2.12 falls between the points -2.58 and 2.58. The area between is the acceptance region. So we cannot reject the null hypothesis.
The given is an example for two tailed test. A two tailed test is used to determine whether the value is greater than or less than the mean value of the population. It represents the area under both tails or sides on a normal distribution curve.
Here the value of the test statistic lies between -2.58 and 2.58. So the values less than -2.58 and greater than 2.58 fall in the rejection region, where the null hypothesis can be rejected.
a) -0.94 falls between -2.58 and 2.58. So it is in the acceptance region. So null hypothesis is accepted.
b) 2.12 lies between -2.58 and 2.58. It is also in acceptance region. So null hypothesis is accepted.
So in both cases null hypothesis cannot be rejected.
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The complete question is :
f the cutoffs for a z test are -2.58 and 2.58, determine whether you would reject or fail to reject the null hypothesis in each of the following cases and explain why:
a. z = −0.94
b. z = 2.12
Use the diagram shown. Lines p and q are parallel.
How many degrees is the measure of ∠4?
Answers
Answer:
61°
Step-by-step explanation:
∠4 is the vertical angle to the 61° angle. This means they will have the same measure, so ∠4 is 61°.
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Penelope and Artemis worked a total of 70 hours this week. Penelope worked 2 hours less than twice what Artemis worked.
1) Let P= hours Penelope worked and A= hours Artemis worked. Write a system of equations for this scenario.
2) Determine how many hours Penelope and Artemis worked.
Answers
Answer:
P + A = 70
2P = A + 2
1) P + A = 70
2P = A + 2
2) Solve the system of equations:
Subtract P from both sides of the first equation:
A = 70 - P
Substitute A for 70 - P in the second equation:
2P = (70 - P) + 2
Simplify:
2P = 72 - P
Add P to both sides of the equation:
3P = 72
Divide both sides of the equation by 3:
P = 24
Substitute P for 24 in the first equation:
A = 70 - 24
A = 46
Penelope worked 24 hours and Artemis worked 46 hours.
Rae's unpaid credit card balance was $1,603. Her APR is 28.6%. What is her new
balance after she makes one new transaction for $51? Round answer to the
hundredths place. If answer doesn't have a hundredths place then include a zero so
that it does. Use a word not a symbol for the units.
Answers
$2010.458 is her new balance after she makes one new transaction for $51.
What does a credit balance mean?
The amount that the credit card company owes you is shown as a credit balance on your billing statement. Each payment you make results in credits being added to your account.
When you return something you purchased with your credit card, you can receive an additional credit.
Credit balance = $1,603
APR = 28.6%
= 28.6% * $1,603
= 458.458
Credit balance = $1,603 + 458.458
= $2061.458
net balance = $2061.458 - 51
= $2010.458
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For the graph, find the average rate of change on the intervals given
See attached picture
Answers
The average rate of change on the intervals [0, 3], [3, 5], [5, 7], and [7, 9] are 2, -1.5, 1, and -1.5, respectively.
What is the average rate in math?It expresses how much the function changed per unit on average during that time period. It is computed by taking the slope of the straight line connecting the interval's endpoints on the function's graph.
To calculate the average rate of change for the intervals shown in the graph, we must first determine the slope of the line connecting the endpoints of each interval.
0-3 interval:
Because the interval's endpoints are (0, 1) and (3, 7), the slope of the line connecting them is:
slope = (y change) / (x change) = (7 - 1) / (3 - 0) = 2
pauses [3, 5]:
Because the interval's endpoints are (3, 7) and (5, 4), the slope of the line connecting them is:
slope = (y change) / (x change) = (4 - 7) / (5 - 3) = -1.5
[5–7] Interval:
Because the interval's endpoints are (5, 4) and (7, 6), the slope of the line connecting them is:
slope = (y change) / (x change) = (6 - 4) / (7 - 5) = 1
Interval 7 and 9:
Because the interval's endpoints are (7, 6) and (9, 3), the slope of the line connecting them is:
slope = (y change) / (x change) = (3 - 6) / (9 - 7) = -1.5
As a result, the average rate of change on the intervals [0, 3], [3, 5], [5, 7], and [7, 9] is 2, -1.5, 1, and -1.5.
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Jamie is going to run for
1
2
2
1
start fraction, 1, divided by, 2, end fraction of an hour at a constant rate, and they want to plan what that rate will be.
1. Write an equation that represents the distance Jamie will run in kilometers (
�
dd) at a rate of
�
rr kilometers per hour.
Answers
The distance Jamie will run is equal to half of the rate in kilometers per hour, the equation is d = r (1/2)
What is speed and velocity?Speed is a scalar number that represents the rate of movement of an item. It is described as the distance covered in a certain amount of time, regardless of direction. In contrast, velocity is a vector quantity that accounts for both speed and direction. It is characterised as the pace at which an item shifts in a certain direction. In physics, the idea of velocity is crucial since it aids in explaining how an object's location varies over time and is used to compute other crucial variables like acceleration and momentum.
The distance is calculated using the given formula:
Distance = rate (time)
Given that, the time is 1/2 hour thus:
d = r (1/2)
Thus, the distance Jamie will run is equal to half of the rate in kilometers per hour, and the equation is d = r (1/2).
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A and B are mutually exclusive.
P(A) = 0.2, P(B) = 0.5. Find P((A ∪ B)′).
Answers
the probability of the complement of (A ∪ B) is 0.3.
How to find and what is Morgan's law?
Since A and B are mutually exclusive, we have:
P(A ∩ B) = 0
The complement of (A ∪ B) is the set of outcomes that are not in A or B. So:
(A ∪ B)′ = A′ ∩ B′
Using De Morgan's law, we have:
A′ ∩ B′ = (A ∪ B)′
We can now use the formula for the probability of the complement:
P((A ∪ B)′) = 1 - P(A ∪ B)
Since A and B are mutually exclusive, we have:
P(A ∪ B) = P(A) + P(B)
So:
P((A ∪ B)′) = 1 - (P(A) + P(B))
Substituting the given probabilities, we get:
P((A ∪ B)′) = 1 - (0.2 + 0.5)
P((A ∪ B)′) = 1 - 0.7
P((A ∪ B)′) = 0.3
Therefore, the probability of the complement of (A ∪ B) is 0.3.
De Morgan's laws are a pair of fundamental laws in Boolean algebra and set theory that describe the relationship between the intersection and union of sets and their complements. The two laws are:
The complement of the union of two sets is equal to the intersection of their complements.
Symbolically: (A ∪ B)′ = A′ ∩ B′
The complement of the intersection of two sets is equal to the union of their complements.
Symbolically: (A ∩ B)′ = A′ ∪ B′
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8. The circle graph shows the favorite game
type of students in Ms. Hunter's class.
3.FR.1.1
Sport
Favorite Game Type
B
Computer
What fraction of the students chose card?
A
1
2
1
12
6
Board
2
10
Card
Answers
The fractiοn οf students whο chοse card as their favοrite game type is: 1/6. Thus, option D is correct.
What is a circle?A circle is a clοsed twο-dimensiοnal shape that is defined as the set οf all pοints in a plane that are equidistant frοm a single fixed pοint called the center οf the circle. The distance frοm the center οf the circle tο any pοint οn the circle is called the radius οf the circle.
A circle can alsο be defined as the lοcus οf a pοint that mοves in a plane such that its distance frοm a fixed pοint (the center) remains cοnstant.
A circle is a very impοrtant and cοmmοn geοmetric shape that has many practical applicatiοns in mathematics, physics, engineering, and οther fields.
Tο determine the fractiοn οf students whο chοse card as their favοrite game type, we need tο find the pοrtiοn οf the circle graph that represents the card categοry.
Frοm the graph, we can see that the card categοry cοvers 16.66% οf the entire circle graph.
i.e.
16.66/100 = 1/6
Therefore, the fraction of students who chose card as their favorite game type is:
1/6
So, the answer is option D: 1/6.
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Complete question:
The circle graph shows the favourite game type of students in Ms. Hunter's class.
What fraction of the students chose card?
a. 2/3
b. 5/9
c. 3/10
d. 1/6
Write a quadratic function f whose zeros is 7
Answers
The quadratic function, x2 + 14x + 49 f, would have 7 as the lone zero.
What are function?Any subset of a Cartesian product is a relation.
For instance, a subset of is known as a "binary relation from A to B," and in specifically, a subset of is known as a "relation on A."
These ordered pairs (a,b) with first components from A and second components from B make up a binary relation from A to B.
A function is a relation that links every item in a set X to a single item in a different set Y. (possibly the same set).
A graph, which is the collection of all ordered pairs (x, f (x)), serves as the sole representation of a function.
As you can see from these definitions, every function is a relation from X to Y, but not vice versa .
(x - 7)(x - 7)
⇒ (x - 7)²
⇒ x² + 7²+ 2 × 7 × x
⇒ x² + 49 + 14x
⇒ x² + 14x + 49
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In the isosceles trapezoid, what is the length of LA?
A) 15
B) 17
C) 16
Answers
Answer:
A) 15 idek
Step-by-step explanation:
which means LA should also equal 15 with LP being 7 and PA being 8
6TH GRADE MATH PLS HELPPPP! TYSM
Answers
Answer:
slope is 1 1/4
Step-by-step explanation:
5/4 = 1 1/4 simplified
srs of 25 seniors 17 respond "yes" confidence interval for true proportion of seniors which of the following conditions were not met?
Answers
The 95% confidence interval for the proportion in the adult population who would say “Yes” of asked is 0.51 and 0.57.
To find the 95% confidence interval for the proportion in the adult population who would say "Yes," we can use the following formula
CI = p ± z × sqrt((p × (1 - p)) / n)
where
p = proportion of the sample who answered "Yes"
z = the z-score corresponding to the desired level of confidence (in this case, 95% corresponds to a z-score of 1.96)
n = sample size
Plugging in the values given in the question, we get
p = 0.54
z = 1.96
n = 1019
CI = 0.54 ± 1.96 × sqrt((0.54 × (1 - 0.54)) / 1019)
CI = 0.54 ± 0.030
CI = (0.51, 0.57)
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I have solved the question in general, as the given question is incomplete,
The complete question is:
Overall, 54% of the sample (550 of 1019 people) answered “Yes.” Find a 95% confidence interval for the proportion in the adult population who would say “Yes” if asked.?
Please help me answer this question ASAP!!
Will mark as brainliest if correct and 50+ points!
Answers
Answer:
See explanation below
Step-by-step explanation:
1. 12x - 18 = 6(2x -3)
2. 15x + 25 = 5(3x + 5)
3. 14x + 21 = 7(2x + 3)
4. 5x - 5 = 5(x - 1)
5. 12x - 30 = 6(2x - 5)
6. 10x + 8 = 2(5x + 4)
7. 27x + 18 = 9(3x + 2)
8. 4x - 20 = 4(x - 5)
9. 20x + 30 = 10(2x + 3)
10. 4(x + 5) = 4x + 20
11. 3(x - 2) = 3x - 6
12. 5(2x + 4) = 10x + 20
13. 5(x - 1) = 5x - 5
14. 1/2(10x + 12) = 5x + 6
15. 4(2x + 4) = 8x + 16
16. 2(5x - 2) = 10x - 4
17. 2(x - 8) = 2x - 16
18. 4(2x + 1) = 8x + 4
16.5% of an amount is 891. What is the original amount?
Answers
Answer:
Jika 16,5% dari suatu jumlah adalah 891, kita dapat menggunakan persamaan:
0,165x = 891
di mana x adalah jumlah aslinya. Kita ingin menyelesaikan persamaan ini untuk x.
Kita dapat memulai dengan membagi kedua sisi dengan 0,165:
x = 891 / 0,165
x = 5400
Jadi, jumlah aslinya adalah 5400.
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19. Hockey Game Two families go to a hockey game. One family purchases two adult tickets and four youth tickets for $28. Another family purchases four adult tickets and five youth tickets for $45.50. Let x represent the cost in dollars of one adult ticket and let y represent the cost in dollars of one youth ticket. a. Write a linear system that represents this situation. b. Solve the linear system to find the cost of one adult and one youth ticket. c. How much would it cost two adults and five youths to attend the game?
Answers
- For the first family: 2x + 4y = 28
- For the second family: 4x + 5y = 45.50
b. To solve this linear system, we can use the elimination method. We can multiply the first equation by -2 and add it to the second equation to eliminate the term for 4x:
-2(2x + 4y = 28) -> -4x - 8y = -56
4x + 5y = 45.50
_____________
-3y = -10.50
y = 3.50
Now, we can substitute this value of y into either equation to solve for x. Let's use the first equation:
2x + 4(3.50) = 28
2x + 14 = 28
2x = 14
x = 7
Therefore, the cost of one adult ticket is $7 and the cost of one youth ticket is $3.50.
c. To find out how much it would cost two adults and five youths to attend the game, we can simply multiply the cost of each ticket by the number of tickets:
2 adults * $7/adult ticket = $14
5 youths * $3.50/youth ticket = $17.50
Therefore, it would cost two adults and five youths a total of $31.50 to attend the game.
Mr yaro left sunyani at 8:30 am. He arrived in Accraat 4.58pm . How long did the journey takes?
Answers
Answer:
4 hours and 28 minutes
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What is the length of AC in the given triangle?
A) 126.6
B) 99.6
C) 66.9
D) 57.1
Answers
Answer:
We can use the Law of Cosines to find the length of side AC:
cos(A) = (b² + c² - a²) / 2bc
cos(A) = (85² + 530² - 850²) / (2 × 85 × 530)
cos(A) = -0.3589 (using a calculator)
Since the cosine of an angle is negative in the second quadrant, we have:
A = 180° - cos⁻¹(-0.3589)
A = 114.49°
Now we can use the Law of Cosines again to find the length of AC:
a² = b² + c² - 2bc cos(A)
AC² = 85² + 530² - 2 × 85 × 530 cos(114.49°)
AC ≈ 99.6
Therefore, the length of AC is approximately 99.6. Answer: (B)
You have one type of chocolate that sells for $3.40/lb and another type of chocolate that sells for $9.00/lb. You would like to have 44.8 lbs of a chocolate mixture that sells for $5.00/lb. How much of each chocolate will you need to obtain the desired mixture?
Answers
Using a system of equations, 32 lbs of the $3.40/lb chocolate and 12.8 lbs of the $9.00/lb chocolate will be needed to obtain the desired mixture.
How to Apply System of Equations?Let x be the amount of the $3.40/lb chocolate needed, and y be the amount of the $9.00/lb chocolate needed to make 44.8 lbs of a $5.00/lb mixture.
We can set up the following system of equations:
x + y = 44.8 (total amount of mixture)
3.4x + 9y = 5(44.8) (total cost of mixture)
Solving this system of equations, we get:
x = 32 lbs of the $3.40/lb chocolate
y = 12.8 lbs of the $9.00/lb chocolate
Therefore, to obtain the desired mixture, 32 lbs of the $3.40/lb chocolate and 12.8 lbs of the $9.00/lb chocolate will be needed.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Answers
The red car is traveling at a pace of about speed of 56.67 feet per second along the road.
How are speed and math related?The mathematical relationship between speed, distance, and time will be explained here. A moving body's speed is the distance it covers in a given amount of time. The speed is calculated using the time in hours and the distance in kilometers per hour. If the distance is in m and the time is in seconds, the speed is m/sec.
Let x represent the distance the red automobile has traveled from where it started, and y represent the separation it has from the police car. We learn the following from the Pythagorean theorem:
[tex]x^2 + y^2 = d^2[/tex]
where d is the separation between the two vehicles.
When we divide the two sides by the passage of time, we obtain:
[tex]2x(dx/dt) + 2y(dy/dt) = 2d(dd/dt)[/tex]
Given that dy/dt = -85 ft/s, we need to get dx/dt.
The police car is also mentioned as being 50 feet off the side of the road. Hence, we can state that [tex]d = sqrt(x^2 + (y - 50)^2)[/tex].When we differentiate this phrase according to time, we get:
[tex]dd/dt = (1/2)*(x^2 + (y - 50)^2)^(-1/2)*(2x*dx/dt + 2(y - 50)*dy/dt)[/tex]
By changing the specified values, we obtain
[tex]-85 = (1/2)*sqrt(x^2 + (180 - 50)^2)^(-1/2)*(2x*dx/dt + 2(180 - 50)*(-85))[/tex]
If we condense this phrase, we get:
[tex]dx/dt = 170/3 ≈ 56.67 ft/s[/tex].
The red car is therefore traveling at a pace of about 56.67 feet per second along the road.
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Imagine
X
in the below is a missing value. If I were to run a median imputer on this set of data what would the returned value be?
50,60,70,80,100,60,5000,x
(It's okay to have to look up how to do this!) An. error 80 100 70 The features in a model.... None of these answers are correct Are always functions of each other Kecp the model validation process stable Are used as proxics for y-hatfy (that is yhat divided by y) Which of the below were discussed as being problems with the hold out method for validation? Outliers can skew the result Validation is sometimes too challenging
K=3
is not sufficiently large cnough Data is not available for test and control differences. The modefis not trained on all of the day
Answers
The returned value would be 70 which is the missing value in the data set. Hence, option D is correct. We have some X values; we called these numeric inputs and some Y value that we are trying to predict.
This set of data would yield a result of 70 if a median imputer were run on it. In regression, we have some X values that are referred to as independent variables and some Y values that are referred to as dependent variables (this is the variable we are trying to predict). Several Y values are possible, but they are uncommon.
Learning a function that can predict Y given X is the fundamental concept behind a regression. Depending on the data, the function may be linear or non-linear.
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Complete question is:
Imagine X in the below is a missing value. If I were to run a median imputer on this set of data. What would the returned value be? 50 , 60 , 70 , 80 , 100 , 60 , 5000 , x (It's okay to have to look up how to do this!)
50
An error
80
70
100
The basic idea of a regression is very simple. We have some X values, we called these ______ and some Y value (this is the variable we are trying to _______.
We could have multiple Y values, but that is not but that is not re-ordered ordinals intercepts features numeric inputs.
a. show that the properties of a probability distribution for a discrete random variable are satisfied.
Answers
To show that the properties of a probability distribution for a discrete random variable are satisfied, we need to verify that the probability distribution function (PDF) satisfies, The PDF must be non-negative for all values of the random variable and The sum of the probabilities for all possible values of the random variable must be equal to 1.
Let X be a discrete random variable taking values x1, x2, ..., xn, and let P(X) be the probability distribution function for X, such that P(X = xi) = pi for all i.
The PDF must be non-negative for all values of the random variable. This means that for any value xi of the random variable, the probability pi must be greater than or equal to zero. That is,
pi ≥ 0 for all i.
This property ensures that probabilities are never negative, which is a necessary condition for a valid probability distribution.
The sum of the probabilities for all possible values of the random variable must be equal to 1. That is,
∑ pi = 1 for all i.
This property ensures that the total probability of all possible outcomes is equal to 1, which is a necessary condition for a valid probability distribution.
Therefore, if the PDF satisfies these two properties, we can conclude that it represents a valid probability distribution for the given discrete random variable.
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you know that a pair of triangles has two pairs of congruent angles. what other information do you need to show that the triangles are congruent?
you need to know that _____ are congruent.
Answers
Answer:
You need to know that the ratio of their sides are congruent
If you make monthly payments of $1,000 for 10th years, determine the total payment over lifetime of loan
Answers
Answer:
hello!!!!
Payment per year
1,000×12months=12,000
total payment over the lifetime of the loan.
12,000×10years=120,000
Answer:
$120,000
Step-by-step explanation:
If you make monthly payments of $1,000 for 10 years, the total payment over the lifetime of the loan would be $1,000 x 12 months x 10 years = $120,000
A penny has a diameter of 0.750 inches. What is the area of a penny to the nearest hundredth?
Answers
The area of a penny is .001m²
What exactly is a circle's area?The quantity of space contained within a circle's perimeter is known as its area. The area that the circle occupies is that which lies inside its perimeter. It is also known as the total number of square units included within that circle. In square units, the area of a circle is equal to πr²or πd²/4 where (Pi) = 22/7 or 3.14.
r stands for circle radius.
circle's diameter is given as d.
Diameter of Penny is 0.750 inches
Converting inch into meter
1 inch=0.0254 meter
0.750 inch= 0.01905 meter
Area of a circle is =π×r²
=π×(0.01905)²
=.001139≈ .001m²
A penny's surface area is.001 m² to the nearest tenth.
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How do you use the discriminant only to determine the number and type of solutions for the following quadratic equation?
Answers
To use the discriminant to determine the number and type of solutions for a quadratic equation, we simply need to calculate b² - 4ac and examine the value.
The discriminant of a quadratic equation is a value that can be used to determine the nature and number of solutions for the equation. The discriminant is found by calculating b² - 4ac, where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
If the discriminant is positive, then the equation has two real solutions. If the discriminant is zero, then the equation has one real solution (a double root). If the discriminant is negative, then the equation has no real solutions but two complex solutions.
If it is positive, there are two real solutions; if it is zero, there is one real solution; if it is negative, there are no real solutions.
For example, consider the quadratic equation 2x² + 4x + 3 = 0. The coefficients are a = 2, b = 4, and c = 3. The discriminant is b² - 4ac = 4² - 4(2)(3) = 16 - 24 = -8. Since the discriminant is negative, the equation has no real solutions but two complex solutions.
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