If the range of f (x) = startroot m x endroot and the range of g (x) = m startroot x endroot are the same, which statement is true about the value of m?

Answers

Answer 1

The only possible value of m that would make the ranges of f(x) and g(x) the same is any positive real number.

The range of a function is the set of all possible output values. In this case, we are given that the ranges of two functions, f(x) and g(x), are the same.

The function f(x) = √(mx) has a domain of x ≥ 0, since the square root of a negative number is not a real number. The function g(x) = m√x has a domain of x ≥ 0 for the same reason.

To find the range of these functions, we need to consider the possible values of the input x. For f(x), as x increases, the output √(mx) also increases, and as x approaches infinity, so does the output. For g(x), as x increases, the output m√x also increases, and as x approaches infinity, so does the output.

Therefore, if the ranges of f(x) and g(x) are the same, this means that they both have the same maximum and minimum values, and these values are achieved at the same inputs.

In particular, if we consider the minimum value of the range, this is achieved when x = 0, since both functions are defined only for non-negative inputs. At x = 0, we have f(0) = g(0) = 0, so the minimum value of the range is 0.

To find the maximum value of the range, we need to consider the behavior of the functions as x approaches infinity. As noted above, both functions increase without bound as x increases, so the maximum value of the range is infinity.

Therefore, the only possible value of m that would make the ranges of f(x) and g(x) the same is any positive real number.

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Related Questions

The figure below shows dimensions of a block of foam used to package a triangular shaped product. The foam is in the shape of a rectangular prism with a small triangular prism removed from the center. How many cubic centimeters of foam are used to package this product?

The figure below shows dimensions of a block of foam used to package a triangular shaped product. The

Answers

Answer:

5,580

Step-by-step explanation:

Rectangle: 36x30x60=6480

Triangle: 1/2x15x20x6=900

6480-900=5,580

The foam are used to package this product is cubic centimeters.

What is the volume of the rectangular prism?

The Area of the rectangular prism is the product of the length, breadth, and height of the given prism.

Area of rectangular prism = 2(length x width + length x height + width x length)

Area of rectangular prism = 2( 36 x 30 + 30 x60 + 60 x 36)

= 10080 cubic centimeters

Let's find the base area:

The formula to find the base area is,

B = ½bh

Triangle area = 1/2 x 15 x 20 x 6

Triangle area = 900

10080 - 900 = 9180

Hence, the foam are used to package this product is cubic centimeters.

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x2 – 11x + 5 = -2x
Solve equation to the nearest tenth

Answers

Answer:

x = 5/7 -> 0.714285 which to the nearest tenth would be 0.7

Step-by-step explanation:

is it x*2 or x^2?

If it were x to the power of two, then the answer would be about x1 = 0.594875 and x2 = 8.40512

Please no fake answers!

Please no fake answers!

Answers

Answer:

X=1.899

I think

Step-by-step explanation:

2X+4.899=X+3

X=1.899

Answer:

x=3

Step-by-step explanation:

:)

need help with this asap!!!!!

need help with this asap!!!!!

Answers

Answer:

that looks hard

Step-by-step explanation:

Which of the following is true about a "cumulative ACK witha sequence number M in the Go-Back-N protocol) A When received by the sender, it retransmits all da packets in the window up to sequence number M When received by the sender, it slides its window by b When sent by the receiver, all packets up to sequer number M were correctly received and delivered D. Both (B) and (C) B. C. 11. The function that is not a cause of extra overhead of routers used to forward IPv4 datagrams is: A. The datagram header checksum B. The datagram fragmentation C. The datagram options D. The datagram reassembly 12. In the Selective-Repeat protocol, if the timer expires, A. All packets in the window are retransmitted and t is restarted B The packet, for which the timer has exp retransmitted immediately and its timeout in Part 1: (20 points, I point each) Choose the best answer for each of the following multiple-choice questions 1. Which of the following Internet transport-layer services provide error checking" A. TCP B. UDP C Neither TCP nor UDP D. Both TCP and UDP 2. The type of delay that is not caused by the store-and-forward strategy used by the switching devices is: A. The processing delay B. The queuing delay C. The transmission delay D. The propagation delay 3. In a statistical multiplexed system, if the average queuing delay is very close to zero, then: A. The system is very well-engineered B. The traffic intensity is greater than 50% C. The system resources are inefficiently utilized D. None of the above

Answers

TCP provides error checking to ensure reliable data delivery, making option A the correct answer. Only the propagation delay is not caused by the store-and-forward strategy employed by switching devices.

TCP (Transmission Control Protocol) provides error checking as part of its services. It ensures reliable data delivery by using acknowledgments and sequence numbers to detect and recover from packet loss, errors, or out-of-order delivery. When a TCP receiver receives data, it sends an acknowledgment (ACK) back to the sender to confirm the successful reception of packets. If the sender does not receive an ACK for a particular packet within a specified timeout period, it assumes the packet was lost or damaged and retransmits it.

TCP provides error checking to ensure reliable data delivery, making option A the correct answer.

The propagation delay is the time it takes for a signal to travel from the source to the destination. It is determined by the physical distance between the devices and the speed of signal propagation in the transmission medium. The propagation delay is an inherent characteristic of the medium and cannot be eliminated by switching devices or other strategies.

The other three options—processing delay, queuing delay, and transmission delay—are all caused by the store-and-forward strategy used by switching devices. Processing delay refers to the time taken to examine and process the packet headers. Queuing delay occurs when packets have to wait in a queue before being transmitted. Transmission delay is the time it takes to push the bits onto the transmission medium.

Among the given options, only the propagation delay is not caused by the store-and-forward strategy employed by switching devices.

3. The correct answer is A. The system is very well-engineered.

In a statistical multiplexing system, the queuing delay is the delay experienced by packets waiting in a queue before being transmitted. If the average queuing delay is very close to zero, it indicates that the system is well-engineered and efficiently managing its resources. A well-designed system can minimize or eliminate queuing delays by appropriately allocating resources and ensuring efficient scheduling algorithms.

Traffic intensity, which represents the ratio of the average traffic load to the transmission capacity, does not directly determine the queuing delay. It is possible to have low queuing delays even with high traffic intensity if the system is well-designed.

When the average queuing delay is close to zero, it suggests that the system is well-engineered and efficiently utilizing its resources, as stated in option A.

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Solve the system by substitution.

x = -2y + 5
-8x – 3y = -1

Answers

Jejdjejjejejejejejjejejeejjeje

^3√-1
0-1
O undefined
01
O-3

^3-10-1O undefined01O-3

Answers

The answer of the given question of radicals is -1.

What is radicals?
A surd or radical is an unresolved root, particularly one that employs the radical symbol. A radical expression is any expression that contains a radical, whether it is a square root, a cube root, or a higher root, while an algebraic expression is any statement that does not contain any transcendental functions or transcendental numbers. The root test is used to determine the radius of convergence of a power series. The nth roots of 1 are known as roots of unity, and they play an important role in many areas of mathematics, including number theory, equation theory, and the Fourier transform.

Given, ∛-1

if we evaluate this radical then,

∛-1 = -1

because 1 perfect cube.

Hence, the answer is option(a) i.e, -1

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Plz help : ) I don't understand

Plz help : ) I don't understand

Answers

Those are alternate interior angles.
Converse statement because usually one is told two lines are parallel first and then the alternate interior angles are congruent second.

Find the distance between the two points in simplest radical form. (0,-8) and (-5,-3)

Answers

Answer:

I dont know the exact numberbut i have clues below

Step-by-step explanation:

Gradient = -1

Rise = 5

Run = -5

What’s 900+900
Just doing this cause it’s fun

Answers

1800??????????? We love fun
900+900=1800 :D !!!!!!!!!!!!!!!!

Write the equation of the line (in slope-intercept form) that has an x-intercept at -6 and a y-intercept at 2. Provide a rough sketch of the line indicating the given points. [1 mark]. Exercise 2. For the polynomial f(x) = −3x² + 6x, determine the following: (A) State the degree and leading coefficient and use it to determine the graph's end behavior. [2 marks]. (B) State the zeros. [2 marks]. (C) State the x- and y-intercepts as points [3 marks]. (C) Determine algebraically whether the polynomial is even, odd, or neither.

Answers

To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.

To write the equation of the line with an x-intercept at -6 and a y-intercept at 2, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.

In this case, the y-intercept is given as 2, so the equation becomes y = mx + 2. To find the slope, we can use the formula (y2 - y1) / (x2 - x1) with the given points (-6, 0) and (0, 2). We find that the slope is 1/3. Thus, the equation of the line is y = (1/3)x + 2.

For the polynomial f(x) = -3x² + 6x, the degree is 2 and the leading coefficient is -3. The end behavior of the graph is determined by the degree and leading coefficient. Since the leading coefficient is negative, the graph will be "downward" or "concave down" as x approaches positive or negative infinity.

To find the zeros, we set the polynomial equal to zero and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two solutions: x = 0 and x = 2.

The x-intercept is the point where the graph intersects the x-axis, and since it occurs when y = 0, we substitute y = 0 into the polynomial and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two x-intercepts: (0, 0) and (2, 0).

To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.

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Find the perimeter of a rectangle
with the following vertices: A (1,1) B
(1,6) C (4,6) D(4,1)

Answers

The perimeter of the rectangle with the given vertices is 21.66 units.

Using Distance Formula, we have

\(AB = \sqrt{(1-1)^{2} +(6-1)^{2} } = \sqrt{25} = 5\)

And \(CD= \sqrt{(4-4)^{2} +(1-6)^{2} } = \sqrt{25} = 5\)

\(BD= \sqrt{(1-4)^{2} +(1-6)^{2} } = \sqrt{9+25} = \sqrt{34} = 5.8\)

\(AC = \sqrt{(4-1)^{2} +(1-6)^{2} } = \sqrt{9+25} = \sqrt{34} = 5.8\)

Hence, the length of the perimeter is 5 units and the breadth of the perimeter is 5.8 units.

Now, the perimeter of a rectangle with length l, and breadth b is given by

Perimeter = 2(l+b)

Perimeter= 2 ( 5 +5.8) = 2 * 10.8 = 21.66 units.

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Which property was used to write the equation in step 2? Step 1: 5 (x minus 7) = 55. Step 2: 5 x minus 35 = 55. Step 3: 5 x = 90. Step 4: x = 18.

Answers

Answer:

Distributive Property

Step-by-step explanation:

If we have an equation where we multiply something in parentheses by a certain term, then we can apply the distributive property to simplify it.

In this case: \(5(x-7)=55\)

We can multiply \(x-7\) by 5 to simplify this equation - this is the distributive property.

\(5x - 35 = 55\)

So the property used to write the equation in Step 2 was the distributive property.

Hope this helped!

Answer:

the answer is didrtbutive

Step-by-step explanation:

hope it helps.

have a good day:)

find the point on the plane 4x − y + 4z = 40 nearest the origin.(x,y,z)=

Answers

The point on the plane 4x - y + 4z = 40 nearest the origin is (-3.048, -0.762, 6.467)

Given data ,

To find the point on the plane 4x - y + 4z = 40 nearest the origin, we need to minimize the distance between the origin and the point on the plane.

The normal vector to the plane 4x - y + 4z = 40 is given by (4,-1,4). To find the perpendicular distance from the origin to the plane, we need to project the vector from the origin to any point on the plane onto the normal vector. Let's choose the point (0,0,10) on the plane:

Vector from origin to (0,0,10) on the plane = <0-0, 0-0, 10-0> = <0,0,10>

Perpendicular distance from the origin to the plane = Projection of <0,0,10> onto (4,-1,4)

= (dot product of <0,0,10> and (4,-1,4)) / (magnitude of (4,-1,4))

= (0 + 0 + 40) / √(4^2 + (-1)^2 + 4^2)

= 40 / √(33)

To find the point on the plane nearest the origin, we need to scale the normal vector by this distance and subtract the result from any point on the plane. Let's use the point (0,0,10) again:

Point on the plane nearest the origin = (0,0,10) - [(40 / √(33)) / √(4^2 + (-1)^2 + 4^2)] * (4,-1,4)

= (0,0,10) - (40 / √(33)) * (4/9,-1/9,4/9)

= (0,0,10) - (160/9√(33), -40/9√(33), 160/9√(33))

= (-160/9√(33), -40/9√(33), 340/9√(33))

Hence , the point on the plane 4x - y + 4z = 40 nearest the origin is approximately (-3.048, -0.762, 6.467)

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What are the steps to solve this

What are the steps to solve this

Answers

Malena's steps arranged sequentially are :

collecting like terms Using the appropriate numerical operator divide both sides by 3

The first step :

2x + 5 = -10 - x

collecting like terms

2x + x = -10 - 5

step 2 : Using the appropriate numerical operator:

3x = -15

step 3 : divide both sides by 3 to isolate x

x = -5

Hence, the required steps as arranged above .

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What additional information is needed to prove the triangles congruent by SSS

What additional information is needed to prove the triangles congruent by SSS

Answers

Answer:

Angle a = Angle D

Answer:

A: Angle A  Angle D

Step-by-step explanation:

Hey id love if yall could fill out this worksheet for me its pretty simple i just have some stuff to do and dont have time currently to work on it

Answers

To be categorized as unemployed, a person has to be without a process, presently available to work, and actively seeking out work within the previous 4 weeks.

Unemployment is a time period regarding people who are employable and actively looking for a process but are not able to discover a process. blanketed in this institution are the ones people in the group of workers who are working but no longer have the precise job.

The situation of now not having a task but being a member of the labor pressure. To be considered unemployed, someone must be jobless but actively trying to find a task by having searched within the last 4 weeks.

Hence, To be categorized as unemployed, a person has to be without a process, presently available to work, and actively seeking out work within the previous 4 weeks.

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complete question:

how do economists define unemployed workers? group of answer choices although currently working, they are not happy with their current job working on contract for a limited time not currently working not currently working but actively searching for work

What is the value of t in the equation 2t-8+4t-13=27

Answers

Answer:

t=8

Step-by-step explanation:

Choose the best estimate for the weight of a cantaloupe. Responses A 2 decigrams2 decigrams B 2 kilograms2 kilograms C 2 grams2 grams D 2 milligrams

Answers

The best estimate for the weight of a cantaloupe is 2 kilograms (B).

A decigram is 1/10th of a gram, which would be too small of weight for a cantaloupe. 2 grams (C) is also too small for a cantaloupe as it would only be the weight of a few small seeds. 2 milligrams (D) is an extremely small weight, only suitable for a single grain of salt or a tiny insect.

Therefore, 2 kilograms (B) is the most reasonable estimate for the weight of a cantaloupe as it falls within the typical range of cantaloupe weights.

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Complete Question:

Choose the best estimate for the weight of a cantaloupe. Responses

A 2 decigrams

B 2 kilograms

C 2 grams

D 2 milligrams

A right triangle has a 12in base and an 8in height. What is the area of the triangle, in in??​

Answers

Answer:

48

Step-by-step explanation:

using the formula 1/2 b*h

8*12=96

96/2=48

help me with this please and thank you

help me with this please and thank you

Answers

Answer:

4, 1, 2, 3

Step-by-step explanation:

let x = cost of 1 bar

cost of 75 bars = $65

cost of one bar => 75/75 = $65/75

x = $0.87

Answer:

4.  c = $0.97 rounded to the nearest hundredth

1.  Let c = cost of one bar

\(\textsf{2.} \quad 75c=\$65\)

\(\textsf{3.} \quad \dfrac{75}{75}c=\dfrac{\$65}{75}\)

Step-by-step explanation:

Step 1

Define the variable:

Let c = cost of one bar

Step 2

Given that one box of 75 Toblerone chocolate bars costs $65:

\(75c=\$65\)

Step 3

To find the cost of one Toblerone chocolate bar, divide both sides of the equation by 75:

\(\dfrac{75}{75}c=\dfrac{\$65}{75}\)

Step 4

Simplify both sides of the equation and round the solution to the nearest hundredth:

c = $0.97 rounded to the nearest hundredth

Numbers of the jerseys of 5 randamty selected Carolina Panthers Quantitative discrete Quantitative continuous. Gualitative

Answers

The numbers of the jerseys of 5 randomly selected Carolina Panthers would fall under the category of quantitative discrete data.

Quantitative data are numerical measurements or counts that can be added, subtracted, averaged, or otherwise subjected to arithmetic operations. Discrete data, on the other hand, can only take on specific, whole number values, as opposed to continuous data which can take on any value within a range.

Qualitative data, on the other hand, are non-numerical data that cannot be measured or counted numerically. Examples include colors, names, opinions, and preferences. Since the numbers of the jerseys are specific numerical values, they are considered quantitative data.

Since they can only take on specific, whole number values (i.e. the jersey numbers are not continuous values like weights or heights), they are considered discrete data. Therefore, the correct option for the given question is option "quantitative discrete".

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If x and y are integers and x = 50y + 69, which of the following must be odd? O xy O x+y O x+2y 3x - 1 O 3x+1

Answers

Since 50 is an even number, we know that x will be even if y is even (50 times an even number is still even) and odd if y is odd (50 times an odd number is odd). Therefore, the only answer choice that must be odd is x+y.

Given that x and y are integers and x = 50y + 69, let's determine which of the following expressions must be odd.

1. xy: Since x is odd (50y + 69), when it is multiplied by any integer y, the result will always be odd. Therefore, xy must be odd.

2. x + y: If x is odd, adding it to an even integer (y) would result in an odd number. However, adding it to an odd integer (y) would result in an even number. Therefore, x + y does not necessarily have to be odd. xy: We can't determine if this is odd or even without knowing the values of x and y.
- x+y: This expression is always odd. To see why, consider two cases:

If x and y are both odd, then x+y is even+odd=odd.
If x and y are both even, then x+y is even+even=even.
If one of x and y is odd and the other is even, then x + y is odd + even =odd.

3. x+2y: We can't determine if this is odd or even without knowing the values of x and y.
3x-1: This expression will be odd if x is odd (3 times an odd number is odd) and even if x is even (3 times an even number is even).
3x+1: This expression will be odd if x is even (3 times an even number plus 1 is odd) and even if x is odd (3 times an odd number plus 1 is even).
x + 2y: Since x is odd and 2y is always even, their sum must be odd. Therefore, x + 2 y must be odd.

4. 3x - 1: This expression is odd, since 3x will always be odd (as x is odd) and subtracting 1 from an odd number results in an even number. Therefore, 3x - 1 does not necessarily have to be odd.

5. 3x + 1: This expression is odd, since 3x will always be odd (as x is odd) and adding 1 to an odd number results in an even number. Therefore, 3x + 1 must be odd.

In conclusion, the expressions that must be odd are xy, x + 2y, and 3x + 1.

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PLEAZE HELPP 50 POINTS If the function f(x) =-3x3 +7x represents the movement of a whale in meters what is the average rate of change of the whale for x=1 and X=3 seconds label your answer

Answers

Answer:

The average rate of change of a function over an interval is found by taking the difference between the function's values at the endpoints of the interval and dividing by the length of the interval. In this case, we have:

f(1) = -3(1)^3 + 7(1) = -3 + 7 = 4

f(3) = -3(3)^3 + 7(3) = -27 + 21 = -6

The average rate of change over the interval from x=1 to x=3 is therefore (-6 - 4) / (3 - 1) = -10 / 2 = -5.

To label your answer, you could write something like: "The average rate of change of the whale's movement over the interval from x=1 to x=3 seconds is -5 meters/second."

Scott purchased furniture for $6702.47 and received an invoice dated May 5, 2021 with terms 4/15 n/30. What is the amount of cash discount available for a payment made on May 12, 2021 to settle the invoice? Round to the nearest tenth Answer:

Answers

The amount of cash discount available is $81.5 .

Given,

Discounted price of furniture  = $14.50 less than the original price.

original price of furniture = p

Paid amount of furniture = $67

Discount is always given on marked price of the article .

So here the discount on furniture will be given on the marked price of the furniture .

Marked price is always more than the cost price .

Now,

First form the equation to find original price .

So,

c = p - 14.5

67 = p - 14.5

p = $81.5

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Ten-year-old Brandon loves baseball and has studied baseball statistics since he was 5 years old. Brandon is currently reading this year's statistics for some of his favorite players. He will easily remember the new statistics because of the knowledge _____ he has for baseball statistics

Answers

Brandon's strong knowledge base of baseball statistics allows him to easily remember and comprehend the new statistics he is reading.

Brandon's extensive knowledge of baseball statistics serves as a foundation or framework that helps him retain and understand the new information he encounters.

By studying baseball statistics since a young age, Brandon has developed a deep understanding of the game, player performance, and statistical trends.

This knowledge base enables him to make connections between the new statistics and his existing knowledge, facilitating the process of remembering and comprehending the information.

Additionally, his passion for baseball likely contributes to his motivation and engagement, further enhancing his ability to retain and recall the statistics effortlessly.

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PLEASE HELP NEED THE ANSWER

-20
-15
-25
-18

PLEASE HELP NEED THE ANSWER-20-15-25-18

Answers

x=-15, because the equation of the graph is y=1/3x+1, and you substitute y for -4.

I need help please with 6, 7 and 8

I need help please with 6, 7 and 8

Answers

6. Solution for |2x-3| = |x| are x = 1,3

7. Solution for 8 + |4v - 7| ≥ 17 is,

          v ≥  4 ,  v ≤ -1/2

8. Number of computer meets in the condition = 6

Average:

                Average of given number is given by sum of all numbers divided by total number of numbers.

6.  |2x-3| = |x|

Case I :

            when x<0

            |2x-3| = |x|

           -(2x-3) = -x

           -2x + 3 = -x

             2x - x = 3

            x = 3 ( Not possible as x<0 )

           No solution in this case.

Case II :

            when   0< x< 3/2

              |2x-3| = |x|

            -(2x -3) = x

            -2x + 3 = x

             2x +x = 3

             3x = 3

              x =1 (Valid solution)

Case III :

             when x>3/2

             |2x-3| = |x|

             2x-3 = x

             2x -x =3

              x = 3 (Valid solution)

Thus solution for |2x-3| = |x| are x = 1,3

7.

          8 + |4v - 7| ≥ 17

               |4v - 7|  ≥ 17 -8

                |4v - 7| ≥ 9

      ⇒   4v - 7 ≥ 9

            4v ≥ 9+7

             v ≥  4

and,

         4v - 7 ≤ - 9

         4v ≤  -2

          v ≤ -1/2

     Thus solution for 8 + |4v - 7| ≥ 17 is,

          v ≥  4 ,  v ≤ -1/2

8.

       We know,

                  Average of quantity =  sum of quantity / Number of quantity

    For the given question,

        Sum of price of all computer =  $ (890+650+ 660+450+        725+750+370+670+650+825)

                                   = $ 6640

  and       Number of computer = 10

Average price of computer = $ 6640/10

                                          = $ 664

      Absolute deviation is  $100

So i can pay price between

                                          ($ 664 - $100) to ($ 664 + $100)

                                         that is $564 to  $764

Number of computer meets in this condition = 6

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-2 + 1/2 what is the answer

Answers

Answer:

-1 1/2

Step-by-step explanation:

1/2 is positive and - 2 is negative

-1 1/2
1/2 is positive and -2 is negative

A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If they are the same color, then you win $1.10; if they are different colors, then you win -$1.00. (That is, you lose $1.00.) Calculate
(a) the expected value of the amount you win;
(b) the variance of the amount you win.
(a) The expected value of the amount you win will be -0.0667.
(b) The variance of the amount you win will be 1.089.

Answers

(a) the expected value of the amount you win 2/9 , (b) the variance of the amount you win 5/18 , c) The expected value of the amount you win is -$0.0667 and d)The variance of the amount you win is 1.2898.

Let's calculate the expected value and variance of the amount you win step by step:

a) Calculate the probability of drawing two marbles of the same color.

First, calculate the probability of drawing two red marbles:

P(RR) = (5/10) * (4/9) = 20/90 = 2/9

Similarly, calculate the probability of drawing two blue marbles:

P(BB) = (5/10) * (4/9) = 20/90 = 2/9

b) Calculate the probability of drawing two marbles of different colors.

P(RB) = (5/10) * (5/9) = 25/90 = 5/18

P(BR) = (5/10) * (5/9) = 25/90 = 5/18

c) Calculate the expected value.

The expected value (EV) is calculated by multiplying each outcome by its probability and summing them up.

EV = (P(RR) * $1.10) + (P(RB) * -$1.00) + (P(BR) * -$1.00) + (P(BB) * $1.10)

= (2/9 * $1.10) + (5/18 * -$1.00) + (5/18 * -$1.00) + (2/9 * $1.10)

= $0.2444 - $0.2778 - $0.2778 + $0.2444

= -$0.0667

Therefore, the expected value of the amount you win is -$0.0667.

d) Calculate the variance.

The variance is a measure of the dispersion of the outcomes around the expected value. It is calculated as the sum of the squared differences between each outcome and the expected value, weighted by their probabilities.

Variance = (P(RR) * ($1.10 - EV)²) + (P(RB) * (-$1.00 - EV)²) + (P(BR) * (-$1.00 - EV)²) + (P(BB) * ($1.10 - EV)²)

Variance = (2/9 * ($1.10 - (-$0.0667))²) + (5/18 * (-$1.00 - (-$0.0667))²) + (5/18 * (-$1.00 - (-$0.0667))²) + (2/9 * ($1.10 - (-$0.0667))²)

= (2/9 * $1.1667²) + (5/18 * -$0.9333²) + (5/18 * -$0.9333²) + (2/9 * $1.1667²)

= 1.2898

Therefore, the variance of the amount you win is 1.2898.

To know more about expected value check the below link:

https://brainly.com/question/30398129

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