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fgiga [73]
2 years ago
7

On most state highways, the fine for speeding depends on the speed of the car. In a certain state, suppose the fine as a functio

n of the number of miles per hour over the speed limit is f(n). The graph of this function is shown below.
Part a) The state determines that the fine at every speed should go up by $5. Write a new function and draw the new graph

Mathematics
1 answer:
Georgia [21]2 years ago
4 0

Graphs can be used to model real world situations.

<em>The coordinates of the graph is gotten by adding 5 to the y-values of the function (see attachment for graph)</em>

The function of the graph is represented as (n, f(n)); where

<em />n \to<em> speed</em>

<em />f(n) \to<em> fine for over speed</em>

When the fine increases by $5 for every speed limit.'

The new function becomes:

g(n) = f(n) +5

<u />

<u>The points on the graph are represented as:</u>

f(5) = 25

f(10) = 50

f(15) = 75

f(20) = 110

f(25) = 150

f(30) = 200

f(35) = 270

So, the new points would be calculated as follows:

g(n) = f(n) +5

g(5) = 25 + 5 = 30

g(10) = 50 + 5 = 55

g(15) = 75 + 5 = 80

g(20) = 110 + 5 = 115

g(25) = 150 + 5 = 155

g(30) = 200 + 5 = 205

g(35) = 270 + 5 = 275

See attachment for the new graph

Read more about graphs and functions at:

brainly.com/question/18806107

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3 years ago
Calculate the expected value, the variance, and the standard deviation of the given random variable X. (Round all answers to two
Tom [10]

Answer:

E (X) = 1.8

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σ = 0.6

Step-by-step explanation:

Solution:-

- Denote the random variable X : is the number of red marbles that Suzan has in her hand after she selects three marbles.

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                Bag : { 3 Red , 2 Green }

- Suzan selects three marbles from the bag. The Event (X) defines the number of red marbles out of 3.

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- The probability distribution of the random variable X, we will use combinations to determine the required probabilities:

  X = 1 red marble:

        P ( X = 1 ) : Suzan chooses 1 Red marble from the available 3 red marble and 2 green marbles.

        P ( X = 1 ) = [ 3C1*2C2 ] / all outcomes = (3*1) / 10 = 0.3

X = 2 red marble:

        P ( X = 2 ) : Suzan chooses 2 Red marble from the available 3 red marble and 1 green marbles.

        P ( X = 2 ) = [ 3C2*2C1 ] / all outcomes = (3*2) / 10 = 0.6

X = 3 red marble:

        P ( X = 3 ) : Suzan chooses 3 Red marble from the available 3 red marble.

        P ( X = 3 ) = [ 3C3] / all outcomes = (1) / 10 = 0.1

- The probability distribution is as follows:

          X :         1                 2                3

       P (X):       0.3            0.6              0.1

- The expected value E(X) for the given random variable X is:

                E ( X ) = ∑Xi*P(Xi)

                           = 1*0.3 + 2*0.6 + 3*0.1

                           =1.8

- The variance Var(X) for the given random variable X is:

                Var ( X ) = ∑Xi^2*P(Xi) - [ E(X) ] ^2

                               = 1^2*0.3 + 2^2*0.6 + 3^2*0.1 - 1.8^2

                               = 0.36

- The standard deviation for the given random variable X is:

                σ = √Var(X)

                σ = √0.36

                σ = 0.6

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