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Lunna [17]
1 year ago
5

A game show contestant is offered the option of receiving a computer system worth $2300 or accepting a chance to win either a lu

xury vacation worth $5400 or a boat worth $8700. If the second option is chosen the contestants probabilities of winning the vacation or the boat are 0.20 and 0.15, respectively. If the contestant were to turn down the computer system. and go for one of the other prizes, what would be the expected winnings?
Mathematics
1 answer:
enot [183]1 year ago
6 0

Step 01:

Game show

Data:

$2300 computer system

$5400 luxury vacation

$8700 boat

Step 02:

Expected winnings

p (luxury vacation) = 0.20

p (boat) = 0.15

E\text{ (game show) = \$5400}\cdot0.20\text{ + \$8700}\cdot0.15

E (game show) = $1080 + $1305 = $2385

The answer is:

The expected winnings are $2385

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Which of the values shown are potential roots of f(x) = 3x3 â€"" 13x2 â€"" 3x 45? Select all that apply.
Verdich [7]

The potential roots of the function are, \pm1, \ \pm3, \ \pm5, \ \pm9,\  \pm15, \ \pm45,\  \pm \dfrac{1}{3},\  \pm \dfrac{5}{3}

And the accurate root is 3 it can be determined by using rules of the rational root equation.

<h2>Given that,</h2>

Function; \rm f(x) = 3x^3 - 13x^2 -3x + 45

<h3>We have to determine,</h3>

Which of the values shown are potential roots of the given equation?

<h3>According to the question,</h3>

Potential roots of the polynomial are all possible roots of f(x).

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Using rational root theorem test. We will find all the possible or potential roots of the polynomial.

\rm p=\dfrac{All\  the \ positive}{Negative\  factors \ of\  45}

\rm q=\dfrac{All\  the \ positive}{Negative\  factors \ of\  3}

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\dfrac{p}{q} = \pm1, \ \pm3, \ \pm5, \ \pm9,\  \pm15, \ \pm45,\  \pm \dfrac{1}{3},\  \pm \dfrac{5}{3}

Now check for all the rational roots which are possible for the given function,

\rm f(x) = 3x^3 - 13x^2 -3x + 45\\\\ f(1) = 3(1)^3 - 13(1)^2 -3(1) + 45 = 3-13-3+45 = 32\neq 0\\\\ f(-1) = 3(-1)^3 - 13(-1)^2 -3(-1) + 45 =- 3-13+3+45 = 32\neq 0\\\\ f(3) = 3(3)^3 - 13(3)^2 -3(3) + 45 = 81-117-9+45 =0\\\\ f(-3) = 3(-3)^3 - 13(-3)^2 -3(-3) + 45 = -81+117+9+45 =-144\neq 0

Therefore, x = 3 is the potential root of the given function.

Hence, The potential roots of the function are, \pm1, \ \pm3, \ \pm5, \ \pm9,\  \pm15, \ \pm45,\  \pm \dfrac{1}{3},\  \pm \dfrac{5}{3}.

For more details about Potential roots refer to the link given below.

brainly.com/question/25873992

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What is the volume of this cone
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