Mathematics, 28.01.2020 15:56, iikatreii

Two students devised a game called “3 pennies & 2 nickels.” each player will choose to play the pennies or the nickels. in each round, the players will flip all their coins on the table and record how many heads and tails they have. the table below includes the point scheme.

point values for “3 pennies & 2 nickels”
penny points nickel points
all pennies heads: –2 both nickels heads: –2
at least one of each: +3 one of each: +5
all pennies tails: –2 both nickels tails: –2

alyssa wants to play the game. choose the statement below that is correct in all aspects.
e(penny) = –0.33 and e(nickel) = 0.33, so she should play with the nickels.
e(penny) = 0.5 and e(nickel) = 1.5, so she should play with the nickels.
e(penny) = 1.75 and e(nickel) = 1.5, so she should play with the pennies.
e(penny) = 2.38 and e(nickel) = 2, so she should play with the pennies.

Answers: 1

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answered: FreyaLouise

E(penny)=1.75 and E(nickel)=1.5 , so she should play with the pennies.

Step-by-step explanation:

We are given Point Values for “3 Pennies & 2 Nickels” as:

Penny Points Nickel Points

All pennies heads: –2 Both nickels heads: –2

At least one of each: +3One of each: +5

All pennies tails: –2 Both nickels tails: –2

Since, the outcome of 3 pennies are given as:

{HHH,TTT,HTH,THH,HHT,HTT,THT,TTH}=8 outcomes.

Now the probability of all head=1/8

( since the outcome is HHH)

Similarly,

Probability of at least one of each= 6/8

( since the outcomes are HTH,THH,HHT,HTT,THT,TTH)

and probability of all pennies tail = 1/8

( Since the outcome is TTT)

Now the outcome of 2 nickel is given as:

{HH,HT,TH,TT}

So, the probability of both nickel head =1/4

( Since, we have the outcome as HH)

Probability of one of each= 2/4

( Since, the outcome is HT,TH)

Probability of both nickels tail= 1/4

( since, the outcome is TT)

Now, Expectation is calculated as sum of the terms obtained by the product of outcomes and it's probability.

E(penny) is calculated as:

$E(penny)=\dfrac{1}{8}\times (-2)+\dfrac{6}{8}\times (3)+\dfrac{1}{8}\times (-2)\\\\E(penny)=\dfrac{-2}{8}+\dfrac{18}{8}+\dfrac{-2}{8}\\\\E(penny)=\dfrac{-2+18-2}{8}\\\\E(penny)=\dfrac{14}{8}\\\\E(penny)=\dfrac{7}{4}\\\\E(penny)=1.75$

Similarly, E(nickel) is calculated as:

$E(nickel)=\dfrac{1}{4}\times (-2)+\dfrac{2}{4}\times (5)+\dfrac{1}{4}\times (-2)\\\\E(nickel)=\dfrac{-2}{4}+\dfrac{10}{4}+\dfrac{-2}{4}\\\\E(nickel)=\dfrac{-2+10-2}{4}\\\\E(nickel)=\dfrac{6}{4}\\\\E(nickel)=\dfrac{3}{2}\\\\E(nickel)=1.5$

answered: daniellealex

E(penny)=1.75 and E(nickel)=1.5 , so she should play with the pennies.

Step-by-step explanation:

We are given Point Values for “3 Pennies & 2 Nickels” as:

Penny Points Nickel Points

All pennies heads: –2 Both nickels heads: –2

At least one of each: +3One of each: +5

All pennies tails: –2 Both nickels tails: –2

Since, the outcome of 3 pennies are given as:

{HHH,TTT,HTH,THH,HHT,HTT,THT,TTH}=8 outcomes.

Now the probability of all head=1/8

( since the outcome is HHH)

Similarly,

Probability of at least one of each= 6/8

( since the outcomes are HTH,THH,HHT,HTT,THT,TTH)

and probability of all pennies tail = 1/8

( Since the outcome is TTT)

Now the outcome of 2 nickel is given as:

{HH,HT,TH,TT}

So, the probability of both nickel head =1/4

( Since, we have the outcome as HH)

Probability of one of each= 2/4

( Since, the outcome is HT,TH)

Probability of both nickels tail= 1/4

( since, the outcome is TT)

Now, Expectation is calculated as sum of the terms obtained by the product of outcomes and it's probability.

E(penny) is calculated as:

Similarly, E(nickel) is calculated as:

answered: Guest

2x^2 -2x -12 = 02(x -3)(x +2) = 0see below for explanation

step-by-step explanation:

equation

you are asked to write the equation

expression = 0

using the given expression. when you do that, you have

2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

(x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

-6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

x - 3 = 0

x = 3 . . . add 3 to both sides of the equation

x +2 = 0

x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

answered: Guest

answer: 48

just remember to use pemdas:

parentheses

expressions

multiplication

division

addition

subtraction

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Two students devised a game called “3 pennies & 2 nickels.” each player will choose to play the...