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Dima020 [189]
1 year ago
10

A game involves rolling a fair six-sided die. If the number facing upward on the die is a whole number multiple of three, the pl

ayer wins an amount equal to the number on the die times $20. If the number is not a multiple of three, the player gets nothing. What is the expected value of a players winnings on each roll.
Mathematics
2 answers:
tamaranim1 [39]1 year ago
7 0

Answer:

$30

Step-by-step explanation:

Multiples of 3: 3,6

Expected profit:

⅙(3×20) + ⅙(6×20) + 0

10 + 20 + 0

30

sweet-ann [11.9K]1 year ago
5 0

Answer:

E = 0 x (4/6) + 60 x (1/6) + 120 x (1/6)  = 30

Step-by-step explanation:

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The height of a stuntperson jumping off a building that is 20 m high is modeled by the equation h = 20 -57, where t is the time
cupoosta [38]

A stuntman jumping off a 20-m-high building is modeled by the equation h = 20 – 5t2, where t is the time in seconds. A high-speed camera is ready to film him between 15 m and 10 m above the ground. For which interval of time should the camera film him?

Answer:

1\leq t\geq \sqrt{2}

Step-by-step explanation:

Given:

A stuntman jumping off a 20-m-high building is modeled by the equation

h =20-5t^{2}-----------(1)

A high-speed camera is ready to making film between 15 m and 10 m above the ground

when the stuntman is 15m above the ground.

height h = 15m  

Put height value in equation 1

15 =20-5t^{2}

5t^{2} =20-15

5t^{2} =5

t^{2} =1

t =\pm1

We know that the time is always positive, therefore t=1

when the stuntman is 10m above the ground.

height h = 10m  

Put height value in equation 1

10 =20-5t^{2}

5t^{2} =20-10

5t^{2} =10

t^{2} =\frac{10}{5}

t^{2} =2

t=\pm\sqrt{2}

t=\sqrt{2}

Therefore ,time interval of camera film him is 1\leq t\geq \sqrt{2}

7 0
2 years ago
Suppose 50 percent of the customers at Pizza Palooza order a square pizza, 70 percent order a soft drink, and 35 percent order b
Firdavs [7]

Answer:

Ordering a soft drink is independent of ordering a square pizza.

Step-by-step explanation:

20% more customers order a soft drink than pizza, therefore they cannot be intertwined.

Given: P(A)=0.5 & P(B)=.7

P(A∩B) =  P(A) × P(B)

=  0.5 × .7

=  0.35

P(A∪B) =  P(A) + P(B) - P(A∩B)

=  0.5 + .7 - 0.35

=  0.85

P(AΔB) =  P(A) + P(B) - 2P(A∩B)

=  0.5 + .7 - 2×0.35

=  0.5

P(A') =  1 - P(A)

=  1 - 0.5

=  0.5

P(B') =  1 - P(B)

=  1 - .7

=  0.3

P((A∪B)') =  1 - P(A∪B)

=  1 - 0.85

=  0.15

7 0
1 year ago
The nth term of a sequence is 2n2 − 1 The nth term of a different sequence is 40 − n2 Show that there is only one number that is
allsm [11]

Answer:

Step-by-step explanation:

nth term of a sequence = 2n² - 1

Therefore, terms of the sequence will be,

1, 7, 17, 31, 49, ........... n terms

nth term of a different sequence = 40 - n²

Therefore, terms of the sequence will be,

39, 36, 31, 24, 15, 4, -9, -24 .......... n terms  

Since, there is no negative number in the first sequence,

Therefore, out of 6 positive terms of second sequence only one number (31) is common in both the sequences.

5 0
1 year ago
Suppose the time required for an auto shop to do a tune-up is normally distributed, with a mean of 102 minutes and a standard de
hammer [34]

Answer:

Step-by-step explanation:

Suppose the time required for an auto shop to do a tune-up is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - u)/s

Where

x = points scored by students

u = mean time

s = standard deviation

From the information given,

u = 102 minutes

s = 18 minutes

1) We want to find the probability that a tune-up will take more than 2hrs. It is expressed as

P(x > 120 minutes) = 1 - P(x ≤ 120)

For x = 120

z = (120 - 102)/18 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.8413

P(x > 120) = 1 - 0.8413 = 0.1587

2) We want to find the probability that a tune-up will take lesser than 66 minutes. It is expressed as

P(x < 66 minutes)

For x = 66

z = (66 - 102)/18 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.02275

P(x < 66 minutes) = 0.02275

4 0
2 years ago
What is the multiplicative rate of change of the function? One-fifth Two-fifths 2 5
nlexa [21]

Answer:

A on edge

Step-by-step explanation:

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4 0
1 year ago
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