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Julli [10]
3 years ago
6

g: Consider the following game. A coin is flipped. If it lands tails we stop playing and winnothing. If it lands heads we spin a

wheel with numbers from1to100, each with equalprobability. We get the amount of money written on the weel and we play again (i.e. weflip the coin again). LetWbe our total winnings from all tosses of the coin. FindE[W]andVar(W).
Mathematics
1 answer:
galben [10]3 years ago
5 0

Answer:

E[W] = $25 (assuming the currency is in dollars)

Var(W) = 1041.67

Step-by-step explanation:

Probability of winning first starts with the coin toss.

For a win, the coin needs to land on heads.

Probability of that = 1/2 = 0.5

Then probability of winning any amount = 1/100 = 0.01

Total probability of winning any amount = 0.5 × 0.01 = 0.005

But expected value is given by

E(X) = Σ xᵢpᵢ

where xᵢ is each amount that could be won

pᵢ is the probability of each amount to be won and it is the same for all the possible winnings = 0.005

So,

E(W) = Σ 0.005 xᵢ

Summing from 0 to 100 (0 indicating getting a tail from the coin toss). This could be done with dome faster with an integral sign

E(W) = ∫ 0.005 x dx

Integrating from 0 to 100

E(W) = [0.005 x²/2]¹⁰⁰₀

E(W) = [0.0025 x²]¹⁰⁰₀ = 0.0025(100² - 0²) = 0.0025 × 10000 = $25

Variance is given by

Variance = Var(X) = Σxᵢ²pᵢ − μ²

μ = expected value

We calculate the expression, Σxᵢ²pᵢ which is another sum from 0 to 100

Σxᵢ²pᵢ = Σ 0.005xᵢ²

Σ 0.005 xᵢ² = ∫ 0.005 x² dx

Integrating from 0 to 100

∫ 0.005 x² dx = [0.005 x³/3]¹⁰⁰₀ = [0.1667x³]¹⁰⁰₀ = 0.1667(100³ - 0³) = 1666.67

Var(W) = 1666.67 - 25² = 1666.67 - 625 = 1041.67.

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The height of a ball dropped from the top of a 450-foot tall building can be described by the expression
BaLLatris [955]

Answer:

The answer is 386 feet.

Step-by-step explanation:

This equation simply asks to plug in a value that gives you the final value of the height. 450 is the initial height, and r (or l) is referred to as the amount of seconds after the item is dropped. 16 is the constant value of feet that the ball drops within one second.

Therefore, by substituting 4 for r (or l) and multiplying it by 16, you will receive 64 feet in 4 seconds. Finally, you need to subtract this from 450 feet, giving you a final answer of 386 feet.

8 0
3 years ago
I really need help with this one please help
Dominik [7]

Yo sup??

a.For this part just draw a triangle with sides 4,8 and 8 inches respectively.

The sides having 8 inches should make equal angle with the base side.

b.One angle is 20

The other two angles be x and y

but x=y because its an isosceles triangle

x+y+20=180

2x=160

x=80

Hope this helps.

5 0
3 years ago
Jill cuts a piece of cardboard in the shape of a trapezoid.The area of the is 43.5sp cm. If bases are cm and 8.5cm long,what is
boyakko [2]

Answer:

7.25cm

Step-by-step explanation:

Let the complete question be;

<em>Jill cuts a piece of cardboard in the shape of a trapezoid. The area of the is 43.5sp cm. If bases are 3.5cm and 8.5cm long, what is the height.</em>

<em />

Area of a trapezoid = 1/2(a+b)*h

a and b are the parallel sides (bases)

h is the height

Given

a = 3.5cm

b = 8.5cm

A = 43.5 sq.cm

Required

Height h

Substitute the given values into the expression

Area of a trapezoid = 1/2(a+b)*h

43.5 = 1/2(3.5+8.5)*h

43.5 = 1/2 * 12h

43.5 = 6h

h = 43.5/6

h = 7.25cm

Hence the height is 7.25cm

8 0
3 years ago
Sims waist is 30 inches. He wants to put on more weight and is hoping to gain enough weight to increase his waist size by 8%. Ho
11Alexandr11 [23.1K]

Sim wants to increase his waist size to 32.4 inches.

<h3>How many inches does Sim want his waist to be?</h3>

Sim wants the increase to be 8% of 30 inches.

The amount of increase Sim wants in his waist size exists

8% × 30 inches.

= 0.08 × 30 inches.

= 2.4 inches.

Adding the wanted increase to his present size would create Sim's waist size to be

30 in + 2.4 in = 32.4 inches.

Sim wants to increase his waist size to 32.4 inches.

Therefore, the correct answer is 32.4 inches.

To learn more about sizes refer to:

brainly.com/question/6285404

#SPJ9

8 0
1 year ago
Helppppp with angles
netineya [11]

Answer:

61

Step-by-step explanation:

8 and 11 are corresponding angles. therefore they add up to 180.

so, 180-119 = 61

8 0
3 years ago
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