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2 years ago

8

In a carnival game, you roll 2 dice. if the sum is 6, you receive a $5 payoff. if the sum is 12, you receive a $9 payoff. otherw

ise, you receive no payoff. what is the expected payoff? (round your answer to two decimal places.) answer

1 answer:

Ray Of Light [21]2 years ago

3 0

P(sum = 6) = 5/36 ; P(sum = 12) = 1/36

expected payoff = (5/36)(5) + (1/36)(9) = $0.94

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A triangle has a perimeter of 126 centimeters. The 2 longer sides are 3 times as long as the shortest side. Find the length of e

Vladimir [108]

The shorter side of the triangle is 18 cm and each of the longer sides are 54 cm

<u>Solution:</u>

Given that triangle has perimeter of 126 cm

Let the length of the shorter side of the triangle be "a"

The 2 longer sides are 3 times as long as the shortest side

So length of 2 longer sides = 3(length of the shorter side)

length of 2 longer sides = 3a

<em><u>The perimeter of triangle is given as:</u></em>

perimeter of triangle = length of the shorter side + length of 2 longer sides

perimeter of triangle = a + 3a + 3a

126 = a + 3a + 3a

7a = 126

a = 18

So length of shorter side = 18 cm

length of 2 longer sides are each = 3a = 3(18) = 54 cm

Thus, the shorter side of the triangle is 18 cm and each of the longer sides is 54 cm

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2 years ago

The lifetime of a certain type of battery is normally distributed with mean value 15 hours and standard deviation 1 hour. There

KIM [24]

Answer:

If the lifetime of batteries in the packet is 40.83 hours or more then, it exceeds for 5% of all packages.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 15

Standard Deviation, σ = 1

Sample size = 4

Total lifetime of 4 batteries = 40 hours

We are given that the distribution of lifetime is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

Standard error due to sampling:

$\displaystyle\frac{\sigma}{\sqrt{n}} = \frac{1}{\sqrt4} = 0.5$

We have to find the value of x such that the probability is 0.05

P(X > x) = 0.05

$P( X > x) = P( z > \displaystyle\frac{x - 40}{0.5})=0.05$

$= 1 -P( z \leq \displaystyle\frac{x - 40}{0.5})=0.05$

$=P( z \leq \displaystyle\frac{x - 40}{0.5})=0.95$

Calculation the value from standard normal z table, we have,

$\displaystyle\frac{x - 40}{0.5} = 1.64\\x = 40.825 \approx 40.83$

Hence, if the lifetime of batteries in the packet is 40.83 hours or more then, it exceeds for 5% of all packages.

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3 years ago

The amount of corn chips in a 16-ounce bag by the dispensing machine has a normal distribution with a mean of 16.5 ounces and a

Elenna [48]

Answer: 1+1=2

Step-by-step explanation: Imagine you have 1 cookie, and a friend gives you 1 more, that means your total amount of cookies is 2. So that proves that 1+1=2!

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2 years ago

Which ordered pair is part of the solution set of the system of inequalities graphed below?

Serjik [45]

They didn't make it easy. Grid lines are apparently 3 apart, but the offered coordinates are all multiples of 4. It appears the only point that is in the doubly-shaded area is ...

... B (-4, -10)

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2 years ago

What is the measure for the following ∠?<br> m∠BOA<br><br> 20<br> 40<br> 60

kaheart [24]

Hello!

First, find angle BOA on the protractor. To do this, look for point B, point O, and point A.

Now, we see some markings that mark what degree point B and point A are at. Point B is marked at 60 degrees, and Point A 40 degrees.

Now, all that's left to do, is subtract the two measurements.

60 degrees - 40 degrees = 20 degrees

Therefore, your answer is 20.

Hope this helps!

8 0

3 years ago