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nalin [4]
3 years ago
10

Suppose there is a 20% chance that revenue will exceed expectations, a 10% chance that costs will be lower than expected, and a

25% chance that the number of defective parts will be lower than expected. Assume that all variables are statistically independent. What is the chance that all 3 favorable outcomes occur together?
Mathematics
1 answer:
Ierofanga [76]3 years ago
7 0

Answer:

The chance that all 3 favorable outcomes occur together is 0.005

Step-by-step explanation:

When two events are independent, the probability of both occurring is the product of the probabilities of the individual events. More formally, if events A and B are independent, then the probability of both A and B occurring is:

P(A and B) = P(A) x P(B)

In this case,

P(A) =P(revenue will exceed expectations)=20%

P(B) = P(costs will be lower than expected)= 10%

P(C)= P(number of defective parts will be lower than expected)=25%

P(A and B and C) = P(A) x P(B) x P(C)

P(A and B and C) = 0.20x0.10x0.25=0.005

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Inga [223]

Answer:

3.75 quarts, rounded to 3.8 quarts

Step-by-step explanation:

3 quarts of solution is 10% antifreeze, so 0.3 quarts are already antifreeze, and 2.7 quarts are not.

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Substitute a for 0.3

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2 years ago
Which answer is equivalent to<br> ??? Help please
grigory [225]

Answer:

\large\boxed{\dfrac{36}{25}}

Step-by-step explanation:

\text{Use}\ a^{-n}=\dfrac{1}{a^n}\\\\\dfrac{5^{-2}\cdot9}{2^4\cdot4^{-3}}=(5^{-2}\cdot9):(2^4\cdot4^{-3})=\left(\dfrac{1}{5^2}\cdot9\right):\left(2^4\cdot(2^2)^{-3}\right)\\\\\text{use}\ (a^n)^m=a^{nm}\\\\=\left(\dfrac{1}{25}\cdot9\right):(2^4\cdot2^{-6})\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=\dfrac{9}{25}:2^{4+(-6)}=\dfrac{9}{25}:2^{-2}=\dfrac{9}{25}:\dfrac{1}{2^2}=\dfrac{9}{25}:\dfrac{1}{4}=\dfrac{9}{25}\cdot\dfrac{4}{1}=\dfrac{36}{25}

7 0
3 years ago
Why are there 27 cubic feet in one cubic yard
kobusy [5.1K]

One cubic yard is equal to 27 cubic feet because one yard is equal to 3 feet

<em><u>Solution:</u></em>

Given that, there 27 cubic feet in one cubic yard

Yard and feet are units of distance

1 Yard (yd) is equal to 3 feet (ft). To convert yards to feet, multiply the yard value by 3.

<em><u>The conversion factor for 1 yard to 1 feet is given as:</u></em>

1 \text{ yard } = 3 \text{ foot }

Now find for 1 cubic yard . Cubic yard means yard raised to power 3

Therefore,

1\ yard^3 = (3)^3\ feet^3\\\\1\ yard^3 = 27 feet^3\\\\1\ cubic\ yard = 27\ cubic\ feet

Thus one cubic yard is equal to 27 cubic feet

Therefore, there are 27 cubic feet in one cubic feet

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