What is the volume of a sphere with a radius of 9 inches
2 answers:
Answer: 972π in.³
Step-by-step explanation: To find the volume of a sphere, start with the formula for the volume of a sphere.
Volume =
Notice that our sphere has a radius of 9 inches, so we can plug a 9 in for the radius in our formula.
Volume =
Start by simplifying the exponent. (9 in.)³ is equal to 9 inches × 9 inches × 9 inches or 729 in.³.
Volume =
Notice that we can cross cancel the 3 in 4/3 and 729 to 1 and 243.
Volume = (4) (243 in³) (π)
Volume = 972π in.³
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Answer:
C
Step-by-step explanation:
When completing the square, we essentially want to create a perfect square trinomial by adding a constant.
If we have the following expression:
And we want to complete the square, we will need to divide the b-coefficient by half and then square it.
Thus, the added term should be:
In the given equation, we have:
The b term here is 8. Therefore:
The value we would add would be 16.
The answer is C.
Further notes:
To complete the square, add 16 like mentioned earlier. However, we also need to subtract 16 to balance things out:
The expression inside the parentheses is now a perfect square trinomial. Factor it:
And we are done!
Answer:
a) 0.1353
b) 0.3679
Step-by-step explanation:
Let's start by defining the random variable T.
T : ''The time (in hours) required to repair a machine''
T ~ exp (λ)
T ~ exp (1)
The probability density function for the exponential distribution is
(In the equation I replaced λ = L)
With L > 0 and x ≥ 0
In this exercise λ = 1 ⇒
For a)
For b)
The event (T ≥ 10 / T > 9) is equivalent to the event T ≥ 1 so they have the same probability of occur