Answer:
The answer is 
Step-by-step explanation:
If we assume that people cannot taste a difference between bottled water, then the probability of identifying tap water is 0.5
Thus, P(identify tap water)=0.5
The probability that at least 8 of the 9 people identify the tap water correctly is the sum of the probabilities
- 8 of 9 people identified correctly or
- 9 of 9 people identified correctly
Since P(identify tap water)=0.5 each probabilities are the same and equal to
=
So we have 
=
∫(t = 2 to 3) t^3 dt
= (1/4)t^4 {for t = 2 to 3}
= 65/4.
----
∫(t = 2 to 3) t √(t - 2) dt
= ∫(u = 0 to 1) (u + 2) √u du, letting u = t - 2
= ∫(u = 0 to 1) (u^(3/2) + 2u^(1/2)) du
= [(2/5) u^(5/2) + (4/3) u^(3/2)] {for u = 0 to 1}
= 26/15.
----
For the k-entry, use integration by parts with
u = t, dv = sin(πt) dt
du = 1 dt, v = (-1/π) cos(πt).
So, ∫(t = 2 to 3) t sin(πt) dt
= (-1/π) t cos(πt) {for t = 2 to 3} - ∫(t = 2 to 3) (-1/π) cos(πt) dt
= (-1/π) (3 * -1 - 2 * 1) + [(1/π^2) sin(πt) {for t = 2 to 3}]
= 5/π + 0
= 5/π.
Therefore,
∫(t = 2 to 3) <t^3, t√(t - 2), t sin(πt)> dt = <65/4, 26/15, 5/π>.
Answer:
the sides are 5ft long
Step-by-step explanation:
since it is a cube we know each side is the same and the cube root of 125 is 5
Answer:
sorry for points
Step-by-step explanation:
