Answer:
The speed of the boat in still water u = 8 ![\frac{mi}{hr}](https://tex.z-dn.net/?f=%5Cfrac%7Bmi%7D%7Bhr%7D)
Step-by-step explanation:
Let speed of the boat = u ![\frac{mi}{hr}](https://tex.z-dn.net/?f=%5Cfrac%7Bmi%7D%7Bhr%7D)
Speed of the current = v
= 4 ![\frac{mi}{hr}](https://tex.z-dn.net/?f=%5Cfrac%7Bmi%7D%7Bhr%7D)
Given that the first boat to travel 3 miles upstream and back in a total 1 hour.
So
![\frac{3}{u - v} + \frac{3}{u + v} = 1](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7Bu%20-%20v%7D%20%2B%20%5Cfrac%7B3%7D%7Bu%20%2B%20v%7D%20%20%3D%201)
![\frac{6 u}{u^{2} - v^{2} } = 1](https://tex.z-dn.net/?f=%5Cfrac%7B6%20u%7D%7Bu%5E%7B2%7D%20-%20v%5E%7B2%7D%20%20%7D%20%3D%201)
![u^{2} - v^{2} - 6 u = 0](https://tex.z-dn.net/?f=u%5E%7B2%7D%20-%20v%5E%7B2%7D%20-%206%20u%20%3D%200)
Since v = 4
![u^{2} - 6 u - 16 = 0](https://tex.z-dn.net/?f=u%5E%7B2%7D%20-%206%20u%20-%2016%20%3D%200)
By solving above equation
![u^{2} + 2 u - 8 u - 16 = 0](https://tex.z-dn.net/?f=u%5E%7B2%7D%20%2B%202%20u%20-%208%20u%20-%2016%20%3D%200)
![u (u + 2) - 8 (u + 2) = 0](https://tex.z-dn.net/?f=u%20%28u%20%2B%202%29%20-%208%20%28u%20%2B%202%29%20%3D%200)
![(u - 8)(u +2) = 0](https://tex.z-dn.net/?f=%28u%20-%208%29%28u%20%2B2%29%20%3D%200)
u = 8 , - 2
Since u = -2 is not valid.
⇒ u = 8 ![\frac{mi}{hr}](https://tex.z-dn.net/?f=%5Cfrac%7Bmi%7D%7Bhr%7D)
This is the speed of the boat in still water.
8 minus 3 equals to 5.
5 subtracted by 15 equals to 10.
Answer:
You are expected to lose $0.05 (or win -$0.05)
Step-by-step explanation:
Since the roulette wheel has the numbers 1 through 36, 0, and 00, there are 38 possible outcomes.
In this bet, you are allowed to pick 3 out of the 38 numbers. Thus, your chances of winning (P(W)) and losing (P(L)) are:
![P(W)=\frac{3}{38}\\P(L) = 1 - P(W)\\P(L) = \frac{35}{38}\\](https://tex.z-dn.net/?f=P%28W%29%3D%5Cfrac%7B3%7D%7B38%7D%5C%5CP%28L%29%20%3D%201%20-%20P%28W%29%5C%5CP%28L%29%20%3D%20%5Cfrac%7B35%7D%7B38%7D%5C%5C)
The expected value of the bet is given by the sum of the product of each outcome pay by its probability. Winning the bet means winning $11 while losing the bet means losing $1. The expected value is:
![EV = (11*\frac{3}{38}) -(1*\frac{35}{38})\\EV = -\$0.0525](https://tex.z-dn.net/?f=EV%20%3D%20%2811%2A%5Cfrac%7B3%7D%7B38%7D%29%20-%281%2A%5Cfrac%7B35%7D%7B38%7D%29%5C%5CEV%20%3D%20-%5C%240.0525)
Therefore, with a $1 bet, you are expected to lose roughly $0.05
Answer: 4y+4z
Step-by-step explanation:
Hey there! :)
Answer:
arc AB = 2.5π in (in terms of pi) or ≈7.85 in. (pi = 3.14)
Step-by-step explanation:
Begin by finding the circumference of the circle. Use the formula:
C = 2rπ
C = 2(9)π
C = 18π.
Since ∠AQB equals 50°, set up a ratio to find the length of arc AB:
![\frac{50}{360} = \frac{x}{18\pi }](https://tex.z-dn.net/?f=%5Cfrac%7B50%7D%7B360%7D%20%20%3D%20%5Cfrac%7Bx%7D%7B18%5Cpi%20%7D)
Cross multiply:
50 · 18π = 360x
900π = 360x
Divide both sides by 360:
x = 2.5π in, or ≈7.85 in.