=
=
A fisherman can row upstream at 4 mph and downstream at 6 mph. He started rowing upstream until he got tired and then rowed down
1 answer:
A fisherman can row upstream at 4 mph and downstream at 6 mph. He started rowing upstream until he got tired and then rowed downstream to his starting point. The distance of how far the fisherman row if the entire trip took 2 hours is 9.6 miles
<u />
The speed of an object refers to the change of the object's distance within a specified time.
Mathematically, we can have;
Distance = speed × time
From the information given;
- The fisherman row upstream for 4 miles/ hour.
- The distance covered by the fisherman = 4 × t₁ ----- (1)
- The fisherman row downstream at 6 miles/ hour
- The distance covered by the fisherman = 6 × t₂ ------ (2)
- SInce it took the entire trip 2 hours, we can infer that:
- t₁ + t₂ = 2
- t₂ = 2 - t₁
From equation (2), replace the above value of t₂ into equation (2)
- d = 6 t₂
- d = 6(2 - t₁)
- d = 12 - 6t₁
From equation (1)
- d = 4 t₁
Equation both distance together, we have:
- 12 - 6t₁ = 4t₁
- 12 = 4t₁ + 6t₁
- 12 = 10t₁
- t₁ = 12/10
- t₁ = 1.2 hours
From t₂ = 2 - t₁
- t₂ = 2 - 1.2
- t₂ = 0.8 hours
From d = 4t₁
Replace t₁ with 1.2 hours
- d = 4(1.2 hours)
- d = 4.8 miles
Also, from d = 6t₂
- d = 6(0.8)
- d = 4.8 miles
Therefore, we can conclude that the distance of how far the fisherman row if the entire trip took 2 hours is (4.8+4.8) miles = 9.6 miles
Learn more about distance here:
You might be interested in
=
=
Answer:
Expected value = 40/26 = 1.54 approximately
The player expects to win on average about $1.54 per game.
The positive expected value means it's a good idea to play the game.
============================================================
Further Explanation:
Let's label the three scenarios like so
- scenario A: selecting a black card
- scenario B: selecting a red card that is less than 5
- scenario C: selecting anything that doesn't fit with the previous scenarios
The probability of scenario A happening is 1/2 because half the cards are black. Or you can notice that there are 26 black cards (13 spade + 13 club) out of 52 total, so 26/52 = 1/2. The net pay off for scenario A is 2-1 = 1 dollar because we have to account for the price to play the game.
-----------------
Now onto scenario B.
The cards that are less than five are: {A, 2, 3, 4}. I'm considering aces to be smaller than 2. There are 2 sets of these values to account for the two red suits (hearts and diamonds), meaning there are 4*2 = 8 such cards out of 52 total. Then note that 8/52 = 2/13. The probability of winning $10 is 2/13. Though the net pay off here is 10-1 = 9 dollars to account for the cost to play the game.
So far the fractions we found for scenarios A and B were: 1/2 and 2/13
Let's get each fraction to the same denominator
- 1/2 = 13/26
- 2/13 = 4/26
Then add them up
13/26 + 4/26 = 17/26
Next, subtract the value from 1
1 - (17/26) = 26/26 - 17/26 = 9/26
The fraction 9/26 represents the chances of getting anything other than scenario A or scenario B. The net pay off here is -1 to indicate you lose one dollar.
-----------------------------------
Here's a table to organize everything so far
What we do from here is multiply each probability with the corresponding net payoff. I'll write the results in the fourth column as shown below
Then we add up the results of that fourth column to compute the expected value.
(1/2) + (18/13) + (-9/26)
13/26 + 36/26 - 9/26
(13+36-9)/26
40/26
1.538 approximately
This value rounds to 1.54
The expected value for the player is 1.54 which means they expect to win, on average, about $1.54 per game.
Therefore, this game is tilted in favor of the player and it's a good decision to play the game.
If the expected value was negative, then the player would lose money on average and the game wouldn't be a good idea to play (though the card dealer would be happy).
Having an expected value of 0 would indicate a mathematically fair game, as no side gains money nor do they lose money on average.
The convex heptagon has 14 distinct diagonals can be drawn
Step-by-step explanation:
A polygon is said to be a heptagon if it has 7 vertices, 7 sides and 7 angles. A heptagon is called a convex heptagon if the lines connecting any two non-adjacent vertices lie completely inside the heptagon
The formula of number of diagonals in any polygon is , where
- d is the number of the diagonals of the polygon
- n is the number of sides of the polygon
∵ The heptagon has 7 sides
∴ n = 7
∵ The number of diagonals =
- Substitute n by 7 in the rule above
∴ The number of diagonals =
∴ The number of diagonals =
∴ The number of diagonals =
∴ The number of diagonals = 14
The convex heptagon has 14 distinct diagonals can be drawn
Learn more:
You can learn more about the polygons in brainly.com/question/6281564
#LearnwithBrainly
Hi, there.
For this question, we can apply the Pythagorean theorem .
I'm sure you've seen this equation before, and they kind of tried to trip you up with this problem. Trust me, it's easier than it looks. Let's break it down.
Lengths a and b both have the value of 48, which means that the value s in is 48, because the length of the hypotenuse is the same as the length and height squared multiplied by 2.
Plug in the value for c:
Plug in the value for s:
Do the innermost exponents first:
The square root symbol and the power of 2 cancel each other out, so we are left with:
s = , so the hypotenuse is 4608 inches.