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Anna11 [10]
3 years ago
6

Matt can plant 27 trees in 3 hours. At that

Mathematics
1 answer:
Bogdan [553]3 years ago
7 0

Answer:

72 trees.

Step-by-step explanation:

27 divided by 3 equals 9. so that means Matt can plant 9 trees in one hour so 9 is our unit rate ( what we multiply by) so now you multiply 9 by 8 and your answer is 72

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Your friend asks if you would like to play a game of chance that uses a deck of cards and costs $1 to play. They say that if you
gtnhenbr [62]

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

\begin{array}{|c|c|c|}\cline{1-3}\text{Scenario} & \text{Probability} & \text{Net Payoff}\\ \cline{1-3}\text{A} & 1/2 & 1\\ \cline{1-3}\text{B} & 2/13 & 9\\ \cline{1-3}\text{C} & 9/26 & -1\\ \cline{1-3}\end{array}

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

\begin{array}{|c|c|c|c|}\cline{1-4}\text{Scenario} & \text{Probability} & \text{Net Payoff} & \text{Probability * Payoff}\\ \cline{1-4}\text{A} & 1/2 & 1 & 1/2\\ \cline{1-4}\text{B} & 2/13 & 9 & 18/13\\ \cline{1-4}\text{C} & 9/26 & -1 & -9/26\\ \cline{1-4}\end{array}

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.

7 0
2 years ago
Convert 13 weeks to seconds.
dimaraw [331]

The value of 13 weeks in seconds is 7862400 seconds

<h3>Conversion of weeks to seconds</h3>

In order to convert weeks to seconds, we will use the following conversion factor

1week = 7 days

13weeks = 91days

<u>Convert days to hours</u>

Since 24 hours = 1 day, then;

91 days = (91*24)

91 days = 2184 hours

Convert hours to seconds

1 hour = 3600secs

Hence 2184 hours = (2184*3600)

2184 hours = 78624000 seconds

Hence the value of 13 weeks in seconds is 7862400 seconds

Learn more on conversion on weeks to seconds here: brainly.com/question/11947673

#SPJ1

8 0
2 years ago
Find the equation of the tangent plane to the surface z=e−x/17ln(y) at the point (3,3,0.920883)
bonufazy [111]
I dont know i will tell you when i find out
5 0
3 years ago
Because all of the ending values are given in feet, find the window dimensions in feet. Convert the length of 3 feet, 9 inches s
MA_775_DIABLO [31]

Answer: 3.75 ft

Step-by-step explanation:

Here we are given the measure of the length of a window. Generally the length is given in the International System of units format (meters); however, in this case we are given the length in feet and inches:

3 ft+9 in

Now, before converting this whole measure to feet, we have to know that 1 ft=12 in, then we can perform the conversion:

9 in \frac{1 ft}{12 in}=0.75 ft

This means 9 in=0.75 ft

Hence:

3 ft+9 i=3 ft+0.75 ft=3.75 ft This is the measure of the length of the window in feet.

8 0
3 years ago
Mr. Wallace took 600 mg of medicine. This was<br> 75% of the full dose. What is the full dose?
Soloha48 [4]

Answer:800

Step-by-step explanation:

75% = 0.75

600/0.75 = x/1

Cross multiply:

0.75x = 600

Divide 0.75 to both sides:

x = 800

So the full does is 800mg.

8 0
3 years ago
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