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frez [133]
3 years ago
5

Please simplify 4a^3 x b^3 / 2ab^2

Mathematics
1 answer:
DedPeter [7]3 years ago
6 0

Answer:

2a^4b^2

Step-by-step explanation:

                b

Simplify   —

                 2

                    b

 (((4 • (a3)) • —) • a) • b

                     2

               b

 ((22a3 • —) • a) • b

                2

3.1    22   divided by   21   = 2(2 - 1) = 21 = 2

(2a3b • a) • b

4.1    b1 multiplied by b1 = b(1 + 1) = b2

2a^4b^2

Hope this helps, have a nice day/night! :D

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78 million converted in scientific notation
Lemur [1.5K]

The <em><u>correct answer</u></em> is:

7.8 × 10⁷

Explanation:

To write a number in scientific notation, we want the decimal behind the first non-zero digit in the number. The first non-zero digit in 78 is 7; this means we want 7.8. In order to have the decimal point behind the 7, we need to move the decimal 7 places. This is the exponent of 10 in our scientific notation, which gives us

7.8 × 10⁷

7 0
3 years ago
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
Is the height of an equilateral triangle the same as the sides?
Hoochie [10]
No,
 although all the sides are the same length on an equilateral triangle the height is calculated by a straight perpendicular line at the mid point of the base.

 The sides are not perpendicular with the base and are angled outwards 

7 0
3 years ago
Margrets parents have her $40 to spend on new video games. Used games are $8 and new games are $14 what is the system of inequal
Artist 52 [7]
8x + 14y = 40
Or
14x + 8y = 40
7 0
3 years ago
Tony bikes 7 miles in one hour predict how far she would go in 4 hours
goblinko [34]

Answer: 28 it should be

Step-by-step explanation: 7x4 is 28 in 1 hour he bikes 7 and he bikes for 4 hours thats an hours worth 4 times

4 0
3 years ago
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