Two number cubes are rolled to determine how a token moves on a game board. The sides of each number cube are numbered 1, 2, 3,
4, 5 and 6.
There are two options describing how the token will be moved.
Option A: If the product is even, move forward 7 spaces. Otherwise, move backward 5.
Option B: If the product is even, move forward 5 spaces. Otherwise, move backward 4.
Use mathematical expectation to determine which option offers the greater likelihood of moving closer to the finish line on the game board.
Which statement best explains the better option?
The mathematical expectation of Option A is 2.75. The mathematical expectation of Option B is 4. Option B offers a greater likelihood of advancing to the finish line.
The mathematical expectation of Option A is 4. The mathematical expectation of Option B is 2.75. Option A offers a greater likelihood of advancing to the finish line.
The mathematical expectation of Option A is 2.75. The mathematical expectation of Option B is 4. Option A offers a greater likelihood of advancing to the finish line.
The mathematical expectation of Option A is 4. The mathematical expectation of Option B is 2.75. Option B offers a greater likelihood of advancing to the finish line.
There are two options describing how the token will be moved.
Option A: If the product is even, move forward 7 spaces. Otherwise, move backward 5.
Option B: If the product is even, move forward 5 spaces. Otherwise, move backward 4.
Use mathematical expectation to determine which option offers the greater likelihood of moving closer to the finish line on the game board.
Which statement best explains the better option?
The mathematical expectation of Option A is 2.75. The mathematical expectation of Option B is 4. Option B offers a greater likelihood of advancing to the finish line.
The mathematical expectation of Option A is 4. The mathematical expectation of Option B is 2.75. Option A offers a greater likelihood of advancing to the finish line.
The mathematical expectation of Option A is 2.75. The mathematical expectation of Option B is 4. Option A offers a greater likelihood of advancing to the finish line.
The mathematical expectation of Option A is 4. The mathematical expectation of Option B is 2.75. Option B offers a greater likelihood of advancing to the finish line.
1 answer:
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Form an equation. Start by representing the number you want to find as X. Now add 1.
X + 1
Now we need to triple it. That basically means multiply X+1 by 3. You can write that as:
3 (X + 1)
Now we write out that the result is 17 more than the number we want to find. So set an equals sign up
3 (X + 1) =
And now write X + 17
3 (X + 1) = X + 17
Now we solve for X.
Firstly, let's get rid of the X on the right.
Remember, if we want to get rid of a number of variable on one side, we need to use opposites, and do the same to the other side of the equation.
In this case, we have a positive X on the right. To get rid of that, we subtract X from both sides. This will leave us with:
2x + 3 = 17
Now let's get rid of the +3 on the left. To do this, we subtract 3 from both sides of the equation.
2x = 17 - 3
2x = 14
Now we just need to get X by itself. The 2 in front of the X multiplies X by 2. Therefore, to get X on its own, we need to divide 2x by 2, which just gives us 2.
We also need to divide the other side by 2, because if we do something on one side, we need to do something on the other too. So divide 14 by 2, and we get 7.
X = 7
But before we celebrate, let's double check the answer. Add 1 to 7. This gives us 8. Triple 8. This is 24. This should be 17 more than 7. So go, 24 - 17. And whaddya know - it's 7!
X + 1
Now we need to triple it. That basically means multiply X+1 by 3. You can write that as:
3 (X + 1)
Now we write out that the result is 17 more than the number we want to find. So set an equals sign up
3 (X + 1) =
And now write X + 17
3 (X + 1) = X + 17
Now we solve for X.
Firstly, let's get rid of the X on the right.
Remember, if we want to get rid of a number of variable on one side, we need to use opposites, and do the same to the other side of the equation.
In this case, we have a positive X on the right. To get rid of that, we subtract X from both sides. This will leave us with:
2x + 3 = 17
Now let's get rid of the +3 on the left. To do this, we subtract 3 from both sides of the equation.
2x = 17 - 3
2x = 14
Now we just need to get X by itself. The 2 in front of the X multiplies X by 2. Therefore, to get X on its own, we need to divide 2x by 2, which just gives us 2.
We also need to divide the other side by 2, because if we do something on one side, we need to do something on the other too. So divide 14 by 2, and we get 7.
X = 7
But before we celebrate, let's double check the answer. Add 1 to 7. This gives us 8. Triple 8. This is 24. This should be 17 more than 7. So go, 24 - 17. And whaddya know - it's 7!