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NeTakaya
3 years ago
5

A game is being played with two players. There are 21 balloons and the player who pops the last balloon wins. One or two can be

popped in a turn. How can a player win every time
Mathematics
1 answer:
34kurt3 years ago
4 0

Answer:

  be the second player, and always leave a multiple of 3 balloons

Step-by-step explanation:

In order to win, a player must force the other player to leave one or two balloons. To do that, the winning player must leave one more balloon than the maximum number that can be popped. That is, the winner will be the player who leaves 3 balloons,

Working backward, we find that the winner must leave a multiple of 3 after each turn. Since the starting number is a multiple of 3, the first player must lose if the second player plays optimally.

The winning strategy is ...

  • be the second player
  • always leave a multiple of 3 balloons.
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16) y intercept is -6
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3 years ago
I need help on this statistic problem.
vladimir1956 [14]

Answer:

Option B.

Step-by-step explanation:

In a regression of y in x, the proportion oh the variation in y explained by the variable x is shown in the R-squared value. So, for answering this question we need to look at the R-squared of such regression.

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3 years ago
What are the solutions to the following system of equations?<br><br> x − y = 6<br> y = x2 −6
anastassius [24]

The solutions to the given system of equations is (0, -6) and (1, -5)  

<h3>Simultaneous equations</h3>

From the question, we are to determine the solutions to the given system of equations

The equations are

x − y = 6 --------- (1)

y = x² −6 ---------- (2)

From equation (1)

x - y = 6

∴ x = 6 + y ------- (3)

Substitute into equation (2)

y = x² −6

y = (6+y)² −6

y = (6+y)(6+y) -6

y = 36 + 6y + 6y +y² -6

y = 36 + 12y + y² - 6

Simplifying

y² + 12y - y + 30 = 0

y² + 11y + 30 = 0

Solve quadratically

y² + 11y + 30 = 0

y² + 6y + 5y + 30 = 0

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(y + 5)(y + 6) = 0

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Substitute the values of y into equation (3)

x = 6 + y

When y = -5

x = 6 + (-5)

x = 6 -5

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When y = -6

x = 6 + (-6)

x = 6 -6

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∴ When x = 0, y = -6 and when x = 1, y = -5

Hence, the solutions to the given system of equations is (0, -6) and (1, -5)  

Learn more on Solving simultaneous equations here: brainly.com/question/16863577

#SPJ!

7 0
2 years ago
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3 years ago
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Natasha_Volkova [10]

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<em>Additional comment</em>

The reminder that these are "points" is to ensure that you write both coordinates as an ordered pair. We know the x-intercepts have a y-value of zero, for example, so there is a tendency to identify them simply as x=2 and x=4. This problem statement is telling you to write them as ordered pairs.

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