All categories

4 years ago

Extension question (provide a full explanation of your method(s):

Mathematics

1 answer:

Volgvan4 years ago

7 0

Answer:

Ann has little chance to win if she is presented with 4 counters.

Ann can always win from a pile of 6 counters.

(both are explained below)

Step-by-step explanation:

If Ann is presented with 4 counters, and

1. if she takes out 3, she will lose since the opponent will pull out 1 and the last one.

2. if she takes 2 her opponent will take out 1 and she can't pull out the last 1 since her opponents last move was to pull out 1 counter so she will lose.

3. If she takes out 1 and her opponent takes out 3 in the next move she loses.

but if instead of 3 her opponent takes out 2 and in the last move Ann takes out the last 1 then she will win.

So, If Ann is presented with 4 counters she has little chance to win provided in the move just before, her opponent didn't move 1 counter.

Now,

if there is 6 counters to Ann, and

1., if Ben's previous move was 1 then Ann can win if she takes out 3 or 2.

If she takes out 3 Ben can take out 1 or 2 and in the last move she will take out 2 or 1 (respectively) and winning the game.

If she takes out 2 Ben can take out 1 or 3 and in the last move Ann wins by pulling out 3 or 1 respectively.

2. if Ben's previous move was 2 then Ann can win if she takes out 1 or 3.

If she takes out 1 Ben can take out 2 or 3 and in the last move she will take out 3 or 2(respectively) and winning the game.

If she takes out 3 Ben can take out 1 or 2 and in the last move Ann wins by pulling out 2 or 1 respectively.

2. if Ben's previous move was 3 then Ann can win if she takes out 1 or 2.

If she takes out 1 Ben can take out 2 or 3 and in the last move she will take out 3 or 2(respectively) and winning the game.

If she takes out 2 Ben can take out 1 or 3 and in the last move Ann wins by pulling out 3 or 1 respectively.

You might be interested in

4) Use the distance formula to find the length of segment BC.

gogolik [260]

Answer:

Step-by-step explanation:

d= √(5-1)^2+(1-4)^2

d= √4^2+(-3)^2

d= √16+9

d=√25

d=5

8 0

3 years ago

Which of the following geometric series converges?

Artist 52 [7]

All three series converge, so the answer is D.

The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.

Consider a geometric sequence with the first term <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is

$S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}$

Multiply both sides by <em>r</em> :

$rS_n=ar+ar^2+ar^3+\cdots+ar^{n-1}+ar^n$

Subtract the latter sum from the first, which eliminates all but the first and last terms:

$S_n-rS_n=a-ar^n$

Solve for $S_n$ :

$(1-r)S_n=a(1-r^n)\implies S_n=\dfrac a{1-r}-\dfrac{ar^n}{1-r}$

Then as gets arbitrarily large, the term $r^n$ will converge to 0, leaving us with

$S=\displaystyle\lim_{n\to\infty}S_n=\frac a{1-r}$

So the given series converge to

(I) -243/(1 + 1/9) = -2187/10

(II) -1.1/(1 + 1/10) = -1

(III) 27/(1 + 1/3) = 18

8 0

3 years ago

What is the equation of the line which

natka813 [3]

Answer:

The equation of the line is y = (-1/2)x + 5

Step-by-step explanation:

$m = \frac{y2 - y1}{x2 - x1 }$

First of all, have to find gradient using the formula above :

(2,4) & (14,-2)

m = (-2-4) / (14-2)

= -6 / 12

= -1/2

Second, using y = mx + b as b is a constant and is a y-intercept. Using any of these 2 coordinates to find the value of b with given gradient :

y = mx + b

Let y=4 & x=2

4 = (-1/2)(2) + b

b = 4 + 1

= 5

Lastly, put the value of gradient and y-intercept into the equation :

y = mx + b

Let m=-1/2 & b=5

y = (-1/2)x + 5

5 0

3 years ago

Square root of 32 x square root of 1 over 18

lisov135 [29]

<h3>Solution:</h3>

$\sqrt{32} \times \sqrt{ \frac{1}{18} } \\ = \sqrt{32} \times \frac{ \sqrt{1} }{ \sqrt{18} } \\ = \sqrt{32} \times \frac{1}{ \sqrt{18} } \\ = \frac{\sqrt{2 \times 2 \times 2 \times 2 \times 2}}{ \sqrt{2 \times 3 \times 3} } \\ = \frac{ \sqrt{ {2}^{2} \times {2}^{2} \times 2} }{ \sqrt{2 \times {3}^{2} } } \\ = \frac{2 \times 2 \times \sqrt{2} }{3 \times \sqrt{2} } \\ = \frac{4 \times \sqrt{2} }{3 \times \sqrt{2} } \\ = \frac{4}{3}$

<h3>Answer:</h3>

$\frac{4}{3}$

<h3>Hope it helps...</h3>

ray4918 here to help

7 0

3 years ago

-3-6x=9 please help solve for x!!!!

Vinil7 [7]

Answer: x= -2

Step-by-step explanation:

Here you go!

7 0

3 years ago