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VARVARA [1.3K]
3 years ago
6

Use Pascal's triangle to find the coefficient of the third term in the expansion of (a + b)2.

Mathematics
1 answer:
Alexxandr [17]3 years ago
4 0

Answer:

B

Step-by-step explanation:

(a+b)^2

using Pascal triangle

1 1

1 2 1

1 3 3 1

so the third term in the expansion of (a+b)^2

we use

1 2 1

a^2 + 2ab+b

hence the coefficient of third term is 1

option B is collect

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You have a spinner with 4 sectors that is spinned twice. Therefore, the possible outcomes are 4 × 4 = 16 pairs of numbers:
(1, 1) (1, 2) (1, 2) (1, 6)
(2, 1) (2, 2) (2, 2) (2, 6)
(2, 1) (2, 2) (2, 2) (2, <span>6)
</span>(6, 1) (6, 2) (6, 2) (6, <span>6)

The possible products are then,
1    2    2    6
2    4    4  12
2    4    4  12
6  12  12  36

Hence, we have:
1 possible product of 1;
4 </span><span>possible products of 2;
4</span><span> possible products of 4;
</span><span>2 possible product of 6;
</span><span>4 possible products of 12;
</span><span>1 possible product of 36.

Since the paint colors are 4, to make a fair decision, each color should be matched with 16 </span>÷ 4 = 4 total possible outcomes: the products 2, 4 and 12 each have 4 possible outcomes, the products 1, 6 and 36 together have 4 possible outcomes.

Therefore, a fair decision is taken if we match:
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product 4 - color 2
product 12 - color 3
products 1, 6 and 36 - color 4.

Hence, the only correct option is A)

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3 years ago
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