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Elena L [17]
2 years ago
8

John always wears a shirt, pants, socks, and shoes. He owns 121212 pairs of socks, 333 pairs of shoes, 555 pairs of pants, and 5

55 shirts.
Mathematics
1 answer:
Pie2 years ago
5 0
If you mean the quantity of ways to dress John, 
he can choose any one of his 12 pairs of socks to combine with any one of his 3 pairs of shoes and any one of his 5 pairs of pants and any one of his 5 <span>shirts.
12 </span>ways to choose pair of socks and 3 ways to choose pair of shoes and 5 ways to choose pant and also 5 ways to choose a shirt.
12*3*5*5=900.
900 ways to dress him...
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2 years ago
Rosa is converting a unit of measure in one system to a unit of measure in another system. 1,760 yd1 mi⋅0.914 m1 yd⋅1 km1,000 m
kodGreya [7K]

Answer: Rosa is finding the number of kilometers in a mile.

Step-by-step explanation:

According to the given information, we have:

1,760 yd=1 mi

0.914 m=1 yd

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So, as we can see, Rosa wants to convert miles to yards, then yards to meters and finally meters to kilometers:

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8 0
2 years ago
What is the binomial expansion of (x + 2)4? x4 + 4x3 + 6x2 + 4x + 1 8x3 + 24x2 + 32x x4 + 8x3 + 24x2 + 32x + 16 2x4 + 8x3 + 12x2
Margaret [11]

<u>Answer-</u>

\boxed{\boxed{(x+2)^4=x^4+8x^3+24x^2+32x+16}}

<u>Solution-</u>

Given expression is (x+2)^4

Applying Binomial Theorem

\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i

Here,

a = x, b = 2 and n = 4

So,

\left(x+2\right)^4=\sum _{i=0}^4\binom{4}{i}x^{\left(4-i\right)}\cdot \:2^i

Expanding the summation

=\dfrac{4!}{0!\left(4-0\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(4-1\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(4-2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(4-3\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(4-4\right)!}x^0\cdot \:2^4

=\dfrac{4!}{0!\left(4\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(3\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(1\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(0\right)!}x^0\cdot \:2^4

=1\cdot x^4\cdot \:1+4\cdot x^3\cdot \:2+6x^2\cdot \:4+4\cdot x\cdot \:8+1\cdot 1\cdot \:16

=x^4+8x^3+24x^2+32x+16

4 0
2 years ago
Read 2 more answers
Given a soda can with a volume of 36 and a diameter of 4, what is the volume of a cone that fits perfectly inside the soda can?
Tomtit [17]
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Now, we can use the height to figure out the volume of a cone. The volume of a cone is V = pi * r^2 *  \frac{h}{3}
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pi * 4 * .96
12.56*.96 = 12.0576
So a cone with a volume of 12.0576 is the largest that will fit into the soda can
5 0
2 years ago
Read 2 more answers
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