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pav-90 [236]
2 years ago
6

The ratio of boys to girls in the gym was 4 to 5. How many boys were in the gym if there were 125 girls in the gym?

Mathematics
1 answer:
Anna007 [38]2 years ago
8 0

Answer:

If there are 125 girls, and the ratio is boys to girls, then you can divide 125 by 5 to get the multiplication factor. This would be 25. Now you can multiply 25 by 4 to get how many boys were in the gym, which would be 100. To get back to your original ratio, you can divide 100/125 by 25 on top and bottom to get 4:5, or 4/5. :)

Step-by-step explanation:


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Which of the following series are convergent?
Westkost [7]

Answer:

All of them

Step-by-step explanation:

According to the ratio test, for a series ∑aₙ:

If lim(n→∞) |aₙ₊₁ / aₙ| < 1, then ∑aₙ converges.

If lim(n→∞) |aₙ₊₁ / aₙ| > 1, then ∑aₙ diverges.

(I) aₙ = 10 / n!

lim(n→∞) |(10 / (n+1)!) / (10 / n!)|

lim(n→∞) |(10 / (n+1)!) × (n! / 10)|

lim(n→∞) |n! / (n+1)!|

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0 < 1

This series converges.

(II) aₙ = n / 2ⁿ

lim(n→∞) |((n+1) / 2ⁿ⁺¹) / (n / 2ⁿ)|

lim(n→∞) |((n+1) / 2ⁿ⁺¹) × (2ⁿ / n)|

lim(n→∞) |(n+1) / (2n)|

1/2 < 1

This series converges.

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lim(n→∞) |(1 / (2(n+1))!) / (1 / (2n)!)|

lim(n→∞) |(1 / (2n+2)!) × (2n)! / 1|

lim(n→∞) |(2n)! / (2n+2)!|

lim(n→∞) |1 / ((2n+2)(2n+1))|

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This series converges.

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Answer:

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