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Hunter-Best [27]

3 years ago

12

Question 6 (1 point) Mrs. Sullivan wants to make a square tablecloth for her dining room table. She has 121 ft? of fabric. What

are the possible side lengths of the tablecloth? A. 11 ft x 11 ft B. 11 ft x 2 ft C. 60.5 ft x 2 ft D. 60.5 ft x 60.5 ft

1 answer:

Mekhanik [1.2K]3 years ago

5 0

Answer:

c 60.5 ft x 2ft

Step-by-step explanation:

60.5 ft x 2 = 121 ft

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There are 4 red marbles and 3 blue marbles in a bag. Once a marble is drawn it is not replaced. Find the probability of drawing

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Answer:

2/7

Step-by-step explanation:

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antiseptic1488 [7]

The given series is geometric with common ratio $6^x - 9$ , which converges if $|6^x - 9|$ (i.e. the interval of convergence). We have the well-known result

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If you're not familiar with that result, it's easy to reproduce.

Let $S_N$ be the $N$ -th partial sum of the infinite series,

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Multiply both sides by the ratio.

$\left(6^x - 9\right) S_N = \left(6^x - 9\right) + \left(6^x - 9\right)^2 + \left(6^x - 9\right)^3 + \cdots + \left(6^x - 9\right)^{N+1}$

Subtract this from $S_N$ to eliminate all the powers of the ratio between 0 and $N+1$ .

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Solve for $S_N$ .

$S_N = \dfrac{1 - \left(6^x - 9\right)^{N+1}}{10-6^x}$

Now as $N\to\infty$ , the exponential term converges to 0 and we're left with

$\displaystyle \sum_{n=0}^\infty \left(6^x-9\right)^n = \lim_{N\to\infty} S_N = \boxed{\frac1{10-6^x}}$

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