Numerade

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Determine whether or not the distribution is a discrete probability distribution and select the reason why or why not. x -1 0 8 P(X=x)P(X=x) 1/8 1/8 5/8 First, decide whether the distribution is a discrete probability distribution, then select the reason for making this decision.

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Prove the following statements by induction 1. $\forall n \ge 1$, $1 + r + r^2 + ... + r^n = \frac{r^{n+1} - 1}{r - 1}$, where $r \ne 1$ 2. $\forall n \ge 1$, $\frac{1}{3} + \frac{1}{15} + \frac{1}{35} + ... + \frac{1}{4n^2 - 1} = \frac{n}{2n + 1}$ 3. $\forall n \ge 1$, $2 + 5 + 8 + ... + (3n - 1) = \frac{1}{2}n(3n + 1)$ 4. $\forall n \ge 2$, $(1 - \frac{1}{2^2})(1 - \frac{1}{3^2})(1 - \frac{1}{4^2})...(1 - \frac{1}{n^2}) = \frac{n+1}{2n}$ 5. Prove that $\forall n \ge 1$, $5^{2n} - 1$ is a multiple of 8

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Classify this reaction: $NaC_2H_3O_2 + H_2O \rightarrow HC_2H_3O_2 + NaOH$

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Molarity is a unit of ________. surface area mass density concentration

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7. (10 points) Find the first three terms in the sequence of partial sums of the series $\sum_{k=3}^{\infty} \frac{k+1}{k-1}$ Write your terms as reduced fractions.

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23. Cart, ball, and plane ** A cart rolls down an inclined plane. A ball is fired from the cart, perpendicularly to the plane. Will the ball eventually land in the cart? Hint: Choose your coordinate system wisely.

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For 2021, Lili Corp., a domestic corporation, has the following financial records: \begin{tabular}{ll} Gross Sales & P7,500,000 \\ Cost of Sales & P3,000,000 \\ Itemized Deductions & $ P 2,500,000 $ \end{tabular}

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Trim Lawn, Inc. has two owners, three highly compensated key employees, and thirty-two rank-and-file employees. Ten of the rank-and-file employees were hired one or two years ago. In addition, Trim Lawn hires ten additional workers in the summer to meet the demand for seasonal lawn care needs. Trim Lawn plans to begin group-term life insurance as an employee benefit. To meet nondiscrimination requirements, Trim Lawn must include ◻ employees. ◻ twenty-two. ◻ twenty-seven. ◻ thirty-two. ◻ thirty-seven. ◻ forty-seven. Trim Lawn, Inc. has two owners, three highly compensated key employees, and thirty-two rank-and-file employees. Ten of the rank-and-file employees were hired one or two years ago. In addition, Trim Lawn hires ten additional workers in the summer to meet the demand for seasonal lawn care needs. Trim Lawn plans to begin group-term life insurance as an employee benefit. To meet nondiscrimination requirements, Trim Lawn must include ◻ employees. ◻ twenty-two. ◻ twenty-seven. ◻ thirty-two. ◻ thirty-seven. ◻ forty-seven.

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Let P(3, 2, 1) and Q(-4, -6, 1) be two points in $\mathbb{R}^3$. Find the distance between P and Q. PQ

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Question 10 ( 3 points ) When managers focus on the stakeholder group that generates the revenue , they are asking " How do we look to shareholders ? " " How do customers see us ? " " At what must we excel ? " " Can we continue to improve and create value ? "

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todd c.