Numerade

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When the price of goods and services rise over time, it is called O stagflation O inflation O deflation O expansion

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5. Let $J = < x^2 + y^2 - 1, y - 1 >$. Find $f \in I(V(J))$ such that $f \notin J$. 6. Compute the Zariski closures $\bar{S} \subset A^2(C)$ a) $S = \{(n^2, n^3) : n \in N\}$

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Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is inconclusive.\\ $\rho = \lim_{n \to \infty} \left| \frac{a_{n+1}}{a_n} \right| = $ (Enter 'inf' for $\infty$).\\ $\sum_{n=1}^{\infty} \frac{n^2}{n^4 + 7}$ is:\\ O A. convergent\\ O B. divergent\\ O C. The Ratio Test is inconclusive

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A. 4. Two sound sources $S_1$ and $S_2$ produce waves with frequencies 1000 Hz and 500 Hz. When we compare the speed of wave 1 to the speed of wave 2 the result is: (C) The same $V = f\lambda$

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Which of the following schools of thought was NOT developed the during the Age when Alexander the Great was taught by Aristotle? Group of answer choices Cynicism Epicureanism Stoicism Sophism

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Suppose the arc own-price elasticity of demand for gasoline is 0.15. Which of the following is correct?

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majority of economists believe that in the long run, real economic variables and nominal economic variables behave independently of one another. For example, an increase in the money supply, a

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Problem 4. Verify if the set of solutions of a system : $X' = AX$ $X_1 = \begin{pmatrix} 1\\6\\-13 \end{pmatrix}$ $X_2 = \begin{pmatrix} 1\\-2\\-1 \end{pmatrix} e^{-4t}$ $X_3 = \begin{pmatrix} 2\\3\\-2 \end{pmatrix} e^{3t}$

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F. The Dayton Corporation began the current year with a retained earnings balance of $32,000. During the year, the company corrected an error made in the prior year, which was a failure to record depreciation expense of $3,000 on equipment. Also, during the current year, the company earned net income of $12,000 and declared cash dividends of $7,000. Compute the year-end retained earnings balance. 1. $34,000 2. $37,000 3. $41,000 4. $44,000 G. When a corporation completes a 3-for-1 stock split 1. the ownership interest of current stockholders is decreased 2. the market price per share of the stock is decreased 3. the par value per share is decreased 4. the market price per share of the stock and the par value per share is decreased H. A corporation has 50,000 shares of $25 par stock outstanding that has a current market value of $150 per share. If the corporation issues a 5-for-1 stock split, the market value of the stock after the split will be approximately 1. $25 2. $150 3.$5 4. $30

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1. Problem: Evaluate the limit, if it exists: $\lim_{x \to 0} \frac{\sqrt{1+x}-1}{x}$ (a) If we try pluggin in $x = 0$ into the function, then numerator $\sqrt{1+x}-1 =$ denominator $x =$ the result of division is (b) Let's try algebra: multiply both numerator and denominator by $(\sqrt{1+x}+1)$ and simplify the numerator only by using the formula $(a-b)(a+b) = a^2 - b^2$. $\frac{\sqrt{1+x}-1}{x} =$ (c) In the obtained expression, factor $x$ appears both in the numerator and the denominator. Simplify further by canceling equal factors of $x$. (d) Find the limit of the simplified form by using Limit Rules. Show your work.

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mary m.