answer:The given series is an infinite geometric series with the first term a = -frac{7}{34} and the common ratio r = frac{1}{10}. To find the sum of the series, we can use the formula for the sum of an infinite geometric series if |r| < 1: [ S = frac{a}{1 - r} ] In this case, |r| = frac{1}{10} < 1. Thus, the sum of the series is: [ S = frac{-frac{7}{34}}{1 - frac{1}{10}} ] [ S = frac{-frac{7}{34}}{frac{9}{10}} ] [ S = -frac{7}{34} times frac{10}{9} ] [ S = -frac{70}{306} ] [ S = -frac{35}{153} ] Therefore, the sum of the infinite geometric series is -frac{35}{153}.

answer:2^7cdot 3^4

answer:False. An inferior good experiences a decrease in demand when its price increases. If the quantity demanded increases despite a price increase, it suggests a normal good, where demand rises as income or affordability increases.

answer:The probability of an increase or decrease in the price of a stock is assumed to be 50%, or 0.5. Therefore, the probability of an increase in the closing price on nine consecutive days is: {eq}begin{align*} & = (0.5) cdot (0.5) cdot (0.5) cdot (0.5) cdot (0.5) cdot (0.5) cdot (0.5) cdot (0.5) cdot (0.5) [2ex] & = 0.001953125 [2ex] & approx 0.0020 end{align*} {/eq} Therefore, the probability that a stock will show an increase in its closing price on nine consecutive days is approximately 0.0020, or 0.2%.