Appearance
question:Compute the median of the following numbers: left{frac{7}{5}, frac{3}{sqrt{5}}, -4 sqrt{5}, 8, frac{10}{3}, 9, -1, -5right}.
answer:To find the median, first arrange the numbers in order from smallest to largest: -4 sqrt{5}, -5, -1, frac{3}{sqrt{5}}, frac{7}{5}, frac{10}{3}, 8, 9 Since there are 8 numbers, the middle two are the 4th and 5th numbers: frac{3}{sqrt{5}}, frac{7}{5} The median is the average of these two numbers: text{Median} = frac{1}{2} left(frac{3}{sqrt{5}} + frac{7}{5}right) To rationalize the denominator, we multiply the first term by frac{sqrt{5}}{sqrt{5}}: text{Median} = frac{1}{2} left(frac{3sqrt{5}}{5} + frac{7}{5}right) Adding the fractions, we get: text{Median} = frac{1}{2} cdot frac{3sqrt{5} + 7}{5} text{Median} = frac{3sqrt{5} + 7}{10} Thus, the median of the given set is frac{3sqrt{5} + 7}{10}.
question:What is the largest underground source of water in Texas?
answer:The largest underground source of water in Texas is the Ogallala Aquifer. This extensive aquifer is a crucial source of water for agricultural and municipal purposes in the region.
question:If there is a shortage of product X in a market with flexible pricing, which of the following will occur? A. The allocation of resources for its production will decrease. B. The market price of product X will increase. C. The market price of product X will decrease. D. The supply curve will shift left, and the demand curve will shift right, eliminating the shortage.
answer:The correct answer is B) The market price of product X will increase. In a situation with a shortage of product X and flexible pricing, the market forces will respond to balance the supply and demand. Since producers cannot satisfy the current demand, they will raise the price of product X. This increase in price will lead to a decrease in demand as consumers become less willing to purchase at higher rates. Eventually, the new equilibrium price will be reached, where the quantity supplied equals the quantity demanded, thereby resolving the shortage.
question:Solve the equation a/4 + a/3 = 21.
answer:To solve the equation a/4 + a/3 = 21, we can first find a common denominator for the two fractions. The least common multiple of 4 and 3 is 12, so we can rewrite the equation as (3a/12) + (4a/12) = 21. Combining the fractions, we get (3a + 4a)/12 = 21. Simplifying the numerator, we get 7a/12 = 21. To isolate a, we can multiply both sides of the equation by 12/7. This gives us a = (21 * 12)/7 = 36. Therefore, the solution to the equation a/4 + a/3 = 21 is a = 36.