If n is an odd integer, which of the following must be an even integer?
Answer(s): D
· Since n is odd, n - 1 is even. Dividing an even number by 2 results in an integer, but it could be odd or even depending on n.· Since n is odd, n + 1 is even. Dividing an even number by 2 results in an integer, but it could be odd or even depending on n.· Since n is odd, adding 2 results in an odd number.· Since n is odd, squaring it keeps it odd, meaning n2 is odd. Adding 3 to an odd number results in an even number. This must be even.· Since n is odd, n2 is odd. Since n is odd, multiplying it by 2 results in an even number. Adding an odd number (n2) and an even number (2n) results in an odd number.
If 0 < r < t and r = 50 - t, what is the greatest possible value of the median of r, t, and 28?
Since r = 50 - t, we substitute it into the inequality 0 < r < t:1. 0 < 50 - t, which simplifies to t < 50.2. 50 - t < t, which simplifies to50 < 2t25 < tSo, the range of t is 25 < t < 50.The median is the middle number when r, t, and 28 are arranged in increasing order.Since r = 50 - t, we note that r decreases as t increases.Case 1: If t < 28r = 50 - t would be greater than 28 because t is small.The numbers in order are t, 28, r.The median is 28.Case 2: If t > 28r = 50 - t would be less than 28 because t is large.The numbers in order are r, 28, t.The median is still 28.From both cases, the median is always 28, regardless of the values of t and r.The greatest possible value of the median is 28.
It costs d dollars to buy n nails. At this rate, what is the cost of n + 1,850 nails, in dollars?
Answer(s): E
Based on the information given, which of the following pairs of energy sources accounted for more than one- half of the world primary energy supply? (Choose all that apply.)
Answer(s): A,B
We sum the percentages for each pair:· Coal and Oil: 24.4 + 34.4 = 58.8% More than 50%· Natural Gas and Oil: 21.2 + 34.4 = 55.6% More than 50%· Natural Gas and Nuclear Power: 21.2 + 6.5 = 27.7% Less than 50% · Natural Gas and Renewable Sources: 21.2 + 13.5 = 34.7% Less than 50%
What fraction of the world primary energy supply was from hydroelectric power or natural gas?
Answer(s): C
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