According to the graph, for which of the years 2002-2006 was the percent increase from the preceding year in the annual gross income greater than 6 percent?Indicate all such years.
Answer(s): A,C,E
2002 vs. 2001:2003 vs. 2002:2004 vs. 2003:2005 vs. 2004:2006 vs. 2005:
FILL BLANKThe operations and are defined for all numbers x and y by x y = 2x - y and x y = x + 3y.If 3 (2z) = z 6, what is the value of z?
Answer(s): A
6 - 2z = z + 186 - 18 = 2z + z-12 = 3z z = -4
If x = 1 + n = 1 + n3 and y = 1 + n2 = 1 + n4, where x y, what is the value of n?
Answer(s): D
x = 1 + n = 1 + n31 + n = 1 + n3n = n3n3 - n = 0n(n2 - 1) = 0n(n - 1)(n + 1) = 0Possible values:n = 0, 1, or -1y = 1 + n2 = 1 + n41 + n2 = 1 + n4n2 = n4n4 - n2 = 0n2(n2 - 1) = 0Possible values:n = 0, 1, or -1We are told x y, so we need a value of n where x y.Try n = 0:x = 1 + 0 = 1y = 1 + 02 = 1x = y -- invalidTry n = 1:x = 1 + 1 = 2y = 1 + 12 = 2x = y -- invalidTry n = -1:x = 1 + (-1) = 0y = 1 + (-1)2 = 2x y -- valid
If k is an integer greater than 3, then
Answer(s): C
k! = k × (k - 1) × (k - 2) × (k - 3)!
Emma made necklaces to sell at a craft fair. The cost of the supplies for each necklace she made was $6.00, and she spent $450 on supplies. She made a profit of at least $300 by selling the necklaces for $12.50 each at the fair. Which of the following could be the number of necklaces Emma sold? (Note: Profit equals revenue minus cost.)Indicate all such numbers of necklaces.
Answer(s): C,D,E,F,G
Let n = number of necklaces soldRevenue = 12.50 × nProfit = Revenue - 450 = 12.50n - 45012.50n - 450 30012.50n 750n 60
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