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QUESTION: 106

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The sequence a1, a2, a3, ..., ak, ... is defined by a1 = 1 and ak = ak-1 +3 for all integers k 2.
What is the remainder when a2009 is divided by 9? (Enter your answer as an integer or a decimal in the answer box.
Backspace to erase.)

Answer(s): A

Explanation:

The recurrence relation ak = ak-1 + 3 means each term increases by 3 from the previous one. Starting from a1 = 1, we have:

a2 = a1 + 3 = 1 + 3 = 4
a3 = a2 + 3 = 4 + 3 = 7
a4 = a3 + 3 = 7 + 3 = 10
a5 = a4 + 3 = 10 + 3 = 13
...
In general, the k-th term of the sequence is:

ak = 1 + (k - 1) × 3 = 3k - 2

Using the formula ak = 3k - 2, we calculate a2009:

a2009 = 3 × 2009 - 2 = 6027 - 2 = 6025

To find the remainder when 6025 is divided by 9, we perform the division:

6025 ÷ 9 = 669 remainder 4

Thus, the remainder when a2009 = 6025 is divided by 9 is 4.

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QUESTION: 107

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The admission price for each child at a certain zoo is of the admission price for each adult. If the admission price for 10 adults and 3 children is $210.80, what is the admission price for each adult? (Enter your answer as an integer or a decimal in the answer box. Backspace to erase.)

Answer(s): A

Explanation:

The equation for the total cost can be written as:

To combine these terms, we need a common denominator. The common denominator between 1 and 5 is 5, so rewrite 10x as

Now, combine the terms on the left-hand side:

62x = 210.80 × 5
62x = 1054

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QUESTION: 108

What was the range of the average amounts spent per visit at Mall Q in 1998 for the seven age-groups?

Answer(s): E

Explanation:

From the graph, the seven average amounts spent per visit are 39, 51, 60, 70, 72, 62, 48 dollars.
Maximum = 72
Minimum = 39
Range = 72 - 39 = 33 dollars.

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QUESTION: 109

For the 45-54 age-group, the average amount spent per visit at Mall Q in 1998 was what percent greater than the corresponding amount for the 25-34 age-group?

Answer(s): C

Explanation:

For the 45 - 54 age-group the average spent per visit was $72.
For the 25 - 34 age-group it was $60.
Difference = 72 - 60 = $12.
Percent greater = 12 ÷ 60 = 0.20 = 20%.

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QUESTION: 110

For the 18-24 age-group, the average amount spent per person at Mall Q in 1998 was closest to which of the following fractions of the corresponding amount for the 25-34 age-group?