FILL BLANKThe circle shown has center O and radius 11. If PR = 12, what is the area of triangle PQR?Give your answer to the nearest 10. (Enter your answer as an integer or a decimal in the answer box.Backspace to erase.)
Answer(s): A
Radius of the circle = 11Diameter (QR) = 2 × 11 = 22Leg PR = 12Since QR is the diameter, and PQR is a right triangle, we can use the Pythagorean Theorem to find PQ.Compute the Area of Triangle PQR:Area 110
FILL BLANKThe 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.)
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 = 4a3 = a2 + 3 = 4 + 3 = 7a4 = a3 + 3 = 7 + 3 = 10a5 = a4 + 3 = 10 + 3 = 13...In general, the k-th term of the sequence is:ak = 1 + (k - 1) × 3 = 3k - 2Using the formula ak = 3k - 2, we calculate a2009:a2009 = 3 × 2009 - 2 = 6027 - 2 = 6025To find the remainder when 6025 is divided by 9, we perform the division:6025 ÷ 9 = 669 remainder 4Thus, the remainder when a2009 = 6025 is divided by 9 is 4.
FILL BLANKThe 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.)
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 asNow, combine the terms on the left-hand side:62x = 210.80 × 562x = 1054
What was the range of the average amounts spent per visit at Mall Q in 1998 for the seven age-groups?
Answer(s): E
From the graph, the seven average amounts spent per visit are 39, 51, 60, 70, 72, 62, 48 dollars.Maximum = 72Minimum = 39Range = 72 - 39 = 33 dollars.
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
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%.
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?
Answer(s): D
Average per person = (average visits per person) × (average amount per visit)
In 2003, what was the ratio of the number of in-store purchases paid for either by check or by credit card to the number of in-store purchases paid for in cash?
Get the percentages from the graph (for 2003):Check = 15%Credit Card = 21%Cash = 33%Add check and credit card:15% + 21% = 36%So we are comparing:36 (check + credit)33 (cash)Write the ratio:36 : 33, or 12 : 11
If the distribution of the number of in-store purchases in 2003 by method of payment is to be represented by a circle graph with a radius of 3.2 centimeters, approximately what will be the length, in centimeters, of the area of the sector representing payment by credit card?
From the graph, in 2003:Credit card purchases = 21% = 0.21Use arc length formula:Arc length = (fraction of circle) × (circumference)Circumference of a circle = 2r r = 3.2 cm 2(3.2) = 6.4 6.4 × 3.14 = 20.1 cmArc length = 0.21 × 20.1 4.221 cm
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