#0 Theta Ciphering MA National Convention 2015 The two lines with equations 17x 8y 159 and intersect at the point, the least common multiple of
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1 #0 Theta Ciphering The two lines with equations 17x 8y 159 and 9x 7y 219 intersect at the point, the least common multiple of Aand B. AB. Find #0 Theta Ciphering The two lines with equations 17x 8y 159 and 9x 7y 219 intersect at the point, the least common multiple of Aand B. AB. Find #0 Theta Ciphering The two lines with equations 17x 8y 159 and 9x 7y 219 intersect at the point, the least common multiple of Aand B. AB. Find #0 Theta Ciphering The two lines with equations 17x 8y 159 and 9x 7y 219 intersect at the point, the least common multiple of Aand B. AB. Find
2 #1 Theta Ciphering f is a polynomial of least degree n such that f Find the value of n. f 1 5, f 2 f 6 0, f 3 9, f 4 16, and #1 Theta Ciphering f is a polynomial of least degree n such that f Find the value of n. f 1 5, f 2 f 6 0, f 3 9, f 4 16, and #1 Theta Ciphering f is a polynomial of least degree n such that f Find the value of n. f 1 5, f 2 f 6 0, f 3 9, f 4 16, and #1 Theta Ciphering f is a polynomial of least degree n such that f Find the value of n. f 1 5, f 2 f 6 0, f 3 9, f 4 16, and
3 #2 Theta Ciphering b A function y a x, where a and b are real, passes through the points 2,1 and 6,5. If log a log c, find the value of c. 5 3 #2 Theta Ciphering b A function y a x, where a and b are real, passes through the points 2,1 and 6,5. If log a log c, find the value of c. 5 3 #2 Theta Ciphering b A function y a x, where a and b are real, passes through the points 2,1 and 6,5. If log a log c, find the value of c. 5 3 #2 Theta Ciphering b A function y a x, where a and b are real, passes through the points 2,1 and 6,5. If log a log c, find the value of c. 5 3
4 #3 Theta Ciphering Find the length of an apothem, in inches, of a regular hexagon that encloses an area of 72 3 square inches. #3 Theta Ciphering Find the length of an apothem, in inches, of a regular hexagon that encloses an area of 72 3 square inches. #3 Theta Ciphering Find the length of an apothem, in inches, of a regular hexagon that encloses an area of 72 3 square inches. #3 Theta Ciphering Find the length of an apothem, in inches, of a regular hexagon that encloses an area of 72 3 square inches.
5 #4 Theta Ciphering In given quadrilateral ABCD, AB is parallel to CD, and the side lengths of the quadrilateral are as shown. Find the area enclosed by the quadrilateral. #4 Theta Ciphering In given quadrilateral ABCD, AB is parallel to CD, and the side lengths of the quadrilateral are as shown. Find the area enclosed by the quadrilateral. #4 Theta Ciphering In given quadrilateral ABCD, AB is parallel to CD, and the side lengths of the quadrilateral are as shown. Find the area enclosed by the quadrilateral. #4 Theta Ciphering In given quadrilateral ABCD, AB is parallel to CD, and the side lengths of the quadrilateral are as shown. Find the area enclosed by the quadrilateral.
6 #5 Theta Ciphering Evaluate: #5 Theta Ciphering Evaluate: #5 Theta Ciphering Evaluate: #5 Theta Ciphering Evaluate:
7 #6 Theta Ciphering When Pablito is dealt three cards from a standard deck of 52 playing cards, the chances of his being dealt three cards of three unique ranks (rank is the number on the card: 2, 3,, Q, K, A) is how many more times likely than being dealt one pair and a third card of a different rank than the pair? Write your answer in decimal form, rounded to the nearest tenth. #6 Theta Ciphering When Pablito is dealt three cards from a standard deck of 52 playing cards, the chances of his being dealt three cards of three unique ranks (rank is the number on the card: 2, 3,, Q, K, A) is how many more times likely than being dealt one pair and a third card of a different rank than the pair? Write your answer in decimal form, rounded to the nearest tenth. #6 Theta Ciphering When Pablito is dealt three cards from a standard deck of 52 playing cards, the chances of his being dealt three cards of three unique ranks (rank is the number on the card: 2, 3,, Q, K, A) is how many more times likely than being dealt one pair and a third card of a different rank than the pair? Write your answer in decimal form, rounded to the nearest tenth. #6 Theta Ciphering When Pablito is dealt three cards from a standard deck of 52 playing cards, the chances of his being dealt three cards of three unique ranks (rank is the number on the card: 2, 3,, Q, K, A) is how many more times likely than being dealt one pair and a third card of a different rank than the pair? Write your answer in decimal form, rounded to the nearest tenth.
8 #7 Theta Ciphering A triangle has vertices at the points 4,7, 7,5, and 6, 3. If the interior of this triangle is revolved about the line with equation 5x y 27, find the volume of the resulting solid. #7 Theta Ciphering A triangle has vertices at the points 4,7, 7,5, and 6, 3. If the interior of this triangle is revolved about the line with equation 5x y 27, find the volume of the resulting solid. #7 Theta Ciphering A triangle has vertices at the points 4,7, 7,5, and 6, 3. If the interior of this triangle is revolved about the line with equation 5x y 27, find the volume of the resulting solid. #7 Theta Ciphering A triangle has vertices at the points 4,7, 7,5, and 6, 3. If the interior of this triangle is revolved about the line with equation 5x y 27, find the volume of the resulting solid.
9 #8 Theta Ciphering Find the sum of the solutions to the equation x 1 x 2 x 3 8. #8 Theta Ciphering Find the sum of the solutions to the equation x 1 x 2 x 3 8. #8 Theta Ciphering Find the sum of the solutions to the equation x 1 x 2 x 3 8. #8 Theta Ciphering Find the sum of the solutions to the equation x 1 x 2 x 3 8.
10 #9 Theta Ciphering Find the equations of the two directrices of the ellipse with equation y 2 x #9 Theta Ciphering Find the equations of the two directrices of the ellipse with equation y 2 x #9 Theta Ciphering Find the equations of the two directrices of the ellipse with equation y 2 x #9 Theta Ciphering Find the equations of the two directrices of the ellipse with equation y 2 x
11 #10 Theta Ciphering Simplify as a single trigonometric function of some angle involving : n 1 sin sin cos... sin cos... #10 Theta Ciphering Simplify as a single trigonometric function of some angle involving : n 1 sin sin cos... sin cos... #10 Theta Ciphering Simplify as a single trigonometric function of some angle involving : n 1 sin sin cos... sin cos... #10 Theta Ciphering Simplify as a single trigonometric function of some angle involving : n 1 sin sin cos... sin cos...
12 #11 Theta Ciphering A right hexagonal prism with all edges of the same length has a volume of 108 cubic inches. Find the length, in inches, of one of the edges of this prism. #11 Theta Ciphering A right hexagonal prism with all edges of the same length has a volume of 108 cubic inches. Find the length, in inches, of one of the edges of this prism. #11 Theta Ciphering A right hexagonal prism with all edges of the same length has a volume of 108 cubic inches. Find the length, in inches, of one of the edges of this prism. #11 Theta Ciphering A right hexagonal prism with all edges of the same length has a volume of 108 cubic inches. Find the length, in inches, of one of the edges of this prism.
13 #12 Theta Ciphering When written as a base-12 number, the base-10 number 2015! ends in how many consecutive zeros? #12 Theta Ciphering When written as a base-12 number, the base-10 number 2015! ends in how many consecutive zeros? #12 Theta Ciphering When written as a base-12 number, the base-10 number 2015! ends in how many consecutive zeros? #12 Theta Ciphering When written as a base-12 number, the base-10 number 2015! ends in how many consecutive zeros?
14
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