Speed Math Maθ National Convention 2012

Speed Math MA θ National Convention 2012

burgundy socks in a row (without . . 1) Assume that Earth replacement)? has a radius of Let the solution 12,000 km and that 1 satisfy the following km = 1.3 miles. If Ali . . 12) . . 17) equations: is placed exactly at . If , what is the the intersection of If a cube has side If the supplement of value of: ? the equator and lengths of 2 inches, angle is nine times Prime Meridian, how what is the longest the length of the . . 2) long will it take him to length in that can be angle, what is half of reach the North Pole drawn between any the complement of What is value of if if he is traveling two corner points? angle ? satisfies the equation northwest at 3 miles ? per hour? . . 13) . . 18) . . 3) Hint: the surface What is the smallest If what is area and volume of solution to the What is the larger a sphere with radius equation: ? . . 19) solution of: is and . ? An economist . . 14) develops a complex . . 4) model for the profit of How many solutions a particular business A very important are there to the that is influenced by theorem in Number . . 7) equation: ? three parameters Theory states: If abbreviated a, b, and and are two How many three digit . . 15) c, as described in the integers, then there numbers contain at following equation: exists integers such least one 0? What is the slope of that . With this in line if it is mind, consider the . . 8) perpendicular to following equations. line , which goes The only constraints What is the oblique through the points: on the parameters angle (in degrees) I) -2: and ? are that they are all formed by a clock’s positive real II) 1: hands if the time is numbers. For which 7:45PM? III) 4: parameter(s) will an increase always IV) 7: . . 9) result in an increased profit? For each of the What is the sum of equations I to IV that the values of k that have integer will make matrix . . 16) . . 20) solutions , add up the have no inverse? bolded number in Sharifa, a huge front (i.e. -2, 1, 4, 7). Hurricanes fanatic, An exponential distribution has the What is the sum of . . 10) has six socks in her the bolded numbers? drawer, and the following characteristics: , Triangle has the socks are either navy where is a positive, . . 5) following or burgundy. If the real number and the characteristics: probability that she rate parameter, What is the smallest angle , angle , side pulls out two navy which is also a prime number that is cm. What is the socks in a row positive real number. bigger than 333? exact length of side ? (without replacement) is 2/3, Further, , the survival parameter, is related . . 6) . . 11) then what is the probability that she to as follows. With pulls out two this information, Page 1 of 2 Speed Math MA θ National Convention 2012 solve the following restrictions on the problem. how you weigh the bars (e.g. you can Suppose scientists weigh two stacks at discover a new once, weigh one bar element, called from one stack, mix Awesome, that is and match bars from very radioactive. Its different stacks). average lifespan (i.e. What is the minimal survival) is 1/1,000th number of uses of of a second. If the the scale you would atom lives for more need to do in order to than 1/200th of a determine which second, what is the stack is lower in probability that it weight? lives for more than 1/100th of a second? . . 23)

. . 21) Evaluate the following expression: Clement the deer, . Shiloh the dog, Vernon the whale, . . 24) Oxy the ox, Clickbileh the A company sells gazelle, and Chantel teddy bears at price the lizard are all in P. Q, the number of the running to be teddy bears the nominated “Animal of company is able to the Year.” If three of sell, is related to P by the six are to be the equation Q = -P nominated and each + 50. The company nomination triplet has paid $1000 to use equal probability of manufacturing occurrence, what is equipment, and each the probability that teddy bear costs neither Oxy nor $0.50 to make. What Chantel is should the value of P nominated? be for the company to achieve maximum . . 22) profit? Assume all bears made are sold. Suppose you have 10 stacks of gold bars, each with 10 . . 25) gold bars in them. The stacks are Consider the identical in following appearance and expressions: weight, except that one stack of gold (A): bars weighs 4.9 kg (B): while the others weight 5 kg. There is Which expression, a scale that you can (A) or (B), is lower in use to weigh the value? bars. There are no