Snow College Mathematics Contest

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Snow College Mathematics Contest Aril, 08 Senior Division: Grades 0- Form: T Bubble in the single best choice for each question you choose to answer.. If log 0 5=0.699 what is log 0 500?.699 5.699 6.

1 Snow College Mathematics Contest Aril, 08 Senior Division: Grades 0- Form: T Bubble in the single best choice for each question you choose to answer.. If log 0 5=0.699 what is log 0 500? Three dice are rolled. What is the robability that none of them show a or? The number of sots on a articular normal Dalmatian dog is divisible by. When the number of sots is divided by the number of legs, a remainder of results. The sots can also be divided by the total of legs, ears, eyes, and tail to leave a remainder of 6. What is the minimum number of sots? Define Z = {..., 9, 6,, 0,, 6, 9,...}. If we define rimes in Z as those ositive numbers that cannot be exressed as roducts of smaller ositive elements of the set, what is the sum of the first three ositive comosite (non-rime) numbers in Z? An equilateral triangle has a side of length a. What is the area of the largest circle which can be drawn within this triangle? 8 a a a a a 6. Ashereisinscribedinacube. Whatis the ratio of the volume of the shere to the volume of the cube? 6 8 6

2 7. Find the measure of an angle that is both the comlement of \A and the sulement of \B if m\a + m\b = Convert the reeating decimal into a fraction. After reducing to lowest terms, find the difference between the denominator and the numerator Simlify. (log 64 65) (log 6 64) (log 6 7) (log 5 6) Acircleandasquarehavethesameerimeter. Then their areas are equal. the area of the circle is the greater. the area of the square is the greater. the area of the circle is times the area of the square. None of these 0. How many two-digit whole numbers are exactly 7 times the sum of their digits? 0 4. Tau, who loves eating ieces of i, discovered that when the digits of a three-digit natural number are rearranged to form a second number, the difference between the two numbers is usually divisible by Given three distinct one-digit numbers (i.e., from the set {,,, 4, 5, 6, 7, 8, 9}), what is the robability that two of them add u to the third one?

What is the area of the shaded region in ft? 4 4 8 4 4 +4 6. Towns A, B, and C are at the corners of a triangle with equal sides.

3 4. Given these rules, how many different aths can you take to sell SNOWMATH? Begin at the to Move only down For each move, go to one of the letters directly below S N N O O O 0 W W W W 0 M M M M M A A A A 5 T T T 70 H H 5. Two semicircles are in a quarter-circle. What is the area of the shaded region in ft? Towns A, B, and C are at the corners of a triangle with equal sides. A car travels at constant seed from A to B at 0 mh, from BtoCat40 mh, andfromcbacktoaat 60 mh. Whatistheaverageseedforthe round tri? 40 mh 4 mh 45 mh 48 mh 50 mh 7. Matrix X is an inverse to matrix A if AX = XA = I. Which of the following cannot have an inverse matrix? ale 4 ale 4 ale ale ale 4 8. How many different ositive integers less than 08 are multiles of 0 or 8 (inclusive)? What is 08 mod 6? Driving on a certain street, Prof. B can hit stolights green 90% of the time. What is the robability that he will hit exactly two of the next three lights green, assuming indeendent events?

4 . At a certain business, ackages are delivered through a square delivery chute, with each side of the chute measuring ft.suosea rectangular box of dimensions 6ft 4ft x is to be delivered through the chute. What is the maximum value of x? An aquarium on a level table has a square base 0 in wide and is 8in tall. When tilted, the water in it just covers one of the 0 in 8inends but only three-fourths of the square bottom. What is the deth of the water when the bottom is again level? in in.5 in 4in 6in. If f(x) =x, findf(f(f())) Suose f(ln x) = x.findf (x). ln x (ln x) e x e x ln x 6. Suose the Earth is a erfect shere and that there is a steel belt fitting snugly around it at the equator. If the length of the belt were increased by 0 feet, how far above the Earth would the belt be raised if it remained circular and centered around the Earth? Less than inch Between inch and inches Between inches and foot Between foot and feet More than feet X5 4. Simlify the sum i n if i =. 0 i i i n= 7. In regular octagon ABCDEF GH, what is the fraction of the total octagon area found in rectangle ADEH? 7 5 G H F A E B D C

5 8. Shannon takes her favorite number, adds 5 to it, multilies the answer by 0, subtracts 0 from the result and then dros the final 0. If Shannon s (correct) answer is 9, what is her favorite number? If the standard order of oerations is reversed (addition and subtraction are done first and exonentiation is done last), what is the value of ^+? Simlify. tan t sin t cos t tan t sin t sin t cos t cos t. Different shades of ink, red, and white can be made by mixing whole numbers of quarts of red and white aint. Shades are different if the ratio of red to white is different. Find the number of different ossible shades that can be made from at most 4 quarts of red and 5 quarts of white aint How many strings of length 7 of a s, b s, and c s are there such that all the a s, if any, show u at the beginning? For examle: aaaabcb is accetable but abbbbab is not Eric the Shee is at the end of a line of 50 shee waiting to be shorn. But being imatient, Eric sneaks u the line two laces every time the shearer takes a shee from the front to be shorn. So, for examle, while the first shee is being shorn, Eric moves ahead so that there are two shee behind him in line. If at some oint it is only ossible for Eric to move one lace, he does so. How many shee get shorn before Eric? Find the values of c such that the trinomial x +cx 4 can be factored over integers. { 5, 9, 9, 5} { 0, 4, 5, 9} { 4,,, 4} {, 5, 5, } { 5,, 9, 5, 5, 9,, 5}

6 5. From my balcony, I measure the angle of elevation to the to of the neighboring building to be 0, andtheangleofderession to the base to be 45. Ifmy(erendicular) distance from the building is 0 m, howtall is the building in meters? Simlify comletely: r q 5 x 40 0 x 40 5 x 0 x 0 40 x 0 x 0 x x x 7. If 0, x, andx are the first three terms of a geometric sequence, what is x? Car A is mi ahead of car B, which is going in the same direction. 8min later car A is only mi ahead of car B. On average, how much faster is car B traveling? 5mh 7.5mh 0 mh 5 mh not enough info 9. Arollofaertowelscontains00aer towels. The tube around which the towels are rolled is cm in diameter. Including the tube, the whole roll is 4 cm in diameter. What is the diameter of the roll (and tube) when there only 50 aer towels left? 6cm 7cm 8cm 0 cm cm 40. During shooting ractice, a basketball layer takes one ste closer if she misses a shot, and one ste farther away if she makes a shot. After a while, she notices she is two stes farther away than when she began. What is the most we can say about her shooting ercentage P (i.e., shots made shots taken)? 5% <P ale 50% P>50% P>67% P>75% not enough info

Solutions to Assignment #07 MATH radians = = 7 (180 ) = 252 : 5

Solutions to Assignment #07 MATH radians = = 7 (180 ) = 252 : 5 Solutions to Assignment #0 MATH 0 Precalculus Section. (I) Comlete Exercises #b & #0b on. 0. (#b) We robabl need to convert this to degrees. The usual wa of writing out the conversion is to alwas multil