Number Stuff
There are 270 cows living in a cave on the first day of June. Every day in June, some number of cows arrive to join the cows already there. At the end of June 30, there are 1000 cows in the cave. On average, how many bats arrived each day in June? Express your answer as a decimal to the nearest tenth.
24.3
Let x be a number between -3.8 and 1.7 such that the distance between x and −3.8 on a number line is exactly two times the distance between x and 1.7. What is the value of x? Express your answer as a decimal to the nearest tenth.
-0.1
What is the degree measure of the acute angle formed by the hour and minute hands at 2:16?
28 degrees
A math textbook is on sale for $45. If this cost represents a 40% discount, what was the original cost of the textbook?
$75
According to “Bus Etiquette”, it is rude to sit directly next to someone. If two people randomly choose two seats into a row of five seats, then what is the probability that they will violate bus etiquette? Express your answer as a common fraction.
2/5
The sum of three distinct primes is 40. What is their product?
434
What is the inverse of the function y=|x-1|?
y= 土x+1
If the sum of the measures of the interior angles of a polygon is 5040 degrees, how many sides does the polygon have?
30
A MATHCOUNTS club has a total of 27 sixth graders and seventh-grade members. If there are 25% more seventh-graders than sixth graders, how many sixth graders are in the club?
12
In how many ways can the letters A, B, C and D be arranged so that no letter is adjacent to any letter that comes immediately before it or immediately after it alphabetically?
2
Using only the eight digits 0, 3, 4, 6, 6, 7, 8 and 8, Erika forms two four-digit numbers whose product is as large as possible. What is the sum of Erika’s numbers?
17403
Kyle subtracts a number from 27 and then multiplies the result by 8. If the product equals the number Kyle first subtracted, what is that number?
216/7
What is the maximum possible area of a rectangle with a diagonal of length 7 cm? Express your answer as a common fraction.
49/2 cm^2
Ramon built a rectangular pen for his dog with dimensions 10 feet by x feet. Heidi builds a circular pen of radius 5 feet for her dog. If the two pens have the same area, what is the value of x? Express your answer as a decimal to the nearest tenth.
7.9
How many distinct pairs of parallel edges are there in a cube?
18
What is the sum of the base-ten numbers from 5 to 50, inclusive, that are palindromes when written in base two?
210
If x is a positive number such that x/18 = 3√x (cube root of x), what is the value of x? Express your answer as a decimal to the nearest tenth.
76.4
Oh there's no question in this one...
whichever team that picked this question just gets 400 points for free.
lol
Suppose hops, skips, and jumps are specific units of length. We know that b hops equal c skips, d jumps equal e hops, and f jumps equal g meters. How many skips are equal to one meter?
cef/bdg skips
One of the dots on a standard 6-sided die is removed randomly. The die is then rolled. What is the probability that the top face has an odd number of dots?
11/21