math counts state countdown 2
Including Gene, 10 individuals audition for the three available parts in a new musical. If everyone is equally likely to be chosen for any part, but no one can be chosen for more than one part, what is the probability that Gene gets a part in the musical? Express your answer as a common fraction.
3/10
What is the area, in square inches, of an isosceles trapezoid with bases of lengths 6 inches and 14 inches and nonparallel sides of length 5 inches?
30
Express your answer as a common fraction.
42/13
James can eat 12 jelly beans per minute, and Jenny can eat 8 jelly beans per minute. How many minutes will it take Jenny and James to eat a combined total of 100 jelly beans?
5
Jenny ran 1 mile up a hill in 15 minutes. If it took her 9 minutes to run back down the hill, along the same path, what was Jenny's average speed, in miles per hour, over the whole run?
5
What is the quotient when 1,000,000,000 is divided by 2⁸ · 5⁷?
50
what is the value of 10⁷ −10⁶/ 18 ?
500000
Together, the total value of 2n nickels, 5n pennies and n dimes is $1.50. What is the value of n?
6
What is the median of the set of all positive divisors of 2020? Express your answer as a decimal to the nearest tenth.
60.5
A giant sequoia tree measures 246 feet tall, and a nearby California redwood tree measures 278 feet tall. If each tree continues to grow exactly one foot per year, in how many years will the California redwood be exactly 10% taller than the giant sequoia?
74
A certain rectangular prism has two faces, each of area 42 m², two faces, each of area 54 m² and two faces, each of area 63 m². What is the sum of the 12 edge lengths of the prism, in meters?
88
11
A magic square is a square in which the sum of the numbers in each row, each column and each diagonal is the same. What is the value of a + k in the magic square shown?
If the lines defined by the equations 3x + 2y = 9 and bx − y = 119 are parallel to each other, what is the value of b? Express your answer as a common fraction.
-3/2
What is the value of 2020² − 2020 × 2019 + 2019²− 2019 × 2020?
1
The sum of the first five terms of an arithmetic sequence is 15. What is the third term of this sequence?
3
In triangle ABC, AB = 10 units and BC = 16 units. What is the sum of the least and greatest possible integer lengths for side AC?
32
Andrea lists six prime numbers whose sum is a multiple of 10. Andrea's numbers, in increasing order, are 13, 29, 31, p, 47, 53. What is the value of p?
37
In 2017, Jonah's income was $57,500. His income increased by 400% in 2018,but then decreased by 80% in 2019. What was Jonah's income in 2019, in dollars?
57500
see picture
2
The arithmetic mean of seven consecutive integers is x. What is the absolute difference between the greatest of the seven integers and x?
3
The sum of the digits of a particular three-digit number is 16. The tens digit of this number is three times the units digit, and the hundreds digit is one more than the units digit. What is the number?
493
The numbers {6, 5, 3, 7, y} have arithmetic mean y. What is the median of these numbers? Express your answer as a decimal to the nearest hundredth.
5.25
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5/24
Jimmy tested the lifespans, in years, of several hard drives. His results are given in the histogram shown. How many years is the average lifespan of the hard drives Jimmy tested? Express your answer as a decimal to the nearest tenth.
9.6
What is the value of √6!+3!+2! +1! ?
27
What is the remainder when 1 + 3 + 3²+3³+.....+3 ²⁰²⁰÷81
40
see picture
6
What is the closest integer to the fourth root of 4000?
8
Rae pays $4.69 for a six-inch sub sandwich, and Elijah pays $8.30 for a foot-long sub sandwich. How many more cents per inch of sub sandwich does Rae pay than Elijah?
9
In how many distinct ways can regular pentagon ABCDE be constructed so that each side is either red or blue and no pair of adjacent sides are the same color?
0
Elias has four $100 bills, three $10 bills and six $1 bills. How many different amounts of money can Elias make using some or all of these bills?
139
A special machine has an input slot and an output slot, such that for every real number, x, if 5x + 8 is dropped into the input slot, 3x + 1 will be the output. If the input is −12, what number will be the output?
-11
What is the ratio of the area of the gray region to the total area of the regular hexagon shown here? Express your answer as a common fraction.
2/3
Circle A has area 16 units2 and circle B has area 64 units2. What is the ratio of the radius of circle A to the radius of circle B? Express your answer as a common fraction.
1/2
For how many ordered pairs of integers (x, y) is the point (x, y) exactly 5 units away from the point (20, 15)?
12
If a and n are positive integers with a ⁿ = 64, what is the sum of all possible values of n
12
What is the value of 111² - 11² + 1² ?
12201
What is the value of 123.45 + 234.51 + 345.12 + 451.23 + 512.34? Express your answer as a decimal to the nearest hundredth.
1666.65
Define the binary operation 🔼 as a 🔼 b = a2 + 2ab + b2. What is the value of (1 🔼 1) 🔼 9?
169
How many ways are there to make exactly 50 cents using quarters, dimes and nickels if at least one of each type of coin must be used?
2