1.How many unique sets of 4 prime numbers exist for which the sum of the members of the set is 45 ?
2. Bobbym wrote on a gigantic piece of paper all the numbers from 1 to 9999 . How many zero digits did he have to write down?
4. Find x.
5. Which is greater?
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6. Find the sum of all perfect squares that divide 2016.
7. Find the greatest possible value of pq + r, where p, q, and r are (not necessarily distinct) prime numbers
satisfying pq + qr + rp = 2016.
8. Positive integers m and n are both greater than 50, have a least common multiple equal to 480, and have a
greatest common divisor equal to 12. Find m + n.
9. Bobbym is stuck fighting his nefarious lizard neighbors yet again though he has another weapon in his math... A LASER! He has 15 health, and the lizard has 20 health. He can deal any integer amount of damage from 1 to 4 and he has a 1/5 chance of dealing 3 damage, a 1/2 chance of dealing 1 damage, and a 1/5 chance of dealing 2 damage, and a 1/10 chance of deleaing 4 damage. Calculate the probability that bobbym will make it out alive, given that bobbym strikes first. The lizards have a 50% chance of dealing 1 damage, and a 50% chance of dealing 2 damage.
10. Find all continuous functions such that
I was doing this triangle problem,
1) There are 3 angles in a triangle, a,b, and c. a < 40, b = c+1, and if c is an integer, what is the least possible value of c?
Is it 71?
2) 15. Let f(a,b) be defined as a^2+b^2-2,(where a and b are positive integers) which of the following CANNOT be the value of f(a,b)?
Is it 2?
3) In a store, 5 customers have bought 7 items, 11 people have bought 6 items, 14 people have bought 5 items, 60 people have bought 4 items, and 10 have bought fewer than 4 items(the number is not specifically known.), which information can be determined?
I. The average amount of items purchased per customer
II. Median number of items purchased per consumer
III. Mode of number of items purchased by consumer
Is it II and III?
4) Flipping y=3x-1 over the y axis obtains -3x-1. Right?
Any chance we can get some clarification on 2,3,8 and
The equation described in 2 equals 0,
In 8, you got equation (1) and your neighbor got (2). For what values of a and b(a and b are distinct), for at least 1 of the solutions are the same?
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For (9), what is the range of
1. Find the sum of all the integers between 50 and 350 whose final digit is 1.
1a. How much greater is this than the sum of all the integers from 1 to 50?
2. Find the complete set of real solutions for the equation where y is real.
3. How many primes can be represented as ? Say NONE if no primes can be represented, say ALL if every prime can be represented.
4. Find all solutions (x,y) where x and y are integers, to the equation
5. For what values of a does
and have at least one root in common?
6. Find the last digit of (2^1232)*(2^5+3^7)?
7.Find the coefficient of p if the difference between the roots in this equation is 9.
8. Bobbym and his neighbor were solving equations late in the night and they were solving two quadratics,
His neighbor switched up bobbym's equation and got (2). For what values of a and b are at least one of the roots the same?
1. How many 2-digit numbers are divisible by 4? Is it 22?
2.Joe began to increase the speed of his car at 2 pm. Since that time, the speed of Joe's car has been increasing by 1.5 miles per hour for each half minute that has passed. If his car is now travelling at 65.5 mph, for how many minutes has the car been exceeding the 55mph speed limit? He starts at 0mph.
3. Ang has x dollars and Julia has y dollars. Ang gives Julia 1/3 of his money. Julia spends 1/4 of the total money she now has. Express the money spent in x and y.
Is it y/4 + x/12
4. A cube has 1000 cubic feet of volume. The container is being filled with 7 cubic feet of water per minute. It is draining at 2 cubic feet per minute. If it is half full at 9 am, at what time is it full? Is it 10:40 am?
A box contains 4 red cards, 6 g blue cards, and 10 green cards.
What is the smallest number of cards we must remove from the box to get 2 cards of THE SAME COLOR?
Is it 4?
2. Max is reading a book. He has read 1/4 of the book. If he stopped at page 67, how many pages are in there fully?
3. 4 lines can intersect at a maximum of... x points. Find x.
4. CD is 6 inches from AB and AB is parallel to CD. Point K is 4 inches from AB and not between the two lines. How many points on CD are exactly 10 inches from K?
5. If 5 different distinct integers sum to 55, what is the largest value any of these numbers can have?