In the game of football, a team can score either a touchdown for six points or field goal for three points. If a team only scores touchdowns or field goals but does not get any extra points, how many different scores which cannot be achieved if the team scored under 30 points?

A poker hand consists of five cards from a deck of 52.  Order does not matter.  In how many ways can the hand consist of 3 hearts and 2 spades?

If Snow White polishes the diamonds that the seven dwarves mine and bring home, she gets to keep 1/8 of the diamonds. One day after work Bashful brought 1 diamond, Doc brought 6 diamonds, Dopey brought 1 diamond, Grumpy brought 4 diamonds, Happy brought 5 diamonds, Sleepy brought 3 diamonds, and Sneezy brought 4 diamonds. Find how many diamonds Snow White kept after she finished polishing the diamonds.

Ms. Nellies has 2 pints of vinegar for her students to use in a science experiment. Each group of students needs/pint of vinegar. Trey draws the number line model and writes the equation below to help Ms. Nellies figure out how many 3-pint servings of vinegar she has. Are Trey's number line model and equation correct? 什 0 1 + 1 1 2+1=3 1 2 اليا 3 N -IN

Most courses offered at a local university worth either 4 or 5 credit hours. The members of the women's basketball team are taking a total of 49 courses that are worth a total of 207 credit hours. How many 4-credit courses and how many 5-credit courses are being taken? The team members are taking... 4-credit hour courses 5-credit hour courses.

There is another surprising way of characterizing the ged. For two numbers a and b, we think about all the numbers you can get by adding multiples of a and b together. We can imaging this by thinking of a and b as dollar values of bills and then asking what prices can paid with them. For example, if your country only issues a 6 dollar bill and a 14 dollar bill, can you buy something that costs 10 dollars? Yes - you pay with two 14 dollar bills and get three 6 dollar bills back in change. Can you buy something that costs 15 dollars? No - all the bills are worth an even number of dollars so there is no way to get an odd net transaction. Formulated more abstractly: Let S(a, b) = {na + mb : n, m e Z}. Problem 0.1. If c is a common divisor of a and b then c|s for all s E S(a,b) Problem 0.2. If s e S(a, b) then gcd(a, b)|s. Problem 0.3. If s e S(a, b) then sx e S(a, b) for all a € Z Problem 0.4. If S(a, b) = Z if and only if 1 E S %3D Problem 0.5. The set S(0,0) is {0}. For any other a and b…

If 10 pens and 12 pads cost $42, and 5 of the same pens and 10 of the same pads cost $29, find the cost of a pen and a pad.

A cashier has a total of 30 bills, made up of ones, fives, and twenties. The number of twenties is 9 more than the number of ones. The total value of the money is $351. How many of each denomination of bill are there? (show work)!!!

During a recent school football game, your quarterback was a sacked and lost 8 yards on the first down. On the second down, a 15 yard passed was completed. On the third down, your team rushed for 4 yards. Did your team get a first down (a gain of 10 yards) As a result of these plays? How many net yards this they play?

A new dormitory is to be constructed.  There will be three types of rooms: single rooms which accommodate just 1 student per room, double rooms which accommodate 2 students per room, and triple rooms which accommodate 3 students per room.  The dorm will contain 151 rooms and accommodate 262 students. Further, there will be 20 more double rooms than single rooms.  Find the number of each type of room. There will be  Blank 1. Calculate the answer by read surrounding text. single rooms. There will be  Blank 2. Calculate the answer by read surrounding text. double rooms. There will be  Blank 3. Calculate the answer by read surrounding text. triple rooms.