There are 10 questions on a discrete mathematics final exam. How many ways are there to assign scores to the problems if the sum of the scores is 100 and each question is worth at least 5 points?

Adam, Ben and Carlos shared some marbles. Adam received 1/5 of the marbles. Ben received 18 more marbles than Adam. Carlos received 54 marbles. How many marbles did they have altogether?

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…

Suppose a student got an 82 on an exam that was worth 25% of the final grade, a 75 on another exam worth 25% of the final grade, and 93 for a homework score worth 10% of the final grade. They only have the final exam left, which is worth 40% of the final grade. What score is needed on the final exam to get a 90 for a final grade?

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)!!!

Bananas cost $0.50 each, and apples cost $1.00 each. Select all the combinations of bananas and apples that Elena could buy for exactly $3.50. 2 bananas and 2 apples 1 banana and 2 apples 3 bananas and 2 apples 1 banana and 3 apples 5 bananas and 2 apples 5 bananas and 1 apple

Blake and April are both taking AP Calculus, but they have different teachers who have two different grading systems. Blake is in Mr. Frey’s class and April is in Coach Smith’s class. Blake is mad because she thinks that with her averages, she would have a higher average in Coach Smith’s class. Given her averages below, what would be her overall average for each class? Round to the nearest whole number. Mr. Frey’s Class (Blake) Coach Smith’s Class (April) Test 35% Quiz 20%Homework 10% Classwork 15%Final Exam 20% Test 45%Quiz 20%Homework 10% Classwork 10%Final Exam 15%   Test Quiz HW CW Final Exam 84 75 90 85 90 Blake’s grade with Mr. Frey Blake’s grade with Coach Smith

Andrew and Ryan shared some chocolates. Andrew gave away 1/4 of his chocolates. 1/4 of the given chocolates were taken by Ryan. Ryan then had the same number of chocolates as Andrew. If Andrew gave away 12 chocolates, how many chocolates did each of them have at first? Answers : Alex = 48 Ryan = 33

Bruce, Clark, and Diana found a box of old baseball cards in the attic. They sold 161 cards to a collector and then split the remaining cards equally among themselves. Then, Bruce gave 1/3 cards to Evan. If Evan was given 6 cards, how many cards were in the box when it was found?

One common system of computing the grade point average (GPA) assigns 4 points to an A, 3 points to a B, 2 points to a C,  1 point to a D, and 0 points to an F. What is the GPA of a student who gets an A in a 3-credit course, a B in each of two 4-credit courses, a C in a 3-credit course, and a D in a 4-credit course? (Round to two decimal places) Group of answer choices 2.75 2.25 2.56 2.60