An instructor gives an exam with fourteen questions. students are allowed to choose any ten to answer. a. how many different choices of ten questions are there?
b. suppose six questions require proof and eight do not.
(i) how many groups of ten questions contain four that require proof and six that do not?
(ii) how many groups of ten questions contain at least one that requires proof?
(iii) how many groups of ten questions contain at most three that require proof?
c. suppose the exam instructions specify that at most one of questions 1 and 2 may be included among the ten. how many different choices of ten questions are there? d. suppose the exam instructions specify that either both questions 1 and 2 are to be included among the ten or neither is to be included. how many different choices of ten questions are there?

The table shows the balance of a money market account over time. write a function that represents the balance y(in dollars) after t years.

Tyler enjoys the fish so much that after his birthday his family decides to take him to a famous aquarium a tank at the aquarium is similar to his tank with the scale factor of 8 how many times greater is the volume of the tank at the aquarium than the volume of tyler tank

At river bank, checking account customers earn 0.75% interest a month on their account balances, pay no service fees for writing checks, and pay a monthly $2.00 financial charge. calculate the income earned in one month on the checking account for a customer with an account balance of $1,000. a. $4.25 b. $5.50 c. $6.75 d. $7.25 checking account earnings at baker’s bank are expressed by the equation: i = -0.09x + 10.2. while the earnings at elite bank are modeled by: i = -0.02x + 7.5. in both cases, x is the number of checks written. at what number of checks will elite bank start generating more checking account income than baker's bank? a. 12 b. 25 c. 39 d. 42 emilio’s checking account had a balance of 728.32 at the beginning of the week. he wrote checks for the following amounts throughout the week: $99.48, $33.50, $18.23, and $72.05. he also deposited his paycheck in the amount of $1,109.90. what is his account balance at the end of the week? a. $1,192.35 b. $1,222.86 c. $1,540.52 d. $1,614.96