A student council consists of three freshmen, four sophomores, four juniors, and five seniors. How many committees of eight members of the council contain at least one member from each class?

How many ways can a committee of 3 freshmen and 4 juniors be formed from a group of 8 freshmen and 11 juniors?

The sports car has a mass of 2.3 Mg, and while it is traveling at 28 m/s the driver causes it to accelerate at 5 m/s^2. If the drag resistance on the car due to the wind is FD =(0.3v^2) N, where v is the velocity in m/s, determine the power supplied to the engine at this instant. The engine has a running efficiency of ε = 0.68.

A function

$$f\left(x\right)$$

has these properties: • The domain of f is the set of natural numbers. •

$$f\left(1\right)=1$$

•

$$f\left(x+1\right)=f\left(x\right)+3x\left(x+1\right)+1$$

a) Determine

$$f\left(2\right)$$

,

$$f\left(3\right)$$

,

$$f\left(4\right)$$

,

$$f\left(5\right)$$

, and

$$f\left(6\right)$$

. b) Describe the function.

Use < or > to complete each statement. 10( -6) ○ -10(-6)

use a graph to solve the equation on the interval -2π, 2π. csc x = - 2√3 / 3

There are equally many boys and girls in the senior class. If 5 seniors are randomly selected to form the student council, find the probability the council will contain at least 3 girls.

Five freshmen, 4 sophomores, and 2 juniors are present at a meeting of students. (a) In how many ways can a six-member committee of three freshmen, two sophomores, and one junior be formed? (b) In how many ways can a six-member committee be selected with no more than two freshmen members?

A student council decides to form a sub-committee of five council members. There are four boys and five girls on council. a) How many different ways can the sub-committee be selected with exactly three girls? b) How many different ways can the sub-committee be selected with at least three girls?

a. A store sells 8 kinds of balloons with at least 30 of each kind. How many different combinations of 30 balloons can be chosen? b. If the store has only 12 red balloons but at least 30 of each other kind of balloon, how many combinations of balloons can be chosen? c. If the store has only 8 blue balloons but at least 30 of each other kind of balloon, how many combinations of balloons can be chosen? d. If the store has only 12 red balloons and only 8 blue balloons but at least 30 of each other kind of balloon, how many combinations of balloons can be chosen?

Suppose you just watched a basketball game between the Knights and the Tornadoes. Create a question about the game that will have a distribution with low variability.

Consider the following definite integrals. a. Write the midpoint Riemann sum in sigma notation for an arbitrary value of $n$.
b.Evaluate each sum using a calculator with $n=20,50,$ and $100$ Use these values to estimate the value of the integral.

$$\int_{0}^{1} \frac{1}{\pi}\left(\sin ^{-1} x+1\right) d x$$

frequency distribution for the class level of students in Professor Weiss's introductory statistics course is as follows.

Two students are randomly selected without replacement. Determine the probability that

a. the first student obtained is a junior and the second a senior.

b. both students obtained are sophomores.

c. Draw a tree diagram for this problem.

d. What is the probability that one of the students obtained is a freshman and the other a sophomore?

a. How many ways can three of the letters of the word ALGORITHM be selected and written in a row? b. How many ways can six of the letters of the word ALGORITHM be selected and written in a row? c. How many ways can six of the letters of the word ALGORITHM be selected and written in a row if the first letter must be A? d. How many ways can six of the letters of the word ALGORITHM be selected and written in a row if the first two letters must be OR?