A random number generator on a computer selects two integers from 1 through 40. What is the probability that both numbers are less than 30.

A random number generator on a computer selects two integers from 1 through 40. What is the probability that the same number is selected twice?

(a) Construct a triangle and measure the three interior angles with a protractor. What is the sum of the measures? (b) Construct three other triangles, measure the angles, and record the sums. Are your answer s the same? (c) Make a conjecture about the sum of the measures of the three interior angles of a triangle .

Let f be continuous on [a, b] and differentiable on (a, b) If there exists c in (a, b) such that f’(c) = 0, does it follow that f(a) = f(b)? Explain.

Let

$$A = \left[ \begin{array} { l l } { 1 } & { 2 } \\ { 3 } & { 5 } \end{array} \right] \text { and } B = \left[ \begin{array} { r r r } { 2 } & { 0 } & { - 1 } \\ { 3 } & { - 3 } & { 4 } \end{array} \right].$$

Compute the indicated matrices, if possible.

$$A ^ { 2 } B ^ { 2 }$$

ATM personal identification number (PIN) codes typically consist of four-digit sequences of numbers. (a) Find the total number of ATM codes possible. (b) Find the total number of ATM codes possible when the first digit is not 0.

In 2014, six of the twelve men's basketball teams in the Big Ten Conference participated in the NCAA Men's Basketball Championship Tournament. What is the probability that a random selection of six teams from the Big Ten Conference will be the same as the six teams that participated in the tournament?

Evaluate the expression if a = 6, b = 15, and c = 9: 8c - 9 + 25

Determine the unit rate. Use mental math when you can. 24 tickets for $480

Solve each inequality. Graph the solution set on a number line.

$$2 x + 6 < 3 ( x - 1 ) \leq 2 ( x + 3 )$$

Find parametric equations for the curve with the given properties. The ellipse

$$\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$$

The temperature (in degrees centigrade) at a point P on a circular wire of radius 2 cm centered at the origin is equal to the square of the distance from P to

$$P_0 = (2, 0).$$

Compute the average temperature along the wire.

The basketball player Shaquille O'Neal makes about half of his free throws over an entire season. We will use the calculator to simulate 100 free throws shots independently by a player who makes 50% of his attempts. We let the number 1 represent the outcome "Hit" and 0 represent a "Miss." Examine the sequence of hits and misses. How long was the longest run of shots made? Of shots missed? (Sequence of random outcomes often show runs longer than we might expect.)

Fish-liver oil is a good source of vitamin A, which is measured spectrophotometrically, after correcting for background, at a wavelength of 329 nm.

Suggest a reason for using this wavelength.