Your friend defines a right angle as an angle that is greater than an acute angle. Use a biconditional to show that this is not a good definition.

A spinner is divided into 8 congruent regions, numbered 1 through 8, is spun once. Let A be the event “even” and let B be the event “6.” Find the probabilities. P(A|B) __________

ANALYZING RELATIONSHIPS You lose track of how many 2-point baskets and 3-point baskets a team makes in a basketball game. The team misses all the 1-point baskets and still scores 54 points. The equation 2x + 3y = 54 models the total points scored, where x is the number of 2-point baskets made and y is the number of 3-point baskets made. Can the number of 3-point baskets made be odd? Explain your reasoning.Find and interpret the intercepts. Graph the equation. Find two more possible solutions in the context of the problem.

In an urn containing n balls, the ith ball has weight W(i), i=1, ..., n. The balls are removed without replacement, one at a time, according to the following rule: At each selection, the probability that a given ball in the urn is chosen is equal to its weight divided by the sum of the weights remaining in the urn. For instance, if at some time

$$i _ { 1 } , \ldots , i _ { r }$$

is the set of balls remaining in the urn, then the next selection will be

$$i_j$$

with probability

$$W \left( i _ { j } \right) / \sum _ { k = 1 } ^ { r } W \left( i _ { k } \right) , j = 1 , \ldots , r$$

. Compute the expected number of balls that are withdrawn before ball number 1 is removed.

A curious event was described in the Minneapolis Star and Tribune . The Minneapolis Community Development Agency (MCDA) makes home improvement grants each year to homeowners in depressed city neighborhoods. Of the $708,000 granted one year,$233,000 was awarded by the city council via a “random selection” of 140 homeowners’ applications from among a total of 743 applications: 601 from the north side, and 142 from the south side, of Minneapolis. Oddly, all 140 grants awarded were from the north side—clearly a highly improbable outcome if, in fact, the 140 winners were randomly selected from among the 743 applicants. a. Suppose the 140 winning applications were randomly selected from among the total of 743, and let x equal the number in the sample from the north side. Find the mean and standard deviation of x . b. Use the results of part a to support a contention that the grant winners were not randomly selected.

If P = 2l + 2w, and if l = 4 and w = 3, what does P equal?

Two wood beams, each of rectangular cross section ($3.0 \mathrm { in. } \times 4.0\mathrm { in. }$, actual dimensions) are glued together to form a solid beam of dimensions $6.0 \mathrm { in. } \times 4.0\mathrm { in. }$ The beam is simply supported with a span of 8 ft. What is the maximum moment $M_{\max }$ that may be applied at the left support if the allowable shear stress in the glued joint is 200 psi? (Include the effects of the beam’s own weight, assuming that the wood weighs $35\ \mathrm{lb} / \mathrm{ft}^{3}$.)

Test each statement below to see if It ls reversible. If so, write It as a true biconditional. ll not, write not reversible.

A rectangle is a four-sided figure with at least one right angle.

If a 1.8-kg brick falls to the ground from a chimney that is 6.7 m high, what is the change in its potential energy?

Solve the linear programming problems stated. Minimize and maximize $z=2 x+3 y$ subject to

$$\begin{aligned} 2 x+y & \geq 10 \\ x+2 y & \geq 8 \\ x, y & \geq 0 \end{aligned}$$

Find the common ratio r for each geometric sequence and use r to find the next three terms. 864, -288, 96, ... r = _____ Next three terms: _____

Refer to the following class. Public Class Point. {, private int myX; private int myY; public Point (), {, myX=0; myY=0; }. public Point(int x, int y), {, myX=x; myY=y; }, public int getX(), {, return myX; }, public int getY(), {, return myY; }, }. Which of the following statements is true regarding the Point class? (A) The calls won't compile because there are two methods named Point. (B) Variables myX and myY can be changed from outside the class. (c) Point objects are immutable. (D) It's impossible to create Point objects with coordinates other than (0, 0). (E) Giving myX and myY private visibility was a poor design decision.

Consider two identical glasses of water, one stationary and the other moving on a horizontal plane with constant acceleration. Assuming no splashing or spilling occurs, which glass will have a higher pressure at the (a) front, (b) midpoint, and (c) back of the bottom surface?

Find an equation for the ellipse that satisfies the given conditions. Eccentricity:

$$\sqrt { 3 } / 2$$

, foci on y-axis, length of major axis: 4