A student wrote the following conjecture. Find a counterexample and explain the error. If x is a positive even number and y is any integer, then the product xy will be positive.

What is the inverse of the following statement? If a building has more than four floors, then it has an elevator.

Find the following for each pair of points: The midpoint of the line segment connecting the points. $(4, -4); (4, 8)$

In the following exercise, label the axes for a sketch to illustrate the given statement.

"Graph the pressure, p, of a gas as a function of its volume. v, where p is in pounds per square inch and v is in cubic inches."

Determine a system of linear inequalities that defines the triangle connecting the points. 60. $(0,-2),(4,6),(4,-2)$

A variable is normally distributed with mean 10 and standard deviation 3. a. Determine and interpret the quartiles of the variable. b. Obtain and interpret the seventh decile. c. Find the value that 35% of all possible values of the variable exceed. d. Find the two values that divide the area under the corresponding normal curve into a middle area of 0.99 and two outside areas of 0.005. Interpret your answer.

What observations or types of telescopes would you use to distinguish a binary system that includes a main-sequence star and a white dwarf star from one containing a main-sequence star and a neutron star?

Seve is training for a long distance walk. He walks for 10 km in the first week, then each week thereafter he walks an additional 500 m. If he continues this pattern for a year, how far does Seve walk: in total?

Write a set of instructions for Otto to walk in a square as shown in earlier figure .

Draw the d-orbital splitting diagrams for the octahedral complex ions of each of the following. $\mathrm { Zn } ^ { 2 + }$

It is known that there are infinitely many positive integers whose square is the sum of the squares of two positive integers. For example, $5^{2}=3^{2}+4^{2}$ and $13^{2}=5^{2}+12^{2}.$ (a) Prove that there are infinitely many positive integers whose square is the sum of the squares of three positive integers. For example, $59^{2}=50^{2}+30^{2}+9^{2}.$ (b) Prove that there are infinitely many positive integers whose square is the sum of the squares of four positive integers.

Consider the following statement: int *num; a. Write the C++ statement that dynamically creates an array of 10 components of type int and num contains the base address of the array. b. Write a C++ code that inputs data into the array num from the standard input device. c. Write a C++ statement that deallocates the memory space of the array to which num points.

What is your average speed if you walk 2 kilometers in 20 minutes?

Sybrina wants to make a 17-inch necklace with a

$$\frac{3}{4}-inch$$

bead, a

$$1\frac{1}{2}-inch$$

bead and another

$$\frac{3}{4}-inch$$

bead on it. What is the length of the remaining part of the necklace?