Make sense of problems. A sale on dog food that costs $10 a bag says buy 1, get one$$$\frac { 1 } { 2 }$ off. What is the true percent discount on the dog food?

Write the correct word in the space next to each definition.

random $\rule{2cm}{0.15mm}$

Scientists think that the global population of tigers is falling exponentially. Estimates suggest that in 1970 there were 37 000 tigers but by 1980 the number had dropped to 22 000. (a) The number T of tigers n years after 1970 can be modelled by

$$T = k a ^ { n }$$

. (i) Write down the value of k. (ii) Show that a = 0.949 to three significant figures. (b) What does the model predict that the population will be in 2020? (c) When the population reaches 1000, the tiger population will be described as ‘near extinction’. In which year will this happen? In the year 2000 a worldwide ban on the sale of tiger products was implemented, and it is believed that by 2010 the population of tigers had recovered to 10 000. (d) If the recovery has been exponential, find a model of the form

$$T = k a ^ { m }$$

connecting the number of tigers (T) with the number of years after 2000 (m). (e) If each year since 2000 the rate of growth has been the same, find the percentage increase in the tiger population each year.

Determine whether the statement is true or false. Use the following sets of numbers.

$N=$ set of natural numbers.

$Z=$ set of integers

$I=$ set of irrational numbers

$Q=$ set of rational numbers

$\mathbb{R}=$ set of real number

$$-1 \in Z$$

Find the Errors. Locate as many as you can.

#include <iostream>
using namespace std;
struct ThreeVals
{
    int a, b, c;
};
int main()
{
    ThreeVals vals = {1, 2, 3};
    cout << vals << endl;
    return 0;
}

As previously discussed, it suggests that using CFLs is a good idea from a purely financial perspective unless you live in an area where power is relatively inexpensive, but there is another wrinkle. Suppose you have a residence with a lot of incandescent bulbs that are used on average 500 hours a year. The average bulb will be about halfway through its life, so it will have 500 hours remaining (and you can’t tell which bulbs are older or newer). At what cost per kilowatt-hour does it make sense to replace your incandescent bulbs today?

Abel and Family Perfumes wants to add one or more of four new products to its current line of colognes. Historically, Abel has used a 5-year project recovery period and a MARR of 20% per year. (a) Determine which of the four options the company should undertake on the basis of a present worth analysis, provided the total amount of investment capital available is $800,000. Use a hand solution, unless assigned otherwise. (b) What products are selected if the investment limit is increased to$900,000? Use a spreadsheet, unless assigned otherwise. (All cash flows are in $1000 units.)$ $$ \begin{matrix} \text{Product Line} & \text{R1} & \text{S2} & \text{T3} & \text{U4}\\ \hline \text{Investment, \$} & \text{$-200$} & \text{$-400$} & \text{$-500$} & \text{$-700$}\\ \text{M&O cost, \$/year} & \text{$-50$} & \text{$-200$} & \text{$-300$} & \text{$-400$}\\ \text{Revenue, \$/year} & \text{150} & \text{450} & \text{520} & \text{770}\\ \hline \end{matrix} $$ $

Find the distance between the points.

$$(-4.2,3.1),(-12.5,4.8)$$

The distance from the surface of a lens to the focal point is the

Let X={a, b, c}. Define a function S from $\mathcal{P}$(X) to the set of bit strings of length 3 as follows. Let Y$\subseteq$X. If a$\in$Y, set $s_1=0$; If a$\notin$Y, set $s_1=1$; If b$\in$Y, set $s_2=0$; If b$\notin$Y, set $s_2=1$; If c$\in$Y, set $s_3=0$; If c$\in$Y, set $s_3=1$. Define S(Y)=$s_1s_2s_3$.

Prove that S is onto.

Use a rotation matrix to rotate the vector

$$\left[\begin{array}{l} -2 \\ -3 \end{array}\right]$$

counterclockwise by the angle $\pi / 9.$

Write always, sometimes, or never to complete a true statement.

A sequence of a rotation and a dilation will $\underline{\text{?}}$ result in an image that is the same size and orientation as the preimage.

Enzymes that are only produced when a substrate is present are termed _____.

Write a program that prompts the user to enter the center of a rectangle, width, and height, and displays the rectangle.