Find the distance between the points.

$$(6.2,5.4),(-3.7,1.8)$$

Use a rotation matrix to rotate the vector

$$\left[\begin{array}{r} 4 \\ -1 \end{array}\right]$$

counterclockwise by the angle $\pi / 3.$

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.

The distance-time graph for Rolf intersects the distance-time graph for Annette at the point (2.5, 7). (Each graph gives the distance in mile s and the time in hours.) What does the common point (2.5, 7) tell you?

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.

Refer to the table. Which lap has the slowest time?

The numbers in Set N are multiples of 5.

The numbers in Set P are multiples of 9.

Which number of the three possibilities could be a number of both Set N and Set P ?

A. 27

B. 25

C. 90

Find the distance between the two points. If necessary, you may draw graphs but you shouldn't need to use the distance formula.

$(0,0)$ and $(3,4)$

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.

Riley and Rhoda plan to buy several bags of dog food and a dog collar. Each bags of dog food costs $7, and the dog collar costs$5. a. Use the information above to write an expression for the amount of money they will spend if they buy b bags of food. b. Riley and Rhoda have $30. Use this information and the expression you wrote for Part (a) to write an inequality for finding the number of bags of food they could buy. c. Solve the inequality and graph the solutions. Check your answer in the original situation.

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

$$Z \subseteq \mathbb{P}$$

Find the number of positive outcomes in the sample space. Then list the possible outcomes. You flip a coin and draw a marble at random from a bag containing two purple marbles and one white marble.

Find the complement of the following set.

The set {x|x is an integer strictly between 0 and 8} if U is the set of all integers.

Find the distance between the points.

$$(1,12),(6,0)$$