Lesson 8 Ancient Treasures Solidify Understanding

Ready

1.

If $A = [\begin{matrix} 6 & - 1 \\ - 4 & 3 \end{matrix}]$ , $I = [\begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix}]$ , and $- A = [\begin{matrix} - 6 & 1 \\ 4 & - 3 \end{matrix}]$ , show that $A + I = A$ and $A + (- A) = I$ .

2.

What is another name for matrix $I$ ?

3.

What is the relationship between matrix $A$ and matrix $- A$ ?

Use $A$ , $B$ , and $C$ to answer questions 4 and 5.

$A = [\begin{matrix} 6 & - 1 \\ - 4 & 3 \end{matrix}]$ , $B = [\begin{matrix} - 5 & 1 \\ 5 & 2 \end{matrix}]$ , and $C = [\begin{matrix} 10 & 4 \\ - 11 & - 5 \end{matrix}]$

4.

Show that $A + B = B + A$ .

5.

Show that $(A + B) + C = A + (B + C)$ .

6.

What is the name of the property described in question 4?

7.

What is the name of the property described in problem 5?

Set

For each of the following problems, the sample size and population information are given. Identify if the conditions for the Central Limit Theorem apply for a sampling distribution of the given sample size. If the conditions are met, then identify the mean, standard deviation, and shape for each sampling distribution.

8.

The sample size is $n = 40$ , $μ = 20$ , $σ = 25$

9.

The sample size is $n = 40$ , $p = 0.6$

10.

The sample size is $n = 10$ , $μ = 20$ , $σ = 25$

11.

The sample size is $n = 40$ , $p = 0.1$

12.

The sample size is $n = 100$ , $p = 0.01$

Go

Draw the terminal ray of the indicated angle of rotation on the unit circle. Find the value of the given trig function at that position.

13.

$θ = (\frac{3 π}{4})$

$\sin θ =$

14.

$θ = (\frac{4 π}{3})$

$\tan θ =$

15.

$θ = (\frac{13 π}{6})$

$\cos θ =$

16.

$θ = k π$ , $k$ is an odd integer

$\cos θ =$

17.

$θ = (\frac{3 π}{2})$

$\sin θ =$

18.

$θ = (\frac{17 π}{6})$

$\tan θ =$

19.

$θ = (\frac{11 π}{4})$

$\tan θ =$

20.

$θ = (\frac{16 π}{4})$

$\sin θ =$