Lesson 10 Meaningful Possibilities Solidify Understanding

Ready

Use the given matrices to perform the indicated operations.

$A = [\begin{array}{rr} 2 & - 4 \\ - 1 & 5 \end{array}] B = [\begin{array}{rrr} 7 & - 10 & 1 \\ 4 & - 6 & - 2 \end{array}] C = [\begin{array}{rr} - 3 & 0 \\ - 1 & 1 \\ 0 & 7 \end{array}] D = [\begin{array}{rrr} 1 & 0 & - 1 \\ 0 & 2 & - 2 \\ 5 & 0 & - 10 \end{array}]$

1.

$A B$

2.

$B C$

3.

$5 D$

4.

$B D$

5.

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

6.

$D C$

Set

7.

A farmer is harvesting his field of potatoes and wonders what the average weight of the potatoes is. He decides to randomly select $50 potatoes$ and finds that the average weight of those $50 potatoes$ is $1.2 pounds$ , and they have a standard deviation of $0.3 pounds$ . Give an interval of plausible values for the actual weight of all the potatoes in the field.

8.

If the farmer were to double the sample size, what would happen to the interval of plausible values? Would the interval increase, decrease, or stay the same? Why?

9.

Based on your interval of plausible values, is it likely that the potatoes for the entire field weigh more than $1.5 pounds$ on average? Why or why not?

10.

Suppose the actual weight of the potatoes in the field is $μ = 1.5 pounds$ with a standard deviation of $σ = 0.5$ . If the farmer were to create a sampling distribution by taking repeated samples of size $50$ and identify the average weight of potatoes in each sample, what would be the shape, center, and standard deviation of this distribution?

11.

If the actual weight of potatoes in the field is really $μ = 1.5 lbs$ , what is the probability of taking a sample of $50 potatoes$ and finding that they weigh $1.2$ or fewer pounds?

Go

Fill in the blanks on the sentences below.

12.

The expression $a^{2} + 2 a b + b^{2}$ is called a perfect square trinomial. I can recognize it because the first and last terms will always be perfect . The middle term will be $2$ times the and . There will always be an sign before the last term. The expression $a^{2} + 2 a b + b^{2}$ factors as .

13.

The expression $a^{2} - b^{2}$ is called the difference of $2$ squares. I can recognize it because it’s a binomial and the first and last terms are perfect . The sign between the first term and the last term is always a .

The expression $a^{2} - b^{2}$ factors as .

14.

The expression $a^{3} + b^{3}$ is called the sum of $2$ cubes. I can recognize it because it’s a binomial and the first and last terms are . The expression $a^{3} + b^{3}$ factors into a binomial and a trinomial. The sign between the terms in the binomial is the as the sign in the expression. The first sign in the trinomial is the of the sign in the binomial. That’s why all of the middle terms cancel when multiplying. The last sign in the trinomial is always . The expression $a^{3} + b^{3}$ factors as .

Factor using what you know about special products.

15.

$25 x^{2} + 30 x + 9$

16.

$x^{2} - 16$

17.

$x^{3} + 27$

18.

$49 x^{2} - 36$

19.

$x^{3} - 1$

20.

$64 x^{2} - 240 x + 225$