Which board geometrically represents 4x2 – 1 using algebra tiles? An algebra tile configuration showing only the product spot, which has 9 tiles in 3 columns with 3 rows. First row: 2 x squared, 1 x. Second row: 2 x squared, 1 x. Third row: 2 negative x, 1. An algebra tile configuration showing only the product spot, which has 9 tiles in 3 columns with 3 rows. First row: 2 x squared, 1 x. Second row: 2 x squared, 1 x. Third row: 2 negative x, 1 negative. An algebra tile configuration showing only the product spot, which has 9 tiles in 3 columns with 3 rows. First row: 2 x squared, 1 negative x. Second row: 2 x squared, 1 negative x. Third row: 2 negative x, 1. An algebra tile configuration showing only the product spot, which has 9 tiles in 3 columns with 3 rows. First row: 2 x squared, 1 x. Second row: 2 x squared, 1 x. Third row: 2 x, 1.

In tossing one coin 10 times, what are your chances for tossing a head? a tail? 2. in tossing one coin 100 times, what are your chances for tossing a head? a tail? 3. in tossing one coin 200 times, what are your chances for tossing a head? a tail? deviation = ((absolute value of the difference between expected heads and observed heads) + (absolute value of the difference between expected tails and observed tails)) divided by total number of tosses. this value should always be positive. 4. what is the deviation for 10 tosses? 5. what is the deviation for the 100 tosses? 6. what is the deviation for 200 tosses? 7. how does increasing the total number of coin tosses from 10 to 100 affect the deviation? 8. how does increasing the total number of tosses from 100 to 200 affect the deviation? 9. what two important probability principles were established in this exercise? 10. the percent of occurrence is the obtained results divided by the total tosses and multiplied by 100%. toss the coins 100 times and record your results. calculate the percent occurrence for each combination. percent head-head occurrence: percent tail-tail occurrence: percent head-tail occurrence:

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

Carl's candies has determined that a candy bar measuring 3 inches long has a z-score of +1 and a candy bar measuring 3.75 inches long has a z-score of +2. what is the standard deviation of the length of candy bars produced at carl's candies?