Question

math 8 unit 2 review
make sure to show the setup for each problem and any additional work.

1. alison has 30 pairs of shoes. half of the shoes are sandals, 10% is running shoes and the rest are dress shoes.

she grabs a pair of shoes, throws them away and then selects another pair. what is the probability the second pair is sandals as a simplified fraction?
a $\frac{1}{20}$ b $\frac{3}{58}$ c $\frac{1}{25}$ d $\frac{6}{145}$

1. alison has 30 pairs of shoes. half of the shoes are sandals, 10% is running shoes and the rest are dress shoes.

what is the probability she will grab dress shoes first put it back, then grab a running shoe as a percent?
a 40% b 4% c 50% d 5%

1. on monday mike paid $7.50 for lunch then $8.25 on thursday. what is his percent of increase?
2. notebooks cost $3.75 each and folders cost $0.55 each. if you buy 3 notebooks and 5 folders, how much money would you need to purchase the 8 items along with 1.5% for tax?
3. yesterday you drank 35 ounces of water and then drink 20 ounces today. determine the percent of change and if it was a percent of increase or decrease.
4. best buy is offering 25% discount on all appliances, batman wants to buy a dishwasher for that originally costs $260.00.

a. how much will be the amount of the discount?
b. what is the sale price?

1. jackson scored 17 points during his first basketball game. during his second game, he scored 27 points. determine the percent of change and if it was a percent of increase or decrease.
2. you want to leave a 16% tip for a $45.86 bill. how much money do you need to cover the bill and tip?

Explanation:

1.

Step1: Calculate number of each type of shoes

Total shoes = 30. Running shoes = 0.1×30 = 3. Half of shoes are sandals, so sandals = 15. Then dress - shoes=30-(3 + 15)=12. After throwing away the first - pair of running shoes, there are 29 shoes left.

Step2: Calculate probability

The probability that the first pair is running shoes and the second pair is sandals: Probability of first pair being running shoes is $\frac{3}{30}$, and probability of second pair being sandals given first was running shoes is $\frac{15}{29}$. The joint probability is $\frac{3}{30}\times\frac{15}{29}=\frac{3}{58}$.

Step1: Calculate number of each type of shoes

Total shoes = 30. Running shoes = 0.1×30 = 3. Half of shoes are sandals, so sandals = 15. Then dress - shoes = 30-(3 + 15)=12.

Step2: Calculate probability

Probability of grabbing dress shoes first and then running shoes (with replacement) is $\frac{12}{30}\times\frac{3}{30}=\frac{36}{900}=0.04 = 4\%$.

Step1: Calculate the increase amount

The increase amount is $8.25 - 7.50=0.75$.

Step2: Calculate the percent increase

Percent increase formula is $\frac{\text{increase}}{\text{original}}\times100\%$. So $\frac{0.75}{7.50}\times100\% = 10\%$.

Answer:

B. $\frac{3}{58}$

2.