700 people went to the amusement park. 500 of them went on a roller-coaster, 100 of them went to the haunted house, and 50 of them went to the water slides.  60 who went on a roller-coaster also went to the haunted house, 10 who went on a roller-coaster also went to the water slides and 5 who went to the haunted house also went to the water slides. 2 people went on all three.  How many people did not go on any of the three?  How many people only went to one?  Create a Venn diagram to show the relationship.

Q: During the fall semester a school is offering science courses in physics, biology, and chemistry,…

A: It is given that there are science courses in physics, biology, and chemistry, and humanities…

Q: A class with 30 students has ten men and nine seniors, and five of the men are seniors. How many…

A: The total number of students is n = 30.

Q: Tom has 16 blue pencils, of which 12 are striped dark blue and light blue, and the rest are solid…

A: There are 16 blue pencils and 9 red pencils out of which 12 are striped dark blue and light blue and…

Q: Your little cousin will have a big animal-themed birthday party and you will help with goody bags.…

A:

Q: What is the probability that a gacha now drawn from the second gift bag is a Naruto gacha?

A: Let us define some events A : Pokemon gacha is placed in second gift bag. B : Naruto gacha is placed…

Q: A basket ball team has 5 guards, 7 forwards, and 3 centers.  How many ways are there to have a…

A: A basket ball team has 5 guards, 7 forwards, and 3 centers. How many ways are there to have a lineup…

Q: Suppose you are at a buffet and there are 10 vegetarian options and 6 options with meat. How many…

A: There are 10 vegetarian options and 6 options with meat at a buffet. The number of ways that exactly…

Q: There are 4 men and 5 women in a room. The leader wants a participation from a group of 2 men and 2…

A:

Q: An ice cream store has 30 flavors to select from. A customer who is a connoisseur of ice cream wants…

A: We have to select three different flavors from a ice cream store which has 30 flavors. Since, here…

Q: Jennifer has 4 black bags. She has 15 seeds in the black bags. She has arranged the seeds in the 4…

A: Given : Number of bags = 4 Number of seeds = 15 None of bag is empty and all bags have different…

Q: You are in a class of 10 students. Three students will be picked to be on a committee. A student…

A: Total number of students in a class = 10 number of students picked to be on a committee = 3 A…

Q: The math club has seven members and will choose a team of three to send to a competition. The…

A: Given that the math club has 7 members and will choose a team of 3 to send to a competition.  The…

Q: Your roommate has six pets (fish, cat, tur- tle, dog, rock, and pony). He will take three of his six…

A: Given that Your roommate has six pets (fish, cat, tur- tle, dog, rock, and pony). He will take three…

Q: At a race track you have the opportunity to buy a ticket that requires you to pick the first and…

A:

Q: There are 24 students in the senior class. Four of the students will be chosen to be the President,…

A: There are total 24 students. We need to select one  President, Vice-President, Secretary, and…

Q: Cameron has five different pairs of shoes that match with six different pairs of socks. How many…

A: There are five different pairs of shoes that match with six different pairs of socks for Cameron.

Q: You have 10 houses in a row on a one side of a street, going from left to right. You are to paint…

A: Number of houses = 10

Q: Joey finds 13 video games that he would like to have. Three of them will run on his operating system…

A: Given: A total of 13 games are there. 10 will run on the operating system and 3 will not.

Q: In a small village with 200 inhabitants, half of the villagers have either a cat or a dog or both.…

A: Given total number of inhabitants = 200 Given half of the total inhabitants have either a cat or a…

Q: The first box contains 5 apples, the second box contains 7 apples, the third box contains 9 apples…

A:

Q: Sally has 2 pairs of shoes, 9 pairs of pants, and 8 shirts. How many different outfits can she make…

A: Sally can make, 2×9×8 = 144 different outfits.    The detailed solution is as follows below:

Q: Jessica knows that her glove drawer contains 12 green gloves, 10 purple gloves, 8 white gloves, and…

A: Given Information: No. of gloves=36Green gloves=12Purple gloves=10White gloves=8Red gloves=6

Q: Of the 30 students in my class, 11 practice taekwondo, 11 play piano, and 20 take lessons in math. 4…

A:

Q: You are buying 10 t-shirts and there are 8 different colors to choose from. How many ways can you…

A: Probability A probability provides the possibility of occurring an event. For example, A school team…

Q: The newest cars have 12 different accessories and the buyer pays for each one separately.  If a…

A: Given, The newest cars have 12 different accessories A buyer wants to buy four accessories

Q: Harry has 4 shirts and some number of pairs of pants in his closet. He has a total of 8 possible…

A:

Q: A manager has 4 people that can play any of positions. How many

A: In the given situation, there are 4 people that can play any of positions. That is, there are 4…

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.