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- 3. Joe's Diner offers an all-you-can-eat buffet at $25.90 per adult and $17.90 per child. On a particular day, the diner had a total buffet revenue of $6609.40 from 266 customers. How many of the customers were children?At the National Baseball Batting Contest, the organizers have set up game booths for the contestants. Richard wants to win a large stuffed animal. The rules of the game are as follows: You are pitched 5 fastballs, and you must hit them into a fair zone to count. • If you successfully hit all 5 pitches, you win a large stuffed animal. If you successfully hit 3 or 4 pitches, you win a small stuffed animal. • If you successfully hit 1 or 2 pitches, you win a bat-shaped pencil. If you miss all the pitches, you do not win a prize. • The game costs $3 to play (each set of 5 fastballs). Everyone has the same chance as Richard to win. If 160 people each play the game once, how many large stuffed animals will be won?To help plan the number of meals to be prepared in a college cafeteria, a survey was conducted, and the following data were obtained. 130 students ate breakfast. 177 students ate lunch. 276 students ate dinner. 65 students ate breakfast and lunch, 115 students ate breakfast and dinner. 86 students ate lunch and dinner. 54 students ate all three meals. How many students ate (a) At least one meal in the cafeteria? students (b) Exactly one meal in the cafeteria? students (c) Only dinner in the cafeteria? students (d) Exactly two meals in the cafeteria? students ***
- Dr. Lawrence has minimized his wardrobe during the fall of 2020, since there's no reason to dress up fancy these days. He has three pairs of jeans, five sweatshirts, and four hats that he puts to regular use. If he were to select his outfit for the day at random, how many different jean-sweatshirt-hat combinations are there? 6.To help plan the number of meals to be prepared in a college cafeteria, a survey was conducted, and the following data were obtained. 127 students ate breakfast.183 students ate lunch.272 students ate dinner.60 students ate breakfast and lunch.111 students ate breakfast and dinner.90 students ate lunch and dinner.53 students ate all three meals. How many students ate (a) At least one meal in the cafeteria? students(b) Exactly one meal in the cafeteria? students(c) Only dinner in the cafeteria? students(d) Exactly two meals in the cafeteria? studentsA pool party is occurring at the Robertson's house this next holiday. They want to invite 64 friends and family. Only 26 friends and 9 family members reply to the invite. The Robertson's are a family of 5 . Their pool is 35 feet long and is 10 feet deep when filled to capacity. They are worried children under 5 will struggle in the pool, so they only fill the pool to 5 feet. The day of the party, 53 people show up. The son, Billy, is 4.5 feet tall. If Billy's height is half the width of the pool, what is the volume of water (in cubic feet) the Robertson's filled the pool with?
- Twelve classmates are taking a picture side by side. A. In how many ways can they take the picture if there are not restrictions? B. In how many ways can they take the picture if two best friends must stand side by side? C. Using the results from A and B, in how many ways can the best friends not stand side by side?During a special promotion, a customer purchasing a computer and a printer is given a choice of 3 free software packages. There are 10 different software packages from which to select. How many different groups of software packages can be selected? Hint: This is a Combination problem! 120 604,800 360 720Bruce, Clark and Diana found a box of old baseball cards in the attic. They sold 131 cards to a collector and then split the remaining cards equally among themselves. Then, Bruce gave 1/4 cards to Evan. If Evan was given 5 cards, how many cards were in the box when it was found? (Hint: work backwards)
- A punch-out card contains 100 spaces. One space pays $300, five spaces pay $20, and the others pay nothing. How much should you pay to punch out one space? (Assume that you wish to pay the fair price.In a survey, 200 restaurants were asked to select which of the following options were on their menu: tacos, burgers. 98 of the restaurants serve tacos and 74 of the restaurants serve burgers. 37 of the restaurants serve neither of these options. How many of the restaurants serve both tacos and burgers? Show your work.