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Points A and B lie along the circumference of a circle with center O. A second circle with center M has a radius one-third as long as that of the circle with center O. If the area of sector AOB is equal to the area of the circle with center M, then what is the measure in degrees of ∠AOB?_____
No line segment with endpoints on the circle with center O is longer than line segment DC.OA = AD = 3

Quantity A

The area of sector OABC

Quantity B

9


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An interior designer decides to accent a wall with an evenly spaced row of stenciled circles. The wall is 31′6″ long and the stencil has an area of 36π square inches. If the designer wants to leave a space of x inches between each circle and at either end of the row, and x is an integer, then what is the greatest possible number of circles that the designer can use?_____
$$\frac{1}{r}$$of a circular pizza has been eaten. If the rest of the pizza is divided into m equal slices, then each of these slices is what fraction of the whole pizza?
A single slice cut from the center of a circular pizza has an edge length (from the center of the pizza to the edge of the crust) of 5″, has an arc length of 1.25π″, and weighs 4 ounces. If a serving weighs 8 ounces, then, to the nearest integer, what is the largest number of servings that six 6″ diameter pizzas can yield? (Note that servings must weigh 8 ounces, but they do not need to be equal in shape.)
A club consists of 8 women and 8 men.The club has a president and a vice president.No club member can hold more than one position.

Quantity A

The number of possible assignments such that a woman is president and a man is vice president

Quantity B

The number of possible assignments such that both the president and vice president positions are filled by women


Given an alphabet of 26 letters, with 21 consonants, and 5 vowels, approximately how many three-letter words can be formed with a vowel as the middle letter and a consonant as the last letter?
Of the 100 eighth-graders at Easton Junior High, 60 students take gym, 40 take a foreign language, and 30 take both gym and a foreign language.

Quantity A

30

Quantity B

The number of students taking neither gym nor a foreign language


Graham`s Catering Service currently employs three chefs and offers three different meals. For an upcoming event, the catering service must provide three meals, with each chef cooking one of the meals.

Quantity A

The number of assign?ments of chefs to meals if each chef must cook a different meal

Quantity B

The number of assign?ments of chefs to meals if each chef may cook any of the three meals


A certain password must contain 3 distinct digits followed by 2 distinct capital letters. Given ten digits and 26 capital letters, how many different passwords are possible?_____
190 students go to a school bake sale. 95 buy a chocolate chip cookie, 75 buy a peanut butter cookie, and at least 12 buy both. What is the least number of students who could have bought neither type of cookie?
Geoff is setting up an aquarium and must choose 4 of 6 different fish and 2 of 3 different plants. How many different combinations of fish and plants can Geoff choose?
If the current day and time is 9:30 p.m. on Tuesday, what time will it be (to the nearest minute) 100,000 seconds from now?
What is the difference between the number of three-member committees that can be formed from a group of nine members and the total number of ways there are to arrange the members of such a committee?
Six students compete in a table tennis tournament. Each student plays each of the other students four times. What is the total number of games played in the tournament?_____
A four-person leadership committee is to be chosen from a student council that consists of seven juniors and five seniors. Q is the total number of different leadership committees that include three seniors and one junior.

Quantity A

Q

Quantity B

75


Contestants at a baking contest must use between 5 and 8 of 10 possible ingredients.

Quantity A

The number of ingre?dients that must be used to get the smallest possible number of different ?combinations

Quantity B

The number of ingredients that must be used to get the largest possible number of different combinations


Depending on the night, a pizza restaurant offers anywhere from seven to nine different choices of toppings. Sam wants a pizza with three toppings. Which of the following could be the number of different ways that Sam can order his pizza with three different toppings?Indicate all possible values.
Depending on the day, an ice cream shop offers seven to nine possible ice cream flavors and three to four possible sauces. A ?Deluxe Sundae consists of two different types of ice cream and two different sauces. Which of the following could be the number of different Deluxe Sundaes that Eva can order?Indicate all possible values.
Six state governors meet at an annual convention. They line up in random order to pose for a photograph. If the governors of Alaska and Hawaii are among the six governors, how many different ways can the governors line up for the picture so that these two governors are adjacent?

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