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And I guess no one answered yesterday :(


The Question of the Day - 30 points

The question is the same as yesterday.

Lucky Prime Hint: I am an odd 2-digit prime number.

Blueeighthnote, I am letting you try to complete the first question of the day.

Question of the Day 1 (Calculators are permitted): Lilly orders a large, orange pineapple-flavored ice cream at the Ice Cream Shack. She immediately realizes that it would be too big for a cone, so she asks them to place it in a cup. Each scoop of ice cream is a perfect sphere with radius 3 inches (a specialty of the Shack). The cup the ice cream is placed in is a cylinder with diameter 7 inches and height 10 inches. If the scoops are gently placed in the cup, a large (3 scoops) would not fit in the cup, so the scoops are pressed into the cup so that all the ice cream fits under the lid. How many centimeters are in the minimum possible height of the ice cream in the cup? Express your answer to the nearest tenth.

Question of the Day 2 (Calculators are permitted): Each of Jonathan's bicycle tires revolved 2327 times as he rode three miles. What is the diameter of one of Jonathan's bicycle tires, in inches? Express your answer to the nearest whole number.

Previous Solution

The lucky prime was 1229.


QUESTION OF THE DAY 2: To be composite, a number must be the product of two natural numbers greater than 1. Since we want the 7 smallest that also aren't divisible by 2, 3, 4, 5, 6, 8, 9, or 10, the smallest factors the numbers could be divisible by are 7, 11, 13, 17, 19... The smallest composite numbers divisible by 7 but not any of the other numbers are 49, 77, 91, 119, 133, etc. The smallest composite numbers divisible by 11 are 121, 143, 187, etc. Together, the smallest 7 are 49, 77, 91, 119, 121, 133, and 143. The sum is 733.



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