HW 2025-03-21 WS

Tags

CCSS.8.EE.C.8C

[BMMT T23.2]

Kaity has a rectangular garden that measures 10 yards by 12 yards. Austin’s triangular garden has side lengths 6 yards, 8 yards, and 10 yards. Compute the ratio of the area of Kaity’s garden to the area of Austin’s garden.

[BMMT T23.3]

Nikhil’s mom and brother both have ages under 100 years that are perfect squares. His mom is 33 years older than his brother. Compute the sum of their ages.

[BMMT T23.4]

Madison wants to arrange 3 identical blue books and 2 identical pink books on a shelf so that each book is next to at least one book of the other color. In how many ways can Madison arrange the books?

[BMMT T23.5]

Two friends, Anna and Bruno, are biking together at the same initial speed from school to the mall, which is 6 miles away. Suddenly, 1 mile in, Anna realizes that she forgot her calculator at school. If she bikes 4 miles per hour faster than her initial speed, she could head back to school and still reach the mall at the same time as Bruno, assuming Bruno continues biking towards the mall at their initial speed. In miles per hour, what is Anna and Bruno’s initial speed, before Anna has changed her speed? (Assume that the rate at which Anna and Bruno bike is constant.)

Tags

CCSS.HSA.CED.A.1

[BMMT T23.6]

Let a number be “almost-perfect” if the sum of its digits is 28. Compute the sum of the third smallest and third largest almost-perfect 4-digit positive integers.

[BMMT T23.8]

Compute the number of ordered pairs (m, n), where m and n are relatively prime positive integers and mn = 2520. (Note that positive integers x and y are relatively prime if they share no common divisors other than 1. For example, this means that 1 is relatively prime to every positive integer.)

[BMMT T23.9]

A geometric sequence with more than two terms has first term x, last term 2023, and common ratio y, where x and y are both positive integers greater than 1. An arithmetic sequence with a finite number of terms has first term x and common difference y. Also, of all arithmetic sequences with first term x, common difference y, and no terms exceeding 2023, this sequence is the longest. What is the last term of the arithmetic sequence?

Tags

CCSS.HSF.BF.A.2

[BMMT T23.10]

Andrew is playing a game where he must choose three slips, uniformly at random and without replacement, from a jar that has nine slips labeled 1 through 9. He wins if the sum of the three chosen numbers is divisible by 3 and one of the numbers is 1. What is the probability Andrew wins?