HW 2025-04-04 WS

[BMMT 19.7]

What is the area of the S-shaped figure below, which has constant vertical height 5 and width 10?

[BMMT 19.9]

The Chan Shun Auditorium at UC Berkeley has room number 2050. The number of seats in the auditorium is a factor of the room number, and there are between 150 and 431 seats, inclusive. What is the sum of all the possible numbers of seats in Chan Shun Auditorium?

Tags

CCSS.4.OA.B.4

Tags

CCSS.8.EE.A.2

[BMMT 19.11]

Jing Jing the Kangaroo starts on the number 1. If she is at a positive integer n, she can either jump to 2n or to the sum of the digits of n. What is the smallest positive integer she cannot reach no matter how she jumps?

Tags

CCSS.3.OA.D.9

Tags

CCSS.HSA.REI.A.2

[BMMT 19.14]

Compute the number of rearrangements of the letters in LATEX such that the letter T comes before the letter E and the letter E comes before the letter X. For example, TLEAX is a valid rearrangement, but LAETX is not.

[BMMT 19.15]

How many integers n greater than 2 are there such that the degree measure of each interior angle of a regular n-gon is an even integer?

[BMMT 19.16]

Students are being assigned to faculty mentors in the Berkeley Math Department. If there are 7 distinct students and 3 distinct mentors and each student has exactly one mentor, in how many ways can students be assigned to mentors given that each mentor has at least one student?

[BMMT 18.8]

How many integers n with 1 ≤ n ≤ 100 have exactly 3 positive divisors?

[BMMT 18.9]

James has three 3 candies and 3 green candies. 3 people come in and each randomly take 2 candies. What is the probability that no one got 2 candies of the same color? Express your answer as a fraction in lowest terms.