BRAlNBOLT

175 Questions
15 Answers

-1

6

0

+204

Counting

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers (1, 2, 3, 4, 5, 6, and 7). Among all the cards of each color, there is exactly one card labeled with each number. mehr ..

BRAlNBOLT 08.12.2024

-1

5

0

+204

Counting

Catherine rolls a standard $6$-sided die six times. If the product of her rolls is $300,$ then how many different sequences of rolls could there have been? (The order of the rolls matters.)

BRAlNBOLT 08.12.2024

-1

4

0

+204

Counting

Joanna has six beads that she wants to assemble into a bracelet. Four of the beads have the same color, and the other two all have different colors. In how many different ways can Joanna assemble her bracelet? (Two bracelets are considered identical mehr ..

BRAlNBOLT 08.12.2024

-1

13

0

+204

Geometry

In triangle ABO, M is the midpoint of \overline{AB}. Points C, D, and N lie on line segments $\overline{AO},$ $\overline{BO},$ and $\overline{MO}$ extended, respectively, so that $DO = BO,$ $NO = MO,$ and $CO = AO.$ If $K$ is the area of triangle mehr ..

BRAlNBOLT 30.10.2024

-1

12

0

+204

Geometry

In the diagram below, ABCD is a square, DE = EF = FG = 2, GH = 1, HB = 5, and \angle DEF = \angle EFG = \angle FGH = \angle GHB = 60^\circ. Find the area of the shaded region.

BRAlNBOLT 30.10.2024

-1

13

0

+204

Geometry

Unit square ABCD is divided into two triangles, which are congruent to each other, and two trapezoids, which are also congruent to each other. These pieces are then re-assembled into rectangle $PQRS,$ as shown below. Find the perimeter of rectangle mehr ..

BRAlNBOLT 30.10.2024

-2

8

0

+204

Counting

Find the number of $7$-digit positive integers, where the sum of the digits is divisible by $3.$

BRAlNBOLT 23.10.2024

-1

10

1

+204

Algebra

Expand (sqrt(x) + 3x)*4 + (sqrt(x) - 3x)*4.

BRAlNBOLT 23.10.2024

-2

7

1

+204

Algebra

Fill in the blanks with positive integers:
(3 + sqrt(6))*3 = ___ + ___ * sqrt(6)

BRAlNBOLT 23.10.2024

-1

10

0

+204

Number Theory

A positive integer is called terrific if it has exactly $10$ positive divisors. What is the smallest number of primes that could divide a terrific positive integer?

BRAlNBOLT 14.10.2024

-1

15

0

+204

Number Theory

A positive integer is called terrific if it has exactly $10$ positive divisors. What is the largest number of primes that could divide a terrific positive integer?

BRAlNBOLT 14.10.2024

-1

15

0

+204

Number Theory

A positive integer is called terrific if it has exactly $10$ positive divisors. What is the smallest terrific positive integer?

BRAlNBOLT 14.10.2024

-1

13

0

+204

Algebra

Let $f(x)$ be a polynomial with integer coefficients. There exist distinct integers $p,$ $q,$ $r,$ $s,$ $t$ such that
f(p) = f(q) = f(r) = f(s) = 1
and $f(t) > 1.$ What is the smallest possible value of $f(t)?$

BRAlNBOLT 01.10.2024

-1

21

0

+204

Algebra

Find the number of ordered pairs $(a,b)$ of integers such that
\frac{a + 2}{a + 1} = \frac{b}{8}.

BRAlNBOLT 11.09.2024

-1

13

0

+204

Algebra

Suppose $f(x)$ is a function defined for all real $x$, and suppose $f$ is invertible (that is, $f^{-1}(x)$ exists for all $x$ in the range of $f$). If the graphs of $y=f(x)$ and $y=f(1/x)$ are drawn, at how many points do they intersect?

BRAlNBOLT 07.09.2024