All Questions ⁺⁰237749 Questions

0

14

0

+1808

Counting

If an ant crawls from one corner to the other corner of a 3 \times 5 rectangle, then it will cross through seven squares.
If the ant crawls from one corner to the other corner of a 15 \times 16 rectangle, then how many squares will read more ..

blackpanther Apr 12, 2025

Apr 11, 2025

0

12

0

+1808

Counting

A survey conducted among 150 high school students revealed that

* 68 students like Math
* 85 students like English
* 55 students like History
* 20 students like both Math and English
* 15 students like both Math and read more ..

blackpanther Apr 11, 2025

Apr 10, 2025

+1

8

1

+608

Counting

Let P be a point chosen uniformly at random inside ABC. Extend ray BP to hit side AC at D. What is the probability that BD < 4?
The sides of triangle ABC are 3, 5, and 7.

onyuIee Apr 10, 2025

0

23

0

+608

Counting

Given a regular octagon, in how many ways can we color one diagonal red and another diagonal blue so that the two colored diagonals intersect at an endpoint? Consider rotations and reflections distinct.

onyuIee Apr 10, 2025

0

15

0

+608

Counting

Find the number of ways of placing three As, three Bs, and three Cs in a 3 \times 3 grid, so that every square contains one letter, and each diagonals contains one A, one B, and one C.

onyuIee Apr 10, 2025

Apr 9, 2025

0

18

1

+190

Counting

How many zeroes do we write when we write all the integers from 1 to 625 in base 4?

HumanBemg Apr 9, 2025

0

14

1

+190

Counting

In how many ways can 5 balls be placed in 4 boxes, if 2$balls are white and 3 balls are black? (Balls of the same color are indistinguishable. The boxes are indistinguishable.)

HumanBemg Apr 9, 2025

Apr 8, 2025

0

21

0

+190

Counting

Now suppose that not only must Sir Lancelot and Sir Gawain be next to each other, but Sir Galahad and Sir Percival also demand to be next to each other. How many seatings of the 8 knights are possible?

HumanBemg Apr 8, 2025

0

13

0

+190

Counting

King Arthur's round table has 8 evenly spaced chairs. In how many ways can 8 knights be seated in the chairs, if Sir Lancelot and Sir Gawain insist on being seated next to each other?

HumanBemg Apr 8, 2025

0

1

14

0

+987

Counting

Suppose for this problem (though it may not be accurate in real life) that the Senate has 48 Republicans and 52 Democrats. In how many ways can we form a committee with 5 senators, in which neither party holds all 5 seats?

booboo44 Apr 8, 2025

0

2

11

0

+987

Counting

In the United States, there are 50 states. Each state is represented by 2 senators. In how many ways can we form a committee with 5 senators, in which no two of the senators are from the same state?

booboo44 Apr 8, 2025

0

1

10

1

+987

Counting

A basket contains 7 green marbles and 6 red marbles. Two marbles are taken from the basket at random without replacement (i.e., the first marble is not put back before the second marble is drawn). What is the probability that the first marble is green, read more ..

booboo44 Apr 8, 2025

0

1

16

1

+987

Counting

A basket contains 7 green marbles and 6 red marbles. A marble is taken from the basket at random; its color is recorded, then the marble is returned to the basket. A second marble is then taken from the basket at random, and its color is recorded. read more ..

booboo44 Apr 8, 2025

Apr 7, 2025

0

1

9

1

+970

Algebra

Let a_1, a_2, a_3, \dots be an infinite geometric series with positive terms. If a_2 = 10, then find the smallest possible value of
a_1 + a_2 + a_3.

gnistory Apr 7, 2025

+1

8

2

+970

Algebra

Compute
1.11111 + 0.11111 + 0.01111 + 0.00111 + 0.00011 + 0.00001

gnistory Apr 7, 2025

0

2

7

1

+448

Free Body Diagram

Tackling Friction in Free body diagrams, would appreciate your generous help.
Problem: A block with a mass of 10 kg is placed on a rough inclined plane that makes a 30° angle with the horizontal. The coefficient of static read more ..

HiylinLink Apr 7, 2025

+1

8

2

+400

Geometry

A and B are two points on a sphere of radius 2. We know the space distance between A and B is 2, What is distance from A to B along the (minor) arc of a great circle?

Stanry Apr 7, 2025

Apr 5, 2025

-1

7

2

+190

Geometry

Three unit squares and two line segments connecting two pairs of vertices are shown. What is the area of triangle ABC?
A is at (0,0), B is at (1,0), and C is at (1,1).

HumanBemg Apr 5, 2025

+1

13

1

+190

Geometry

In \triangle ABC, we have AB = AC = 4 and \angle BAC = 45^\circ. If M is the midpoint of BC, then find AM^2.

HumanBemg Apr 5, 2025

+1

5

1

+190

Geometry

What is the equation of the reflection of the line y = 2x + 1 across the line y = 5x - 3? Give your answer in slope-intercept form.

HumanBemg Apr 5, 2025

-1

2

13

1

+970

Geometry

In the diagram below, ABCD is a rectangle with AD=6 and B=10. Point M is the intersection of its diagonals and point E lies on \overline{AD} such that BE=2. Find CE^2. (Diagram not to scale)

gnistory Apr 5, 2025

+1

1

4

1

+970

Geometry

Let R=(a,b) be the image of rotating point P=(7,2) clockwise by 150^\circ degrees around Q=(12,-5). What is b?

gnistory Apr 5, 2025

0

1

19

0

+970

Geometry

Let R be the image of rotating point P=(4,0) counterclockwise by 60^\circ$ degrees around Q=(12,-7). What is PR?

gnistory Apr 5, 2025

Apr 4, 2025

0

1

12

1

+970

Geometry

Point B is the reflection of point A=(2,-1) over the line y=1. Point C is the reflection of point B over the line x + 2y = a. If C=(-5,8), what is a?

gnistory Apr 4, 2025

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