All Questions ⁺⁰235549 Questions

0

21

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+279

Counting

Four children and four adults are to be seated at a circular table. In how many different ways can they be seated if all the children are next to each other, and all the adults are next to each other? (Two seatings are considered the same if read more ..

fjeihqoO Apr 11, 2024

0

25

0

+279

Counting

At a meeting, four scientists, two mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if the mathematicians must sit next to each other? (Two seatings are considered equivalent if read more ..

fjeihqoO Apr 11, 2024

0

36

0

+279

Counting

A standard six-sided die is rolled $7$ times. You are told that among the rolls, there was one $1,$ one $2$, one $3$, one $4$, one $5$, and two $6$s. How many possible sequences of rolls could there have been? (For example, 2, 3, read more ..

fjeihqoO Apr 11, 2024

+1

10

2

+21

Try to solve this difficult probability question: [DUPLICATE]

Try to solve this difficult probability question:
A fair coin is tossed repeatedly until either heads comes up three times in a row or tails comes up three times in a row. What is the probability that the coin will be tossed more than $10$ times? read more ..

blueorange Apr 11, 2024

0

16

2

+4

Exploring the properties of Isosceles triangles

Hello,
Given an isosceles triangle ABC where AB=AC and the base BC is of length 8 cm. The height from A to the base BC divides it into two segments, BD and DC. If the length of BD is 3 cm, what is the length of segment DC and the height read more ..

yvonne910rhodes Apr 11, 2024

0

19

1

+20

Geometry

In triangle ABC, angle A = p + 2q degrees, angle B = 6p - 5q degrees, and angle C = 14p + 8q degrees. Find p (in degrees) in terms of q.

MasterUtopia Apr 11, 2024

0

20

3

+6

Math question help

Question 1) How many positive five-digit integers contain the digit grouping "24" at least once? For instance, 24380 and 24440 are two such integers to include, but 23480 and 42034 do not meet the restrictions.
Question 2) For how many read more ..

timmynotjimmy Apr 11, 2024

0

18

1

+1234

help geometry

The area of a trapezoid is $80$. The length of one base is $16$ units greater than the other base, and one base of the trapezoid is $12$. Find the length of the median of the trapezoid.

Akhain1 Apr 11, 2024

0

22

0

+1234

help geometry

Let P_1 P_2 P_3 \dotsb P_{10} be a regular polygon inscribed in a circle with radius $1.$ Compute
P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1

Akhain1 Apr 11, 2024

0

35

0

+1234

help geometry

In rectangle $EFGH$, let $M$ be the midpoint of $\overline{EF}$, and let $X$ be a point such that $MH = MX$, as shown below. If $\angle EFH = 30^\circ$ and $\angle MHX = 60^\circ,$ then find $\angle XHG,$ in degrees.

Akhain1 Apr 11, 2024

0

18

0

+2653

Trapzoid

In trapezoid ABCD, \overline{AB} \parallel \overline{CD}. Find the area of the trapezoid.

LiIIiam0216 Apr 11, 2024

0

27

0

+2653

Trapezoid

In trapezoid $PQRS,$ $\overline{PQ} \parallel \overline{RS}$. Let $X$ be the intersection of diagonals $\overline{PR}$ and $\overline{QS}$. The area of triangle $PQX$ is $2,$ and the area of triangle $RSX$ is $2.$ Find the area of trapezoid read more ..

LiIIiam0216 Apr 11, 2024

Apr 10, 2024

+1

11

2

+35

Counting problems

Problem 1.
Andy is placing pieces on a 3 × 3 square board such that pieces are placed on non-adjacent squares (squares that are not directly above, below, left, or right of another square). How many ways are there for Andy to place 4 pieces on his read more ..

Mather459 Apr 10, 2024

0

9

1

+4

Pls help!!!

Find the sum of all solutions to

types0uls Apr 10, 2024

0

19

0

+2653

Geometry

In parallelogram $EFGH,$ let $M$ be the point on $\overline{EF}$ such that $FM:ME = 1:1,$ and let $N$ be the point on $\overline{EH}$ such that $HN:NE = 1:1.$ Line segments $\overline{FH}$ and $\overline{GM}$ intersect at $P,$ and line segments $\overline{FH}$ read more ..

LiIIiam0216 Apr 10, 2024

0

30

0

+2653

Geometry

In triangle $PQR,$ let $X$ be the intersection of the angle bisector of $\angle P$ with side $\overline{QR}$, and let $Y$ be the foot of the perpendicular from $X$ to side $\overline{PR}$. If $PQ = 8,$ $QR = 5,$ and $PR = 1,$ then compute the length read more ..

LiIIiam0216 Apr 10, 2024

0

22

0

+830

Triangle

In triangle ABC, angle ACB = 90 degrees. Let H be the foot of the altitude from C to side AB.
If BC = 1 and AH = 2, find CH.

magenta Apr 10, 2024

0

29

0

+306

help with geometry

In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 1$, and $PR =1$, then read more ..

nathanl6656 Apr 10, 2024

0

31

0

+306

help plz

In triangle $STU$, let $M$ be the midpoint of $\overline{ST},$ and let $N$ be on $\overline{TU}$ such that $\overline{SN}$ is an altitude of triangle $STU$. If $ST = 8$, $SU = 8$, $TU = 8$, and $\overline{SN}$ and $\overline{UM}$ intersect at $X$, read more ..

nathanl6656 Apr 10, 2024

0

22

0

+306

need help

Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is $6$, then find the volume of the resulting read more ..

nathanl6656 Apr 10, 2024

0

23

0

+306

Triangle

Altitudes $\overline{AD}$ and $\overline{BE}$ of acute triangle $ABC$ intersect at point $H$. If $\angle AHB = 144^\circ$ and $\angle BAH = 66^\circ$, then what is $\angle HCA$ in degrees?

nathanl6656 Apr 10, 2024

0

19

0

+1431

help geometry

Points $M$, $N$, and $O$ are the midpoints of sides $\overline{KL}$, $\overline{LJ}$, and $\overline{JK}$, respectively, of triangle $JKL$. Points $P$, $Q$, and $R$ are the midpoints of $\overline{NO}$, $\overline{OM}$, and $\overline{MN}$, respectively. read more ..

kittykat Apr 10, 2024

0

23

0

+1431

help angles

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 60^\circ$ and $\angle STU = 45^\circ$, read more ..

kittykat Apr 10, 2024

0

32

0

+1431

Help coordinates

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $4,$ and the slope of line segment $\overline{OQ}$ is $5.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

kittykat Apr 10, 2024

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