All Questions ⁺⁰230861 Questions

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+387

Counting

I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if there must be a mathematics textbook exactly in the middle, and all the psychology textbooks are read more ..

magenta Apr 21, 2024

0

1

0

+387

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 ..

magenta Apr 21, 2024

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2

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+387

Counting

At a meeting, $5$ scientists, $2$ mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if each scientist must sit next to a mathematician? (Two seatings are considered equivalent read more ..

magenta Apr 21, 2024

0

2

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+1036

Algebra

Fill in the blanks to make a quadratic whose roots are $1$ and $-1.$
x^2 + ___ x + ___

kittykat Apr 21, 2024

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2

1

+1036

Algebra

Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$

kittykat Apr 21, 2024

0

4

1

+1036

Algebra

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

kittykat Apr 21, 2024

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3

0

+1133

Geometry

In triangle $PQR,$ $M$ is the midpoint of $\overline{PQ}.$ Let $X$ be the point on $\overline{QR}$ such that $\overline{PX}$ bisects $\angle QPR,$ and let the perpendicular bisector of $\overline{PQ}$ intersect $\overline{PX}$ at $Y.$ If $PQ = 36, find read more ..

parmen Apr 21, 2024

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3

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+1133

Geometry

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 12$, find $BC$.

parmen Apr 21, 2024

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+1133

Geometry

In triangle $ABC,$ let the angle bisectors be $\overline{BY}$ and $\overline{CZ}$. Given $AB = 12$, $AY = 12$, and $AC = 12$, find $BZ$.

parmen Apr 21, 2024

+1

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+5

probability help

A history class is comprised of 9 female and 5 male students. If the instructor of the class randomly chooses 6 students from the class for an oral exam, what is the probability that 4 female students and 2 male students will be selected? Round your answer read more ..

hawtkitty84 Apr 21, 2024

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4

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+1133

Geometry

Angle bisectors $\overline{AX}$ and $\overline{BY}$ of triangle $ABC$ meet at point $I$. Find $\angle C,$ in degrees.

parmen Apr 21, 2024

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3

0

+1133

Geometry

As shown in the diagram $\angle BAC=90^\circ$. Let $X$ be the foot of the altitude from $A$ to $\overline {BC}$, $\overline{AY}$ be the bisector of $\angle BAC$, and $\overline{AZ}$ be the median of $\triangle ABC$. If $\angle BAY = 16^\circ$, then read more ..

parmen Apr 21, 2024

0

3

0

+1133

Geometry

In quadrilateral $PQRS$, $PQ = QR = RS = SP$, $PR = \sqrt{2}$, and $QS = \sqrt{2}$. Find the perimeter of $PQRS$.

parmen Apr 21, 2024

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4

1

+1133

Geometry

In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $90^\circ.$ Find the area of the rhombus.

parmen Apr 21, 2024

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4

1

+1133

Geometry

The perimeter of a rectangle is $40,$ and the length of one of its diagonals is $10 \sqrt{2}.$ Find the area of the rectangle.

parmen Apr 21, 2024

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4

1

+1133

Geometry

Rectangle $ABCD$ contains a point $X$ such that $AX = 3$, $BX = 3$, and $CX = 3$. Find $DX$.

parmen Apr 21, 2024

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+1133

Geometry

A rectangle contains a strip of width $1,$ as shown below. Find the area of the strip.

parmen Apr 21, 2024

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3

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+1133

Geometry

Two rectangles overlap, as shown below. Find the area of the overlapping region (which is shaded) if $AB = BE = 3$ and $FB = BC = 3.$

parmen Apr 21, 2024

Apr 20, 2024

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+132

This is rlly hard, PLS HELP

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may not sit next to each other in the same row?

Lilliam0216 Apr 20, 2024

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+132

HELP

Find the number of positive integers that satisfy both the following conditions:
Each digit is a 1 or a 3
The sum of the digits is 12

Lilliam0216 Apr 20, 2024

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3

1

+132

PLS HELP

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may not sit next to each other in the same row?

Lilliam0216 Apr 20, 2024

0

2

1

+132

HELP

In how many ways can the numbers 1 through 5 be entered once each into the five boxes below so that all the given inequalities are true?

Lilliam0216 Apr 20, 2024

0

3

0

+866

Counting

A speech class has $4$ freshmen and $3$ sophomores. (Everyone is distinguishable.) In how many ways can they stand in line, so that all the freshmen are standing together?

ABJeIIy Apr 20, 2024

0

4

0

+866

Counting

I have $4$ different mathematics textbooks and $3$ different psychology textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if there must be a mathematics textbook exactly in the middle, and all the psychology textbooks are read more ..

ABJeIIy Apr 20, 2024

0

2

0

+866

Counting

At a meeting, $5$ scientists, $2$ mathematicians, and a journalist are to be seated around a circular table. How many different arrangements are possible if each scientist must sit next to a mathematician? (Two seatings are considered equivalent read more ..

ABJeIIy Apr 20, 2024

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