AUnVerifedTaxPayer

18 Questions
7 Answers

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Counting

Let n be a positive integer, and let S = {1, 2, 3, ..., n}. Three subsets A, B, C of S are chosen at random.
(a) Find the probability that A contains all elements 1, 2, 3, ..., n.
(b) Find the probability that B contains mehr ..

AUnVerifedTaxPayer 03.10.2024

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1

1

+76

Algebra

Let $x$ and $y$ be nonnegative real numbers. If $x + y = 25$, then find the minimum value of $6x + 3y.$

AUnVerifedTaxPayer 28.09.2024

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1

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+76

Algebra

For certain values of k and m, the system
3a + 2b = 2
a + 2b = k - 8a - mb
has infinitely many solutions (a,b). What are k and m? mehr ..

AUnVerifedTaxPayer 28.09.2024

0

3

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+76

Algebra

The function $f(x)$ is defined only on domain $[-1,2]$, and is defined on this domain by the formula
$$f(x) = 2x^2-8x+1.$$
What is the range of $f(x)$? Express your answer as an interval or as a union of intervals.

AUnVerifedTaxPayer 28.09.2024

0

2

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+76

Algebra

Let
$$f(x) = \frac{1}{1+\frac{2}{1+\frac 3x}}.$$
There are three real numbers $x$ that are not in the domain of $f(x)$. What is the sum of those three numbers?

AUnVerifedTaxPayer 28.09.2024

0

1

1

+76

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.

AUnVerifedTaxPayer 25.09.2024

+1

1

1

+76

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.

AUnVerifedTaxPayer 25.09.2024

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1

1

+76

Geometry

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

AUnVerifedTaxPayer 25.09.2024

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1

+76

Geometry

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

AUnVerifedTaxPayer 25.09.2024

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4

1

+76

Counting

A baking club wants to form an executive committee. There are $20$ people in the baking club, including Mark. In how many ways can the baking club form an executive committee with $7$ people, including Mark?

AUnVerifedTaxPayer 12.09.2024

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3

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+76

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, mehr ..

AUnVerifedTaxPayer 12.09.2024

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2

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+76

Counting

You are given the 4 x 4 grid below.
(a) Find the number of ways of placing 8 counters in the squares (at most one counter per square), so that each row contains exactly two counters.
(b) Find the number of ways mehr ..

AUnVerifedTaxPayer 12.09.2024

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3

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+76

Geometry

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 $4,$ and the area of triangle $PSR$ is $8.$ Find the area of trapezoid mehr ..

AUnVerifedTaxPayer 11.09.2024

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3

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+76

Geometry

Lines $XQ$ and $XR$ are tangent to a circle, as shown below. If $\angle QTA = 45^\circ$ and $\angle RUA = 45^\circ,$ then find $\angle QXR,$ in degrees.

AUnVerifedTaxPayer 07.09.2024

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4

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+76

Geometry

The tangent to the circumcircle of triangle $WXY$ at $X$ is drawn, and the line through $W$ that is parallel to this tangent intersects $\overline{XY}$ at $Z.$ If $XZ = 5$ and $YZ = 2,$ find $WX.$

AUnVerifedTaxPayer 07.09.2024

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2

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+76

Geometry

In triangle $ABC,$ $\angle C = 90^\circ.$ A semicircle is constructed along side $\overline{AC}$ that is tangent to $\overline{BC}$ and $\overline{AB}.$ If the radius of the semicircle is equal to $1$ and $AB = 2$, then find $AC.$

AUnVerifedTaxPayer 07.09.2024

+1

1

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+76

need help

A circular table is pushed into a corner of the room, where two walls meet at a right angle. A point $P$ on the edge of the table (as shown below) has a distance of $3$ from one wall, and a distance of $3$ from the other wall. Find the radius mehr ..

AUnVerifedTaxPayer 07.09.2024

0

4

1

+76

help geometry

Two tangents $\overline{PA}$ and $\overline{PB}$ are drawn to a circle, where $P$ lies outside the circle, and $A$ and $B$ lie on the circle. The length of $\overline{PA}$ is $5,$ and $AB$ has a length of 6. Find the radius of the circle.</ mehr ..

AUnVerifedTaxPayer 07.09.2024

+76

0

The expression simplifies to 6 - 3*3^(1/3).

AUnVerifedTaxPayer09.10.2024, 14:54