CInsbstnkng

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Math

A fair coin is tossed repeatedly until either heads comes up three times in a row or tails comes up four times in a row. What is the probability that the coin will be tossed more than 10 times? Express your answer as a common fraction.

CInsbstnkng 07.10.2025

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Math

In triangle ABC, cos A=sqrt(7/10) and cos B=sqrt(3/10) Find cos C

CInsbstnkng 07.10.2025

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Trapezoid ABCD has bases \overline{AB} and \overline{CD}. The extensions of the two legs of the trapezoid intersect at $P$. If $[PBC] = 15$ and $CD = 3 \cdot AD,$ what is $[ABCD]$?

CInsbstnkng 19.08.2025

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Trapezoid ABCD has bases \overline{AB} and \overline{CD}. The extensions of the two legs of the trapezoid intersect at $P$. If $[ABD]=8$ and $[PBC]=8$, then what is $[PAB]$?

CInsbstnkng 19.08.2025

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An equilateral triangle, a regular heptagon, a square, a 20-gon, a regular pentagon, a regular hexagon, and a regular n-gon, all with the same side length also completely surround a point. Find n.

CInsbstnkng 18.08.2025

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Let ABCDE be an equilateral pentagon. If the pentagon is concave, and $\angle A = \angle B = 90^{\circ},$ then what is the degree measure of $\angle E$?

CInsbstnkng 18.08.2025

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Find all ordered pairs x, y of real numbers such that x+y=10 and x^3+y^3=300.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

CInsbstnkng 17.08.2025

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For an integer n, the inequality
x^2 + nx + 15 < -89 - 3x^2
has no real solutions in $x$. Find the number of different possible values of $n$.

CInsbstnkng 17.08.2025

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Shown below is rectangle EFGH. Its diagonals meet at Y. Let $X$ be the foot if an altitude is dropped from $E$ to $\overline{FH}$. If EX = 24 and $GY = 30$, find the perimeter of rectangle $EFGH$.

CInsbstnkng 13.08.2025

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Find the sum of the squares of the roots of $2x^2+4x-1=x^2-8x+3$.

CInsbstnkng 11.08.2025

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Let $m$ be a real number. If the quadratic equation $x^2+mx+4 = 2x^2 + 17x + 8$ has two distinct real roots, then what are the possible values of $m$? Express your answer in interval notation.

CInsbstnkng 11.08.2025

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Solve the system of equations
y = \log_2 (2x)
y = log_4 (16 + x)

CInsbstnkng 11.08.2025

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Find one ordered pair $(x,y)$ of real numbers such that $x + y = 10$ and $x^3 + y^3 = 162 + x^2 + y^2.$

CInsbstnkng 11.08.2025

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In triangle ABC, the angle bisector of angle BAC meets BC at D, such that AD = AB. Line segment AD is extended to E, such that angle DBE = angle BAD = 17 degrees. Find angle ABD.

CInsbstnkng 10.08.2025

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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 mehr ..

CInsbstnkng 09.08.2025

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We have a triangle $\triangle ABC$ and a point $K$ on $BC$ such that $AK$ is an altitude to $\triangle ABC$. If $AC = 8,$ $BK = 2$, and $CK = 3,$ then what is $AB$?

CInsbstnkng 08.08.2025

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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 $\overline{AB}$ is $4,$ and the circle has a radius of $5.$ Find the length $AB.$ mehr ..

CInsbstnkng 08.08.2025

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Lines $XQ$ and $XR$ are tangent to a circle, as shown below. If $\angle XTU = 47^\circ$ and $\angle QAU = 65^\circ,$ then find $\angle QXR,$ in degrees.

CInsbstnkng 08.08.2025

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For an integer $n,$ let $f(n)$ be the remainder when $n^8 + n^{16}$ is divided by $5.$ Compute $f(0) + f(1) + f(2) + f(3) + f(4).$

CInsbstnkng 07.08.2025