BlackoutMiIkshake

29 Questions
0 Answers

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help CPhill

In the diagram, a semicircle is centered at $O,$ and $\overline{AB}$ is tangent to the semicircle at $B.$ Find $\angle BCD,$ in degrees.

BlackoutMiIkshake 2 hours ago

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Math

Distinct prime numbers p, q, and r satisfy the equation p(q + r) = 16. Which of the following prime numbers must either q or r be equal to?
2 3 5 7 11

ElectricPavlov ●●

BlackoutMiIkshake 24 oct. 2025

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Math

The triangle with vertices at (1,0), (0,1), and (k,k) has area 1/2. Find k.

BlackoutMiIkshake 24 oct. 2025

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Math

Mrs. Monstrous Millie wants to throw a party for a group of monsters and aliens. The monsters each have 5 heads with 7 ears on each head, and the aliens each have 5 heads with 3 ears on each head. As party favors, Mrs. Millie wants to give each guest a lire plus ..

BlackoutMiIkshake 24 oct. 2025

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Math

Siva starts at vertex A of square ABCD with side length 10. He walks towards vertex C, along the diagonal AC. He then walks towards B, then towards D. What is the length of his path?

BlackoutMiIkshake 22 oct. 2025

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Math

William writes the integers from 2 through 15 from left to right on a piece of paper, then does the following:

* He begins by circling the leftmost uncircled integer, then circles all its powers. Afterwards, he repeats this process until every lire plus ..

BlackoutMiIkshake 22 oct. 2025

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Math

Two chords with length r are drawn on a circle of radius r. What is the maximum possible distance between their endpoints?

BlackoutMiIkshake 22 oct. 2025

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Math

In the diagram below, AB = AC = 1, and arc BC is centered at A with \angle BAC = 60^\circ. Point D is on \overline{AB}, and point E is on arc BC so that BD = DE, and arc BE (centered at D) is tangent to \overline{AC}. Point F is on \overline{DB}, lire plus ..

BlackoutMiIkshake 21 oct. 2025

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Math

Let ABC be a triangle with \angle B = 90^{\circ}. Suppose that point D lies on segment BC such that angle BAD = \angle CAD, and suppose that point E lies on segment AC such that angle EDA = 60^{\circ}. Given that AD = AC and that CE = 17, find BD.
<lire plus ..

BlackoutMiIkshake 21 oct. 2025

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Math

A number is chosen at random from among all 9-digit numbers that use each of the digits 1 through 9 exactly once. What is the probability that this number is a multiple of 2?

BlackoutMiIkshake 20 oct. 2025

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Math

Three squares of a 5 \times 5 grid are colored. Two colorings are conisdered equivalent if one coloring can be rotated to form the other coloring, such as the two colorings below, and the grid can be reflected as well. We also want the three lire plus ..

BlackoutMiIkshake 20 oct. 2025

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Math

Selma multiplies the number 9 the two-digit number \overline{AB}, and the three-digit number \overline{CDE}. She finds that the product of all three numbers is the five-digit number 41409. Compute the sum \overline{AB} + \overline{CDE}. lire plus ..

BlackoutMiIkshake 20 oct. 2025

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Math

Given a positive integer N, a multiplication decomposition of N is a sequence of positive integers (d_1, d_2, \dots, d_k) such that
* d_1 \neq 1,
* d_i divides d_{i + 1} for 1 \le i \le k - 1, and
* d_1 d_2 \dotsm d_k = N.
The last lire plus ..

BlackoutMiIkshake 20 oct. 2025

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Math

A traffic light runs repeatedly through the following cycle: green for 40 seconds, then yellow for 5 seconds, then red for 35 seconds, which repeats indefinitely. Oliver picks a random time and watches the light for 75 seconds. What is the probability lire plus ..

BlackoutMiIkshake 20 oct. 2025

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Math

Consider a cube with side length 1, together with 14 congruent spheres each of radius r, with 8 of the spheres centered at the 8 vertices of the cube and the remaining $6$ spheres centered at the centers of the $6$ faces of the cube. Suppose $r$ is chosen lire plus ..

BlackoutMiIkshake 20 oct. 2025

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Math

What is the units digit of 1^1 + 2^2 + 3^4 + 4^8?

BlackoutMiIkshake 18 oct. 2025

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Math

A square has two of its vertices at (12, 34) and (-98, 56),$ and another vertex at (a, b). What is the sum of all possible values of the area of the square?

BlackoutMiIkshake 18 oct. 2025

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Math

At Patty the panda's pizza parlor, the possible pizza toppings are pesto, pepperoni, peppers, and pineapple, and the possible desserts are pumpkin pie, powdered-sugar pretzels, and papaya popsicles. If Prajwal the porcupine, Petunia the peacock, and Pete lire plus ..

BlackoutMiIkshake 17 oct. 2025