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230399 Questions
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65
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counting
When two standard 6-sided dice are rolled, there are 36 possible outcomes for the sum of the two rolls: one sum of 2, two sums of 3, and so on, up to one sum of 12.
Find all possible ways of numbering two 6-sided dice
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Guest
Mar 12, 2023
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76
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counting
A coin is tossed 12 times. How many different sequences of tosses could there have been, if the number of heads was at least ?
Guest
Mar 12, 2023
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70
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geometry
In triangle PQR, let M be the midpoint of QR, let N be the midpoint of PR, and let O be the intersection of QN and RM, as shown. If QN perp PR, QN = 12, and PR = 14, then find the area of triangle PQR.
Guest
Mar 12, 2023
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79
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geometry
In tetrahedron ABCO, angle AOB = angle AOC = angle BOC = 90^\circ. A cube is inscribed in the tetrahedron so that one of its vertices is at O, and the opposite vertex lies on face ABC. Let OA = 1, OB = 1, OC = 1. Show that the
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Guest
Mar 12, 2023
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72
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Polygon
Let B, A, and D be three consecutive vertices of a regular -gon. A regular heptagon is constructed on AB with a vertex C next to A Find angle BCD in degrees.
Guest
Mar 12, 2023
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69
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Probability
A standard six-sided die is rolled twice. What is the probability that the product of the rolls is 1, 2, or 3?
Guest
Mar 12, 2023
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66
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Counting
Six children are each offered a single scoop of any of 3 flavors of ice cream from the Combinations Creamery. How many ways can each child choose a flavor for their scoop of ice cream so that some flavor of ice cream is selected by exactly two children?
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Guest
Mar 12, 2023
0
80
1
Help on geometry
Point A is on side XZ of triangle XYZ such that XA = XY. Given that YXZ = 90˚, YZX = 30˚, and ZA = 6-sqrt12, find the area of triangle XYZ.
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Guest
Mar 12, 2023
Mar 11, 2023
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73
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Probability
I need the answer to this
Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. What is the probability that the area of triangle XYD is at most 20?
Guest
Mar 11, 2023
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95
1
counting
I don't get this
Sam wants to color the three sides of an equilateral triangle. He has two different colors to choose from. In how many different ways can Sam color the sides of the triangle? (Two colorings are considered
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Guest
Mar 11, 2023
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92
1
+1
Why is b^2 kept?
why is b^2 kept in the function a^2 + b^2 - 2ab?
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Bokor
Mar 11, 2023
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84
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Algebra
Need to work with variables
Let a and b be real numbers such that a^3 + 3ab^2 = 679 and a^3 - 3ab^2 = 673. Find a - b.
Guest
Mar 11, 2023
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69
0
counting
At a meeting, five scientists, two mathematicians, five journalists, two biologists, and three politicians are to be seated around a circular table. How many different arrangements are possible if the scientists must all sit together (in
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Guest
Mar 11, 2023
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73
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counting
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?
Guest
Mar 11, 2023
0
73
0
counting
In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?
Guest
Mar 11, 2023
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