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230955 Questions
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75
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Inequality
Prove that if a, b, and c are positive real numbers, then
sqrt(a^2 + ab + b^2) + sqrt(a^2 + ac + c^2) + sqrt(b^2 + bc + c^2) >= sqrt(3) (sqrt(ab) + sqrt(ac) + sqrt(bc))
When does equality occur?
Guest
Mar 13, 2023
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65
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Coordinates
Points A, B, and C are given in the coordinate plane. There exists a point Q and a constant k such that for any point P,
PA^2 + PB^2 + PC^2 = 3PQ^2 + k
If A = , B = , and C = , then find the constant k.
Guest
Mar 13, 2023
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64
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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 13, 2023
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86
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KURKI MURKI
3 kury za 3 dni zniosą 3 jajka. Ile jajek zniosą 9 kur za 9 dni?
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Guest
Mar 13, 2023
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79
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tetrahedron
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 13, 2023
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80
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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 13, 2023
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66
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Probability
A stick is broken at two points, chosen at random. If the length of the stick is 6 then what is the probability that all three resulting pieces are shorter than 2 units?
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Guest
Mar 13, 2023
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75
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Probability
Can anyone help with this?
Let PQR be an equilateral triangle, centered at O. A point X is chosen at random inside the triangle. Find the probability that X is closer to O than to any of the sides. (In
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Guest
Mar 13, 2023
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71
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Algebra
Help this is hard
Let S be the set of all real numbers of the form
a1/3 + a2/3^2 + a3/3^3 + ....
where a_i \in {0, 1, 2} for all i.
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Guest
Mar 13, 2023
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70
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counting
I don't know how to count
In a regular decagon, the sides are to be colored with five different colors, so that sides are diametrically opposite have the same color. (Not all five colors need to be used.) One possible
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Guest
Mar 13, 2023
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73
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counting
Plz I need help
Let n be a positive integer. Let k be a positive integer.
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Guest
Mar 13, 2023
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70
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Counting
Need help plz
At my office, 16 people own cats, people own dogs, and people own both cats and dogs. How many people own a cat or a dog?
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Guest
Mar 13, 2023
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75
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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.
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Guest
Mar 13, 2023
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70
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Probability
What do I do
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 13, 2023
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95
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Interest rates
Help I don't know the formula
Chuck deposits $2000 into a bank account that compounds annually at an interest rate of . Assuming there are no other transactions, what will the balance be after years, in dollars?
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Guest
Mar 13, 2023
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72
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counting
Sam writes down the numbers 1, 2, 3, ..., 99
(a) How many digits did Sam write, in total?
(b) Sam chooses one of the digits written down, at random. What is the probability that Sam chooses a 0?
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Guest
Mar 13, 2023
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99
7
+1124
Pascal's triangle
Hi friends,
just a question...If I look at the sums of each row in Pascal's triangle, I see a ratio of 2. Is it therefore save to say that a Geometric sequence is formed in the triangle?
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juriemagic
Mar 13, 2023
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91
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need me help
1. Определить количество информации (по Хартли), содержащееся в системе, информационная емкость которой характеризуется десятичным
числом Q (750). Закодировать это число по двоичной системе счисления.
I= log2Q= log2750 ≈ 9,550 бит ≈ 10 бит.
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Guest
Mar 13, 2023
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76
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чему равно выражение 12:2(3-1)
чему равно выражение 12:2(3-1)
Guest
Mar 13, 2023
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87
1
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 13, 2023
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79
1
Counting
Help how do you do this
There is a group of five children, where two of the children are twins. How many ways can I distribute 10 identical pieces of candy to the children, if the twins must get an equal amount of candy?
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Guest
Mar 13, 2023
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91
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Geometry
Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF, which intersect at I. If DI = 3, BD = 4, and BI = 8, then find the area of triangle ABC.
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Guest
Mar 13, 2023
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