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Lê Quốc Trần Anh Coordinator
08/07/2018 at 06:17
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If the mean of the integers 7, 3, 11, 13, 5 and x is 4 more than the mode of the six integers, what is the value of x? 

Mathcounts


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Face586
03/08/2018 at 14:17
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Your body is old in bamboo
Winter re-open summer.
What is the trick?

  • ...
    Cristiano Ronaldo 03/08/2018 at 14:18

    Your body is old in bamboo
    Winter re-open summer.
    What is the trick?

     Answer: That is a fan

    Face586 selected this answer.

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Nếu Có Thể
21/03/2017 at 17:14
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The provincial : \(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+.......+\dfrac{1}{99.101}\)

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    Nguyễn Việt Hoàng 21/03/2017 at 17:22

    We have : \(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+.......+\dfrac{1}{99.101}\)

                  \(=\dfrac{1}{2}\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+.......+\dfrac{2}{99.101}\right)\)

                  \(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+......+\dfrac{1}{99}-\dfrac{1}{101}\right)\)

                   \(=\dfrac{1}{2}\left(1-\dfrac{1}{101}\right)\)

                    \(=\dfrac{1}{2}.\dfrac{100}{101}\)

                    \(=\dfrac{50}{101}\)

    Nếu Có Thể selected this answer.
  • ...
    →இے๖ۣۜQuỳnh 22/03/2017 at 20:14
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      We have : x < -0.8 ⇒ x + 0,8 < 0 ⇒|x + 0.8| = -(x + 0.8)

                       x < -0.8 ⇒ x < 25 ⇒ |x - 25| = 25 - x

      Candle A = -(x + 0.8) - (25 - x) + 1.9

                      = -x + 0,8 - 25 + x + 1,9

                      = -x + x - 0,8 - 25 + 1,9

                      = -25,8 + 1,9

                  A = -23,8

           A = -x - 0.8 - 25 + x + 1.9

           A = -23.9 

       
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      EDM Sang copy my post you review time go

       
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      Nguyễn Xuân Sáng you never copy my name again

       
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      Thanks You Nếu Có Thể 

       
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      Put A = 1.2 + 2.3 + 3.4 + ....... + 199.200

       => 3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ....... + 199.200.201

      => 3A = 199.200.201

      => A = 199.200.201/3

      => A = 2666600

       
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      That worker makes 3 tools out of time is:

                                12 hours - 7 hours 30 minute = 4 hours 30 minute = 4,5 hours

      The worker makes 1 product time out is :  

                                4,5 : 3 = 1,5 (hours)

                                       Answer : 1,5 hours

       
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      That worker makes 3 tools out of time is:

                                12 hours - 7 hours 30 minute = 4 hours 30 minute = 4,5 hours

      The worker makes a product time out is :  

                                 4,5 : 3 = 1,5 (hours)

                                       Answer : 1,5 hours

       
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      Land : A = 1.3 + 3.5 + 5.7 + ...... + 99.101

      => 4A = 1.3.(5 - 1) + 3.5.(7 - 3) + ...... + 99.101.(103 - 99)

      => 4A = 1.3.5 - 1.3.5 + 3.5.7 - 3.5.7 + ...... + 99.100.101

      => 4A = 99.100.101

      => A = 99.100.101/4

      => A = 249975

       
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      From 7m + 5n = 31, we can see that 7m or 5n is even.

      - If 7m is even, m is even and prime => m = 2.

      => 5n = 31 - 7 x 2 = 17. n ⋮̸⋮̸ 5, so no numbers sastify the problem.

      - If 5n is even, n is even and prime => n = 2.

      => 7m = 31 - 5 x 2 = 21 => m = 3 is a prime number.

      The value of: mn + nm = 32 + 23 = 9 + 8 = 17.

       
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      Land A = 1.2 + 2.3 + 3.4 + ....... + 199.200

       => 3A = 1.2.3 - 1.2.3 + 2.3.4 - 2.3.4 + ....... + 199.200.201

      => 3A = 199.200.201

      => A = 199.200.201/3

      => A = 2666600

       
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      We have : 11.3+13.5+15.7+.......+199.10111.3+13.5+15.7+.......+199.101

                    =12(21.3+23.5+25.7+.......+299.101)=12(21.3+23.5+25.7+.......+299.101)

                    =12(1−13+13−15+......+199−1101)=12(1−13+13−15+......+199−1101)

                     =12(1−1101)=12(1−1101)

                      =12.100101=12.100101

                      =50101

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    Nguyễn Xuân Sáng 21/03/2017 at 20:49

    We have:

    \(\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{99.101}\)

    \(=\dfrac{2.1}{2.1.3}+\dfrac{2.1}{2.3.5}+\dfrac{2.1}{2.5.7}+...+\dfrac{2.1}{2.99.101}\)

    \(=\dfrac{1}{2}.\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}\right)\)

    \(=\dfrac{1}{2}.\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)

    \(=\dfrac{1}{2}.\left(1-\dfrac{1}{101}\right)\)

    \(=\dfrac{1}{2}.\dfrac{100}{101}\)

    \(=\dfrac{50}{101}\)


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John
13/04/2017 at 08:54
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Consider the set of all solutions (x,y) to the equation 3x2 = 3y4 + 2013, where x and y are integers. What is the sum of all values of y occurring in such pairs (x,y) ?

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    ♫ ♪ ♥► EDM Troop ◄♥ ♪ ♫ 13/04/2017 at 17:48

    Suppose there are \(a\) values of y = \(k\) satisfy the equation above.

    When k is satisfied the equation, -k is also satisfied the equation, because \(y^4=k^4=\left(-k\right)^4\)

    So the sum of all values of y  is \(a.k+a.\left(-k\right)=0\)

    Ans : 0. 

    John selected this answer.

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Bùi Vân
16/05/2017 at 08:56
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2 lines make 1 intersection at the most.
3 lines make 3 intersection at the most.
4 lines make 6 intersection at the most.
How many intersections at the most do n lines make?

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    Phan Thanh Tinh Coordinator 16/05/2017 at 12:13

    n lines make \(\dfrac{n\left(n-1\right)}{2}\)intersections at the most

    Bùi Vân selected this answer.

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Summer Clouds moderators
08/08/2017 at 08:40
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Bailey is estimating the volume of a container. The container is a cube that measures 2 feet 7 inches on each edge. Bailey estimates the volume by using 3 feet for each edge. In cubic inches, what is the positive difference between Bailey’s estimate and the actual volume? 

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    Phan Thanh Tinh Coordinator 08/08/2017 at 09:00

    Convert : 2 feet 7 inches = 31 inches ; 3 feet = 36 inches

    The positive diference between Bailey's estimate and the actual volume is :

    363 - 313 = 46656 - 29791 = 16865 (cubic feet)

    Selected by MathYouLike
  • ...
    Lê Quốc Trần Anh Coordinator 08/08/2017 at 09:04

    Convert: 1 feet = 12 inches

    The differance between the measure of Balley and the actual size is: \(3ft-2ft7inch=5inches\)

    So the positive differance is: \(5.5.5=125\left(cubic-inches\right)\)


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Vương Ngọc Như Quỳnh
29/08/2017 at 20:53
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Give a,b are two real intergers \(a\ge-\dfrac{1}{4},b\ge-\dfrac{1}{4},a+b=1\)

Prove : \(\sqrt{4a+1}+\sqrt{4b+1}\le\sqrt{12}\)

  • ...
    VTK-VangTrangKhuyet 29/08/2017 at 20:56

    Using Bunhiakovski's inequaility :

    \(\left(1\cdot\sqrt{4a+1}+1\cdot\sqrt{4b+1}\right)^2\le\left(1^2+1^2\right)\cdot\left(4a+1+4b+1\right)=2\cdot6=12\)

    => \(\sqrt{4a+1}+\sqrt{4b+1}\le\sqrt{12}\)

    The "=" happens when a = b = \(\dfrac{1}{2}\)

    Vương Ngọc Như Quỳnh selected this answer.

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Summer Clouds moderators
14/09/2017 at 08:43
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Namakshi wants to arrange her marching band in a rectangular array with the same number of band members in each row. But when she tried putting them in 3 rows, she had 1 band member left over; in 5 rows, she had 2 members left over; in 7 rows, she had 3 members left over; and in 9 rows, she had 4 members left over. What is the least number of members that could be in the band?

  • ...
    Phan Thanh Tinh Coordinator 14/09/2017 at 10:45

    Let x be the least number of members in the band, then x is divided by 3, 5, 7, 9 with remainders 1, 2, 3, 4 respecitvely.

    Since 3 = 1.2 + 1 ; 5 = 2.2 + 1 ; 7 = 3.2 + 1 ; 9 = 4.2 + 1,

     2x + 1 is divisible by 3 ; 5 ; 7 ; 9.

    So, 2x + 1 = LCM(3,5,7,9) = 315 or x = 157

    Hence, the answer is 157

    We need to 

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    →இے๖ۣۜBoy™†hïếuGîa 16/09/2017 at 13:39

    Let x be the least number of members in the band, then x is divided by 3, 5, 7, 9 with remainders 1, 2, 3, 4 respecitvely.

    Since 3 = 1.2 + 1 ; 5 = 2.2 + 1 ; 7 = 3.2 + 1 ; 9 = 4.2 + 1,

     2x + 1 is divisible by 3 ; 5 ; 7 ; 9.

    So, 2x + 1 = LCM(3,5,7,9) = 315 or x = 157

    Hence, the answer is 157

    We need to 


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Lê Quốc Trần Anh Coordinator
13/11/2017 at 17:49
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For how many positive integers containing no digit of zero is the sum of the digits equal to 5?

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    Lê Quốc Trần Anh Coordinator 13/11/2017 at 17:50

    In ΔABC, shown here, the measure of angle BCA is 90°, AC = 12 units and BC = 9 units.
    If D is a point on hypotenuse AB , such that AD = 5 units, what is the length of
    segment CD? Express your answer in simplest radical form.


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Cloud moderators
30/11/2017 at 13:49
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The mean of x and y is 12 and the mean of y and 12 is \(\dfrac{z}{2}\)  . What is the mean of x and z?

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    Dao Trong Luan Coordinator 30/11/2017 at 17:53

    \(\dfrac{x+y}{2}=12\Leftrightarrow x+y=24\Rightarrow x=24-y\)

    \(\dfrac{y+12}{2}=\dfrac{z}{2}\Leftrightarrow y+12=z\)

    => \(\dfrac{x+z}{2}=\dfrac{24-y+y+12}{2}=\dfrac{36}{2}=18\)

    So the mean of x and z is 18

    Selected by MathYouLike

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Trigonometric
sin cos tan cot sinh cosh tanh
Lim-log

Combined operations

 

α β γ δ θ σ ∂ ε ω φ ϕ π μ λ Ψ ξ η χ ζ ι κ ν ψ Ω ρ τ υ Γ Δ Λ Φ Π Σ Υ Ξ ϑ Θ ς ϰ
∞ ⊻ ⩞ ⋎ ⋏ ≀ ∪ ⊎ ⋓ ∩ ⋒ ⊔ ⊓ ⨿ ⊗ ⊙ ⊚ ⊛ ⊘ ⊝ ⊕ ⊖ ⊠ ◯ ⊥
⇔ ⇒ ⇐ → ← ↔ ↑ ↓
Operations
+ - ÷ × ≠ = ⊂ ⊃ ⊆ ⊇ ≈ ∈ ∉ ∃ ∄ ≤ ≥ ± ∓ ≠ ∅ ≃ ≅ ≡ ⋮ ⋮̸ ∀
(□) [□] {□} |□|

The type of system

m×n 1×2 1×3 1×4 1×5 1×6
2×1 2×2 2×3 2×4 2×5 2×6
3×1 3×2 3×3 3×4 3×5 3×6
4×1 4×2 4×3 4×4 4×5 4×6
5×1 5×2 5×3 5×4 5×5 5×6
6×1 6×2 6×3 6×4 6×5 6×6

Recipe:

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