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Lê Quốc Trần Anh Coordinator
04/03/2018 at 04:21
Answers
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A five-digit number is made by randomly ordering the digits 1, 2, 3, 4 and 5. What is the probability that this number is divisible by 4? Express your answer as a common fraction.

  • ...
    Lê Quốc Trần Anh Coordinator 07/03/2018 at 04:41

    ANSWER:

    Recall that a number is divisible by 4 if the two-digit number formed by the tens and ones digits is divisible by 4. Using the digits 1, 2, 3, 4 and 5, the following two-digit multiples of four can be formed: 12, 24, 32 and 52. There are 5 × 4 = 20 permutations of two digits chosen from the digits 1, 2, 3, 4 and 5. Therefore, the probability that the five-digit number is divisible by 4 is 4/20 = 1/5.


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Lê Quốc Trần Anh Coordinator
07/05/2018 at 11:45
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Describe all constants $\color[rgb]{0.35,0.35,0.35}a$ and $\color[rgb]{0.35,0.35,0.35}b$ such that $\color[rgb]{0.35,0.35,0.35}f(x) = \dfrac{2x + a}{bx - 2}$ and $\color[rgb]{0.35,0.35,0.35}f(x) = f^{-1}(x)$ for all $\color[rgb]{0.35,0.35,0.35}x$ in the domain of $\color[rgb]{0.35,0.35,0.35}f$.


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Mr Puppy
23/07/2018 at 10:39
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0
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Suppose that the polynomial \(f\left(x\right)=2x^5-9x^3+2x^2+9x-3\) has 5 solutions x1 ; x2; x3; x4; x5. The other polynomial \(k\left(x\right)=x^2-4\). Find the value of \(P=k\left(x_1\right)\times k\left(x_2\right)\times k\left(x_3\right)\times k\left(x_4\right)\times k\left(x_5\right)\).

Polynomial


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Quoc Tran Anh Le Coordinator
06/08/2018 at 02:38
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Convert 113 in Base10 to Base7.

Math Puzzles

  • ...
    Lê Anh Duy 06/08/2018 at 06:50

    113 = 2 x 72 + 2 x 71 + 1 x 70 = 2217

    (How can I get those number?

    CLUE: Keep dividing 113 by 7:

    113 \(\div\) 7 = 16 (remainder 1)

    16 \(\div\) 7 = 2 (remainder 2)

    Because 2  \(\div\) 7 = 0, we stop here.

    We get three number: 2, 2, 1)

    Selected by MathYouLike

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Huỳnh Anh Phương
09/01/2019 at 12:34
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3
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Linda has oranges and bunch of grapes. She wants exchange to get watermelons. 5 oranges can exchange for 1 bunch of grapes. 5 bunch of grapes can exchange for 1 watermelons. How many oranges can exchange for 3 watermelons?

Mathcounts

  • ...
    Nguyen Thu An 31/01/2019 at 15:53

    75 oranges

    Huỳnh Anh Phương selected this answer.
  • ...
    kakalot 25/01/2019 at 05:30

    need 75 fruit

  • ...
    omgomgomg 10/01/2019 at 17:36

    aaaaa


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Jeff Bezos
19/03/2017 at 00:54
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2
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If x = 1 is the solution for px + 4q = 161, where both p and q are primes, find the value of p2 - q.

simple equation

  • ...
    FA KAKALOTS 03/02/2018 at 12:40

    i will you to make this topic :)
    replace x=1 into the polution above , we have 
    p+4q=161 
    => q= (161-p)/4 
    => q=40-(p-1)/4 => q<40(1)
    because the p and q are primes so (p-1) divisible for 4 =>p-1 >=4 => p>=5 (2)
    Merged (1) with (2) we have q ={2;3;5;7;11;13;17;19;23;29;31}
    then you try to the each of case : it will have 2 cases (correct satisfies) 
    this case p=37 <=> q=31 and p=133 <=> q=7

  • ...
    Tạ Đức Duy 23/06/2017 at 23:10

    i will you to make this topic :)
    replace x=1 into the polution above , we have 
    p+4q=161 
    => q= (161-p)/4 
    => q=40-(p-1)/4 => q<40(1)
    because the p and q are primes so (p-1) divisible for 4 =>p-1 >=4 => p>=5 (2)
    Merged (1) with (2) we have q ={2;3;5;7;11;13;17;19;23;29;31}
    then you try to the each of case : it will have 2 cases (correct satisfies) 
    this case p=37 <=> q=31 and p=133 <=> q=7 


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Summer Clouds
30/05/2017 at 14:22
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1
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At National School, 50% of the students have bicycles. Of the students who have bicysles, 30% have black bicycles. What percent os students of National School have black bicycles?

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    Trần Quang Linh 30/05/2017 at 16:43

    30 percent :)


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Summer Clouds moderators
05/07/2017 at 14:07
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Show that \(A=3+3^2+3^3+3^4+......+3^{99}+3^{100}\) is divisible by 4.

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    Phan Thanh Tinh Coordinator 05/07/2017 at 17:11

    \(A=3+3^2+3^3+3^4+...+3^{99}+3^{100}\)

    \(=3\left(3+1\right)+3^3\left(3+1\right)+...+3^{99}\left(3+1\right)\)

    \(=\left(3+1\right)\left(3+3^3+...+3^{99}\right)⋮4\)

    Selected by MathYouLike

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Phan Thanh Tinh Coordinator
11/08/2017 at 14:41
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WARNING

There has been some Vietnamese problems since my last warning. Although most of the members can understand the questions, we shouldn't answer them from now. Mathulike doesn't select any answers for Vietnamese questions.

P/S : Summer Clouds sent me a message : Các câu hỏi bằng tiếng Việt em ko trả lời nhé. Có trả lời cô cũng ko tích đâu.

  • ...
    phanhuytien 12/08/2017 at 09:45

    ok thank

  • ...
    Kaya Renger Coordinator 11/08/2017 at 14:45

    I don't see the picture :V :V :V 

  • ...
    Lê Quốc Trần Anh Coordinator 11/08/2017 at 14:41

    Ok, I agree.


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Lê Quốc Trần Anh Coordinator
04/09/2017 at 20:59
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The Population Reference Bureau reported a net gain of 155 people on Earth each minute. At this rate, how many more people are there on Earth every day?

  • ...
    VTK-VangTrangKhuyet 04/09/2017 at 21:03

    We have :

    1 minute : 155 people gained.

    1 day : x people gained.

    We have : 1 day = 1440 minutes.

    So at the rate 155 people/1 minute, there are \(155\cdot1440=223200\) more people on Earth every day.

    Lê Quốc Trần Anh selected this answer.
  • ...
    Dao Trong Luan 04/09/2017 at 21:06

    Everyday have 24h; a hour have 60minutes

    => Everyday have:

    24 . 60 = 1440 [minutes]

    So everyday, there are more people on Earth are:

    1440 . 155 = 223 200 [people]

    So everyday, there are more 223 200 people on Earth


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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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