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Home » There are \(\boxed1800\) positive 4-digit numbers divisible by 5. - Crosslake

There are \(\boxed1800\) positive 4-digit numbers divisible by 5. - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Die größte 5-stellige Zahl ist 99999. Wir finden die größte durch 11 teilbare Zahl:

📌 \left\lfloor \frac{99999}{11} \right\rfloor = \left\lfloor 9090.8181\ldots \right\rfloor = 9090, \quad \text{also} \quad 11 \times 9090 = 99990.

📌 Die Zahlen, die durch 11 von 10010 bis 99990 teilbar sind, bilden eine arithmetische Folge mit Differenz 11. Die Anzahl der Terme ist:

📌 \frac{99990 - 10010}{11} + 1 = \frac{89980}{11} + 1 = 8180 + 1 = 8181.

📌 Somit gibt es \(\boxed{8181}\) positive 5-stellige Zahlen, die durch 11 teilbar sind.

📌 Frage: Ein Wissenschaftler misst zwei Drahtstücke: Eine ist 3,2 cm lang und die andere 7,8 cm lang. Wie lang ist die durchschnittliche Länge der beiden Stücke in Zentimetern?

📌 Lösung: Um die durchschnittliche Länge zu finden, addieren wir die Längen und teilen durch die Anzahl der Stücke:

📌 \text{Durchschnitt} = \frac{3.2 + 7.8}{2} = \frac{11.0}{2} = 5.5 \text{ cm}.

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T(3) = (3)^2 - 6(3) + 13 = 9 - 18 + 13 = 4
Thus, the minimum time predicted by the model is $ \boxed{4} $.
Question: Factor the expression $ 16x^2 - 40x + 25 $ completely.
Check if the trinomial is a perfect square trinomial:
16x^2 = (4x)^2, \quad 25 = (5)^2, \quad -40x = 2(4x)(-5)
This confirms the expression is of the form $ a^2 - 2ab + b^2 = (a - b...
16x^2 - 40x + 25 = (4x - 5)^2
Thus, the factored form is $ \boxed{(4x - 5)^2} $.
Question: If $ x + \frac{1}{x} = 4 $, what is the value of $ x^2 + \fr...
We square both sides of the given equation:

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