https://file.aiquickdraw.com/mathbot/file/1726485861980w7qrlhvk.jpg

Let's analyze and solve each of the questions provided in the image:

### 1. **Rezultatul calculului \( 2^{-3} \cdot 40 \)**
We need to evaluate \( 2^{-3} \cdot 40 \).

First, calculate \( 2^{-3} \):
\[
2^{-3} = \frac{1}{2^3} = \frac{1}{8}
\]

Now multiply by 40:
\[
\frac{1}{8} \cdot 40 = \frac{40}{8} = 5
\]
Thus, the correct answer is **b) 5**.

### 2. **Dintre numerele de mai jos, cel care este cuprins între 9 și 10 este:**
We need to evaluate the options and check which value is between 9 and 10:

a) \( 4\sqrt{5} \):
\[
4\sqrt{5} = 4 \times 2.236 \approx 8.944
\]
This is less than 9.

b) \( 6\sqrt{2} \):
\[
6\sqrt{2} = 6 \times 1.414 \approx 8.484
\]
This is also less than 9.

c) \( \sqrt{9.5} \):
\[
\sqrt{9.5} \approx 3.082
\]
Clearly not between 9 and 10.

d) \( 3\sqrt{10} \):
\[
3\sqrt{10} = 3 \times 3.162 \approx 9.486
\]
This is **between 9 and 10**, so the correct answer is **d) 3\(\sqrt{10}\)**.

### 3. **Suma divizorilor naturali ai lui 9 este egală cu:**
The divisors of 9 are 1, 3, and 9.

Sum of the divisors:
\[
1 + 3 + 9 = 13
\]
Thus, the correct answer is **b) 13**.

### 4. **Media aritmetică a numerelor 6 și 7 cu ponderile 3 și 2 este egală cu:**
We are given the weighted average formula:
\[
\text{Weighted Average} = \frac{6 \times 3 + 7 \times 2}{3 + 2}
\]

First, calculate the weighted sum:
\[
6 \times 3 = 18, \quad 7 \times 2 = 14
\]
The total weighted sum is:
\[
18 + 14 = 32
\]
Now divide by the total weight (3 + 2 = 5):
\[
\frac{32}{5} = 6.4
\]
Thus, the correct answer is **b) 6.4**.

---

Would you like further explanations on any of these questions? 

Here are 5 related questions to deepen your understanding:
1. How do you compute exponents with negative bases?
2. What is the geometric meaning of a square root?
3. How do you find the divisors of any number?
4. Can you explain how to calculate the weighted average with different weights?
5. How does changing the weights in a weighted average affect the result?

**Tip**: Always double-check if you are working with proper units and ranges when solving square root and exponent problems.

Rezultatul calculului 2^(-3) . 40, Dintre numerele de mai jos, cel care este cuprins între 9 și 10, Suma divizorilor naturali ai lui 9, Media aritmetică a numerelor 6 și 7 cu ponderile 3 și 2

This page covers a variety of math problems, including exponent calculations, finding the number between 9 and 10 using square roots, summing the divisors of 9, and calculating a weighted average. Suitable for students in Grades 7-9.

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