2. Mandie claims that $$ 2^{5}

Question

2. Mandie claims that $$ 2^{5}<4^{2}+3^{2} $$. Is she correct? Justify your answer by showing your complete solution.

UpStudy AI · Accepted Answer

Let's analyze Mandie's claim that $$ 2^{5} < 4^{2} + 3^{2} $$.

**Step 1: Calculate $$ 2^{5} $$**

$$
2^{5} = 2 \times 2 \times 2 \times 2 \times 2 = 32
$$

**Step 2: Calculate $$ 4^{2} + 3^{2} $$**

$$
4^{2} = 4 \times 4 = 16
$$
$$
3^{2} = 3 \times 3 = 9
$$
$$
4^{2} + 3^{2} = 16 + 9 = 25
$$

**Step 3: Compare the two results**

$$
2^{5} = 32
$$
$$
4^{2} + 3^{2} = 25
$$
$$
32 < 25 \quad \text{?}
$$

**Conclusion:**

The statement $$ 32 < 25 $$ is **false**. Therefore, Mandie's claim that $$ 2^{5} < 4^{2} + 3^{2} $$ is **incorrect**.
Mandie's claim is incorrect because $$ 2^{5} = 32 $$ and $$ 4^{2} + 3^{2} = 25 $$, so $$ 32 $$ is not less than $$ 25 $$.

2. Mandie claims that \( 2^{5}<4^{2}+3^{2} \). Is she correct? Justify your answer by showing your complete solution.

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