Classify 15 as odd or even and composite or prime. Find the reciprocal of the production rate (8 units/hr). Determine if sqrt(49) and sqrt(2) are rational or irrational. Find the reciprocal of 0.25. E

Here are the answers to your questions:

1. Classification of 15
The number 15 is an odd number because it is not divisible by 2.
It is also a composite number because it has factors other than 1 and itself (its factors are 1, 3, 5, and 15).

2. Reciprocal of production rate

Step 1: Identify the production rate.
The production rate is 8 units per hour.

Step 2: Find the reciprocal.
The reciprocal of a number $a$ is $\frac{1}{a}$.
The reciprocal of 8 is $\frac{1}{8}$.

$$\boxed{\frac{1}{8}}$$

3. Rational or irrational numbers

a) $\sqrt{49}$

Step 1: Evaluate the square root.

$$\sqrt{49} = 7$$

Step 2: Determine if it's rational or irrational.
Since 7 can be expressed as a fraction $\frac{7}{1}$, it is a rational number.

b) $\sqrt{2}$

Step 1: Evaluate the square root.

$$\sqrt{2} \approx 1.41421356...$$

Step 2: Determine if it's rational or irrational.
Since $\sqrt{2}$ cannot be expressed as a simple fraction of two integers and its decimal representation is non-terminating and non-repeating, it is an irrational number.

4. Reciprocal of 0.25

Step 1: Convert 0.25 to a fraction.

$$0.25 = \frac{25}{100} = \frac{1}{4}$$

Step 2: Find the reciprocal of the fraction.
The reciprocal of $\frac{1}{4}$ is $\frac{4}{1} = 4$.

$$\boxed{4}$$

5. Express $5^3 \times 5^4$ as a single power of 5

Step 1: Apply the law of indices $a^m \times a^n = a^{m+n}$.

$$5^3 \times 5^4 = 5^{3+4}$$

Step 2: Simplify the exponent.

$$5^{3+4} = 5^7$$ $$\boxed{5^7}$$

6. Simplify $\frac{2^5 \times 2^3}{2^4}$

Step 1: Simplify the numerator using $a^m \times a^n = a^{m+n}$.

$$2^5 \times 2^3 = 2^{5+3} = 2^8$$

Step 2: Substitute the simplified numerator back into the expression.

$$\frac{2^8}{2^4}$$

Step 3: Apply the law of indices $\frac{a^m}{a^n} = a^{m-n}$.

$$\frac{2^8}{2^4} = 2^{8-4} = 2^4$$ $$\boxed{2^4}$$

7. Find log250 to 4 decimal places

Step 1: Use a calculator or logarithm tables to find the value of $\log_{10}(250)$.

$$\log_{10}(250) \approx 2.39794000867...$$

Step 2: Round the value to 4 decimal places.

$$2.3979$$ $$\boxed{2.3979}$$

8. Simplify log100 + log0.1

Step 1: Evaluate each logarithm.

$$\log_{10}(100) = \log_{10}(10^2) = 2$$ $$\log_{10}(0.1) = \log_{10}(10^{-1}) = -1$$

Step 2: Add the values.

$$2 + (-1) = 1$$

Alternatively, using the logarithm law $\log a + \log b = \log (ab)$:

$$\log_{10}(100) + \log_{10}(0.1) = \log_{10}(100 \times 0.1)$$ $$\log_{10}(10) = 1$$ $$\boxed{1}$$

9. Evaluate $(27)^{\frac{2}{3}}$

Step 1: Rewrite the expression using the property $a^{\frac{m}{n}} = (\sqrt[n]{a})^m$.

$$(27)^{\frac{2}{3}} = (\sqrt[3]{27})^2$$

Step 2: Calculate the cube root of 27.

$$$$