4.2 Find the value of the following: \( 4.2 .15^{3}+\sqrt{10000} \) \( \qquad \) \( \qquad \) \( 4.2 .2(-6)^{2} \div(-10)^{2} \) \( \qquad \) \( \qquad \) \( \qquad \)

We begin by evaluating each expression step by step. ### 1. Evaluate \( 4.2 \cdot (0.15)^3 + \sqrt{10000} \) 1. Compute the cube of \(0.15\): \[ (0.15)^3 = 0.15 \times 0.15 \times 0.15 = 0.003375. \] 2. Multiply this result by \(4.2\): \[ 4.2 \cdot 0.003375 = 0.014175. \] 3. Compute the square root of \(10000\): \[ \sqrt{10000} = 100. \] 4. Add these results together: \[ 0.014175 + 100 = 100.014175. \] Thus, the value of the first expression is \[ 100.014175. \] ### 2. Evaluate \( 4.2 \cdot 0.2 \cdot (-6)^2 \div (-10)^2 \) 1. Multiply \(4.2\) by \(0.2\): \[ 4.2 \cdot 0.2 = 0.84. \] 2. Evaluate \((-6)^2\): \[ (-6)^2 = 36. \] 3. Evaluate \((-10)^2\): \[ (-10)^2 = 100. \] 4. Multiply \(0.84\) by \(36\): \[ 0.84 \cdot 36 = 30.24. \] 5. Divide the result by \(100\): \[ \frac{30.24}{100} = 0.3024. \] Thus, the value of the second expression is \[ 0.3024. \]