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Xavier mixes \( 2 \frac{4}{5} \) buckets of coarse sand with \( 1 \frac{1}{5} \) buckets of cement to make a special type of concrete. How many buckets of concrete will he make? Tasneem is an intern at ZX Communications Agency. She earns R4 500 a month. \( \begin{array}{l}1.2 .1 \\ 1.2 .2\end{array} \quad \) Write the number 4500 in scientific notation. 10 A Gudani MX 360 Pro laptop could be bought at a cash price of R6 500 or through

Ask by Ball Hardy. in South Africa
Feb 20,2025

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Xavier will make 4 buckets of concrete. The number 4500 in scientific notation is \(4.5 \times 10^3\).

Solución

Let's break down the problem step by step. ### Part 1: Mixing Sand and Cement 1. **Convert Mixed Numbers to Improper Fractions:** - For coarse sand: \[ 2 \frac{4}{5} = 2 + \frac{4}{5} = \frac{10}{5} + \frac{4}{5} = \frac{14}{5} \] - For cement: \[ 1 \frac{1}{5} = 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5} \] 2. **Add the Two Fractions:** - To add \(\frac{14}{5}\) and \(\frac{6}{5}\): \[ \frac{14}{5} + \frac{6}{5} = \frac{14 + 6}{5} = \frac{20}{5} = 4 \] Thus, Xavier will make **4 buckets of concrete**. ### Part 2: Writing 4500 in Scientific Notation To express the number 4500 in scientific notation, we need to write it in the form \( a \times 10^n \), where \( 1 \leq a < 10 \). 1. **Convert 4500:** - Move the decimal point 3 places to the left: \[ 4500 = 4.5 \times 10^3 \] Thus, **4500 in scientific notation is \( 4.5 \times 10^3 \)**. ### Summary of Answers: 1. Xavier will make **4 buckets of concrete**. 2. The number 4500 in scientific notation is **\( 4.5 \times 10^3 \)**.

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To find the total number of buckets of concrete Xavier makes, you need to add the two quantities together. First, convert the mixed numbers to improper fractions. \( 2 \frac{4}{5} \) becomes \( \frac{14}{5} \) and \( 1 \frac{1}{5} \) turns into \( \frac{6}{5} \). Adding these gives \( \frac{14}{5} + \frac{6}{5} = \frac{20}{5} = 4 \). So, Xavier makes 4 buckets of concrete! Now, for that scientific notation! When converting R4 500, you rewrite it as \( 4.5 \times 10^3 \). This means you move the decimal point 3 places to the left, hence putting it in the scientific form that scientists and mathematicians love. Keep up with the numbers, Tasneem, and you'll be a pro!

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