6. Calculate the final amount if R8 500 is invested for 5 years at a compound interest rate of $$ 7 \% $$ p.a. (Round off your answer to the nearest cent.) 7. Calculate the following without using a calculator: $$ 7.1 \quad 17-9+3-5 $$ $$ 7.2 \quad-22-(-16) $$ $$ 7.3 \quad 9 imes(-4) \div(-3) $$ $$ 7.4 \quad-10+7 imes(-2) $$ $$ 7.5 \quad-20 \div 5+(-6) imes(-7) $$ 8. Calculate the following without using a calculator: $$ 8.1 \quad-3^{2}+(-3)^{3} $$ $$ 8.2 \quad \sqrt{144}-\sqrt[3]{-125} $$ Calculate the following without using a calculator. Show your work. $$ 9.1 \quad 1 \frac{3}{4}+2 \frac{7}{8}-4 \frac{1}{2} $$ $$ 9.2 \quad 2 \frac{1}{5} imes 1 \frac{3}{7} \div 7 \frac{1}{3} $$ $$ 9.3 \quad\left(1 \frac{1}{4} ight)^{2}+\left(-\frac{1}{2} ight)^{3} $$ $$ 9.4 \quad \sqrt{1 \frac{9}{16}} imes \sqrt[3]{-\frac{8}{125}} $$

Question

6. Calculate the final amount if R8 500 is invested for 5 years at a compound interest rate of $$ 7 \% $$ p.a. (Round off your answer to the nearest cent.) 7. Calculate the following without using a calculator: $$ 7.1 \quad 17-9+3-5 $$ $$ 7.2 \quad-22-(-16) $$ $$ 7.3 \quad 9 	imes(-4) \div(-3) $$ $$ 7.4 \quad-10+7 	imes(-2) $$ $$ 7.5 \quad-20 \div 5+(-6) 	imes(-7) $$ 8. Calculate the following without using a calculator: $$ 8.1 \quad-3^{2}+(-3)^{3} $$ $$ 8.2 \quad \sqrt{144}-\sqrt[3]{-125} $$ Calculate the following without using a calculator. Show your work. $$ 9.1 \quad 1 \frac{3}{4}+2 \frac{7}{8}-4 \frac{1}{2} $$ $$ 9.2 \quad 2 \frac{1}{5} 	imes 1 \frac{3}{7} \div 7 \frac{1}{3} $$ $$ 9.3 \quad\left(1 \frac{1}{4}ight)^{2}+\left(-\frac{1}{2}ight)^{3} $$ $$ 9.4 \quad \sqrt{1 \frac{9}{16}} 	imes \sqrt[3]{-\frac{8}{125}} $$

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$\frac{-20}{5}+\left(-6\right)\left(-7\right)$$
- step1: Remove the parentheses:
  $$\frac{-20}{5}-6\left(-7\right)$$
- step2: Divide the terms:
  $$-4-6\left(-7\right)$$
- step3: Multiply the numbers:
  $$-4+42$$
- step4: Add the numbers:
  $$38$$
Calculate or simplify the expression $$ -22-(-16) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$-22-\left(-16\right)$$
- step1: Remove the parentheses:
  $$-22+16$$
- step2: Add the numbers:
  $$-6$$
Calculate or simplify the expression $$ 8500*(1+0.07)^5 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$8500\left(1+0.07\right)^{5}$$
- step1: Add the numbers:
  $$8500\times 1.07^{5}$$
- step2: Convert the expressions:
  $$8500\left(\frac{107}{100}\right)^{5}$$
- step3: Simplify:
  $$8500\times \frac{107^{5}}{100^{5}}$$
- step4: Rewrite the expression:
  $$100\times 85\times \frac{107^{5}}{100^{5}}$$
- step5: Reduce the numbers:
  $$85\times \frac{107^{5}}{100^{4}}$$
- step6: Rewrite the expression:
  $$5\times 17\times \frac{107^{5}}{100^{4}}$$
- step7: Rewrite the expression:
  $$5\times 17\times \frac{107^{5}}{25^{4}\times 4^{4}}$$
- step8: Rewrite the expression:
  $$5\times 17\times \frac{107^{5}}{5^{8}\times 4^{4}}$$
- step9: Reduce the numbers:
  $$17\times \frac{107^{5}}{5^{7}\times 4^{4}}$$
- step10: Multiply the fractions:
  $$\frac{17\times 107^{5}}{256\times 5^{7}}$$
Calculate or simplify the expression $$ (7/4)+(23/8)-(9) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{7}{4}+\frac{23}{8}-9$$
- step1: Reduce fractions to a common denominator:
  $$\frac{7\times 2}{4\times 2}+\frac{23}{8}-\frac{9\times 4\times 2}{4\times 2}$$
- step2: Multiply the numbers:
  $$\frac{7\times 2}{8}+\frac{23}{8}-\frac{9\times 4\times 2}{4\times 2}$$
- step3: Multiply the numbers:
  $$\frac{7\times 2}{8}+\frac{23}{8}-\frac{9\times 4\times 2}{8}$$
- step4: Transform the expression:
  $$\frac{7\times 2+23-9\times 4\times 2}{8}$$
- step5: Multiply the numbers:
  $$\frac{14+23-9\times 4\times 2}{8}$$
- step6: Multiply the terms:
  $$\frac{14+23-72}{8}$$
- step7: Calculate:
  $$\frac{-35}{8}$$
- step8: Rewrite the fraction:
  $$-\frac{35}{8}$$
Calculate or simplify the expression $$ -3^2+(-3)^3 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$-3^{2}+\left(-3\right)^{3}$$
- step1: Simplify:
  $$-3^{2}-3^{3}$$
- step2: Evaluate the power:
  $$-9-3^{3}$$
- step3: Evaluate the power:
  $$-9-27$$
- step4: Subtract the numbers:
  $$-36$$
Calculate or simplify the expression $$ (11/5)*(10/7)/(22/3) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\frac{11}{5}\times \frac{10}{7}}{\frac{22}{3}}$$
- step1: Multiply the numbers:
  $$\frac{\frac{22}{7}}{\frac{22}{3}}$$
- step2: Multiply by the reciprocal:
  $$\frac{22}{7}\times \frac{3}{22}$$
- step3: Reduce the numbers:
  $$\frac{1}{7}\times 3$$
- step4: Multiply:
  $$\frac{3}{7}$$
Calculate or simplify the expression $$ (5/4)^2+(-1/2)^3 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{5}{4}\right)^{2}+\left(\frac{-1}{2}\right)^{3}$$
- step1: Rewrite the fraction:
  $$\left(\frac{5}{4}\right)^{2}+\left(-\frac{1}{2}\right)^{3}$$
- step2: Simplify:
  $$\frac{5^{2}}{4^{2}}-\left(\frac{1}{2}\right)^{3}$$
- step3: Evaluate the power:
  $$\frac{25}{16}-\left(\frac{1}{2}\right)^{3}$$
- step4: Evaluate the power:
  $$\frac{25}{16}-\frac{1}{8}$$
- step5: Reduce fractions to a common denominator:
  $$\frac{25}{16}-\frac{2}{8\times 2}$$
- step6: Multiply the numbers:
  $$\frac{25}{16}-\frac{2}{16}$$
- step7: Transform the expression:
  $$\frac{25-2}{16}$$
- step8: Subtract the numbers:
  $$\frac{23}{16}$$
Calculate or simplify the expression $$ 9*(-4)/(-3) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{9\left(-4\right)}{\left(-3\right)}$$
- step1: Remove the parentheses:
  $$\frac{9\left(-4\right)}{-3}$$
- step2: Multiply the terms:
  $$\frac{36}{3}$$
- step3: Reduce the fraction:
  $$12$$
Calculate or simplify the expression $$ 17-9+3-5 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$17-9+3-5$$
- step1: Calculate:
  $$6$$
Calculate or simplify the expression $$ -10+7*(-2) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$-10+7\left(-2\right)$$
- step1: Multiply the numbers:
  $$-10-14$$
- step2: Subtract the numbers:
  $$-24$$
Calculate or simplify the expression $$ \sqrt(1+9/16) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{1+\frac{9}{16}}$$
- step1: Add the numbers:
  $$\sqrt{\frac{25}{16}}$$
- step2: Use the properties of radicals:
  $$\frac{\sqrt{25}}{\sqrt{16}}$$
- step3: Simplify the expression:
  $$\frac{5}{4}$$
Let's solve the problems step by step.

### 6. Compound Interest Calculation
To calculate the final amount $$ A $$ when $$ P $$ is invested at a compound interest rate $$ r $$ for $$ t $$ years, we use the formula:
$$
A = P(1 + r)^t
$$
Where:
- $$ P = 8500 $$
- $$ r = 0.07 $$
- $$ t = 5 $$

Calculating:
$$
A = 8500(1 + 0.07)^5
$$

Now, let's compute this value:
$$
A = 8500(1.07)^5
$$

Calculating $$ (1.07)^5 $$:
$$
(1.07)^5 \approx 1.402552
$$

Now, substituting back:
$$
A \approx 8500 \times 1.402552 \approx 11921.69
$$

Thus, the final amount is approximately **R 11,921.69**.

### 7. Basic Arithmetic Calculations
#### 7.1 $$ 17 - 9 + 3 - 5 $$
$$
17 - 9 = 8 \
8 + 3 = 11 \
11 - 5 = 6
$$
Final result: **6**

#### 7.2 $$ -22 - (-16) $$
$$
-22 + 16 = -6
$$
Final result: **-6**

#### 7.3 $$ 9 \times (-4) \div (-3) $$
$$
9 \times (-4) = -36 \
-36 \div (-3) = 12
$$
Final result: **12**

#### 7.4 $$ -10 + 7 \times (-2) $$
$$
7 \times (-2) = -14 \
-10 - 14 = -24
$$
Final result: **-24**

#### 7.5 $$ -20 \div 5 + (-6) \times (-7) $$
$$
-20 \div 5 = -4 \
(-6) \times (-7) = 42 \
-4 + 42 = 38
$$
Final result: **38**

### 8. More Calculations
#### 8.1 $$ -3^2 + (-3)^3 $$
$$
-3^2 = -9 \
(-3)^3 = -27 \
-9 - 27 = -36
$$
Final result: **-36**

#### 8.2 $$ \sqrt{144} - \sqrt[3]{-125} $$
$$
\sqrt{144} = 12 \
\sqrt[3]{-125} = -5 \
12 - (-5) = 12 + 5 = 17
$$
Final result: **17**

### 9. Mixed Numbers and Fractions
#### 9.1 $$ 1 \frac{3}{4} + 2 \frac{7}{8} - 4 \frac{1}{2} $$
Convert to improper fractions:
$$
1 \frac{3}{4} = \frac{7}{4}, \quad 2 \frac{7}{8} = \frac{23}{8}, \quad 4 \frac{1}{2} = \frac{9}{2} = \frac{36}{8}
$$
Now calculate:
$$
\frac{7}{4} + \frac{23}{8} - \frac{36}{8} = \frac{14}{8} + \frac{23}{8} - \frac{36}{8} = \frac{14 + 23 - 36}{8} = \frac{1}{8}
$$
Final result: **$$\frac{1}{8}$$**

#### 9.2 $$ 2 \frac{1}{5} \times 1 \frac{3}{7} \div 7 \frac{1}{3} $$
Convert to improper fractions:
$$
2 \frac{1}{5} = \frac{11}{5}, \quad 1 \frac{3}{7} = \frac{10}{7}, \quad 7 \frac{1}{3} = \frac{22}{3}
$$
Now calculate:
$$
\frac{11}{5} \times \frac{10}{7} \div \frac{22}{3} = \frac{11 \times 10}{5 \times 7} \times \frac{3}{22} = \frac{330}{770} = \frac{33}{77} = \frac{3}{7}
$$
Final result: **$$\frac{3}{7}$$**

#### 9.3 $$ \left(1 \frac{1}{4}\right)^{2} + \left(-\frac{1}{2}\right)^{3} $$
Convert to improper fractions:
$$
1 \frac{1}{4} = \frac{5}{4}
$$
Now calculate:
$$
\left(\frac{5}{4}\right)^{2} + \left(-\frac{1}{2}\right)^{3} = \frac{25}{16} - \frac{1}{8} = \frac{25}{16} - \frac{2}{16} = \frac{23}{16}
$$
Final result: **$$\frac{23}{16}$$**

#### 9.4 $$ \sqrt{1 \frac{9}{16}} \times \sqrt[3]{-\frac{8}{125}} $$
Convert to improper fractions:
$$
1 \frac{9}{16} = \frac{25}{16}
$$
Now calculate:
$$
\sqrt{\frac{25}{16}} \times \sqrt[3]{-\frac{8}{125}} = \frac{5}{4} \times -\frac{2}{5} = -\frac{1}{2}
$$
Final result: **$$-\frac{1}{2}$$**

### Summary of Results
- **6:** R 11,921.69
- **7.1:** 6
- **7.2:** -6
- **7.3:** 12
- **7.4:** -24
- **7.5:** 38
- **8.1:** -36
- **8.2:** 17
- **9.1:** $$\frac{1}{8}$$
- **9.2:** $$\frac{3}{7}$$
- **9.3:** $$\frac{23}{16}$$
- **9.4:** $$-\frac{1}{2}$$
- **6:** R 11,921.69 - **7.1:** 6 - **7.2:** -6 - **7.3:** 12 - **7.4:** -24 - **7.5:** 38 - **8.1:** -36 - **8.2:** 17 - **9.1:** 1/8 - **9.2:** 3/7 - **9.3:** 23/16 - **9.4:** -1/2

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