College

a. Calculate the expression:
\[ 19 - 8 \times 2 + \left( \frac{12}{3} \right) \]

b. The formula to calculate the volume of a rectangular prism is:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]

c. Calculate:
\[ 7.83 \times 1000 \]

d. Calculate:
\[ 7.83 \div 1000 \]

e. Convert
\[ 19.7 \, \text{m} \]
to centimeters.

f. Convert
\[ 2348 \, \text{g} \]
to kilograms.

g. Round 18974 to the nearest 10000.

h. Round 323 to the nearest 5.

i. Convert the fraction to a percentage:
\[ \frac{24}{30} \]

Answer :

Sure! Let's go through each part of the question step-by-step:

a. Calculate [tex]\(19 - 8 \times 2 + \left(12 \div 3\right)\)[/tex]:

- First, perform the multiplication: [tex]\(8 \times 2 = 16\)[/tex].
- Next, perform the division: [tex]\(12 \div 3 = 4\)[/tex].
- Now, substitute back into the expression: [tex]\(19 - 16 + 4\)[/tex].
- Perform the subtraction and addition: [tex]\(19 - 16 = 3\)[/tex], then [tex]\(3 + 4 = 7\)[/tex].
- Result: 7

b. The formula to calculate the volume of a rectangular prism:

- The volume is calculated by multiplying the length, width, and height.
- The formula is: Volume = length × width × height.

c. Calculate [tex]\(7.83 \times 1000\)[/tex]:

- To solve this, multiply: [tex]\(7.83 \times 1000 = 7830\)[/tex].
- Result: 7830

d. Calculate [tex]\(7.83 \div 1000\)[/tex]:

- To solve this, divide: [tex]\(7.83 \div 1000 = 0.00783\)[/tex].
- Result: 0.00783

e. Convert [tex]\(19.7 \, \text{m}\)[/tex] to [tex]\(\text{cm}\)[/tex]:

- Since 1 meter equals 100 centimeters, you multiply: [tex]\(19.7 \times 100 = 1970\)[/tex].
- Result: 1970 cm

f. Convert 2348 g to kg:

- Since 1000 grams equals 1 kilogram, divide: [tex]\(2348 \div 1000 = 2.348\)[/tex].
- Result: 2.348 kg

g. Round 18974 to the nearest 10000:

- 18974 is closer to 20000 than 10000.
- Result: 20000

h. Round 323 to the nearest 5:

- 323 divided by 5 gives 64.6, which rounds to 65.
- Multiplying 65 by 5 gives: [tex]\(65 \times 5 = 325\)[/tex].
- Result: 325

i. Convert to percentage: [tex]\(\frac{24}{30}\)[/tex]:

- First, divide: [tex]\(\frac{24}{30} = 0.8\)[/tex].
- Convert to percentage by multiplying by 100: [tex]\(0.8 \times 100 = 80\)[/tex].
- Result: 80%

I hope these detailed explanations help you understand each step! If you have any more questions, feel free to ask.