Let's tackle each part of the problem step by step.
Simplify the algebraic expression:
We are given the expression:
[tex]\[ 4a^2 b^3 \times 5bc^3 \div 10ab^2c \][/tex]
First, we handle the multiplication in the numerator:
[tex]\[ 4a^2 b^3 \times 5bc^3 = (4 \times 5) \times a^2 \times b^3 \times b \times c^3 = 20a^2 b^4 c^3 \][/tex]
Now, we perform the division:
[tex]\[ \frac{20a^2 b^4 c^3}{10ab^2c} \][/tex]
We can simplify this by dividing both the numerator and the denominator:
1. [tex]\( \frac{20}{10} = 2 \)[/tex]
2. [tex]\( \frac{a^2}{a} = a \)[/tex]
3. [tex]\( \frac{b^4}{b^2} = b^2 \)[/tex]
4. [tex]\( \frac{c^3}{c} = c^2 \)[/tex]
So, the simplified expression is:
[tex]\[ 2ab^2c^2 \][/tex]
How much more did Tapaba receive compared to Palibe:
Palibe and Tapaba shared [tex]$30.00 in the ratio \(2:3\) respectively. To find out how much more Tapaba received compared to Palibe, we proceed as follows:
1. Calculate the total parts of the ratio:
\[ 2 + 3 = 5 \]
2. Determine the amount each part represents:
\[ \text{One part} = \frac{30.00}{5} = 6.00 \]
3. Calculate the amount received by Palibe (2 parts):
\[ \text{Amount received by Palibe} = 2 \times 6.00 = 12.00 \]
4. Calculate the amount received by Tapaba (3 parts):
\[ \text{Amount received by Tapaba} = 3 \times 6.00 = 18.00 \]
5. Find the difference between the amounts received by Tapaba and Palibe:
\[ \text{Difference} = 18.00 - 12.00 = 6.00 \]
Therefore, Tapaba received $[/tex]6.00 more than Palibe.
