Understand place values in base 5.

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14. Find the value of 2 in $4203_{\text{five}}$

Understand place values in base 5.
In base 5, the place values are powers of 5, starting from the right:
$5^0$ (ones place)
$5^1$ (fives place)
$5^2$ (twenty-fives place)
$5^3$ (one hundred twenty-fives place)
Identify the position of the digit 2.
In the number $4203_{\text{five}}$ , the digit 2 is in the $5^2$ place.
Calculate the value of the digit 2.
The value of 2 is $2 \times 5^2$ .
$2 \times 5^2 = 2 \times 25 = 50$ $\boxed{50}$
15. The Executive meeting for DFCU Bank ended at 1:25 pm. If it lasted for 3 hours and 30 minutes, when did it start?
Convert the end time to 24-hour format.
1:25 pm is 13:25 in 24-hour format.
Subtract the duration of the meeting from the end time.
First, subtract the hours:
$13:25 - 3 \text{ hours} = 10:25$
Subtract the minutes.
We need to subtract 30 minutes from 10:25. Since 25 minutes is less than 30 minutes, we borrow 1 hour (60 minutes) from the hours.
10 hours becomes 9 hours, and 25 minutes becomes $25 + 60 = 85$ minutes.
Now subtract 30 minutes:
$9:85 - 30 \text{ minutes} = 9:55$
Convert the start time back to 12-hour format.
9:55 in 24-hour format is 9:55 am.
$\boxed{9:55 \text{ am}}$
16. Solve the equation $2(k + 1) = 10$
Divide both sides of the equation by 2.
$\frac{2(k + 1)}{2} = \frac{10}{2}$ $k + 1 = 5$
Subtract 1 from both sides of the equation to isolate $k$ .
$k + 1 - 1 = 5 - 1$ $k = 4$ $\boxed{4}$

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