💡First, I need to determine the total amount Shara has returned to her brother over the past 6 months. Since she returns 10 each month, the total returned is 10 multiplied by 6, which equals 60.Next, the problem states that Shara has returned half of the money she originally borrowed. This means the total amount she borrowed was twice the amount she has returned so far. Therefore, the total borrowed amount is 60 multiplied by 2, which equals 120.Currently, Shara has returned 60, so the remaining amount she owes is 120 minus 60, which is 60.To find out how much she will still owe 4 months from now, I need to calculate how much more she will return in the next 4 months. She returns 10 each month, so over 4 months, she will return 10 multiplied by 4, which equals 40.Finally, subtract the amount she will return in the next 4 months from her current debt to find out how much she will still owe. That is 60 minus 40, which equals 20.

💡First, I need to understand what it means to convert a percentage to a decimal fraction.A percentage represents a part per hundred, so 3% means 3 per 100.To convert this to a decimal, I divide the percentage by 100.Dividing 3 by 100 gives me 0.03.Therefore, 3% expressed as a decimal fraction is 0.03.

💡First, I need to determine the number of votes required to win the election. Since a candidate needs more than 50.5% of the votes, I'll calculate 50.5% of 6000 votes.Next, I'll find out how many votes Geoff initially received by subtracting the additional 3000 votes he needed from the total votes required to win.Finally, I'll calculate the percentage of votes Geoff received by dividing the number of votes he initially received by the total number of votes and then multiplying by 100.

💡First, I recognize that the product of two numbers is equal to the product of their Least Common Multiple (LCM) and Highest Common Factor (HCF).Given that one of the numbers is 8, and the LCM is 24 while the HCF is 4, I can set up the equation:8 * n = 24 * 4Solving for n:8n = 96n = 96 / 8n = 12Therefore, the other number is 12.

💡First, I note that there were initially 42.0 students in the fourth grade at the start of the year.During the year, 4.0 students left the fourth grade. To find out how many students remained after these departures, I subtract the number of students who left from the initial number:42.0 - 4.0 = 38.0 students.Next, 10.0 students were transferred to the fifth grade. To determine the final number of students in the fourth grade, I subtract the number of transferred students from the remaining number:38.0 - 10.0 = 28.0 students.Therefore, at the end of the year, there were 28.0 students in the fourth grade.

💡First, I need to evaluate the absolute value of (-3), which is straightforward.Next, I'll calculate the square root of (3) multiplied by the sine of (60^circ). I remember that (sin 60^circ) is (frac{sqrt{3}}{2}), so multiplying that by (sqrt{3}) gives me (frac{3}{2}).Then, I'll determine the value of (2^{-1}), which is the same as (frac{1}{2}).Finally, I'll add all the evaluated terms together: (3 + frac{3}{2} - frac{1}{2}). Combining the fractions, I get (3 + 1), which equals (4).