answer：First, I need to determine how many candy bars Nicole has. Since Lena has 5 more candy bars than Nicole, and Lena has 16 candy bars, Nicole must have 16 - 5 = 11 candy bars.Next, I'll find out how many candy bars Kevin has. Kevin has 4 fewer candy bars than Nicole, so Kevin has 11 - 4 = 7 candy bars.Lena currently has 16 candy bars and needs 5 more to reach a multiple of Kevin's candy bars. After receiving 5 more candy bars, Lena will have 16 + 5 = 21 candy bars.Finally, I'll calculate the ratio of Lena's candy bars to Kevin's candy bars after she gets the additional 5 candy bars. Lena will have 21 candy bars, and Kevin has 7 candy bars. The ratio is 21:7, which simplifies to 3:1.

answer：First, I need to calculate the amount of money the freelancer has after the initial three-month investment. The annual interest rate is 8%, so for three months, the interest rate is 8% divided by 4, which is 2%. Applying this interest to the initial investment of 15,000, the amount after three months becomes 15,300.Next, this 15,300 is invested in another savings certificate for nine months. I need to determine the annual interest rate ( r ) that, when applied for nine months, will grow the investment to 16,500 after a total of twelve months.The interest for nine months is calculated as ( frac{9}{12} times r ), which simplifies to ( frac{3r}{4} ). Applying this interest to the 15,300 investment gives the equation:[15300 times left(1 + frac{3r}{400}right) = 16500]Solving for ( r ) involves isolating it in the equation. First, divide both sides by 15,300 to simplify:[1 + frac{3r}{400} = frac{16500}{15300} approx 1.0784313725]Subtracting 1 from both sides:[frac{3r}{400} = 0.0784313725]Finally, multiply both sides by ( frac{400}{3} ) to solve for ( r ):[r = 0.0784313725 times frac{400}{3} approx 10.464052288]Therefore, the annual interest rate of the second certificate is approximately 10.464%.

answer：First, I need to understand that the set consists of consecutive even integers, meaning each number increases by 2.Given that the smallest integer is 140 and the median is 150, I can determine how many numbers are in the set.Since the median is 150, it is the middle number when the set has an odd number of terms. This means there are an equal number of integers below and above 150.Starting from 140, I can list the numbers until I reach 150. Each step increases by 2:140, 142, 144, 146, 148, 150There are 6 numbers from 140 to 150. To make 150 the median, there should be an equal number of numbers above 150. Therefore, I add the next even numbers:152, 154, 156, 158, 160Now, the complete set is:140, 142, 144, 146, 148, 150, 152, 154, 156, 158, 160The greatest integer in this set is 160.

answer：First, I need to calculate the residue of each term in the expression (240 cdot 15 - 21 cdot 9 + 6) modulo 18.Starting with (240 cdot 15):- (240) divided by (18) leaves a remainder of (6), so (240 equiv 6 pmod{18}).- (15) divided by (18) leaves a remainder of (15), so (15 equiv 15 pmod{18}).- Multiplying these remainders: (6 cdot 15 = 90).- (90) divided by (18) leaves a remainder of (0), so (90 equiv 0 pmod{18}).Next, for (21 cdot 9):- (21) divided by (18) leaves a remainder of (3), so (21 equiv 3 pmod{18}).- (9) divided by (18) leaves a remainder of (9), so (9 equiv 9 pmod{18}).- Multiplying these remainders: (3 cdot 9 = 27).- (27) divided by (18) leaves a remainder of (9), so (27 equiv 9 pmod{18}).Lastly, for the constant term (6):- (6) divided by (18) leaves a remainder of (6), so (6 equiv 6 pmod{18}).Now, combining these results:- (0 - 9 + 6 = -3).- To find the positive equivalent modulo (18), add (18) to (-3): (-3 + 18 = 15).Therefore, the residue of the expression modulo (18) is (15).

answer：First, I recognize that the expression ((25+15)^2 - (25-15)^2) can be simplified using the difference of squares formula.I recall that the difference of squares formula is (a^2 - b^2 = (a + b)(a - b)).Applying this formula to the given expression, I set (a = 25 + 15) and (b = 25 - 15).Next, I calculate (a + b) and (a - b):- (a + b = (25 + 15) + (25 - 15) = 50)- (a - b = (25 + 15) - (25 - 15) = 30)Finally, I multiply these results to find the value of the original expression:(50 times 30 = 1500).

answer：First, I need to calculate the values of ( a ), ( b ), ( c ), and ( d ) based on the given expressions.For ( a ), the expression is ( -1^2 ). Since the exponent applies only to 1, and the negative sign is outside, ( a = -(1^2) = -1 ).Next, for ( b ), the expression is ( (-2)^2 - 1 ). Squaring -2 gives 4, and subtracting 1 results in ( b = 3 ).For ( c ), the expression is ( -3^2 + 5 ). Squaring 3 gives 9, applying the negative sign gives -9, and adding 5 results in ( c = -4 ).Lastly, for ( d ), the expression is ( frac{3}{4} div (-frac{1}{4}) ). Dividing by a fraction is the same as multiplying by its reciprocal, so ( d = frac{3}{4} times (-4) = -3 ).Now, using these values, I can compute the defined operation:[begin{vmatrix} a & c b & d end{vmatrix} = ad - bc]Substituting the calculated values:[= (-1) times (-3) - 3 times (-4)]Calculating the products:[= 3 + 12]Summing the results:[= 15]