You can acquire 42 cookies through 12 different combinations. The first method involves purchasing 2 packs of 21 (21x2 = 42). The second consists of acquiring 1 pack of 21 alongside 3 packs of 7 (21 + 3x7 = 42). The third way is to buy 1 pack of 21 and 21 individual cookies (21 + 21 = 42). The fourth option combines 1 pack of 21, 1 pack of 7, and 14 single cookies (21 + 7 + 14 = 42). The fifth strategy includes 1 pack of 21, 2 packs of 7, and 7 individual cookies (21 + 14 + 7 = 42). The sixth way is to opt for 6 packs of 7 (7x6 = 42). The seventh option is to purchase 5 packs of 7 along with 7 individual cookies (7x5 + 7 = 42). For the eighth method, you can buy 4 packs of 7 and 14 single cookies (7x4 + 14 = 42). The ninth way is to get 3 packs of 7 with 21 single cookies (7x3 + 21 = 42). The tenth consists of acquiring 2 packs of 7 plus 28 individual cookies (7x2 + 28 = 42). The eleventh strategy involves 1 pack of 7 and 35 single cookies (7 + 35 = 42). Lastly, the twelfth method is simply buying 42 individual cookies (42 = 42).
The final amount comes to $2313.51. Explanation: We compute the future value of each cash flow and aggregate them. Initially, $700 is deposited after year one. Considering a timeframe of three years at an interest rate of 6%. Next, $500 is deposited at the end of the second year, maturing in two years. Finally, $300 is deposited after three years, maturing in one year. Moreover, an additional $600 is deposited at the end of year four with no interest accrued on that amount. Therefore, the terminal value equals $833.71 plus $561.80 plus $318 plus $600 totals $2313.51.
The watch is less expensive in Geneva, Switzerland by £20. Step-by-step explanation: To identify the city where the watch is cheaper, we need to convert the watch's price to the same currency. Since pounds are utilized in part b of the question, using this currency would simplify the calculations. In Geneva, the watch's price is 193.75 CHF from our conversion: £1 = 1.55 CHF, thus, £x = 193.75 CHF. By cross-multiplying, we solve for x: (193.75 * 1) / 1.55 = 193.75/1.55 = £125. This demonstrates that the watch is cheaper in Geneva and more expensive in Manchester. To find out by how much, we simply deduct the Geneva price from the Manchester price: 145 - 125 = £20 cheaper.
Utilizing the Law of Sines (sinA/a=sinB/b=sinC/c) and recognizing that the angles in a triangle add up to 180°.
The angle C calculates to 180-53-17=110°
Thus, we have 27/sin53=b/sin17=c/sin110
This leads to b=27sin17/sin53, c=27sin110/sin53
The perimeter is defined as a+b+c, so
p=27+27sin17/sin53+27sin110/sin53 units
p≈68.65 units (rounded to the nearest hundredth of a unit)
The maximum area that can be enclosed is 64 ft². To achieve the largest area while minimizing the perimeter, the dimensions should be as equal as possible. Allocating 32 feet of fencing for four sides gives us 8 feet per side, resulting in a square with a side length of 8; thus, the area equals 8*8 = 64.
