answer:Solution 1: Let's assume the total cost of the meal is M dollars. If the two friends who don't have enough money paid their full share, let's call their combined contribution F. The rest of the friends (let's call their number R) would then pay (M-F)/R dollars each. However, these two friends only paid 10 less than they should, so they actually paid F-20 dollars. Because of this, everyone else had to pay an additional 5, meaning the new amount paid by each of the other friends is (M-F)/R + 5. We know that F-20 divided among the two friends must be equal to what they should have paid, which is F, since if they had paid this amount, the rest of the friends wouldn't need to chip in extra money to cover the bill. Therefore, we can write the equation 2*(F-20) = F. Solving this equation gives us F = 40. Substituting F back into the equation (M-40)/R + 5 = (M-40)/R + 5*R = (M-F)/R gives us R^2 = 8, so R = 2*sqrt(2), which isn't a whole number. This means our assumption about the distribution of friends was incorrect. Final answer: The problem doesn't make sense with the given conditions. Solution 2: Let's again assume the total cost of the meal is M dollars. This time, let's assume that there are three levels of payment: full payment, half payment, and no payment. Let's call the number of friends who pay nothing N, those who pay half H, and those who pay fully F. The total contribution from the N friends would be 0, from the H friends would be H*10 (since they each pay 10 less), and from the F friends would be M - 10*H. The combined contribution from all friends should equal the total cost of the meal, so we have the equation 0*N + 10*H + (M - 10*H) = M. Since some friends are not paying their full share, the rest must cover for them, increasing their share by 5. Therefore, we also have the equation (M - 10*H)/(H + F) = (M - 10*H)/(H + F) + 5. Simplifying the second equation leads to H = 2/3 * F. Substituting this into the first equation leads to F = 3*M/5. Therefore, H = 2*M/5. Since H and F must both be whole numbers (as they represent numbers of friends), M must be a multiple of 5. If M = 5, then F = 3 and H = 2, which seems reasonable as a small group of friends. Final answer: There are 3 + 2 = 5 friends in total. Solution 3: Let's consider a scenario where the two friends who didn't have enough money ended up not paying anything. In this case, the equation becomes (M-20)/(n-2) = (M/n) + 5, where n is the total number of friends. Solving this equation leads to n = 4 + sqrt((4*M)/(M-95)). For certain values of M, n will be an integer. For example, if M = 9500, then n = 10, which could represent a group of 8 friends who pay fully, and 2 who don't pay anything. Final answer: There are more than 10 friends in total, assuming two friends didn't pay anything. Ranking of solutions from best to worst: 1. Solution 2: This solution fits the problem statement most accurately by introducing three categories of payment: full, half, and none. It uses simple algebraic manipulations to arrive at a reasonable answer. 2. Solution 3: While this solution also produces valid results, it makes a very specific assumption about the payment behavior of the two friends who didn't have enough money. The problem statement does not provide enough information to make this assumption. 3. Solution 1: This solution makes the most straightforward interpretation of the problem but fails to produce a valid answer using standard mathematical methods. Best and final answer: There are 3 + 2 = 5 friends in total, with 2 friends paying half and 3 friends paying fully.,Solution 1: The first solution assumes that the two friends who paid 10 less did so individually, not collectively. This means they each underpaid by 10, which totals to a shortfall of 20. The other friends had to cover this cost, and it increased their share by 5 each. If we divide the total shortfall (20) by the increase in everyone else's share (5), we get the number of friends who covered the shortfall. Reasoning: Total shortfall = 2 * 10 = 20 Number of friends covering the shortfall = Total shortfall / Increase in share = 20 / 5 = 4 However, this does not include the two friends who underpaid. So, the total number of friends is 4 (who covered the shortfall) + 2 (who underpaid). Final answer: There are 6 friends in total. Solution 2: The second solution considers the possibility that the two friends who didn't have enough money paid 10 less collectively, not individually. In this case, the total shortfall would be 10, not 20. Using similar reasoning as above, we can find out how many friends covered the shortfall: Reasoning: Total shortfall = 10 Number of friends covering the shortfall = Total shortfall / Increase in share = 10 / 5 = 2 Again, this doesn't include the two friends who underpaid. Therefore, the total number of friends is 2 (who covered the shortfall) + 2 (who underpaid). Final answer: There are 4 friends in total. Ranking of solutions from best to worst: 1. Solution 1: This solution seems more plausible because it interprets "two friends do not have enough money and pay 10 less than they should" as each friend paying 10 less individually, resulting in a total shortfall of 20. This interpretation makes sense given the context of the problem. 2. Solution 2: While possible, this solution seems less likely because it interprets the same statement as both friends paying 10 less collectively. This interpretation might not be accurate given the wording of the problem. Best and final answer: There are 6 friends in total.,Solution 1: Let the total number of friends be F. Two friends don't have enough money and pay 10 less, so the original total contribution would have been (F-2) x (their share). Now, everyone else increases their share by 5, which means the total contribution is (F-2) x (their share + 5). Since the two friends paid 10 less each, the total contribution should be (F-2) x (their share + 10). By setting these two amounts equal, we get: (F-2) x (their share + 5) = (F-2) x (their share + 10) This simplifies to: (their share + 5) = (their share + 10) F = 10 However, this answer is not possible because if there were only 10 people, including the two who paid 10 less, then there would be only 8 friends who should contribute fully, and they would each pay 10 less. This would mean that there would be no one left to pay 5 more, which is a contradiction. Therefore, this solution is incorrect. Solution 2: Let's rework the problem noticing that two friends pay 10 less each. Let the total number of friends be F and the original cost of the meal be 'x'. So, each friend should pay x/F. However, two friends don't have enough and pay x/F-10, increasing the rest's share by 5. This implies: x/F = x/(F-2) + 5 Dividing both sides by x and then rearranging terms gives: 1/F = 1/(F-2) + 5/x Subtracting 1/(F-2) from both sides we get: 1/F - 1/(F-2) = 5/x By cross multiplication and simplification, we get: (F-2) - F + 2 = 5/x Simplifying further: -2 = 5/x Now, since x cannot be 5, the equation is not true. Therefore, neither the solutions provided here nor others are not correct due to contradictions

answer:First, let's calculate how many widgets are produced daily: Widgets produced daily = Production rate * Hours per day = 200 widgets/hour * 8 hours = 1600 widgets Next, let's find out how many widgets are rejected daily due to defects: Defective widgets daily = Total widgets produced daily * Defect rate = 1600 widgets * 0.05 = 80 widgets Now, we can calculate the number of non-defective widgets produced daily: Non-defective widgets daily = Total widgets produced daily - Defective widgets daily = 1600 widgets - 80 widgets = 1520 widgets Finally, to find out how many non-defective widgets are produced in a week, we multiply the daily production by the number of days per week: Non-defective widgets weekly = Non-defective widgets daily * Days per week = 1520 widgets * 5 days = 7600 widgets So, the factory produces 7,600 non-defective widgets in a week.,To calculate the number of non-defective widgets produced in a week, we need to consider the total number of widgets produced in a week, minus the defective ones. First, let's find the widgets produced per day: Widgets per hour = 200 (given) Widgets per day = 200 widgets per hour * 8 hours (in a day) Widgets per day = 1600 widgets Now, let's find the number of non-defective widgets produced in a day: Defective rate per hour = 100% - 95% = 5% (given) Defective rate per day = 5% for 8 hours (since the defect rate doesn't change over the day) Defective rate per day = 40 widgets (5% of 800) Now, let's find the number of non-defective widgets produced in a day: Total widgets per day = 1600 widgets (from above) Non-defective widgets per day = 1600 widgets - 40 defective widgets Non-defective widgets per day = 1560 widgets Finally, let's find the number of non-defective widgets produced in a week: Non-defective widgets per week = 1560 widgets per day * 5 days Non-defective widgets per week = 7800 widgets So, the factory produces 7,800 non-defective widgets in a week., First, let's calculate how many widgets the factory produces in one hour without considering the defective rate: Widgets produced per hour = 200 Next, let's find out the number of widgets produced in one day by multiplying the hourly production rate by the number of operating hours: Widgets produced per day = Widgets produced per hour * Operating hours per day = 200 * 8 = 1600 Since the factory operates for 5 days a week, we can now calculate the total number of widgets produced in a week: Widgets produced per week = Widgets produced per day * Days per week = 1600 * 5 = 8000 Now, we need to account for the defective rate. Since 5% of the produced widgets are rejected as defective, this means that 95% of the widgets are non-defective. To find the number of non-defective widgets produced in a week, we can multiply the total weekly production by the percentage of non-defective widgets: Non-defective widgets = Total weekly production * Percentage of non-defective widgets = 8000 * 0.95 = 7600 So, the factory produces 7,600 non-defective widgets in a week.

answer:New Zealand While it's essential to acknowledge the breadth and depth of Maori history and culture, I'll provide a succinct response as requested. The Maori people are the indigenous inhabitants of New Zealand, an island nation in the South Pacific Ocean, prior to the European settlers' arrival. They have a rich and unique heritage that significantly contributes to the country's cultural landscape.,New Zealand,The Maori people are indigenous to New Zealand, an island nation located in the southwestern Pacific Ocean.

answer:The average distance between the Earth and the Moon is about 238,900 miles (384,400 kilometers). To determine how long it would take to travel this distance at an average speed of 60 miles per hour, we can use the formula: Time = Distance / Speed Time to reach the Moon = Distance to the Moon / Average speed = 238,900 miles / 60 miles per hour = 3,981.67 hours Since there are 24 hours in a day, we can convert this time into days: Days to reach the Moon = Time in hours / Hours per day = 3,981.67 hours / 24 hours = 165.9 days So, it would take approximately 165.9 days to travel from the Earth to the Moon at an average speed of 60 miles per hour.,It would take much longer than you think! The average distance between Earth and the Moon is about 238,900 miles. If you were able to maintain a speed of 60 miles per hour, it would take approximately 3,981 hours or 165.87 days to reach the Moon. However, realistically it would be impossible to reach the Moon at such a slow speed because there's no atmosphere or way to float above the Earth's surface like an airplane. Rockets would be needed to propel you into space and astronauts do not travel to the Moon in a straight line as they need to use a trajectory called Lunar Orbit Insertion, so the distance covered can range between over 400,000 miles to about 600,000 miles taking account of the tilting rotation and location of the Moon., The average distance between the Earth and the Moon is about 238,900 miles (384,400 kilometers). To determine how long it would take to travel this distance at an average speed of 60 miles per hour, we can use the formula: Time = Distance / Speed In this case: Distance = 238,900 miles Speed = 60 miles/hour So, Time = 238,900 miles / 60 miles/hour = 3,981.67 hours Now, let's convert this value into days: We know that: 1 day = 24 hours So, Number of days = Time (in hours) / Hours per day = 3,981.67 hours / 24 hours/day = 165.9 days Therefore, it would take approximately 165.9 days to travel from the Earth to the Moon at an average speed of 60 miles per hour.