answer:Let's denote the weight of the 7th person as W. The total weight of the 6 people before the 7th person enters is: 6 people * 160 lbs/person = 960 lbs When the 7th person enters, the average weight becomes 151 lbs for 7 people. So the total weight is: 7 people * 151 lbs/person = 1057 lbs The weight of the 7th person is the difference between the total weight with 7 people and the total weight with 6 people: W = 1057 lbs - 960 lbs W = 97 lbs Therefore, the weight of the 7th person is boxed{97} lbs.

answer:To determine John's overall average speed, we need to calculate the total distance he traveled and then the total time he spent traveling. 1. **Calculate the distance traveled while driving:** John drove at a speed of 20 mph for 45 minutes. Since the time is given in minutes, we convert it to hours: [ text{Time in hours} = frac{45}{60} = 0.75 text{ hours} ] Using the formula for distance, ( text{Distance} = text{Speed} times text{Time} ): [ text{Distance driving} = 20 text{ mph} times 0.75 text{ hours} = 15 text{ miles} ] 2. **Calculate the distance traveled while horse riding:** John rode a horse at a speed of 6 mph for 30 minutes. Convert time to hours: [ text{Time in hours} = frac{30}{60} = 0.5 text{ hours} ] Using the formula for distance: [ text{Distance horse riding} = 6 text{ mph} times 0.5 text{ hours} = 3 text{ miles} ] 3. **Calculate the total distance traveled:** [ text{Total distance} = text{Distance driving} + text{Distance horse riding} = 15 text{ miles} + 3 text{ miles} = 18 text{ miles} ] 4. **Calculate the total time spent traveling:** [ text{Total time} = text{Time driving} + text{Time horse riding} = 0.75 text{ hours} + 0.5 text{ hours} = 1.25 text{ hours} ] 5. **Calculate the overall average speed:** Average speed is calculated by dividing the total distance by the total time: [ text{Average speed} = frac{text{Total distance}}{text{Total time}} = frac{18 text{ miles}}{1.25 text{ hours}} = 14.4 text{ mph} ] Thus, John's overall average speed is 14.4 text{ mph}. The final answer is boxed{E) 14.4 mph}

answer:Let's first identify the prime numbers that are greater than 2 but less than 6. These are 3 and 5. Next, let's identify the prime numbers that are greater than 8 but less than 24. These are 11, 13, 17, 19, and 23. Now, we need to find the product of one prime from the first set and one prime from the second set that results in a number between 15 and 36. Let's try each combination: - 3 * 11 = 33 (This is within the range) - 3 * 13 = 39 (This is outside the range) - 3 * 17 = 51 (This is outside the range) - 3 * 19 = 57 (This is outside the range) - 3 * 23 = 69 (This is outside the range) - 5 * 11 = 55 (This is outside the range) - 5 * 13 = 65 (This is outside the range) - 5 * 17 = 85 (This is outside the range) - 5 * 19 = 95 (This is outside the range) - 5 * 23 = 115 (This is outside the range) The only product that falls within the range of 15 to 36 is 3 * 11, which equals 33. Therefore, the value of z is boxed{33} .

answer:If each bag holds 11 cookies and you have 33 cookies, you would divide the total number of cookies by the number of cookies per bag: 33 cookies ÷ 11 cookies/bag = 3 bags So, you would have boxed{3} bags of cookies.