answer:If there are 12 floors in the parking garage, and every 3rd floor requires ID, then there are 12 / 3 = 4 floors that require ID. If it takes 2 minutes for drivers to show ID on each of these 4 floors, then it takes a total of 4 * 2 = 8 minutes to show ID on all 4 floors. Since there are 60 seconds in a minute, it takes 8 * 60 = 480 seconds to show ID on all 4 floors. If it takes drivers 800 feet at a speed of 10 feet/second to go from one floor to the next, then it takes 800 / 10 = 80 seconds to go from one floor to the next. Since there are 12 floors in total, it takes 80 * 12 = 960 seconds to go from the top of the garage to the bottom without stopping for ID. Adding the time it takes to show ID on the 4 floors, it takes a total of 960 + 480 = 1440 seconds to go from the top to the bottom, including stopping for ID. 1440 The answer is: 1440, First, let's find out how many ID checks a driver would need to go through when driving from the top to the bottom of the garage. Since every 3rd floor requires an ID check, that means there are 4 floors between each ID check (the checked floor and the 3 floors above it). As there are 12 floors in total, there will be 3 ID checks (with the last one potentially being only 1, 2 or 3 floors from the bottom). Now let's calculate the time taken for all the ID checks: 2 minutes per ID check * 3 ID checks = 6 minutes Since we want the answer in seconds, convert minutes to seconds: 6 minutes * 60 seconds/minute = 360 seconds Next, we need to find out how long it takes to travel between floors. The drivers take 800 feet to go from one floor to the next at a speed of 10 feet/second. To find out how long it takes to travel between floors, divide the distance by the speed: 800 feet / 10 feet/second = 80 seconds However, there is no information given about the floors being located at specific heights, so we cannot determine the vertical distance between the floors accurately. Therefore, we cannot calculate the exact time it takes to travel between floors. But we do have the time it takes for all the ID checks: 360 seconds. So, the minimum time it would take to go from the top to the bottom of the garage (ignoring travel time between floors) is 360 seconds.,To calculate the time it takes from the top to the bottom, we first need to know the total number of floors in the parking garage. We are given that the garage has 12 floors, but every 3rd floor requires showing ID. Therefore, there are 12/3 = 4 floors where there is a delay due to showing the driver's ID. Since there is a delay of 2 minutes, or 120 seconds, for every ID check, we need to multiply the total number of ID checks by the time for each check: 4 floors * 120 seconds each = 480 seconds. Now we need to calculate the time it takes to travel between the remaining floors, which are not affected by the ID checks. As stated, it takes drivers 10 feet/second to go from one floor to the next, and there are 8 floors without ID checks. So, we can calculate the travel time for these floors as: 800 feet / 10 feet/second = 80 seconds. Finally, we can sum the time spent on both the travel between floors and the ID checks to find the total time: 480 seconds (for ID checks) + 80 seconds (for travel between floors) = 560 seconds. So, it takes a driver 560 seconds to go from the top of the garage to the bottom, considering the time spent showing ID and traveling between floors.

answer:If Lexie is 8 years old, her sister is twice her age, so her sister is 8 x 2 = 16 years old. If Lexie is 6 years older than her brother, her brother is 8 - 6 = 2 years old. The age difference between her brother and her sister is 16 - 2 = 14 years. 14 The answer is: 14, Let's break this down step-by-step: 1. We know that Lexie is 8 years old. 2. Her sister is twice as old as her, so the sister is 16 years old (2 * 8). 3. Lexie is 6 years older than her brother, so her brother is 2 years old (8 - 6). 4. Now, we want to find the age difference between Lexie's sister and her brother. 5. The sister is 16 years old, and the brother is 2 years old. 6. Therefore, the age difference between them is 14 years (16 - 2). The answer is that there is a 14-year age difference between Lexie's sister and her brother.,If Lexie is 8 years old and her sister is twice her age, her sister is 8 * 2 = 16 years old. Since Lexie is 6 years older than her brother, her brother is 8 - 6 = 2 years old. The age difference between her brother and sister is 16 - 2 = 14 years.

answer:To solve this problem, we need to determine the value of x, which represents the number of hat options available. Let's break down the information given: Number of shirt options: 6 Number of pant options: 4 Number of hat options: x Total number of outfit choices: 140 We can set up the equation as follows: Number of shirt options * Number of pant options * Number of hat options = Total number of outfit choices 6 * 4 * x = 140 Let's simplify and solve for x: 24x = 140 To isolate x, we divide both sides of the equation by 24: 24x / 24 = 140 / 24 x = 5.8333... Since the number of hat options must be a whole number, we round x to the nearest whole number: x = 6 The value of x is 6. The answer is: 6,To determine the value of x, let's first analyze how many choices there are for each color combination: Shirts and hats come in total 6 colors (Tan, Black, Blue, Gray, White, and Yellow) while pants come in less, i.e., only 4 colors (Tan, Black, Blue, and Gray). Therefore, we must consider the possible combinations of colors inclusive of the 4 pants colors. - There are 6 color choices for shirts and hats, but as you cannot have all 3 items the same color, consider the cases: 1. All 3 items have different colors. In this case, there are (6 choose 3) = 20 possible combinations. Each of these combinations can be created using any of the 4 pant colors. Which gives us a total of 20 * 4 = 80 options (including the ones with former pants colors that have been excluded previously). 2. Two items have the same color. There are 10 ways to choose two colors (from 6) and then 3 ways to match them to the items (since there are 3 items and two have the same color). This gives 10 * 3 = 30 ways. We must consider that there are 4 possible pants colors. So we have 30 * 4 = 120 options for these cases. The total number of options becomes: 80 + 120 = 200 options. But there are only 140 outfits. Therefore, there are 200 possible combinations but 60 of them consist of an outfit where all 3 items have the same color. Let's figure out how many hats are there. Originally, you had x hats, and then from the 4 pants colors' outfits (30 * 4 = 120 outfits), there are 60 outfits where all 3 items have the same color. This implies that (120 - 60) = 60 outfits have hats that can be paired with pants of different colors. Since in each of these outfits, the hat could be paired with any of the 60 outfits with different colored pants, there must be 60 hats that can be paired with pants of different colors. So, x = 60., To solve this problem, let's break it down step-by-step: 1. We need to find the number of ways to choose a shirt, hat, and pair of pants without having them all be the same color. 2. There are 6 shirts, 4 pants, and X hats available. 3. Let's first calculate the total number of ways to pick one shirt, one hat, and one pair of pants without any restrictions. This can be calculated using combinations: C(10,3) + C(6,2) * C(4,1) * X + C(6,1) * C(4,2) * X + C(4,1) * C(6,2) * X, where C(n,k) represents the number of combinations of n items taken k at a time. 4. The term C(10,3) represents the number of ways to choose 3 items from the 10 available colors (tan, black, blue, gray, white, and yellow for both shirts and hats). 5. The second term, C(6,2) * C(4,1) * X, represents the number of ways to choose 2 shirts and 1 pant, multiplied by the number of hats (X). 6. The third and fourth terms represent the number of ways to choose 1 shirt and 2 pants or 2 hats and 1 pant, respectively. 7. Now, let's set up the equation using the given information that there are 140 possible outfits: C(10,3) + C(6,2) * C(4,1) * X + C(6,1) * C(4,2) * X + C(4,1) * C(6,2) * X = 140 8. After calculating all the combinations, we get: 120 + 45X = 140 9. Solving for X, we get X = 140 - 120 / 45 ≈ 2.22 10. Since there cannot be a fraction of a hat, we need to round up to the nearest whole number, which is 3. So, the value of the unknown variable X is 3.

answer:Johann initially had 60 oranges, and he ate 10, leaving him with 60 - 10 = 50 oranges. Next, half of the oranges were stolen by Carson, so Johann had 50 / 2 = 25 oranges left. Carson returned exactly 5 oranges, so Johann now has 25 + 5 = 30 oranges.,Johann had 60 oranges. He decided to eat 10, so he now has 60 - 10 = 50 oranges. Half of the oranges were stolen by Carson, so Johann now has 50 / 2 = 25 oranges. Carson returned exactly 5 oranges, so Johann now has 25 + 5 = 30 oranges. 30 The answer is: 30, Johann has 40 oranges now. Here's the step-by-step breakdown: 1. Johann starts with 60 oranges. 2. He eats 10, leaving him with 60 - 10 = 50 oranges. 3. Carson then steals half of what Johann has left, which is 50 / 2 = 25 oranges. 4. After being stolen from, Johann has 50 - 25 = 25 oranges remaining. 5. Carson returns exactly 5 oranges to Johann, so Johann now has 25 + 5 = 40 oranges.