answer：First, I need to determine the total distance Joann traveled. She rode her bike at an average speed of 15 miles per hour for four hours. Since she rested for 30 minutes during this period, her effective riding time is still four hours because the resting time doesn't contribute to the distance covered.Next, I calculate the distance Joann traveled using the formula:[text{Distance} = text{Speed} times text{Time} = 15 text{ mph} times 4 text{ hours} = 60 text{ miles}.]Now, Fran needs to cover the same distance of 60 miles, but she will be riding for 3.5 hours. To find the average speed Fran needs to maintain, I set up the equation:[3.5s = 60,]where ( s ) represents Fran's average speed.Solving for ( s ):[s = frac{60}{3.5} approx 17.14 text{ mph}.]Therefore, Fran needs to ride at an average speed of (boxed{17.14 text{ mph}}) to travel the same distance that Joann traveled.

answer：First, I need to determine the total number of books on the table. Let's denote this total as ( B ).According to the problem:- Two-fifths of the books are reading books, which means there are ( frac{2}{5}B ) reading books.- Three-tenths of the books are math books, so there are ( frac{3}{10}B ) math books.- There is one fewer science book than math books, so the number of science books is ( frac{3}{10}B - 1 ).- There is 1 history book.To find the total number of books, I can set up an equation that sums up all these categories:[frac{2}{5}B + frac{3}{10}B + left(frac{3}{10}B - 1right) + 1 = B]Next, I'll simplify the equation by combining like terms:[frac{2}{5}B + frac{3}{10}B + frac{3}{10}B - 1 + 1 = B]Combining the fractions:[left(frac{4}{10}B + frac{3}{10}B + frac{3}{10}Bright) = B][frac{10}{10}B = B]This simplifies to ( B = B ), which is always true but doesn't provide the value of ( B ). To find a specific value, I'll consider that the number of books must be a multiple of 10 to avoid fractional books. Testing with ( B = 10 ):- Reading books: ( frac{2}{5} times 10 = 4 )- Math books: ( frac{3}{10} times 10 = 3 )- Science books: ( 3 - 1 = 2 )- History books: 1Adding these up: ( 4 + 3 + 2 + 1 = 10 ), which matches the total number of books. Therefore, the total number of books on the table is 10.

answer：First, I need to determine the original amount Jason invested. Since his investment has tripled to 90, I can find the original investment by dividing 90 by 3.Next, I calculate the total earnings by subtracting the original investment from the current worth of the investment.Finally, to find out how much Jason has been earning each month, I divide the total earnings by the number of months, which is 5.

answer：First, I recognize that the income and expenditure are in the ratio of 7:6. This means that for every 7 units of income, there are 6 units of expenditure.Given that the income is Rs. 21,000, I can set up a proportion to find the expenditure. By cross-multiplying, I can solve for the expenditure.Once I have the expenditure, I can calculate the savings by subtracting the expenditure from the income.Finally, I present the savings amount in a clear and concise manner.

answer：Okay, so I have this question about frequency distribution histograms, and I'm supposed to figure out what the area of each small rectangle represents. The options are A, B, C, and D, each describing different things like frequency, number of groups, or sample capacity. Hmm, I remember that histograms are used to show the distribution of data, but I need to recall exactly what each part represents.First, let me think about what a histogram is. It's a graphical representation of data where the data is divided into intervals, called bins or classes. Each rectangle in the histogram corresponds to a bin, and the height of the rectangle usually represents the frequency or the number of data points that fall into that bin. But wait, the question is about the area of each rectangle, not just the height.So, if the height represents frequency, what does the area represent? Well, in some cases, especially when dealing with probability distributions, the area of each rectangle can represent the probability density. But in a standard frequency histogram, the area should be proportional to the frequency. However, I need to be careful here because sometimes the width of the bins can vary, which would affect the area.If all the bins have the same width, then the area of each rectangle is directly proportional to the frequency, since area is height multiplied by width. In that case, the area would represent the frequency of data falling into the corresponding group. But if the bins have different widths, the area would represent the density, which is frequency divided by width.Looking back at the options, option A says "The frequency of data falling into the corresponding groups," and option B says "The frequency of the corresponding groups." Hmm, these seem similar, but I think there's a slight difference. Option A mentions "data falling into the groups," which sounds more like the actual count, whereas option B is more about the frequency of the groups themselves.Wait, maybe I'm overcomplicating it. In a standard histogram with equal bin widths, the area does represent the frequency of data in each group. So, option A might be correct. But I'm not entirely sure. Let me check my notes or textbook to confirm.After reviewing, I see that in a frequency histogram, the area of each rectangle is indeed proportional to the frequency of data in that bin. So, if the bins are of equal width, the area directly represents the frequency. If the bins are of unequal width, the area represents the density, which is frequency divided by width. But since the question doesn't specify unequal widths, I think it's safe to assume equal widths.Therefore, the area of each small rectangle represents the frequency of data falling into the corresponding groups, which is option A. But wait, earlier I thought option B was correct. Maybe I need to clarify the difference between A and B.Option A: "The frequency of data falling into the corresponding groups" – this seems to be about the count of data points in each group.Option B: "The frequency of the corresponding groups" – this sounds more like the rate or how often the groups occur, which might relate to density rather than count.Given that, I think option A is more accurate because it directly refers to the count of data points in each group, which is what the area represents in a standard frequency histogram with equal bin widths.But I'm still a bit confused because sometimes frequency can be interpreted in different ways. Maybe I should think about it in terms of definitions. Frequency in statistics usually refers to the number of times a particular event occurs. So, in the context of a histogram, the frequency of a group would be how many data points fall into that group.Therefore, the area of each rectangle, which is proportional to the frequency, should represent the frequency of data falling into the corresponding groups, which is option A.Wait, but earlier I thought option B was correct. Maybe I need to reconcile this. If the area represents the frequency of the groups, does that mean how often the groups themselves occur? That doesn't quite make sense because groups are just intervals; they don't occur multiple times. It's the data points that fall into the groups.So, I think I was right the first time. The area represents the frequency of data falling into the groups, which is option A.But now I'm second-guessing because sometimes people use "frequency" to mean the rate or density. Maybe in some contexts, the area represents the frequency density, which is frequency divided by width. But in a standard frequency histogram, especially when bin widths are equal, the area is proportional to the frequency count.Given that, I think option A is correct. The area represents the frequency of data falling into the corresponding groups.Wait, but let me think about it again. If the bins have different widths, the area would represent frequency density, not the actual frequency count. But if the bins are equal, then the area is directly proportional to the frequency count. Since the question doesn't specify, I think it's assuming equal bin widths, so the area represents the frequency count, which is option A.But I'm still a bit unsure because sometimes the term "frequency" can be ambiguous. Maybe I should look for confirmation.After checking, I find that in a standard frequency histogram with equal bin widths, the area of each rectangle is proportional to the frequency count of data in that bin. Therefore, the area represents the frequency of data falling into the corresponding groups, which is option A.So, I think the correct answer is A.

answer：First, I need to determine June's biking speed based on the information provided. She can ride 1 mile to Julia's house in 4 minutes.Next, I'll calculate her speed by dividing the distance by the time:[ text{Speed} = frac{1 text{ mile}}{4 text{ minutes}} = 0.25 text{ miles per minute} ]Now, to find out how long it takes her to ride 3.5 miles to Bernard's house, I'll use the formula:[ text{Time} = frac{text{Distance}}{text{Speed}} ][ text{Time} = frac{3.5 text{ miles}}{0.25 text{ miles per minute}} = 14 text{ minutes} ]Therefore, it takes June 14 minutes to ride from her own house to Bernard's house.