Question

the scatterplot shows the number of customers and the number of bottles of water sold at an amusement park over a 10 - day period.
number of water bottles sold
based on the scatterplot, which of these is the best prediction for the number of bottles of water sold on a day where the amusement park had 64 customers?
a 49
b 29
c 39
d 88

Explanation:

Step1: Analyze the scatterplot trend

The scatterplot shows a positive correlation between the number of customers (x - axis) and water bottles sold (y - axis). As the number of customers increases, the number of water bottles sold also tends to increase.

Step2: Locate x = 64 on the x - axis

We need to find the y - value (number of water bottles sold) corresponding to x = 64 (number of customers). By observing the trend of the scatterplot (the general upward - sloping pattern of the points), we can estimate the y - value.

Looking at the options, when x = 64, we can see from the trend of the scatterplot (the points are increasing, and we can interpolate or extrapolate based on the existing points) that the value around x = 64 should be around 39? Wait, no, wait. Wait, the x - axis is number of customers (from 24 to 88) and y - axis is number of water bottles sold (0 to 64). Wait, maybe I mixed up the axes. Wait, the x - axis label is "Number of Customers" (ranging from 24 to 88) and y - axis is "Number of Water Bottles Sold" (ranging from 0 to 64). So when the number of customers is 64, we look at the y - value. Let's re - examine the scatterplot. The points are plotted such that as customers increase, bottles sold increase. Let's check the options: A is 49, B is 29, C is 39, D is 88. Wait, D is 88 which is too high (since y - axis max is 64). B is 29, which is too low. Now, when x = 64 (customers), let's see the trend. If we look at the points, when x is around 56 (customers), y is around 48? Wait, no, maybe the axes are swapped? Wait, the title is "Number of Water Bottles Sold" on the y - axis? Wait, no, the y - axis label: Wait, the left - hand side is "Number of Customers" (x - axis is from 24 to 88, bottom x - axis) and the y - axis (vertical) is "Number of Water Bottles Sold" (from 0 to 64). Wait, maybe the scatterplot has x as number of customers (horizontal, 24 - 88) and y as number of water bottles (vertical, 0 - 64). So when x = 64 (customers), we need to find y (bottles). Let's look at the points: when x is 32 (customers), y is around 16? No, wait, maybe I misread the axes. Wait, the top y - axis is "Number of Water Bottles Sold" (0 - 64) and the bottom x - axis is "Number of Customers" (24 - 88). So the points are plotted with x (customers) and y (bottles). So as x (customers) increases from 24 to 88, y (bottles) increases from 0 to 64. Now, when x = 64 (customers), what's y? Let's see the options. The correct trend: if we draw a line of best fit, the line would have a positive slope. Let's check the options. Option C is 39, option A is 49. Wait, maybe I made a mistake. Wait, let's count the grid. Each grid square: x - axis (customers) from 24 to 88, so the range is 88 - 24 = 64, and the number of grid squares: from 24 to 88, there are (88 - 24)/8 = 8 squares (since each square is 8 units: 24, 32, 40, 48, 56, 64, 72, 80, 88). Y - axis: 0 to 64, 8 squares (each square 8 units: 0, 8, 16, 24, 32, 40, 48, 56, 64). Now, when x = 64 (customers, which is at the 5th square from 24: 24 + 8*5 = 64), the y - value (bottles) should be at the corresponding square. Looking at the points, when x is 32 (24+8*1), y is around 16? No, maybe the points are: when x = 32 (customers), y = 16? No, the first point: when x is 32 (customers), y is around 16? Wait, no, the first visible point: when x is 32 (customers), y is around 16? Then x = 40, y = 24? x = 48, y = 32? x = 56, y = 40? x = 64, y = 48? But the options don't have 48. Wait, the options are A.49, B.29, C.39, D.88. Wait, maybe the axes are swapped. Maybe the x - axis is number of water bottles sold and y - axis is number of customers? That would make more sense. Let's re - interpret: x - axis: number of water bottles sold (0 - 64), y - axis: number of customers (24 - 88). Then the question is: when the number of water bottles sold is 64, what's the number of customers? No, the question is: "which of these is the best prediction for the number of bottles of water sold on a day where the amusement park had 64 customers?" So x is customers (64), y is bottles. So we need to find y when x = 64. Let's look at the scatterplot again. The points are plotted such that as x (customers) increases, y (bottles) increases. Let's list the approximate x - y pairs: when x = 32 (customers), y = 16 (bottles); x = 40, y = 24; x = 48, y = 32; x = 56, y = 40; x = 64, y = 48? But the options are 49 (A), 29 (B), 39 (C), 88 (D). Wait, 49 is close to 48. So the best prediction is A? No, wait, maybe I messed up the axes. Wait, the y - axis is "Number of Water Bottles Sold" (0 - 64) and x - axis is "Number of Customers" (24 - 88). So when x = 64 (customers), the y - value (bottles) should be around 39? No, let's check the options again. Wait, the correct answer is C? Wait, no, let's think again. The scatterplot: if we have a positive correlation, and when x = 64 (customers), the y (bottles) should be around 39? Wait, the options: C is 39. Let's see, if x = 64, and the trend is that for every increase in customers, bottles increase. Let's take two points: (32, 16) and (88, 64). The slope would be (64 - 16)/(88 - 32)=48/56 = 6/7≈0.857. Then for x = 64, y = 16+(64 - 32)*(6/7)=16 + 32*(6/7)=16+27.43≈43.43. Close to 49 (option A) or 39 (option C). Wait, maybe the points are different. Alternatively, maybe the correct answer is C (39). Wait, no, let's look at the options again. The answer is C? Wait, no, I think I made a mistake in axis interpretation. Let's start over. The problem says: "the scatterplot shows the number of customers and the number of bottles of water sold at an amusement park over a 10 - day period." So x - axis: number of customers, y - axis: number of bottles sold. We need to find y when x = 64. Looking at the scatterplot, the points are plotted such that when x (customers) is 64, the y (bottles) is around 39? Wait, no, the option C is 39, B is 29, A is 49, D is 88. D is too big (y - axis max is 64), B is too small. Between A and C, if we look at the scatterplot, the trend line: if we draw a line through the points, when x = 64, y is around 39? Wait, maybe the correct answer is C.

Answer:

C. 39