lesson 13 practice problems
1 a group of ten friends played a number guessing game. they were asked to pick a number between 1 and 20. the person closest to the target number wins. the ten people made the guesses in the first row of this table:
| guess | 2 | 15 | 10 | 8 | 12 | 19 | 20 | 5 | 7 | 9 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| absolute guessing error | | | | | | | | | | |

a. the actual number was 14. complete the table with the absolute guessing errors.

b. graph the guess and absolute guessing errors.

c. is the absolute guessing error a function of the guess? explain how you know.

(graph for part b: x - axis: guess (2,4,6,8,10,12,14,16,18,20,22), y - axis: absolute guessing error (0,2,4,6,8,10,12,14,16,18,20))

2 bags of walnuts from a food producer are advertised to weigh 500 grams each. in a certain batch of twenty bags, most bags have an absolute error that is less than 4 grams.

could this scatter plot represent those twenty bags and their absolute errors? explain your reasoning.

(scatter plot: x - axis: weight (grams) (495,500,505,510,515), y - axis: absolute error (grams) (0,2,4,6,8,10,12))

Question

lesson 13 practice problems
1 a group of ten friends played a number guessing game. they were asked to pick a number between 1 and 20. the person closest to the target number wins. the ten people made the guesses in the first row of this table:
| guess | 2 | 15 | 10 | 8 | 12 | 19 | 20 | 5 | 7 | 9 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| absolute guessing error |  |  |  |  |  |  |  |  |  |  |

a. the actual number was 14. complete the table with the absolute guessing errors.

b. graph the guess and absolute guessing errors.

c. is the absolute guessing error a function of the guess? explain how you know.

(graph for part b: x - axis: guess (2,4,6,8,10,12,14,16,18,20,22), y - axis: absolute guessing error (0,2,4,6,8,10,12,14,16,18,20))

2 bags of walnuts from a food producer are advertised to weigh 500 grams each. in a certain batch of twenty bags, most bags have an absolute error that is less than 4 grams.

could this scatter plot represent those twenty bags and their absolute errors? explain your reasoning.

(scatter plot: x - axis: weight (grams) (495,500,505,510,515), y - axis: absolute error (grams) (0,2,4,6,8,10,12))

Accepted Answer

### Part 1a:
# Explanation:
## Step1: Recall absolute error formula
Absolute guessing error = $ |\text{guess} - \text{actual number}| $. Actual number is 14.
## Step2: Calculate for each guess
- For guess 2: $ |2 - 14| = 12 $
- For guess 15: $ |15 - 14| = 1 $
- For guess 10: $ |10 - 14| = 4 $
- For guess 8: $ |8 - 14| = 6 $
- For guess 12: $ |12 - 14| = 2 $
- For guess 19: $ |19 - 14| = 5 $
- For guess 20: $ |20 - 14| = 6 $
- For guess 5: $ |5 - 14| = 9 $
- For guess 7: $ |7 - 14| = 7 $
- For guess 9: $ |9 - 14| = 5 $
# Answer:
The absolute guessing errors (from left to right) are: 12, 1, 4, 6, 2, 5, 6, 9, 7, 5

### Part 1b:
# Explanation:
## Step1: Identify coordinates
For each guess (x - axis) and its absolute error (y - axis), the points are: (2,12), (15,1), (10,4), (8,6), (12,2), (19,5), (20,6), (5,9), (7,7), (9,5).
## Step2: Plot points
On the given graph, plot each (guess, absolute error) point. For example, at x = 2, y = 12; at x = 15, y = 1, etc.
# Answer:
Points are plotted as (2,12), (15,1), (10,4), (8,6), (12,2), (19,5), (20,6), (5,9), (7,7), (9,5) on the graph.

### Part 1c:
# Explanation:
## Step1: Recall function definition
A function is a relation where each input (guess) has exactly one output (absolute error).
## Step2: Check each guess
Each guess (input) has only one absolute error (output) since for a single guess, $ |\text{guess}-14| $ gives one value. No guess is repeated, so each input has unique output.
# Answer:
Yes, the absolute guessing error is a function of the guess. Because for each guess (input), there is exactly one absolute guessing error (output) (by the definition of absolute value, each input gives one output, and no guess is repeated).

### Part 2:
# Explanation:
## Step1: Analyze the scatter plot
The scatter plot has points with absolute error (y - axis) values. We need to check how many points have absolute error < 4.
## Step2: Count points with error < 4
Looking at the plot: Most points on the left (lower x - values) have higher errors, but the points around x = 500 have absolute errors (y) close to 0, 1, 2, 3, 4? Wait, the problem says "most bags have an absolute error less than 4 grams". In the scatter plot, let's check the y - values (absolute error). The points with y < 4: let's see, the ones near x = 500 have y around 0,1,2,3? Wait, no, the left - most points (x ~ 495) have y ~ 7 - 8, then a point at y = 4, then y = 2, then near x = 500, y ~ 0 - 1, then at x ~ 505, y ~ 6 - 7, x ~ 510, y ~ 8 - 12. Wait, no, maybe mis - reading. Wait, the x - axis is weight (grams), y - axis is absolute error (grams). The problem says "most bags have an absolute error less than 4 grams". In the scatter plot, how many points have y < 4? Let's count: the points with y < 4: the ones near x = 500 (y ~ 0,1,2,3) – maybe 5 - 6 points? But "most" of twenty bags? Wait, no, maybe I mis - see. Wait, the scatter plot: left cluster (x ~ 495) has y ~ 7 - 8 (2 points), then a point at y = 4, then y = 2, then near x = 500 (y ~ 0 - 1, 2 points), then x ~ 505 (y ~ 6 - 7, 2 points), x ~ 510 (y ~ 8 - 12, 3 points). Wait, total points: let's count the dots. Left cluster: 2, then y = 4 (1), y = 2 (1), x = 500: 2, x = 505: 2, x = 510: 3. Total: 2 + 1+1 + 2+2 + 3=11? No, maybe 20? Wait, the problem says "twenty bags". The scatter plot has, let's see: left (x ~ 495): 2 points, then a point at (497,4), then (498,2), then at x = 500: 2 points, x = 503: 2 points, x = 505: 2 points, x = 508: 1, x = 510: 3, x = 512: 2? Wait, no, maybe the plot has around 10 - 12 points? Wait, no, the problem says "twenty bags" but the scatter plot might be a sample. Wait, the key is: the problem says "most bags have an absolute error less than 4 grams". In the scatter plot, how many points have absolute error (y) < 4? Let's check y - axis: y < 4 means y = 0,1,2,3. In the plot, the points with y < 4: the ones near x = 500 (y ~ 0,1,2,3) – maybe 5 - 6 points? But "most" of twenty? Wait, maybe I made a mistake. Wait, the problem says "most bags have an absolute error less than 4 grams". In the scatter plot, if we look at the points: the ones with y < 4 are the ones where the absolute error is less than 4. Let's count: the points with y - value (absolute error) < 4: let's see, the point at y = 2, y = 0 (if any), y = 1, y = 3. Wait, the scatter plot: the left - most points (x ~ 495) have y ~ 7 - 8 (2 points, error ≥ 4), then a point at y = 4 (error = 4, not less than 4), then y = 2 (error < 4), then near x = 500 (y ~ 0,1,2 – 3 points, error < 4), then x = 505 (y ~ 6 - 7, 2 points, error ≥ 4), x = 510 (y ~ 8 - 12, 3 points, error ≥ 4). Wait, total points: 2 + 1+1 + 3+2 + 3=12? No, maybe 20? Wait, the problem says "twenty bags" but the scatter plot has, say, 12 points? No, the user's plot: let's count the dots. Left: 2, then 1 (y = 4), 1 (y = 2), 2 (x = 500), 2 (x = 505), 3 (x = 510). Total: 2 + 1+1 + 2+2 + 3=11. Wait, maybe the plot is a sample. Wait, the problem says "most bags have an absolute error less than 4 grams". In the scatter plot, how many have error < 4? The points with y < 4: y = 2, and the ones near x = 500 (y ~ 0,1,2) – let's say 4 points. The rest (11 - 4 = 7) have error ≥ 4. So "most" would mean more than half (10 out of 20). But in the plot, less than half have error < 4. Wait, no, maybe I misread the x - axis. Wait, x - axis is weight (grams), so the bags are around 500 grams. So the points near x = 500 (weight ~ 500) should have smaller errors. Wait, the points at x = 500 (weight) have y (error) ~ 0 - 1 (small, < 4), then x = 505 (weight 505, error ~ 6 - 7, which is |505 - 500| = 5, so error 5 ≥ 4), x = 510 (weight 510, error |510 - 500| = 10, ≥ 4), x = 495 (weight 495, error |495 - 500| = 5, ≥ 4), x = 497 (weight 497, error |497 - 500| = 3, which is < 4! Wait, I missed that. The point at x ~ 497, y ~ 4? No, y - axis is absolute error. Wait, x = 497 (weight), y = 7? No, maybe x - axis is weight, so absolute error is |weight - 500|. So for x = 495, error = 5; x = 497, error = 3 (since |497 - 500| = 3 < 4); x = 498, error = 2 (|498 - 500| = 2 < 4); x = 500, error = 0; x = 501, error = 1; x = 502, error = 2; x = 505, error = 5; x = 506, error = 6; x = 510, error = 10; x = 511, error = 11; x = 512, error = 12. Oh! I see, I misread the x - axis. The x - axis is weight (grams), so the absolute error is |weight - 500|. So for the points:

- x = 495: error = 5 (y = 5? Wait, no, the y - axis is absolute error. Wait, the left - most points (x ~ 495) have y ~ 7 - 8? No, that can't be. Wait, the problem says "bags of walnuts... advertised to weigh 500 grams each". So absolute error = |actual weight - 500|. So the x - axis is actual weight, y - axis is |actual weight - 500|. So for a point at x = 495, y = |495 - 500| = 5; x = 497, y = 3; x = 498, y = 2; x = 500, y = 0; x = 501, y = 1; x = 502, y = 2; x = 505, y = 5; x = 506, y = 6; x = 510, y = 10; x = 511, y = 11; x = 512, y = 12. Now, the problem says "most bags have an absolute error less than 4 grams". So how many points have y < 4? Let's count:

- x = 497: y = 3 (1)
- x = 498: y = 2 (2)
- x = 500: y = 0 (3)
- x = 501: y = 1 (4)
- x = 502: y = 2 (5)

That's 5 points with y < 4. The other points: x = 495 (y = 5), x = 505 (y = 5), x = 506 (y = 6), x = 510 (y = 10), x = 511 (y = 11), x = 512 (y = 12), and the left - most two points (x ~ 495? No, x = 495 is one point, then two points at x ~ 495? Wait, the scatter plot: left cluster (x ~ 495) – 2 points, y ~ 7 - 8? No, that would mean |495 - 500| = 5, but y is 7 - 8, which is wrong. So maybe the x - axis is not weight but something else? No, the problem says "bags of walnuts... absolute error". So my initial mistake was misinterpreting the x - axis. Let's start over.

The scatter plot: x - axis is weight (grams), y - axis is absolute error (grams). The problem states "most bags have an absolute error less than 4 grams". So we need to check if in the scatter plot, more than half (10 out of 20) have y < 4. Looking at the plot:

- Points with y < 4: the ones near x = 500 (y ~ 0,1,2,3) – let's say 10 - 12 points? Wait, the plot has:

Left side (x ~ 495): 2 points, y ~ 7 - 8 (error ≥ 4)

Middle (x ~ 497 - 502): points with y ~ 2, 4, 2, 0, 1, 2 (so y < 4: y = 2, 2, 0, 1, 2 – 5 points; y = 4: 1 point (error = 4, not less than 4))

Right side (x ~ 505 - 512): points with y ~ 6, 7, 8, 10, 12 (error ≥ 4)

Total points: 2 + 1+5 + 5=13? No, the plot has, let's count the dots:

- Left: 2 (y ~ 7 - 8)
- Then y = 4 (1)
- Then y = 2 (1)
- Then x = 500: 2 (y ~ 0 - 1)
- Then x = 505: 2 (y ~ 6 - 7)
- Then x = 510: 3 (y ~ 8 - 12)

Total: 2 + 1+1 + 2+2 + 3=11.

Now, "most" of 20 bags? Wait, the problem says "in a certain batch of twenty bags", but the scatter plot is a representation. Maybe the plot has 20 points? No, the image shows a scatter plot with around 10 - 12 points. Maybe the question is: does the scatter plot show that most bags have error < 4? Let's see: the points with y < 4: the ones near x = 500 (y ~ 0,1,2,3) – let's say 5 points, and the ones with y ≥ 4: 6 points. So "most" would mean more than half, but here less than half have error < 4. Wait, no, maybe I'm wrong. Wait, the problem says "most bags have an absolute error that is less than 4 grams". In the scatter plot, if we look at the y - axis (absolute error), the points with y < 4 are the ones below the horizontal line y = 4. How many are below? Let's see:

- The points with y < 4: the ones near x = 500 (y ~ 0,1,2,3) – let's count:

- A point at y = 2 (1)
- A point at y = 1 (1)
- Two points at y ~ 0 (2)
- A point at y = 3 (1)

Total: 5 points. The rest have y ≥ 4. So "most" would require more than 10 (half of 20), but here only 5. So the answer is: No, because in the scatter plot, fewer than half of the points (representing bags) have an absolute error less than 4 grams, so it does not match the description that most bags have an absolute error less than 4 grams.

# Answer:
No, this scatter plot cannot represent those twenty bags. Because in the plot, only a few points (fewer than half) have an absolute error less than 4 grams, while the problem states "most bags" (more than half of twenty, i.e., more than 10) have

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Part 1a:

Step1: Recall absolute error formula

Step2: Calculate for each guess

Step1: Identify coordinates

Step2: Plot points

Step1: Recall function definition

Step2: Check each guess

Answer:

Part 1b: