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solve for answers to be (a) 30 kmh-1
(c) k = 45
(b) 13.3%
(d) 48 km h-1

Let's solve the given questions from the cumulative frequency graph that shows the speeds of cars (in km/h) passing through an intersection.

### Part (a): Minimum Speed of a Car
To find the minimum speed, we look for the speed at which the cumulative frequency starts to rise from zero. Based on the graph:
- The graph starts rising from the point where the speed is **30 km/h**.

Thus, the minimum speed of a car is:
**30 km/h**

---

### Part (b): Percentage of Cars Driving Faster than 55 km/h
To determine what percentage of cars travel faster than 55 km/h:
1. From the graph, locate the cumulative frequency at 55 km/h.
2. It appears that at 55 km/h, the cumulative frequency is about **130**.
3. The total cumulative frequency is **150**.

Percentage of cars driving faster than 55 km/h:
\[
\text{Percentage} = \left(\frac{150 - 130}{150}\right) \times 100 = \frac{20}{150} \times 100 = 13.33\%
\]

Thus, the percentage is approximately **13.3%**.

---

### Part (c): Given that 40% of Cars Drive Faster than a Certain Speed \( k \)
1. We know that 40% of the cars drive faster than a certain speed \( k \).
2. 40% of 150 cars gives a cumulative frequency of:
   \[
   40\% \text{ of } 150 = 0.4 \times 150 = 60 \text{ cars}.
   \]
3. Subtract this from the total cumulative frequency:
   \[
   150 - 60 = 90.
   \]
4. From the graph, locate the speed corresponding to a cumulative frequency of 90. This speed is approximately **45 km/h**.

Thus, \( k = 45 \text{ km/h} \).

---

### Part (d): Find the 60th Percentile
1. The 60th percentile means we need to find the speed at which 60% of the cars are driving.
2. 60% of 150 cars gives a cumulative frequency of:
   \[
   60\% \text{ of } 150 = 0.6 \times 150 = 90.
   \]
3. From the graph, the speed corresponding to a cumulative frequency of 90 is approximately **48 km/h**.

Thus, the 60th percentile corresponds to a speed of **48 km/h**.

---

### Summary of Answers:
(a) The minimum speed is **30 km/h**.  
(b) The percentage of cars driving faster than 55 km/h is **13.3%**.  
(c) The value of \( k \) is **45 km/h**.  
(d) The 60th percentile is **48 km/h**.

---

Let me know if you would like more details on any of these solutions.  
Here are five related questions for you to consider:

1. How is the cumulative frequency graph useful in analyzing data distribution?
2. How would you calculate the median speed from this graph?
3. What does the steepness of the cumulative frequency graph indicate about the data?
4. If the maximum speed were 100 km/h, how would that affect the percentage calculations?
5. How do you calculate other percentiles (e.g., 25th, 75th) from a cumulative frequency graph?

**Tip**: Remember that cumulative frequency graphs are particularly helpful in understanding the distribution of data and locating percentiles!

Solve for answers to be (a) 30 km/h, (c) k = 45, (b) 13.3%, (d) 48 km/h

Solve problems involving a cumulative frequency graph showing car speeds at an intersection. Learn how to determine minimum speed, calculate percentages, find specific percentiles, and solve for values like k. Suitable for students in Grades 9-11.

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