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2 months ago

The frequency distribution of weights (in kg) of 40 persons is given below.

Mathematics

1 answer:

AnnZ [12.3K]2 months ago

8 0

Answer: (a) 4

(b) 5

(c) 14

(d)

Class interval Class mark

30 - 35 $\dfrac{35+30}{2}=32.5$

35 - 40 $\dfrac{35+40}{2}=37.5$

40 - 45 $\dfrac{40+45}{2}=42.5$

45 - 50 $\dfrac{45+50}{2}=47.5$

50 - 55 $\dfrac{50+55}{2}=52.5$

Step-by-step explanation:

The data consists of 40 individuals:

Weights (in kg) Frequency

30 - 35 6

35 - 40 13

40 - 45 14

45 - 50 4

50 - 55 3

(a)

The lower limit refers to the smallest value in a class interval.

Accordingly, the lower limit for the fourth-class interval (45 - 50) is 4.

(b)

The class size is calculated by subtracting the lower limit from the upper limit.

For the first class interval, class size = 35 - 30 = 5.

Thus, all intervals share a consistent class size of 5.

(c)

The highest frequency in this data is 14, corresponding to the class interval of 40 - 45.

This class interval thus demonstrates the greatest frequency.

(d)

Class mark is the middle value of each class interval.

Class interval = $\dfrac{(\text{Upper limit+Lower limit})}{2}$

Class interval Class mark

30 - 35 $\dfrac{35+30}{2}=32.5$

35 - 40 $\dfrac{35+40}{2}=37.5$

40 - 45 $\dfrac{40+45}{2}=42.5$

45 - 50 $\dfrac{45+50}{2}=47.5$

50 - 55 $\dfrac{50+55}{2}=52.5$

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A) The speed of pedestrian BC is 5 km/h

The speed of pedestrian CD is 0 km/h

The speed of pedestrian DE is 5 km/h

B) He reached E since the stop after 6 hours

C) The formula for section BC is d(t) = 40 - 5t

The formula for section CD is d(t) = 20

The formula for section DE is d(t) = 50 - 5t

Step-by-step breakdown:

In the time-distance graph, speed represents the change in distance with respect to time

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For line BC:

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2. Δt = 10 - 6 = 4 hours

3. The speed = 20 ÷ 4 = 5 km/h

The speed for pedestrian DE is 5 km/h

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1. f(x) is referenced as d(t)

2. m is the speed

3. x corresponds to t

4. You can calculate c by substituting any coordinates of a point along the line into the formula

Line BC has a negative slope because d decreases as t increases

∵ m = -5 and c = 40

Thus, d(t) = 40 - 5t

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Line CD is a horizontal line (which follows the form of any horizontal line represented as y = c)

Thus, m = 0 and c = 20

Therefore, d(t) = 20

The equation for section CD is d(t) = 20

Line DE

Line DE features a negative slope as d decreases along with an increase in t

∵ m = -5

Thus, d(t) = -5t + c

The value of c can be determined by substituting point D's coordinates into the equation

∵ D's coordinates are (6, 20)

Thus, 20 = -5(6) + c

So, 20 = -30 + c

Adding 30 to both sides yields

∴ c = 50

Thus, d(t) = 50 - 5t

The equation for section DE is d(t) = 50 - 5t

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