Commercial dredging operation in ancient rivers occasionallyuncover archaeological artifacts of great importance. one suchartifact is bronze age spearheads recovered from ancient rivers inireland. a recent study gave the following information regardingdiscoveries of ancient bronze spearheads in irish rivers
river bann blackwater erne shannon barrow
#spearheads = 19 8 15 33 14
(a). make a pareto chart for these data
(b). make a circle graph for these data

A) Refer attached fig. or pareto chart

Step-by-step explanation:

Given data

Rivers               Bann    Blackwater    Erne     Shannon    Barrow

Spearheads(fi)     19          8                    15          33               14

a)

Pareto charts are those charts  who has both bars and lines.  bars are shown in descending order and the cumulative total is represented by the line.

b) Circle graph

Circle graph is also known as pie chart

In this chart we divided into circle in to different segments according to formula.

Total  frequency of spreads in = 19+8+15+33+14=90

i) Bann

fi =19

percentage = %

Segment size = 21.35% × 360 = 77°

ii) Black water

fi = 8

percentage = = 8.99%

Segment size = 8.99% × 360 = 32°

iii) Erne

fi = 15

percentage = = 16.85%

Segment size = 16.85% × 360 = 61°

iv) Shannon

fi = 33

percentage = = 37.08%

Segment size = 37.08% × 360 = 133°

iv) Barrow

fi = 14

percentage = = 15.73%

Segment size = 15.73% × 360 = 57°

1. d.90

2. e. none of these (80)

3. a. 0

4. b. 6

5. e. none of these (10)

6. a. 5

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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