Commercial dredging operation in ancient rivers occasionallyuncover archaeological artifacts of great importance. One suchartifa
ct 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
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
1 answer:
Answer:
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°
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"I can find the maximum or minimum by looking at the factored expression of a quadratic function by reading off its roots and taking the arithmetic average of them to obtain the -coordinate of the quadratic function, and then substituting that value into the function."
Step-by-step explanation:
Because of the symmetry of quadratics (which is the case here because we have two factors of degree 1, so we are dealing with a <em>polynomial</em> of degree 2, which is a fancy way of saying that something is a quadratic), the -coordinate of the extremum (a fancy way of saying maximum or minimum) is the (arithmetic) average of the two roots.
In the factored form of a quadratic function, we can immediately read the roots: 3 and 7. Another way to see that is to solve , which gives
(the 'V' stands for 'or'). We can take the average of the two roots to get the
-coordinate of the minimum point of the graph (which, in this case, is
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Having the -coordinate of the extremum, we can substitute this value into the function to obtain the maximum or minimum point of the graph, because that will give the
-coordinate of the extremum.