Answer:
< CFE = 40°
Step-by-step explanation:
To better understand the solution, see attachment for the diagram.
Given:
BC parallel to DE
Measure of Arc BD = 58°
Measure of Arc DE = 142°
First step: Draw a diameter that passes through the centre of the circle and name it. In this case, the diameter is line ST.
The line ST divides the arc BD and arc DE into half.
That is:
Arc SC = 1/2(arc BC) =1/2(58)
Arc SC = 29°
Arc TE = 1/2(arc DE) =1/2(142)
Arc TE = 71°
Arc SC + Arc CE + Arc TE = 180° (Sum of angles in a semicircle
29° + Arc CE + 71° = 180°
Arc CE + 100° = 180°
Arc CE = 180-100
Arc CE = 80°
Inscribed angle = 1/2(intercepted angle)
<CFE = 1/2(Arc CE )
<CFE = 1/2(80)
< CFE = 40°
Answer:
Step-by-step explanation:
Matching each vocabulary word with its corresponding example:
(1). All Americans = f. Population (a group of items, units or subjects under reference of study e.g. inhabitants of a region, numbers of cars in a city, workers in a factory and so on)
(2). The proportion of all Americans who strongly agree that prisoners with life sentences who have Alzheimer's should be released = c. Parameter ( the number that summarizes some characteristic of a population)
(3). The proportion of the 85 Americans surveyed who strongly agree that prisoners with life sentences who have Alzheimer's should be released = d. Statistic (the sample characteristic corresponding to a population parameter used when a sample is used to make statistical inference about a population)
(4). The answer-Strongly Agree' or 'Agree, or Disagree, or Strongly Disagree = b. Variable (any quality, characteristic, quantity or number that can be counted or measured)
(5). The 85 Americans who participated in the survey = e. Sample (a part or fraction of a population selected on some basis)
(6). The list of answers that the 85 Americans gave = a. Data (the pieces of information collected to be used for the analysis)
600.34 All you need to do is subtract and that will be your answer.
Each candle in the set is a different size.
The smallest candle has a radius of 0.5 inches and a height of 3 inches.
The other two candles are scaled versions of the smallest, with scale factors of 2 and 3.
How much wax is needed to create one set of candles?
in cubic inches
Answer
pi 0.5^2 *3 = 0.75pi is the volume of the first candle.
The second volume is 8 * 0.75pi = 6pi.
And the last volume is 27 * 0.75 pi = 20.25 pi So in total we just take the sum and that is 27pi
Answer: (a) 4
(b) 5
(c) 14
(d)
Class interval Class mark
30 - 35 
35 - 40 
40 - 45 
45 - 50 
50 - 55 
Step-by-step explanation:
The data of 40 persons is given as :
Weights (in kg) Frequency
30 - 35 6
35 - 40 13
40 - 45 14
45 - 50 4
50 - 55 3
(a)
<em>Lower limit is the lowest number in a class interval .</em>
So, is the lower limit of fourth-class interval (45 - 50) is 4.
(b)
<em>Class size = Upper limit - lower limit </em>
So, Class size of first class interval = 35-30=5
Thus , class size of each interval is 5. [ class size remains same]
(c)
Highest frequency in table = 14 which is corresponding to 40 - 45 .
Thus , 40 - 45 is the class interval has the highest frequency.
(d)
<em>Class mark is the mid value of each class interval.</em>
<em>Class interval = </em>
Class interval Class mark
30 - 35
35 - 40
40 - 45
45 - 50
50 - 55
