Answer:
f⁻¹(x) = (8-x)/3 and it is a Function.
Step-by-step explanation:
Given is f(x) = -3x+8
Suppose y = f(x), then y = -3x + 8
Solving for x:-
-3x + 8 = y
-3x = y - 8
3x = 8 - y
x = (8-y)/3
Now interchanging x and y:-
y = (8-x)/3
Here, y is inverse function i.e. f⁻¹(x)
Hence, f⁻¹(x) = (8-x)/3
Since f⁻¹(x) is a linear expression of x, therefore it is a function.
Answer:
(a) Mean =243.0909
(b) Median = 240
In other words it is the middle value of the data arranged in order.
(c) Mode = 221 and 257
(d) Mid Range = 247.5
e)
Variance = 1578.5037
Standard Deviation = 39.730
Range = 309-186= 123
(e) No the results are not likely to be representative of all players in that sport's league because they are not similar.
Step-by-step explanation:
First arranging the data in ascending order
186 187 221 221 229 240 257 257 274 293 309
(a) Mean = Sum of observations/ No of observations
= 186 + 187 + 221 +221 + 229 + 240 + 257 + 257 + 274 + 293 + 309 /11
= 2674/11=
= 243.0909
(b) Median for un grouped data is
Here n = 11 and n/2 = 11/2 is not an integer
Median = Results obtained by ([n/2] +1) player
= (11/2 +1) = 6th player in ordered data
= 240
In other words it is the middle value of the data arranged in order.
(c) Mode = Most frequent values.
There are two modes : 221 and 257 . These both values occur repeatedly.
(d) Mid Range = Maximum Value + minimum value/ 2= 186+ 309/2= 247.5
Now we will find the variance and standard deviation
The variance is given by
s² = (186-243.0909)²+ (187-243.0909)²+ (221-243.0909)²+ (221 -243.0909)²+(229-243.0909)²+ (240-243.0909)²+( 257-243.0909)²+ (257 -243.0909)²+ (274-243.0909)²+ ( 293-243.0909)²+ (309 -243.0909)²/11-1
s²= 3259.370 + 3146.139+ 488.008+ 488.008+ 198.553+ 9.554+ 193.463 + 193.463 + 955.372 + 2509.098 + 4344.009/10
s²= 15,785.037/10= 1578.5037
And Standard Deviation = s= √1578.5037= 39.730
Variance = 1578.5037
Standard Deviation = 39.730
Range = 309-186= 123
(e) No the results are not likely to be representative of all players in that sport's league because they are not similar.
#1 - 3, 1, 2
#2 - x+2y=4
#3 - y=3x-1
75 cm
2 m
980 mm
The most accurate measurement to describe the height of a door given the options is 2 m. Other options such as 10 m, 980 mm, and 75 cm are either unrealistically tall for a door or convert to less than 1 meter making them shorter than typical doors.
To determine the most accurate measurement to describe the height of a door, we need to consider the typical height of a door in most buildings. This generally ranges from 2.0 to 2.1 meters. Given the options provided, the closest and most accurate measurement to this range would be 2 m.
Let's break down the other options as well: The option of 10 m is quite unrealistic as that would make a door taller than the size of most two-story buildings. The options of 980 mm and 75 cm both convert to less than 1 meter (0.98 m and 0.75 m respectively), which would be shorter than a typical door.
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