Solution:
Rewrite 3 ≥ y - 2 for easier calculation:
y - 2 ≤ 3
Move the term:
y ≤ 3 + 2
y ≤ 5
When graphing the solution, filled dot (black arrow) is used for ≤ and ≥ while empty dot (white arrow) is used for < >
Answer:
a)
90% confidence interval for the mean grading time of all composition papers.
(12.47981 , 13.52019)
b)
Appropriate inequality
The interval is ( 12.47981 < μ < 13.52019)
Step-by-step explanation:
<u><em>Explanation</em></u>:-
a)
Given sample size 'n' = 40
Mean of the sample = 13 minutes
standard deviation = 2 min
level of significance = 0.10 or 90%
90% confidence interval for the mean grading time of all composition papers.
( 13 - 0.52019 , 13 + 0.52019)
(12.47981 , 13.52019)
b)
The interval is ( 12.47981 < μ < 13.52019)
Answer:
1) If sum of the two smaller sides of a triangle is greater than the third longer side, then its a triangle.
<h3>In our case, 20 + 23 > 41. Hence its a triangle .</h3>
Use the side lengths to classify the triangle as acute, right, or obtuse. Compare the square of the length of the longest side with the sum of the squares of the lengths of the two shorter sides
2) Square root of sum of the squares of the two smaller sides is equal to the third longer side, then its a right triangle.
In our case,
√20^2+23^2≈30.4795<41.
<h3>Hence not a right triangle.</h3>
Since the sum of the squares of the two shorter sides is < the square of the longer side, its an obtuse angle triange
Step-by-step explanation:
Hope it is helpful....
It follows from the definition of the binomial coefficient:
So we have
That is, 
gets absorbed into the numerator's factorial, and we introduct 
into the denominator. Now, 
, so we get
as required.
We know that for all B:
![\csc\text{B}\in(-\infty,-1]\cup[1,\infty)](https://tex.z-dn.net/?f=%5Ccsc%5Ctext%7BB%7D%5Cin%28-%5Cinfty%2C-1%5D%5Ccup%5B1%2C%5Cinfty%29)
So the answer is 0,5 (b.)
