Answer:
The given statement is false.
Step-by-step explanation:
We are given the following in the question:
95% confidence interval: (4.53,5.18)
Sample mean, 
= 4.85 seconds
Sample size, n = 20
Alpha, α = 0.05
Sample standard deviation, σ = 1.47 seconds
Degree of freedom = n - 1 = 19
95% Confidence interval:
Putting the values, we get,
Thus, the calculated confidence interval is different from the given confidence interval.
Hence, the given statement is false.
Answer:
The height of water in the second tank is 2ft
Step-by-step explanation:
In this question, we are asked to calculate the height of water in a second tank if the content of a first tank is poured into the second tank.
The plot twist to answering this question is that we need to note the volume of water in the first tank. Although the first tank has dimensions of 2ft by 3ft by 2ft height, the water in the tank only rose to a height of 1 feet.
Hence, to calculate the volume of the water in the first tank, the width and the length of the tank still remain the same, the only difference here is that we work with a height of 1 feet since the Water is not full.
Mathematically, the volume of water present in the tank will be;
V = l * b * h
V = 4 * 3 * 1 = 12 cubic feet
Now, this content is emptied into a second tank. Since the volume of water here is the same; this means;
12 cubic feet = 3 * 2 * h
We ignore the 4ft height as it is just the height of the tank and not the height of the water in the tank
6h = 12 cubic feet
h = 12/6 = 2 ft
Answer:
The even numbers between 0 and X represents an arithmetic sequence with a common difference of 2
The rule of arithmetic sequence = a + d(n - 1)
Where a is the first term and n is the number of terms
So, for the even numbers between 0 and X
The first term = a = 0
d = 2
So, we need to find n at the last term which is X
∴ X = 0 + 2 ( n -1 )
∴ n - 1 = X/2
∴ n = X/2 + 1
The sum of the arithmetic sequence = (n/2) × (2a + (n−1)d)
Substitute with a and d and X
So, the sum = (n/2) * (2*0 + (n−1)*2)
= (n/2) * ((n−1)*2)
= n(n-1)
= (X/2 + 1) * (X/2)
= X/2 by (X/2 + 1)
So, The quick way to add all even numbers between 0 and X always works.
Answer:
sin θ = 
Step-by-step explanation:
Given that,
cos θ = 
From the trigonometric functions,
cos θ = 
⇒ adjacent = 
, and the hypotenuse = 3
Let the opposite side be represented by x, applying the Pythagoras theorem we have;
= 
+ 
= 
+ 
9 = 3 +
= 9 - 3
= 6
x = 
Thus, opposite side =
So that,
sin θ = 
=
Therefore,
sin θ =
