Given:
The logarithmic expression is:
To find:
The equivalent expression of given expression by using change-of-base formula.
Solution:
The change-of-base formula is:
The given expression is:
Using the change-of-base formula, we get
Where, is a constant and c>0.
Let 
, then
Therefore, the correct option is a.
Answer:
1/216
Step-by-step explanation:
The ratio of volumes of similar shapes is the cube of the scale factor. The filled portion of the cone is similar to the entire cone.
<h3>Linear scale factor</h3>
If the filled height is 1/6 of the total height, the scale factor for linear dimensions is 1/6.
<h3>Volume scale factor</h3>
The scale factor for the volume is the cube of the scale factor for linear dimensions. it is ...
(1/6)³ = 1/216
The volume of the filled portion of the cup is 1/216 of the volume of the cup.
Answer:
b
Step-by-step explanation:
Answer: option (b)
1 billion = 1, 000, 000, 000
In scientific notation, a number is rewritten as a simple decimal multiplied by 10 raised to some power n.
10 =101
100= 102
1, 000 = 103
1, 0000 = 104.
..............
Therfore 1 billion can be written as
1 billion =1, 000, 000, 000=10^{9}
Then 1.5 billion = 1.54 10^{9}
Hence option (b) is the correct answer
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Answer:
12 seconds.
Step-by-step explanation:
Let t represent time taken by code to sort an array of 24 elements.
We have been given that an algorithm takes 4 seconds to sort an array of 8 elements. We are asked to find the time it will take for same code to sort an array of 24 elements.
We will use proportions to solve our given problem.
Therefore, it will take 12 seconds for the same code to sort an array of 24 elements.
The point-slope form:
We have the point (-1, 6) and the slope m = -3. substitute:
