Determine which graph represents a reflection across the x-axis of f(x) = 3(1.5)x.
1 answer:
The reflection is written as:
And the graph can be seen below.
<h3>How to get the graph of the reflection?</h3>
Here we have the function:
A reflection across the x-axis is given by:
Then, replacing the function f(x) by the actual equation:
The graph of the function g(x) can be seen below:
If you want to learn more about reflections:
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Given:
Length of the cuboid tank = 4 m
Breadth = 2.5 m
Height = 2.4 m
One third of the tank is filled with water.
1 cubic meter = 1000 liters.
To find:
The quantity of the water in the tank.
Solution:
Volume of a cuboid is:
Where, l is length, b is breadth and h is the height.
The volume of the tank is :
Volume of tank is 24 cubic meter.
One third of the tank is filled with water. So, the volume of the water is
The volume of water is 8 cubic meters.
We have,
1 cubic meter = 1000 liters.
8 cubic meter = 8000 liters.
Therefore, the quantity of the water in the tank is 8000 liters.
In statistics, mean is the average in a set of data collected. To calculate the mean, you have to add up all the numbers in the table and divide it by the number of data that exists. For example, if the data set is 2 4 1 5 2 8, the mean will be:
mean = = 3.6
So, for this data set, the mean is 3.6.
The median is also a average number, however, the median is the middle value in the list. For example, with the data set above, the median is 3, because, as the set has an even number of data, the middle term would be the mean of the two middle number, in other words:
median = = 3
The standard deviation (σ) is the spread of data distribution, which means it's how "far" a number is from the mean of the set. The formula is
σ = √∑ (x - μ)²/N, where ∑ is the total sum; μ is the mean; and N is the number of data points in the sample. So, to calculate the standard deviation, using the example:
1) Calculate the mean of the set: μ=3.6
2) Find the difference between each data point and the mean and then, the square of each one:
(2-3.6)² = 2.56;
(4-3.6)² = 0.16
(1-3.6)² = 6.76
(5-3.6)² = 1.96
(2-3.6)² = 2.56
(8-3.6)² = 19.36
3) Add up all the squares: ∑= 33.36
4) Divide by the number of data points: =5.56
5) Take the square root: σ = 2.36
For the set of numbers above (2,4,1,5,2,8), the standard deviation is
σ = 2.36.