Answer:
- The graph that represents a reflection of f(x) across the x-axis is the blue line on the picture attached.
Explanation:
The function f(x) is:
Which is an exponential function with these features:
- y-intercept: f(0) = 6(0.5)⁰ = 6(1) = 6
- multiplicative rate of change: 0.5 (the base of the exponential term), which means that it is a decaying function (decreasing)
- Horizontal asympote: y = 0 (this is the limit of f(x) when x approaches +∞.
The reflection of f(x) across the x-axis is a function g(x) such that g(x) = - f(x).
Thus, the reflection of f(x) across the x-axis is:
The features of that function are:
- Limit when x approaches - ∞: -∞ (thus the function starts in the third quadrant).
- y-intercerpt: g(0) = -6 (0.5)⁰ = -6(1)= - 6.
- Horizontal asympote: y = 0 (this is the limit of f(x) when x approaches +∞.
- Note that the function never touches the x-axis, thus the function increases from -∞, crosses the y-axis at (0, -6) and continous growing approaching the x-axis but never touchs it. So, this is an increasing frunction, that starts at the third quadrant and ends in the fourth quadrant.
With those descriptions, you can sketch the graph, which you can see in the figure attached. There you have the function f(x) (the red increasing line) and its reflection across the x-axis (the blue increasing line).
Answer:
40
Step-by-step explanation:
To find how much gasoline is needed for 480 kilometers, we will need to find how much is needed per kilometers:
13 liters is used for 156 kilometers
156/13 = 12 so 1 liter gasoline is spent per 12 kilometers
So for 480 kilometers we would need 40 liter gasoline because
480/12 = 40
You write it as $101,000.
120 miles divided by 25 = 4.8
4.8 x 4 = 19.2 inches
Answer:
Step-by-step explanation:
Given that a research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=1096 and x=542 who said yes.
i.e. sample size = 
who said yes =
Sample proportion = 
Std error of proportion = 
Margin of error 95% 
Hence confidence interval for proportions
=
a) Point estimate 
B) Margin of error = 
C) Conf interval = 
D) We are 95% confident that for large random samples representing the population, the proportion of yes will lie between these two values.