Answer:
No. g(6) is undefined.
Step-by-step explanation:
A function is continuous when the left limit is equal to the right limit at a point, and the function is defined as the limit value at that point.
This function is not defined at x=6, so cannot be continuous there. (Also, the limit values from the different directions are different.)
The area of the rectangle shown is expressed as 4x² - 2x - 6
The diagram is attached below:
Area of a rectangle = Length * width
From the diagram;
Length = 4x - 6
Width = x+1
Substitute the given parameters into the formula as shown:
Area = 4x-6(x+1)
Area = 4x(x) + 4x (1) - 6x - 6
Area = 4x² + 4x - 6x - 6
Area = 4x² - 2x - 6
Hence the area of the rectangle shown is expressed as 4x² - 2x - 6
Learn more here: brainly.com/question/20968176
Answer:
B: Retain the null hypothesis
Step-by-step explanation:
In the relationship between the confidence interval and hypothesis, it is stated that:
When the confidence interval is constructed, all values that fall inside the interval are considered possible values for the parameter that we are estimating while values that fall outside the interval are rejected as they are considered not possible or realistic values.
Now, If the value of the parameter specified by the null hypothesis falls inside the given confidence interval, then we will fail to reject the null hypothesis at the corresponding significance level. However, If the value specified by the null hypothesis doesn't fall inside the given confidence interval, then the null hypothesis can be rejected at the corresponding significance level.
See attachment for the graph of the reflection of f(x) across the y-axis
<h3>How to reflect the function?</h3>
The function is given as:
f(x) = 1.5(0.5)^x
The rule of reflection across the y-axis is
(x, y) = (-x, y)
So, we have the following equation
f'(x) = 1.5(0.5)^-x
Rewrite the function as
g(x) = 1.5(0.5)^-x
So, we plot the graph of the function g(x)
See attachment for the graph of the reflection of f(x)
Read more about function transformation at:
brainly.com/question/17586310
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Answer:
2000 meters
Step-by-step explanation:
When the motorboat is moving downstream, its speed relative to the ground is 18 km/h, so its speed relative to the raft is 15 km/h.
When the motorboat is moving upstream, its speed relative to the ground is 12 km/h, so its speed relative to the raft is again 15 km/h.
Converted to m/min, the relative speed is:
15 km/h × (1000 m/km) × (1 h / 60 min) = 250 m/min
It takes the motorboat 16 minutes to travel to the front of the raft and back. Since the speed is the same in both directions, the motorboat takes 8 minutes to travel the length of the raft.
So the length of the raft is 250×8 = 2000 meters.
