Answer:
x = 1.24
Step-by-step explanation:
In order to get that x down from its current position of exponential, you need to take either the log or the natural log of both sides. The power rule tells us that we can then pull the exponent down in front. So let's take the natural log of both sides:
We can bring the x down in front to give us:
ln(83) = x ln(35)
The right side of this is "stuck" together by multiplication, so we can undo that multilication by division of the ln(35). That leaves us with just x on the right:
Do this on your calculator and find that x = 1.24
Answer:
The vertex of this parabola is
Step-by-step explanation:
One way of finding the x-coordinate of the vertex of a parabola is by using the equation
From the function , we can see that
This means that
So, the x-value of the vertex is -2. Now, we can plug this x-value into the function to find the y-coordinate of the point.
Thus, the vertex of this parabola is
Using the Normal distribution, it is found that 0.0359 = 3.59% of US women have a height greater than 69.5 inches.
In a <em>normal distribution</em> with mean and standard deviation
, the z-score of a measure X is given by:
US women’s heights are normally distributed with mean 65 inches and standard deviation 2.5 inches, hence .
The proportion of US women that have a height greater than 69.5 inches is <u>1 subtracted by the p-value of Z when X = 69.5</u>, hence:
has a p-value of 0.9641.
1 - 0.9641 = 0.0359
0.0359 = 3.59% of US women have a height greater than 69.5 inches.
You can learn more about the Normal distribution at brainly.com/question/24663213
The infinite geometric series is converges if |r| < 1.
We have r = 0.7 < 1, therefore our infinite geometric series is converges.
The sum S of an infinite geometric series with |r| < 1 is given by the formula :
We have:
Substitute:
Answer: c. Converges, 40.