Reading that as

By the fundamental theorem of calculus, the first derivative is

and so the second derivative would be

which means
Answer:
The z-score of a male bird of this species with a weight of 29.37 grams is 1.7.
Step-by-step explanation:
We are given that the weights of adult male birds of a certain species are normally distributed with a mean of 27.5 grams and a standard deviation of 1.1 grams.
<u><em>Let X = weights of adult male birds of a certain species</em></u>
So, X ~ Normal(
)
The z score probability distribution for normal distribution is given by;
Z =
~ N(0,1)
where,
= population mean weight = 27.5 grams
= standard deviation = 1.1 grams
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
SO, the z-score of a male bird of this species with a weight of 29.37 grams is given by;
<u>Z score</u> =
=
= <u>1.7</u>
Answer:
c
Step-by-step explanation:
Answer:

Step-by-step explanation:
The standard equation for a circle is given by:

Where (h, k) is the center and r is the radius.
We know that the center is (-4, 8). So, substitute -4 for h and 8 for k:

Simplify:

Now, we will need to find r.
We know that it passes through the point (-2, -1). So, we can substitute -2 for x and -1 for y and solve for r. So:

Evaluate:

Square:

Add:

So, r squared is 85.
We don’t actually have to solve for r itself, since we will have to square it anyways.
So, we have:

Substituting 85 for r squared, we get:

And we have our equation.