Jeremy had 3/4 of a submarine sandwich and gave

Answer:

Step-by-step explanation:

Previous concepts

Normal distribution, is defined as a symmetric "probability distribution centered around the mean, indicating that values near the mean are more common than those further away".

The Z-score measures a value's relation to the mean of a set of values, displayed in terms of how many standard deviations away it is from that mean.

According to the central limit theorem, "with a population having mean μ and standard deviation σ, if we draw sufficient random samples from this population with replacement, the means of those samples will resemble a normal distribution, regardless of the original population's shape, as long as the sample size is large enough".

Solution to the problem

In this scenario, we select a sample size of n = 100

The central limit theorem informs us that the distribution of the sample mean is defined by:

Thus, the mean for the sample would be:

And the standard deviation would be:

Answer:

Step-by-step explanation:

The trigonometric expression given is:

11 cos² x +3 sin² x + 6sin x cos x + 5

Alternatively, we can present it as:

(9 cos² x + 2 cos² x) + (2 sin² x + sin² x) + 6sin x cos x + 5

After rearranging, the expression can be rewritten as:

(9 cos² x + sin² x + 6sin x cos x) + (2 cos² x + 2 sin² x) + 5

If we factor the highlighted part similarly to a polynomial:

(9 cos² x + sin² x + 6sin x cos x) + (2 cos² x + 2 sin² x) + 5

This results in:

(3 cos x + sin x)² + 2 (cos² x + sin² x) + 5

Notably, the term in the second set of brackets (cos² x + sin² x) is a well-known trigonometric identity and equals one.

Consequently, the expression simplifies to:

(3 cos x + sin x)² + 7

The maximum and minimum values of the entire expression rely on the max and min values of (3 cos x + sin x), which follows the format (a cos x + b sin x).

The max and min values can be easily determined.

I've included a screenshot from related material below:

Here, a=3 and b=1, thus, R= √10

As the cosine value for any angle ranges between -1 and 1, the value of cos(x − α) will also fall within this range.

This means the max and min for (a cos x + b sin x) will be -R to R, and all resultant values will be between those limits.

In this case, we observe that it falls between (-√10) and √10.

Returning to our original expression:

(3 cos x + sin x)² + 7

The bracketed term ranges between (-√10) and √10.

Nevertheless, since squaring a negative value yields a positive result, we cannot use a negative value for determining the minimum. The minimum occurs at the lowest non-negative value, which is zero.

Thus, the minimum value is:

(0)² + 7 = 7

And the maximum is:

(√10)² + 7 = 17

Answer:

For a 90º clockwise rotation, the vertex q' (–3, 4) maps to q(4, 3).

According to the 90º counterclockwise rotation rule, q' (–3, 4) transforms to q(–4, –3).

Step-by-step explanation:

Given the rectangle with vertices r'(–4, 4), s'(–4, 1), p'(–3, 1), and q'(–3, 4),

Find the image of vertex q after a 90º rotation.

The rotation rules are:

90º clockwise: (x, y) → (y, –x)

90º counterclockwise: (x, y) → (–y, x)

Applying the clockwise rule to q'(–3, 4) yields q(4, 3).

Applying the counterclockwise rule to q'(–3, 4) yields q(–4, –3).

Thus, clockwise rotation of q' (–3, 4) results in q(4, 3),

and counterclockwise rotation results in q(–4, –3).

The likely equation for the ellipse is given by

This can be parameterized as a segment of the curve using

with . Then we can proceed with

and other related calculations.

Response:

To settle their disagreement over who does the dishes, flip a fair coin. There is an equal 50% probability of it showing heads or tails, hence the choice will be random.