Trapezoid GHJK was rotated 180° about the origin to determine the location of G'H'J'K', as shown on the graph. What are the coor

Answer:

F' = (7, 6)

R' = (-1, 7)

I' = (-2, -5)

O' = (6, -6)

Step-by-step explanation:

The reflection rule across the y-axis states that (x, y) ---> (-x, y). Thus, all x coordinates must be converted to their negative counterparts. The -7 from F becomes 7, the 1 from R becomes -1, the 2 from I turns into -2, and the -6 from O changes to 6.

The complete question reads:

Peter created two rays, AC and AP, sharing a common vertex at point A. Which of the following statements

might accurately describe Peter's drawing?

I. AC and AP are parallel.

II. PAC represents an angle.

III. AC and AP are at right angles.

A. I and II

B. II and III

C. I and III

D. I, II, and III

Answer:

Option B: II & III

Step-by-step explanation:

We know Peter has drawn rays AC and AP.

Since the point A is shared as the endpoint, it indicates an angular relationship at this common point.

This angle could potentially be 90°, suggesting that rays AC and AP may be perpendicular.

Thus, the valid statements that characterize his drawing are: II & III.

Answer:

  $200

Step-by-step explanation:

The yearly tax obligation is...

  2.4% × $100,000 = $2,400

Monthly, this amounts to...

  $2400/(12 mo) = $200/mo

This means taxes will increase Bonnie's monthly mortgage payment by $200.

Response:

Regarding this scenario, we have the following details about the timeframe to organize a return

And we select a sample size =49>30, and we aim to find the standard deviation for the sample mean. Based on the central limit theorem, we understand that the sample mean distribution is represented by:

The standard deviation would then be:

Therefore, the most accurate response would be

b. 2 minutes

Step-by-step explanation:

Prior concepts

Normal distribution, defines a probability distribution that is symmetric around the mean, showing that occurrences near the mean are more frequent than those that are further away.

The central limit theorem states that "when we have a population with mean μ and standard deviation σ and draw sufficiently large random samples from the population with replacement, then the distribution of the sample means will resemble a normal distribution. This applies regardless of whether the original population is normal or skewed, given that the sample size is large enough".

Solution to the problem

For this case, we have the following information about the time to prepare a return

A sample size =49>30 also indicates that we are focused on determining the standard deviation for the sample mean. Based on the central limit theorem, we recognize that the sample mean distribution is described by:

Hence, the most accurate answer would be

b. 2 minutes