In 2015, in Buffalo, New York, there were 8,625 arrests, 2,678 robberies, 865 assaults, and 20 murders. The population of Buffal

Response: 8

Detailed Explanation:

Answer: The graph corresponds to the inequality y > 3x + 2

Step-by-step explanation:

A linear inequality is similar to a linear equation, but it consists of inequality symbols (<, >, ≤, ≥) rather than the equal sign (=).

In the question, the linear inequality is depicted through a graph.

The line in the graph intersects the point (-3,-7).

Now, let’s evaluate which option meets the conditions of this point.

1) y < 3x + 2 implies the line should be y = 3x + 2.

⇒ -7 = 3(-3) + 2.

⇒ -7 = -9 + 2 ⇒ -7 = -7, which holds true.

2) y > 3x + 2, which is analogous to the first.

3) y < x + 2 means the line should be y = x + 2.

⇒ -7 = -3 + 2.

⇒ -7 = -1, which is false.

4) y > x + 2 parallels the third scenario.

Thus, options 3) and 4) cannot represent the required linear inequality.

From options 1) and 2), option 2) is the correct linear inequality since the graph indicates shading above the line, suggesting y (>) must be greater. [Conversely, for y (<) to be lower, the shading would be below the line.]

Consequently, the correct linear inequality presented by the graph is 2) y > 3x + 2.

Answer:

He should plan to stop at Springfield.

Step-by-step explanation:

Gilmore is located 26 miles away, so half of this distance is 13 miles.

The town closest to 13 miles is Springfield.

Answer:

(a) The data point that is considered an outlier is $810.

(b) The distribution regarding expenditures on textbooks among the 34 students is right skewed.

Step-by-step explanation:

The provided data regarding how much 34 college students spent on textbooks is:

S = {120, 130, 130, 140, 150, 150, 160, 170, 180, 210, 220, 230, 240, 250, 260, 280, 280, 290, 290, 290, 310, 320, 320, 370, 380, 390, 410, 440, 450, 470, 510, 530, 620, 810}

(a)

An outlier is defined as a value significantly different from the rest of the dataset, being either excessively high or low.

A widely-used approach for identifying outliers involves:

• Identifying values that fall below Q₁ - 1.5 IQR as outliers.
• Identifying values that exceed Q₃ + 1.5 IQR as outliers.

In our case,

Q₁ = first quartile

Q₃ = third quartile

IQR = Interquartile range = Q₃ - Q₁.

The first quartile value corresponds to more than 25% of the data points. It can be found by examining the median of the first half of the data.

Calculate the first quartile with the set below:

Initial half of data: {120, 130, 130, 140, 150, 150, 160, 170, 180, 210, 220, 230, 240, 250, 260, 280, 280}

This subset contains 17 values.

The median in an odd-sized dataset is the central point.

The central value here is: 180

Thus, the first quartile is Q₁ = 180.

The third quartile value corresponds to more than 75% of the data points.

We determine the third quartile from the second half of the data:

Final half of data: {290, 290, 290, 310, 320, 320, 370, 380, 390, 410, 440, 450, 470, 510, 530, 620, 810}

The median of an odd dataset serves as the middle value.

The central point is: 390

Hence, the third quartile is Q₃ = 390.

Calculate the interquartile range as follows:

IQR = Q₃ - Q₁

      = 390 - 180

      = 210

Next, we compute the value of [Q₁ - 1.5 IQR]:

And then we compute [Q₃ + 1.5 IQR]:

There are no values below [Q₁ - 1.5 IQR]. However, one value exceeds [Q₃ + 1.5 IQR].

X = 810 > [Q₃ + 1.5 IQR] = 705

Consequently, the outlier identified within the dataset is $810.

(b)

A distribution is classified as positively skewed or right-skewed when the majority of the data congregates on the lower end of the spectrum.

The stem plot indicates that most of the data values are concentrated on the left side, confirming that the distribution is indeed right skewed.