6. It is now 10:29 a.m., but when the bell rings at 10:30 a.m. Suzette will be late for French class for the third time this wee

a) The sequence is geometric.

b) The subsequent term is 486

c) The rule is:

The 20th term will be: a_{20}=6973568802

Step-by-step explanation:

The series 6, 18, 54, 162, ... depicts the number of push-ups Kendall performed each week, starting from her initial week of exercise.

Part a) Is this sequence arithmetic or geometric?

An arithmetic sequence has a constant difference between consecutive terms.

In the given series 6, 18, 54, 162,

18-6 = 12

54-18= 36

The differences are not constant, thus it isn’t arithmetic.

A geometric sequence maintains a constant ratio between consecutive terms.

In this series 6, 18, 54, 162,

18/6 = 3

54/18 = 3

162/54 = 3

The ratios remain constant; therefore, the sequence is geometric.

The sequence in question is geometric.

Part b) How can you determine the next number in the series?

The next number can be calculated using the following formula:

where a_n= nth term

a= first term

r= common ratio

The next number represents the 5th term of the sequence.

To find the 5th term:

Thus, the next term in the sequence is 486

Part c) What is the rule for determining the 20th week? Calculate the 20th week.

The rule for determining the 20th week is:

Here n=20

Calculating the 20th week

Answer:

The inequality used to calculate the number of articles written by Mustafa for his school paper is .

Mustafa has authored over 8 articles.

Step-by-step explanation:

Details given:

Total combined number of articles = 22

Let 'x' represent the articles written by Mustafa.

Now stated:

Heloise has authored as many articles as Mustafa.

Heloise's articles number =

Gia has penned as many articles as Mustafa.

Gia's article count =

It follows that;

The total of articles from Mustafa, Heloise, and Gia must be more than or equal to the total combined articles.

Expressing it in an equation gives us;

Thus the inequality for finding the number of articles penned by Mustafa for his school project is .

Now simplifying the inequality:

By taking the LCM to standardize the denominator, we get:

Thus, Mustafa has written in excess of 8 articles.

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.

Answer: 23.89%

Detailed solution:

The empirical rule indicates that about 95% of data points lie within two standard deviations from the mean.

Given: The GMAT scores follow a normal distribution with the mean near .

Additionally, 95% of classmates scored between 400 and 680.

Applying the empirical rule, 95% of scores are within ,

which corresponds to  (1)

and  (2)

Subtracting (1) from (2) yields:

Let x symbolize the scores of students.

z-score formula:

For x = 490, calculate

Then, the p-value equals:

This means that 23.89% of his peers scored below his score.