Three irrational numbers are given below. Select the option that correctly plots the approximate value of each me on live where

A geometric sequence models the bounce heights:
Use the formula
A (subscript n) = Ar(n-1)
a = the first-term value
n = the index of the term you want (for the fourth peak, n = 4) 
r = common ratio, found by dividing the second term by the first
Here r = 18/27 = 2/3 because 27×(2/3) = 18, and similarly 18×(2/3) = 12
For the fourth peak n = 4
Compute: 4th term = 27(2/3)^(4-1) = 8
Therefore the height at the fourth peak is 8

Answer: There exists a distinction between rote counting and rational counting. Rote counting requires memorizing sequences of numbers, whereas rational counting informs children about "how many items there are." For children to engage in rational counting, they must exhibit one-to-one correspondence.

Answer: Acquire a systematic sample by selecting every 20th vehicle that travels past (irrespective of the lane or direction).

Step-by-step explanation:

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}

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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.

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Answer:

5.83

Step-by-step explanation:

To determine the mean:

10(0.1) + 15(0.2) + 20(0.2) + 25(0.4) + 30(0.1)

u = 21

To find the standard deviation:

= 5.83