Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 18: Problem 710

The arithmetic mean of 7 consecutive integers starting with a is \(m\) then the arithmetic mean of 11 consecutive integers starting with \(a+2\) is (a) \(2 \mathrm{a}\) (b) \(2 \mathrm{~m}\) (c) \(a+4\) (d) \(m+4\)

Short Answer

Expert verified
The arithmetic mean of the second set of 11 consecutive integers in terms of the mean of the first set is (d) \(m+4\).

Step by step solution

01

Find the mean of the first set of integers

To find the arithmetic mean of the 7 consecutive integers starting with a, we need to add all the integers and then divide the sum by 7. The integers are: a, a+1, a+2, a+3, a+4, a+5, and a+6. Mean of 7 integers, m = \(\frac{a+(a+1)+(a+2)+(a+3)+(a+4)+(a+5)+(a+6)}{7}\)
02

Simplify the mean for the first set

Now, we can simplify the mean expression by adding all the terms and dividing by 7: m = \(\frac{7a+21}{7}\) Divide both numerator and denominator by 7: m = \(a+3\) Now we have the arithmetic mean of the first set of consecutive integers in terms of a.
03

Find the mean of the second set of integers

Now we need to find the arithmetic mean of the 11 consecutive integers starting with a+2. The integers are: a+2, a+3, a+4, a+5, a+6, a+7, a+8, a+9, a+10, a+11, and a+12. Mean of 11 integers = \(\frac{(a+2)+(a+3)+(a+4)+(a+5)+(a+6)+(a+7)+(a+8)+(a+9)+(a+10)+(a+11)+(a+12)}{11}\)
04

Simplify the mean for the second set

Next, we simplify the expression by adding all the terms and dividing by 11: Mean of 11 integers = \(\frac{11a+77}{11}\) Divide both numerator and denominator by 11: Mean of 11 integers = \(a+7\) Now we have the arithmetic mean of the second set of consecutive integers in terms of a.
05

Compare the means and choose the correct option

We know the mean of the first set of 7 integers is m = \(a+3\), and the mean of the second set of 11 integers is \(a+7\). The question asks for the arithmetic mean of the second set in terms of m or a. Comparing the mean of the second set with the first set (m = \(a+3\)), we notice that the mean of the second set is 4 more than the first set's mean: Mean of 11 integers = m + 4 This matches option (d). So the correct answer is (d) \(m+4\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A box contains 4 Red and 3 White balls. Every time one ball is drawn randomly and is placed back along with two more balls of opposite colour. What is the probability that among first 3 trials in first two one get red colour ball and in 3 rd he get white ball. (a) \((8 / 27)\) (b) \((16 / 99)\) (c) \((16 / 231)\) (d) none

If the mean and standard deviation of \(\mathrm{x}\) is \(\mathrm{b}\) and a respectively then the standard deviation of \([(x-b) / a]\) is (a) 1 (b) \((\mathrm{a} / \mathrm{b})\) (c) (b/a) (d) \(a b\)

If \(\mathrm{n}=100, \underline{\mathrm{x}}=3\) and \(\mathrm{S}^{2}=11\) then \(\left[\left(\sum \mathrm{xi}^{2}\right) /\left(\sum \mathrm{xi}\right)\right]\) is (a) 10 (b) 22 (c) \(6.66\) (d) 2000

The sum of the squares of deviation for 10 observations taken from their mean 30 is 90 . The coefficient of variation is (a) \(20 \%\) (b) \(10 \%\) (c) \(11 \%\) (d) \(12 \%\)

A \(2 \times 2\) determinant is such that all its entries are \(1,-1\) or \(0 .\) If one determinant is chosen from such determinants what is the probability that the value of the determinant is zero? (a) \((3 / 8)\) (b) \((11 / 27)\) (c) \((2 / 9)\) (d) \((25 / 81)\)
See all solutions

Recommended explanations on English Textbooks

Rhetorical Analysis Essay

Read Explanation

Rhetoric

Read Explanation

Language Acquisition

Read Explanation

Multiple Choice Questions

Read Explanation

Research and Composition

Read Explanation

History of English Language

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free