1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Zinaida [17]
3 years ago
11

Prove that for every pair of integers m and n, if n − m is even, then n 2 − m is also even. (You may freely use the fact that th

e sum of two odd numbers is even, that the sum of an odd number and an even number is odd, the product of an odd and an even is even, etc.)
Mathematics
1 answer:
Romashka [77]3 years ago
7 0

Answer with Step-by-step explanation:

We are given that  n and m are two integers

We have to prove that if n-m is even , then n^2-m is also even.

We know that sum of two odd numbers is even.Sum of an odd number and even number is odd.

Product of an odd number and even number is even.

Case 1.Suppose m and n are both even n=4 , m=2

4-2=2

(4)^2-2=14 =Even

Case 2.Suppose m odd and n odd

n=9,m=5

9-5=4

(9)^2-5=76=Even

Hence, proved.

You might be interested in
The distribution of IQ scores can be modeled by a normal distribution with mean 100 and standard deviation 15.
evablogger [386]

Answer:

4.4% of the population with IQ between 120 and 125.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 100

Standard Deviation, σ = 15

We are given that the distribution of IQ scores is a bell shaped distribution that is a normal distribution.

a) Let X be a person's IQ score.

Then, density functions for IQ scores is given by:

P(x) = \displaystyle\frac{1}{2\sqrt{2\pi}}e^{-\frac{z^2}{2}}\\\\\text{where,}\\\\z = \frac{x-\mu}{\sigma}\\\\P(x) = \displaystyle\frac{1}{2\sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}\\\\P(x) = \displaystyle\frac{1}{2\sqrt{2\pi}}e^{-\frac{(x-100)^2}{450}}

b) P(population with IQ between 120 and 125.)

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

P(120 \leq x \leq 125) = P(\displaystyle\frac{120 - 100}{15} \leq z \leq \displaystyle\frac{125-100}{15}) = P(1.33 \leq z \leq 1.66)\\\\= P(z \leq 1.66) - P(z < 1.33)\\= 0.952 - 0.908 = 0.044 = 4.4\%

P(120 \leq x \leq 125) = 4.4\%

6 0
3 years ago
A yogurt costs 45 pence how many yogurts can be bought for 5 pounds
Oliga [24]
11.
for a total of 4.95
you would have 5 pence remaining.
6 0
3 years ago
Read 2 more answers
Define table represents a group frequency discretion of the number of hours spent on the computer per week for 49 student. What
Scilla [17]

Observe the given data distribution table carefully.

The 5th class interval is given as,

14.0-17.4

The upper limit (UL) and lower limit (LL) of this interval are,

\begin{gathered} UL=17.4 \\ LL=14.0 \end{gathered}

Thus, the upper-class limit of this 5th class is 17.4.

6 0
1 year ago
Kelli spent 18 hours per week practicing for a gymnastics meet.She practiced for 35 weeks.How many hours did she practice in all
adell [148]
She practiced 630 hours in all because you multiply 18x35
5 0
3 years ago
Read 2 more answers
The following events took place at a manufacturing company for the current year: (1) Purchased $115,000 in direct materials. (2)
Elden [556K]

The question was not written properly. Here is the appropriate form of question:

The following events took place at a manufacturing company for the current year:

(1) Purchased $115,000 in direct materials.

(2) Incurred labor costs as follows: (a) direct, $76,000 and (b) indirect, $33,600.

(3) Other manufacturing overhead was $127,000, excluding indirect labor.

(4) Transferred 75% of the materials to the manufacturing assembly line.

(5) Completed 60% of the Work-in-Process during the year.

(6) Sold 80% of the completed goods.

(7) There were no beginning inventories.

1- What is the company's Cost of Goods Sold?

Options:

a. $193,710

b. $154,968

c. $322,850

d. $258,280

Answer:

1- b. $154,968

Step-by-step explanation:

1- Cost of goods sold (COGS) is the is the expense of securing or assembling the items that an organization sells during a period, so the main costs remembered for the measure are those that are directly attached to the creation of the items, including the expense of work (labor cost), materials, and assembling overhead.

0.6*[$0 + 0.75*($115,000) + $76,000 + ($127,000 + $33,600)] <em>(because completed 60% of the Work-in-Process during the year)</em>

= $193,710

80% of $193,710 <em>(because sold 80% of the completed goods)</em>

0.8*$193,710

= $154,968

5 0
3 years ago
Other questions:
  • it takes Sarah 50 minutes to walk to her friend's house 1 3/4 miles away. What is her walking pace in miles per hour?
    5·1 answer
  • Six times the sum of a number and twelve is forty
    6·1 answer
  • True or false -3&gt;7(1)-10
    5·2 answers
  • Find the value of n<br> (2n + 4)º
    15·1 answer
  • Evaluate 2 - (-4) + 3 + (-6) - (-2)
    13·1 answer
  • Which of these shapes have the same perimeter
    8·1 answer
  • A company that makes​ hair-care products had 7,000 people try a new shampoo. Of the 7,000 people, 28 had a mild allergic reactio
    12·1 answer
  • It costs $8 for admission to the Park City Ice Arena. In addition, renting skates costs $1 per hour. Write an equation that show
    9·1 answer
  • Can i please get help now
    6·1 answer
  • Write the expression two-cubed times seven as a numerical expression.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!