if x < y < z and all three are consecutive non-zero integers, then which of the following must be a positive odd integer?

Answers

Answer 1

Option (A) x+1 is a positive odd integer.

Given that, x < y < z and all three are consecutive non-zero integers.Let the first number be x, then the other two consecutive non-zero integers will be (x+1) and (x+2).To find out the positive odd integer among these, let us take each of them and verify if they are positive odd integers.∴ x+1 is odd, x+2 is even∴ x+1 is the only positive odd integer out of the three.

Learn more about Non-zero integers

brainly.com/question/2032387

#SPJ11


Related Questions

What is the Smallest Positive Integer with at least 8 odd Factors and at least 16 even Factors?

Answers

Therefore, the smallest positive integer with at least 8 odd factors and at least 16 even factors is N = 1800.

what is Combination?

In mathematics, combination is a way to count the number of possible selections of k objects from a set of n distinct objects, without regard to the order in which they are selected.

The number of combinations of k objects from a set of n objects is denoted by [tex]nCk[/tex] or [tex]C(n,k),[/tex] and is given by the formula:

[tex]nCk = n! / (k! *(n-k)!)[/tex]

where n! denotes the factorial of n, i.e., the product of all positive integers up to n.

by the question.

Now, let's consider the parity (evenness or oddness) of the factors of N. A factor of N is odd if and only if it has an odd number of factors of each odd prime factor of N. Similarly, a factor of N is even if and only if it has an even number of factors of each odd prime factor of N. Therefore, the condition that N has at least 8 odd factors and at least 16 even factors can be expressed as:

[tex](a_{1} +1) * (a_{2} +1) * ... * (an+1) = 8 * 2^{16}[/tex]

Let's consider the factor 2 separately. Since N has at least 16 even factors, it must have at least 16 factors of 2. Therefore, we have a_i >= 4 for at least one prime factor p_i=2. Let's assume without loss of generality that p[tex]1=2[/tex] and [tex]a1 > =4.[/tex]

Now, let's consider the remaining prime factors of N. Since N has at least 8 odd factors, it must have at least 8 factors that are not divisible by 2. Therefore, the product (a2+1) * ... * (an+1) must be at least 8. Let's assume without loss of generality that n>=2 (i.e., N has at least three distinct prime factors).

Since a_i >= 4 for i=1, we have:

[tex]N > = 2^4 * p2 * p3 > = 2^4 * 3 * 5 = 240[/tex]

Let's now try to find the smallest such N. To minimize N, we want to make the product (a2+1) * ... * (an+1) as small as possible. Since 8 = 2 * 2 * 2, we can try to distribute the factors 2, 2, 2 among the factors (a2+1), (a3+1), (a4+1) in such a way that their product is minimized. The only possibility is:

[tex](a2+1) = 2^2, (a3+1) = 2^1, (a4+1) = 2^1[/tex]

This gives us:

[tex]N = 2^4 * 3^2 * 5^2 = 1800[/tex]

To learn more about distribute:

https://brainly.com/question/29062095

#SPJ

a normal distribution of exam scores has a standard deviation of 8. a score that is 12 points above the mean would have a z-score of: a score that is 20 points below the mean would have a z-score of:

Answers

The standard deviation of a normal distribution of exam scores is 8. A score that is 12 points above the mean would have a z-score of 1.5, and a score that is 20 points below the mean would have a z-score of -2.5.

What is the z-score?

The z-score can be calculated by dividing the difference between a data value and the mean of the data set by the standard deviation of the data set.

The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8.

z = (x−μ)/σ = (x−μ)/σ = (12−0)/8 = 1.5

The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8 is 1.5.

The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8.

z = {x-μ}/{σ}  = {-20-0}/{8}  = −2.5

The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8 is -2.5.

Learn more about Z-score here:

https://brainly.com/question/15016913

#SPJ11

we assume there is sometimes sunny days and sometimes rainy days, and on day 1, which we're going to call d1, the probability of sunny is 0.9. and then let's assume that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance. so, what are the chances that d2 is sunny?

Answers

Probability of D2 being sunny = 0.78.

On day 1, which is called D1, the probability of sunny is 0.9. It is also given that a sunny day follows a sunny day with 0.8 chance, and a sunny day follows a rainy day with 0.6 chance.

Therefore, we need to find the chances that D2 is sunny.

There are two possibilities for D2: either it can be a sunny day, or it can be a rainy day.

Now, Let us find the probability of D2 being sunny.

We have the following possible cases for D2.

D1 = Sunny; D2 = Sunny

D1 = Sunny; D2 = Rainy

D1 = Rainy; D2 = Sunny

D1 = Rainy; D2 = Rainy

The probability of D1 being sunny is 0.9.

When a sunny day follows a sunny day, the probability is 0.8.

When a sunny day follows a rainy day, the probability is 0.6.

Therefore, the probability of D2 being sunny is given by the formula:

Probability of D2 being sunny = (0.9 × 0.8) + (0.1 × 0.6) = 0.72 + 0.06 = 0.78.

Therefore, the probability that D2 is sunny are 0.78 or 78%.

To learn more about probability refer :

https://brainly.com/question/13957582

#SPJ11

Other Questions
y=x^2+7x-3 complete the square to re-write the quadratic function in vertex form.pls help students conducting research observe the rate of an enzyme-catalyzed reaction under various conditions with a fixed amount of enzyme in each sample. when will increasing the substrate concentration likely result in the greatest increase in the reaction rate? Which of the following is NOT one of the options Gorgias invites his audience to consider in discussing the "bad reputation" of Helen? -her noble birth - fortune -persuasion - r*pe - her own free will Uri paid a landscaping company to mow his lawn. The company charged $74 for the service plus 5% tax. After tax, Uri also included a 10% tip with his payment. How much did he pay in all? Chang, the founder of a multinational corporation, believes that his business should mainly focus on the benefit of those people who own its stock. In this scenario, he most likely follows _______, a model of business management.a. Stakeholders modelb. Shareholders primacyc. Customer value Immigration vs emigration in the American Rocky Mountains chart How was the Montgomery Bus Boycott an influential part of the Civil Rights Movement?ResponsesIt brought the leadership of Thurgood Marshall to national attention.It led to the desegregation of interstate transportation.It demonstrated the effectiveness of nonviolent protest.It resulted in the integration of the citys schools. The Kingston County Basketball Conference (KCBC) is an amateur basketball association. Each city in the county has one team that represents it. Each team has a maximum of twelve players and a minimum of nine players. Each team also has up to three coaches (offensive, defensive, and PT coaches.) Each team plays two games (home and visitor) against each of the other teams during the season.a. Draw the ER diagram.b. Create a relational model based on the ER diagram. Un smbolo es _________ de una idea. La semilla la representacin el argumento el opuesto 2. La lupa en esta obra representa _________. La guerra la ceguera la opresin la creacin artstica 3. Las aves en la obra representan _________. La libertad la muerte el miedo la sabidura 4. El personaje de la obra parece _________ mundo exterior. Interesado en el inspirado por el aislado del creado por el 5. La mquina de pinturas puede reflejar la influencia de _________. Los artistas de la vanguardia la guerra Benjamn Peret su padre During the Meiji Restoration, fought to as fast as possible and as a result changed its significantly. mrs. grundy believes that boarding schools provide the best education because after attending such a school, she found herself well prepared for college. the fallacy in her thinking is Which evidence suggests that some of the first life on earth was prokaryotic bacteria? in a peptide bond, which parts of the two amino acids are joined together? Solve please geometry, solve for x which of the following pharmacologic features is shared by all of the medications that have received fda approval for maintenance treatment of opioid use disorder?A. FDA approved medications for maintenance or detoxificationB. Medications in schedules III, IV, or VC. Buprenorphine or Buprenorphine/naloxoneD. Methadone the muscle name literally meaning below the tongue is blank.target 1 of 5 the muscle connecting the hyoid bone to the styloid process of the temporal bone is the blank.target 2 of 5 the shorter of the muscles over the fibula is the blank.target 3 of 5 the muscle extending from the arm to the lateral forearm is the blank.target 4 of 5 the hamstring that becomes tendinous midway along its length is the on what part of the face was a female moai tatooed a market shortage results from an excess of quantity over quantity at a given price. (insert one word in each blank.) which idea of evolution is supported by the existence of vestigial structures? Help me. Do you think people have a responsibility to learn how to use new technologies? Why or why not?