Statistics

Oh, what a lovely question! You see, when we have 8 numbers and we want to choose 4 of them, we can use a special formula called combinations. The number of combinations we can make is calculated using the formula 8! / (4! * (8-4)!), which simplifies to 70 combinations. Isn't that just delightful? Just imagine all the beautiful possibilities waiting to be created!

To calculate the probability of getting only one head and an even number on the tetrahedral die, we need to consider the total number of possible outcomes. There are 2 outcomes for the coin toss (HH, HT), and 2 outcomes for the tetrahedral die (2, 4). Therefore, there are a total of 2 x 2 = 4 possible outcomes. The favorable outcome for getting only one head and an even number is (HT, 2) or (HT, 4), which is 2 out of the 4 possible outcomes. Thus, the probability is 2/4 = 0.5 or 50%.

Product means the answer to a multiplication.

e.g. 2 x 3 = 6 ( 6 is the product).

For Addition ; Sum, Total,

Subtraction ; Minus, Difference

Multiplication ; as given

Division ' Quotient.

3 + 3 + 3 + 3 + 3 = 15 total possible outcomes.

You can 'prove' this by laying out a table of possibles where a user might tick the result of each game.....

Match....1....2....3....4....5

Win......._...._...._...._...._

Lose......_...._...._...._...._

Draw....._...._...._...._...._

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The only three-digit prime number that can be formed using the digits 4, 1, and 0 is 401. This number is prime because it is not divisible by any other number except 1 and itself.

The only three-digit number that fits the criteria of being a square number and having a product of its digits equal to two is 128. This is because 128 is a square number (11^2 = 121, 12^2 = 144) and the product of its digits (1 x 2 x 8) equals 16, which is not equal to two. Therefore, there is no three-digit number that meets all the given conditions.

There are 238 - 1 = 237 numbers between 1 and 238. To find the number of digits, we need to consider the range of numbers from 1 to 9 (1-digit numbers), 10 to 99 (2-digit numbers), and 100 to 238 (3-digit numbers). There are 9 one-digit numbers, 90 two-digit numbers, and 139 three-digit numbers between 1 and 238, totaling 9 + 90 + 139 = 238 digits.

Statistics and logic are analytical tools used by political science.

To calculate the number of four-digit numbers that can be made using the digits 1, 4, 5, and 9 without repetition, we use the permutation formula. Since there are 4 digits to choose from for the first digit, 3 for the second, 2 for the third, and 1 for the fourth, the total number of permutations is 4 x 3 x 2 x 1 = 24. Therefore, there are 24 different four-digit numbers that can be formed using the digits 1, 4, 5, and 9 without repetition.

To find numbers with a mean of 7, we need to consider the sum of the numbers and the total count of numbers. If we have two numbers, they must add up to 14 to have a mean of 7. For three numbers, their sum must be 21. In general, any set of numbers that sum up to 7 times the count of numbers will have a mean of 7.

Six

* * * * *

No, that is the number of PERMUTATIONS (not combinations).

With 3 numbers, the number of combinations, including the null combination, is 23 = 8.

With the three numbers 1,2 and 3, these would be

{None of them}, {1), {2), {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}.

The calendar for the year 1987 will repeat exactly in the year 2018. This is because the Gregorian calendar repeats every 28 years. The calendar for any specific year will repeat in the year that is a multiple of 28 years later.

There are various ways to organize data. Chronological or data management via a measure of time that runs either forward or backward is often used. Value and size, in which items are measured based on either largest of smallest size comparisons is another method of data organization. Deductive organization states the conclusions with clearly stated information.

social are always used when we are going to talk about society ,these values are always like "to say thanx , welcome, help others whereas personal values are always related with your good principle towards life like as "to be puntual ,to maintain discipline etc.

Well, darling, 843 rounded to the nearest thousand is still 1000. It's not rocket science, honey. Just bump up that 843 to the next thousand like it's nobody's business.

right angled triangle

To calculate the number of 4-number combinations using the numbers 1, 2, 3, 4, and 5 without repetition, you can use the formula for permutations. Since order matters in a combination, you would use the formula for permutations, which is nPr = n! / (n - r)!. In this case, you would have 5 choices for the first number, 4 choices for the second number, 3 choices for the third number, and 2 choices for the fourth number. Therefore, the total number of 4-number combinations would be 5P4 = 5! / (5-4)! = 5 x 4 x 3 x 2 = 120 combinations.

Statistics is the name of the subject. It is the general definition which deals with the collection, presentation and interpretation of data. On the other hand, statistic is a test used to test a hypothesis. It is commonly applied to sample cases.

A statistic is a description of some measure, such as your height, weight, or age. Such measures may be collected in large numbers to be analyzed statistically to determine some characteristic of a population. For example, the collection of a population's ages make up a data base that may be analyzed by statistical methods to determine the proportion of the population that will retire and start drawing pension funds during the next decade.

Well, honey, it doesn't take a rocket scientist to figure this one out. The two numbers you're looking for are 20 and 21. Add those bad boys together and you've got yourself a grand total of 41. Math can be a real piece of cake sometimes, don't you think?

Statistics is crucial in Nigeria for various reasons. It helps in monitoring and evaluating the country's economic growth, informing policy decisions, and assessing the effectiveness of government programs. Additionally, statistics play a vital role in identifying trends, patterns, and disparities within the population, which is essential for targeted interventions and resource allocation. Overall, accurate and reliable statistical data is fundamental for evidence-based decision-making and sustainable development in Nigeria.

IELTS stands for the International English Language Testing System, a globally recognized test designed to assess the English language proficiency of non-native speakers. It evaluates listening, reading, writing, and speaking skills, and is essential for those seeking to study, work, or migrate to English-speaking countries. The test has two formats: Academic, for students applying to universities, and General Training, for work or migration purposes.

Success in IELTS requires strong command of English and familiarity with the test format. Many individuals opt for an IELTS Preparation Course to enhance their skills, practice with mock tests, and receive expert guidance. These courses help improve vocabulary, grammar, and test strategies, ensuring better performance. Scores are graded on a 9-band scale, with higher bands indicating greater proficiency. Preparing well for IELTS is crucial as it plays a key role in opening opportunities for global education and career advancement.

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Phone No: 09216008300

Oh, dude, like, yeah, Friday the 13th does have some nudity. It's like a staple of those classic slasher films, you know? So, if you're looking for a little skin with your scares, you're in luck. But hey, don't get too excited, it's all in the name of horror movie tradition, right?

Let us first define a combination and a permutation. Say we have 5 letters and we want to pick two at a time. First let's say the order matters and we allow repetition.

There are 5 letters and we have 5 choices for the first letter and then 5 choices for the second. The total choices is 5x5 or 52. In general if we have n objects and we are picking r of them and allowing for repetition, then there are nr ways to do that. Remember that the order matters here.

If we don't allow for repetitions, then we have n! divided by (n-r)! where ! means factorial. For example, 3! means simply 3x2x1 and 5! means 5x4x3x2x1.

So in the case of the 5 letters taken two at a time where order matters we have

5!/((5-2)! which is 5x4x3x2x1 divided by 3x2x1. Cancel out the 3x2x1 and you are left with

5x4 or 20.

There is no need to remember this formula, just remember there are 5 choices for the first letter, but whatever you pick for the first one, you can't use that one again so there are 4 choices for the second. The total is given by the multiplication rule and we have 5x4=20.

In the case of the entire alphabet with 26 letters, if we allow repetitions, we have 262 permutations. There are 26 choices for the first letter and 26 for the second.

But if we don't allow repetitions, there are 26x25 permutations.

Now combination is the same thing, but order does not matter. So AB is the same as BA.

Let's just worry about either lower case or upper case letters first. Forget about things like Ab or cB for now. Only combinations we are looking at are like ab or AB, but NOT aB.

First let's talk about combinations where we don't allow repeats. This is much easier to understand. I will leave combinations with repetitions for last. So AB is OK, but not AA.

When we figures out how many permutations there were without repeats, we found that if we are taking r objects taken from n of them, we had n!/(n-r)!. Now since ab is the same as ba, for example, if we know how many permutations we have of two letters taken from the alphabet, we could just divide that by 2. This is because ever time we have something like dc and CD, they are the same as a combination since order no longer matters.

So in general we have n!/(n-r)! now divide by r! since if you have r items the number of ways to arrange all r of them is r!. For example, say you pick 5 letters out of the alphabet instead of 2, then there would be 26!/(26-5)! permutations, but each one of the 5 letter permutations can be arranged in 5! ways. For example, 5 choices for the first letter, 4 for the second, 3 for the third etc, which is 5!.

So the final formula for finding how many combinations of r items you have if you take the r of them from a total of n items ( such as 5 letters from 26) is n!/(n-r)!r!.

This is usually written nCr.

Now combinations with repetitions is the toughest one to see. This problem did not say if you have repeats or not. So the answer to the problem using ONLY lower or ONLY upper case an allowing no repeats is 26!/24!2!=325. If you allow upper and lower case letters, think of the the upper and lower case as totally separate things. So your alphabet now has

52 objects and the solutions becomes 52x51/2=1326

Now let's say we allow repetitions of the letters. So AA is ok for example. So we are looking at combinations so order does not matter and we allow repetitions.

Here is one common way to see this that is taught in many stats classes.

The method is commonly called bars and stars. Say we have n objects. Lets say 5.

Write down 5-1 or 4 vertical bars. In the case of n, draw n-1 vertical bars.

The 4 vertical bars look like this: | | | | you can see how they create 5 spaces from left to write. I will label the space in case you don't see it. 1| 2 |3 | 4 |5 where 1 is the first space etc. Now put stars in each space. The number or stars can be anything from 0 ( no stars) to r where you are picking r objects from n. BUT, the total number of stars is r. So for example is I pick 5 letters out of 26 and allow repetitions and only worry about combinations, then I have 25 bars and 5 stars. If I put all 5 stars in the first space, I am done. If I put 2 in the first space, I have 3 more to put anywhere I want.

Here is an example you can see: Example: n=3, r=5,

* | * | *** -> 1 object of type 1, 1 of type 2, 3 of type 3

| * | **** -> zero objects of type 1, 1 object of type 2, 4 objects of type 3.

Now, the number of combinations using bars and stars is equal to the number of rows of n-1 bars and r stars. The total number of bars and stars is n+r, then subtract 1 since we have n-1 bars. So we have n+r-1 items (bars and stars combined) and we are selecting the locations of the r stars out of the n+r-1 locations. The order does not matter. Therefore, the number of such rows is C(n+r-1,r), and this is also the number of combinations with repetitions allowed. It might be hard to remember unless you think of n-1 bars plus r stars is n+r-1 and you are finding where to place the r stars, but it does not matter which space they go in.

So in the case of 2 letter combinations taken from 26 letters and allowing repetitions, we have C(26+2-1,2) or C(27,2) This is 27x26/2=351 The general formula for this comes from just plugging the n+r-1 chose r into the formula for combinations.

This is just considering upper or lower case letters. Now how many combinations are there if you use both? I will leave that one for you!

In this question, the issue of repititions is now mentioned and upper or lower case is not noted either. In math we need precision, so the questions does not have a unique answer without that information.

In the context of a research study, money can be considered an independent variable if it is being manipulated or controlled to observe its effects on other variables. For example, in a study on consumer behavior, researchers may manipulate the amount of money given to participants to see how it influences their purchasing decisions. However, money can also be considered a dependent variable if it is being measured or observed to understand how other factors, such as income level or economic policies, impact its distribution or circulation in an economy.