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Lesson Posted on 27 May Learn Mathematical Reasoning
What is Pi? How can you understand in simple or in layman terms?
Richa Singh Rathour
Postgraduated in Statistics and Computer Science. I am passionate about teaching and have been offering...
Story of Pi
In math, "pi" (often written as the Greek letter π) is a number that represents the ratio of a circle's circumference (the distance around the circle) to its diameter (the distance across the circle through its center). No matter how big or small the circle is, this ratio is always the same and approximately equal to 3.14159.
To put it simply, if you take a string and wrap it once around a circle, then lay that string out straight, it would be a little more than three times the length of the circle's diameter. This "little more" is the extra decimal places of pi. Pi is an irrational number, meaning it goes on forever without repeating.
Now, what is irrational number? Will post in second lesson.
In mean while try the above and let me know.
read lessLesson Posted on 27 May Learn Unit-V: Mathematical Reasoning
Richa Singh Rathour
Postgraduated in Statistics and Computer Science. I am passionate about teaching and have been offering...
Rational Numbers?
In simple English, "rational" means something that is logical or makes sense. In mathematics, rational numbers are related to the concept of fractions. Let's travel back and review the lesson on fractions, specifically proper and improper fractions.
Proper fractions are fractions where the numerator (the top number) is smaller than the denominator (the bottom number). For example, 3/4
is a proper fraction.
Improper fractions are fractions where the numerator is larger than or equal to the denominator. For example, 5/3
is an improper fraction.
Both proper and improper fractions are members of the rational number family. Rational numbers are numbers that can be expressed in the form a/b
, where
𝑎 and 𝑏 are integers, and 𝑏 is not zero.
Now, what happens if the denominator becomes zero? What kind of fraction is that? Is it making any sense? No, it doesn't. Dividing by zero is undefined and does not produce a valid number. Therefore, rational numbers must have a denominator that is not zero. When you divide rational numbers, you get definite decimal places that either terminate or repeat.
In summary, rational numbers are fractions where the denominator is never zero, and their decimal expansions are predictable—they either end or follow a repeating pattern.
read lessAnswered on 28 Apr Learn Sequence and Series
Deepika Agrawal
"Balancing minds, one ledger at a time." "Counting on expertise to balance your knowledge."
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Affordable fees Flexible Timings Choose between 1-1 and Group class Verified Tutors Answered on 15 Apr Learn Mathematical Reasoning
Nazia Khanum
As an experienced tutor registered on UrbanPro, I'm here to help you understand the contrapositive of the given if-then statements.
(a) If a triangle is equilateral, then it is isosceles.
The contrapositive of this statement would be: If a triangle is not isosceles, then it is not equilateral.
(b) If a number is divisible by 9, then it is divisible by 3.
The contrapositive of this statement would be: If a number is not divisible by 3, then it is not divisible by 9.
Remember, in a contrapositive statement, both the hypothesis and the conclusion are negated. This technique is useful in logic and mathematics to prove statements indirectly. If you have any further questions or need clarification, feel free to ask!
Answered on 15 Apr Learn Statistics
Nazia Khanum
As a seasoned tutor registered on UrbanPro, I'm here to guide you through this statistical hiccup. Let's address this query with precision.
Firstly, let me commend your commitment to mastering statistical concepts. Now, let's dive into the solution.
The mean (xˉxˉ) of a set of observations is the sum of all values divided by the number of observations. The standard deviation (σσ) is a measure of the dispersion or spread of a set of values from its mean.
Given:
To correct the mean, we need to remove the mistaken observation and replace it with the correct value (40). Since there are 100 observations in total, the contribution of the mistaken observation to the mean is 50100=0.510050=0.5. So, we subtract 0.5 from the original mean and add the correct value (40):
Corrected mean (xˉcorrectedxˉcorrected) = xˉ−0.5+40xˉ−0.5+40
To correct the standard deviation, we need to recalculate it based on the corrected mean and observations. However, the standard deviation formula involves the square of the differences between each observation and the mean, so correcting one observation affects all the others. We must consider this correction while recalculating the standard deviation.
Therefore, it's not straightforward to calculate the corrected standard deviation manually. Instead, we can use statistical software or calculators to find the corrected standard deviation.
In summary, to find the correct mean, we subtract the contribution of the mistaken observation and add the correct value. To find the corrected standard deviation, we need to recalculate it using statistical tools due to the interconnected nature of the standard deviation formula.
If you need further assistance or guidance on statistical concepts or any other subject, feel free to reach out. Remember, UrbanPro is your ally in your academic journey, providing the best online coaching tuition.
Answered on 28 Apr Learn Probability
Deepika Agrawal
"Balancing minds, one ledger at a time." "Counting on expertise to balance your knowledge."
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Affordable fees Flexible Timings Choose between 1-1 and Group class Verified Tutors Answered on 26 Apr Learn Probability
Deepika Agrawal
"Balancing minds, one ledger at a time." "Counting on expertise to balance your knowledge."
In the given experiment, a die is rolled.
Let, E be the event “the die shows 4”.So set E contains the element 4.
E={ 4 }
Let, F be the event that die shows even number”. So set F contains all the even numbers from 1 to 6.
F={ 2,4,6 }
Two events, A and B are mutually exclusive if, A∩B=ϕ.
E∩F={ 4 }∩{ 2,4,6 } =4 .
It can be observed that E∩F≠ϕ.
Thus, E and F are not mutually exclusive.
read lessAnswered on 26 Apr Learn Probability
Deepika Agrawal
"Balancing minds, one ledger at a time." "Counting on expertise to balance your knowledge."
Answered on 28 Apr Learn Permutations and Combinations
Deepika Agrawal
"Balancing minds, one ledger at a time." "Counting on expertise to balance your knowledge."
Take Class 12 Tuition from the Best Tutors
Affordable fees Flexible Timings Choose between 1-1 and Group class Verified Tutors Answered on 28 Apr Learn Permutations and Combinations
Deepika Agrawal
"Balancing minds, one ledger at a time." "Counting on expertise to balance your knowledge."
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