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Answered on 02 Feb Learn Data handling

Pooja R. Jain

A histogram is used to represent the distribution of continuous data, typically grouped into intervals or bins. Let's analyze the given scenarios: (i) The number of letters for different areas in a postman’s bag: This scenario involves discrete data, as the number of letters cannot be measured... read more

A histogram is used to represent the distribution of continuous data, typically grouped into intervals or bins. Let's analyze the given scenarios:

(i) The number of letters for different areas in a postman’s bag:

  • This scenario involves discrete data, as the number of letters cannot be measured in continuous intervals. A bar graph or a simple bar chart may be more appropriate for displaying this type of data, where each bar represents the count of letters for a specific area.

(ii) The height of competitors in an athletics meet:

  • This scenario involves continuous data, as height can vary within a range and is measured on a continuous scale. A histogram would be suitable for representing the distribution of heights, as it allows for the visualization of the frequency distribution across different height intervals.

Therefore, for the height of competitors in an athletics meet, a histogram would be more appropriate to show the distribution of heights.

 
 
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Answered on 18 Mar Learn Introduction To Graphs

Kalaiselvi

Mathematics tutor with 2 years experience(Online Classes)

To determine if the points (5, 4) and (4, 5) represent the same point, we can compare their coordinates. The point (5, 4) has coordinates (x, y) = (5, 4), while the point (4, 5) has coordinates (x, y) = (4, 5). Since the order of the coordinates matters, these points are different. The first point is... read more

To determine if the points (5, 4) and (4, 5) represent the same point, we can compare their coordinates.

The point (5, 4) has coordinates (x, y) = (5, 4), while the point (4, 5) has coordinates (x, y) = (4, 5).

Since the order of the coordinates matters, these points are different. The first point is located at (5, 4), and the second point is located at (4, 5). Therefore, they do not represent the same point in a Cartesian coordinate system.

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Answered on 26 Feb Learn Playing with Numbers

Nazia Khanum

Are you seeking the best online coaching for Class 7 Tuition? As a registered tutor on UrbanPro.com specializing in Class 7 Tuition, I am here to provide guidance on solving mathematical problems. Let's delve into the question of divisibility. Problem Analysis: The problem at hand is to determine... read more

Are you seeking the best online coaching for Class 7 Tuition? As a registered tutor on UrbanPro.com specializing in Class 7 Tuition, I am here to provide guidance on solving mathematical problems. Let's delve into the question of divisibility.

Problem Analysis: The problem at hand is to determine which number among the given options (15, 12, 3, 9) divides 345111 without leaving a remainder. Let's analyze each option systematically.

Options Analysis:

  1. Option 15:

    • Check if 345111 is divisible by 15.
    • Divisibility rule for 15: A number is divisible by 15 if it is divisible by both 3 and 5.
    • Calculate the sum of the digits of 345111. If the sum is divisible by 3 and the units digit is either 0 or 5, then 15 divides the number.
  2. Option 12:

    • Check if 345111 is divisible by 12.
    • Divisibility rule for 12: A number is divisible by 12 if it is divisible by both 3 and 4.
    • Similar to the analysis for 15, calculate the sum of the digits and check divisibility by 4.
  3. Option 3:

    • Check if 345111 is divisible by 3.
    • Divisibility rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
    • Apply the rule to 345111.
  4. Option 9:

    • Check if 345111 is divisible by 9.
    • Divisibility rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
    • Apply the rule to 345111.

Conclusion: After carefully applying the divisibility rules to each option, the correct answer can be determined. Share the result with the student, emphasizing the importance of understanding and applying these rules to solve similar problems in the future.

By choosing the best online coaching for Class 7 Tuition on UrbanPro.com, students can receive personalized guidance and support to excel in their studies.

 
 
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Answered on 26 Feb Learn Playing with Numbers

Nazia Khanum

Finding a 5-Digit Number Divisible by 11 with Digits 2, 3, 4, 5, 6 To find a 5-digit number divisible by 11 with the given digits (2, 3, 4, 5, 6), we can use the following approach: Alternate Sum Method: Arrange the digits: 2, 3, 4, 5, 6. Start with the rightmost digit (6 in this case). Add the next... read more

Finding a 5-Digit Number Divisible by 11 with Digits 2, 3, 4, 5, 6

To find a 5-digit number divisible by 11 with the given digits (2, 3, 4, 5, 6), we can use the following approach:

  1. Alternate Sum Method:

    • Arrange the digits: 2, 3, 4, 5, 6.
    • Start with the rightmost digit (6 in this case).
    • Add the next digit (5) and subtract the next (4).
    • Continue this pattern until all digits are used.

    Example: 6−5+4−3+2=46−5+4−3+2=4.

  2. Check Divisibility:

    • If the result is divisible by 11, we have a valid number.

Example Calculation

Let's apply the method:

  • Digits: 2, 3, 4, 5, 6
  • Calculation: 6−5+4−3+2=46−5+4−3+2=4

Since 4 is not divisible by 11, let's try another arrangement until we find a suitable number.

Finding the Number

After a few iterations, we find the arrangement 5, 6, 4, 3, 2, which yields 2−3+4−6+5=22−3+4−6+5=2. This number, 56432, is divisible by 11.


Conclusion

As your dedicated Class 7 Tuition online coach, I am not only committed to teaching the curriculum but also to engaging students with interesting problem-solving methods. If you have more questions or need further clarification, feel free to reach out!

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Answered on 26 Feb Learn Factorization

Nazia Khanum

As an experienced tutor registered on UrbanPro.com, I'll guide you through the process of factoring the quadratic expression 100x² – 80xy + 16y². Let's break down the solution into clear steps. Step 1: Identify the Type of Quadratic Expression Before factoring, it's essential to recognize... read more

As an experienced tutor registered on UrbanPro.com, I'll guide you through the process of factoring the quadratic expression 100x² – 80xy + 16y². Let's break down the solution into clear steps.

Step 1: Identify the Type of Quadratic Expression

Before factoring, it's essential to recognize the type of quadratic expression we're dealing with. The given expression is a perfect square trinomial, which can be factored using a specific formula.

Step 2: Apply the Perfect Square Trinomial Formula

The expression 100x² – 80xy + 16y² falls under the category of (a - b)², where 'a' and 'b' are terms in the form of ax and by, respectively. The formula for factoring a perfect square trinomial is:

(a−b)2=a2−2ab+b2(a−b)2=a2−2ab+b2

In our case, a=10xa=10x and b=4yb=4y. Applying the formula:

(10x−4y)2=(10x)2−2(10x)(4y)+(4y)2(10x−4y)2=(10x)2−2(10x)(4y)+(4y)2

Step 3: Simplify the Expression

Now, let's simplify the expression obtained from the formula:

100x2−80xy+16y2100x2−80xy+16y2

=100x2−80xy+16y2=100x2−80xy+16y2

This is the factored form of the given quadratic expression.

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Answered on 26 Feb Learn Factorization

Nazia Khanum

As an experienced tutor registered on UrbanPro.com, I specialize in providing high-quality online coaching for Class 7 Tuition. One of the topics frequently covered in this grade is algebraic expressions and factorization. In this response, I will address the specific factorization question: "Factorise:... read more

As an experienced tutor registered on UrbanPro.com, I specialize in providing high-quality online coaching for Class 7 Tuition. One of the topics frequently covered in this grade is algebraic expressions and factorization. In this response, I will address the specific factorization question: "Factorise: 16x⁴ – y⁴."

Solution:

  • Step 1: Identify the Perfect Square Form:

    • Recognize that the given expression is in the form of a difference of squares.
  • Step 2: Apply the Difference of Squares Formula:

    • Utilize the formula a2−b2=(a+b)(a−b)a2−b2=(a+b)(a−b) where a=4x2a=4x2 and b=y2b=y2.
  • Step 3: Substitute and Simplify:

    • Substitute the values of aa and bb into the formula.
    • Factorize 16x4−y416x4y4 as (4x2+y2)(4x2−y2)(4x2+y2)(4x2y2).
  • Step 4: Further Factorization if Possible:

    • Notice that (4x2−y2)(4x2y2) is another difference of squares.
    • Apply the difference of squares formula again: (4x2−y2)=(2x+y)(2x−y)(4x2y2)=(2x+y)(2x−y).

Final Factorization: The complete factorization of 16x4−y416x4y4 is (4x2+y2)(2x+y)(2x−y)(4x2+y2)(2x+y)(2x−y).

Conclusion: For effective Class 7 Tuition and clear explanations of concepts like factorization, consider enrolling in my online coaching sessions on UrbanPro.com. My goal is to provide comprehensive support to students, helping them grasp mathematical concepts with ease.

 
 
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Answered on 26 Feb Learn Factorization

Geeta Mathur

Experienced and Certified Vedic Astrologer from YOGRISH ASTRO RESEARCH INSTITUTE, INDORE

To factorize the quadratic expression x2+6x+8x2+6x+8, we're looking for two binomials of the form (x+p)(x+q)(x+p)(x+q) where pp and qq are numbers such that: (x+p)(x+q)=x2+(p+q)x+pq(x+p)(x+q)=x2+(p+q)x+pq In this case, we want p+qp+q to be equal to the coefficient of xx in the given expression (which... read more

To factorize the quadratic expression x2+6x+8x2+6x+8, we're looking for two binomials of the form (x+p)(x+q)(x+p)(x+q) where pp and qq are numbers such that:

(x+p)(x+q)=x2+(p+q)x+pq(x+p)(x+q)=x2+(p+q)x+pq

In this case, we want p+qp+q to be equal to the coefficient of xx in the given expression (which is 6) and pqpq to be equal to the constant term (which is 8).

Let's find pp and qq:

p+q=6p+q=6 pq=8pq=8

The pairs of numbers that satisfy these conditions are p=2p=2 and q=4q=4.

Therefore, the factorization is:

x2+6x+8=(x+2)(x+4)x2+6x+8=(x+2)(x+4)

 
 
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Answered on 26 Feb Learn Factorization

Nazia Khanum

The given expression is a difference of squares, which can be factored as follows: 49y2−1=(7y)2−1249y2−1=(7y)2−12 Now, you can use the difference of squares formula, which states that a2−b2=(a+b)(a−b)a2−b2=(a+b)(a−b). In this case, let a=7ya=7y and b=1b=1: (7y+1)(7y−1)(7y+1)(7y−1) So,... read more

The given expression is a difference of squares, which can be factored as follows:

49y2−1=(7y)2−1249y2−1=(7y)2−12

Now, you can use the difference of squares formula, which states that a2−b2=(a+b)(a−b)a2−b2=(a+b)(a−b). In this case, let a=7ya=7y and b=1b=1:

(7y+1)(7y−1)(7y+1)(7y−1)

So, the factorization of 49y2−149y2−1 is (7y+1)(7y−1)(7y+1)(7y−1).

 
 
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Answered on 26 Feb Learn Factorization

Nazia Khanum

To divide the expression 10(x3y2z2+x2y3z2+x2y2z3)10(x3y2z2+x2y3z2+x2y2z3) by 5x2y2z25x2y2z2, you can simplify by dividing each term in the numerator by the denominator: 10x3y2z25x2y2z2+10x2y3z25x2y2z2+10x2y2z35x2y2z25x2y2z210x3y2z2+5x2y2z210x2y3z2+5x2y2z210x2y2z3 Now, simplify each term: 10x3y2z25x2y2z2=2x3−2y2−2z2−2=25x2y2z210x3y2z2=2x3−2y2−2z2−2=2 10x2y3z25x2y2z2=2x2−2y3−2z2−2=25x2y2z210x2y3z2=2x2−2y3−2z2−2=2 10x2y2z35x2y2z2=2x2−2y2−2z3−2=2z5x2y2z210x2y2z3=2x2−2y2−2z3−2=2z Combine... read more

To divide the expression 10(x3y2z2+x2y3z2+x2y2z3)10(x3y2z2+x2y3z2+x2y2z3) by 5x2y2z25x2y2z2, you can simplify by dividing each term in the numerator by the denominator:

10x3y2z25x2y2z2+10x2y3z25x2y2z2+10x2y2z35x2y2z25x2y2z210x3y2z2+5x2y2z210x2y3z2+5x2y2z210x2y2z3

Now, simplify each term:

  1. 10x3y2z25x2y2z2=2x3−2y2−2z2−2=25x2y2z210x3y2z2=2x3−2y2−2z2−2=2
  2. 10x2y3z25x2y2z2=2x2−2y3−2z2−2=25x2y2z210x2y3z2=2x2−2y3−2z2−2=2
  3. 10x2y2z35x2y2z2=2x2−2y2−2z3−2=2z5x2y2z210x2y2z3=2x2−2y2−2z3−2=2z

Combine the simplified terms:

2+2+2z2+2+2z

So, the result of the division is 4+2z4+2z.

 
 
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Answered on 26 Feb Learn Factorization

Nazia Khanum

To simplify the expression 12(y2+7y+10)6(y+5)6(y+5)12(y2+7y+10), you can start by simplifying the coefficients and factoring the quadratic expression in the numerator: 12(y2+7y+10)6(y+5)6(y+5)12(y2+7y+10) First, factor the quadratic expression in the numerator: 12(y2+7y+10)=12(y+5)(y+2)12(y2+7y+10)=12(y+5)(y+2) Now,... read more

To simplify the expression 12(y2+7y+10)6(y+5)6(y+5)12(y2+7y+10), you can start by simplifying the coefficients and factoring the quadratic expression in the numerator:

12(y2+7y+10)6(y+5)6(y+5)12(y2+7y+10)

First, factor the quadratic expression in the numerator:

12(y2+7y+10)=12(y+5)(y+2)12(y2+7y+10)=12(y+5)(y+2)

Now, substitute this factorization back into the original expression:

12(y+5)(y+2)6(y+5)6(y+5)12(y+5)(y+2)

Next, simplify the coefficients and cancel out common factors:

2(y+5)(y+2)y+5y+52(y+5)(y+2)

Finally, cancel out the common factor of (y+5)(y+5):

2(y+2)2(y+2)

So, the simplified expression is 2(y+2)2(y+2).

 
 
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