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The table given below shows the ages of patients being treated in a hospital. Construct a cumulative frequency distribution table for the same:
| Age | No. of patients |
| 10 - 20 | 90 |
| 20 - 30 | 50 |
| 30 - 40 | 60 |
| 40 - 50 | 80 |
| 50 - 60 | 50 |
| 60 - 70 | 30 |
Concept: undefined >> undefined
The electricity bills of 45 houses in a particular locality are given below. Tabulate the given data and present it as a cumulative frequency table with one of the classes being 300 - 450:
784, 567, 890, 231, 150, 458, 356, 762, 386, 824, 525, 663, 724, 841, 315, 641, 156, 715, 156, 317, 814, 547, 879, 456, 463, 664, 175, 584, 515, 487, 871, 511, 522, 454, 247, 819, 412, 326, 445, 311, 321, 545, 344, 266, 351.
Concept: undefined >> undefined
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From the cumulative frequency distribution given below, construct a frequency distribution table:
| Marks | c.f. |
| Less than 10 | 10 |
| Less than 20 | 18 |
| Less than 30 | 32 |
| Less than 40 | 45 |
| Less than 50 | 50 |
Concept: undefined >> undefined
Construct a frequency distribution table from the given cumulative frequency distribution showing the weights of 750 students in a school:
| Weight (in kg) | c.f. |
| More Than 25 | 750 |
| More Than 30 | 640 |
| More Than 35 | 615 |
| More Than 40 | 485 |
| More Than 45 | 370 |
| More Than 50 | 220 |
| More Than 55 | 124 |
| More Than 60 | 49 |
| More Than 65 | 24 |
| More Than 70 | 0 |
a. Find the number of students whose weight lie in the interval 40-45
b. Find the interval which has the most number of students.
Concept: undefined >> undefined
Prove that the area of a rhombus is equal to half the rectangle contained by its diagonals.
Concept: undefined >> undefined
Simplify:
`(sqrt(x^2 + y^2) - y)/(x - sqrt(x^2 - y^2)) ÷ (sqrt(x^2 - y^2) + x)/(sqrt(x^2 + y^2) + y)`
Concept: undefined >> undefined
Evaluate, correct to one place of decimal, the expression `5/(sqrt20 - sqrt10)`, if `sqrt5` = 2.2 and `sqrt10` = 3.2.
Concept: undefined >> undefined
If x = `sqrt3 - sqrt2`, find the value of:
(i) `x + 1/x`
(ii) `x^2 + 1/x^2`
(iii) `x^3 + 1/x^3`
(iv) `x^3 + 1/x^3 - 3(x^2 + 1/x^2) + x + 1/x`
Concept: undefined >> undefined
Show that Negative of an irrational number is irrational.
Concept: undefined >> undefined
Draw a line segment of length `sqrt5` cm.
Concept: undefined >> undefined
Draw a line segment of length `sqrt3` cm.
Concept: undefined >> undefined
Draw a line segment of length `sqrt8` cm.
Concept: undefined >> undefined
Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
Concept: undefined >> undefined
Show that: `x^3 + 1/x^3 = 52`, if x = 2 + `sqrt3`
Concept: undefined >> undefined
Show that: `x^2 + 1/x^2 = 34,` if x = 3 + `2sqrt2`
Concept: undefined >> undefined
Show that: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`
Concept: undefined >> undefined
Using the following figure, show that BD = `sqrtx`.
Concept: undefined >> undefined
If 3( log 5 - log 3 ) - ( log 5 - 2 log 6 ) = 2 - log x, find x.
Concept: undefined >> undefined
If x = (100)a , y = (10000)b and z = (10)c , find log`(10sqrty)/( x^2z^3)` in terms of a, b and c.
Concept: undefined >> undefined
Given 3log x + `1/2`log y = 2, express y in term of x.
Concept: undefined >> undefined
