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The median of the first prime ten prime numbers is
The first ten prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. To find the median, arrange the numbers in ascending order (already done above). Since there are 10 numbers (an even count), the median is the average of the two middle numbers. The two middle numbers are the 5th and 6th numbers inRead more
The first ten prime numbers are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
To find the median, arrange the numbers in ascending order (already done above). Since there are 10 numbers (an even count), the median is the average of the two middle numbers. The two middle numbers are the 5th and 6th numbers in the list:
5th number = 11,
6th number = 13.
The median is calculated as:
Median = (11 + 13) / 2,
Median = 24 / 2,
Median = 12.
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Class mark and Class size of the class intervals are 25 and 10 respectively then the class interval is
The class mark and class size are given as 25 and 10, respectively. The class mark is the midpoint of the class interval, and the class size is the difference between the upper and lower limits of the class interval. Let the class interval be represented as: Lower Limit = L, Upper Limit = U. The claRead more
The class mark and class size are given as 25 and 10, respectively. The class mark is the midpoint of the class interval, and the class size is the difference between the upper and lower limits of the class interval.
Let the class interval be represented as:
Lower Limit = L, Upper Limit = U.
The class mark is calculated as:
Class Mark = (L + U) / 2.
Substitute the given class mark (25):
25 = (L + U) / 2.
Multiply through by 2:
L + U = 50. — (1)
The class size is the difference between the upper and lower limits:
Class Size = U – L.
Substitute the given class size (10):
10 = U – L. — (2)
Now solve the system of equations (1) and (2):
From (2): U = L + 10.
Substitute U = L + 10 into (1):
L + (L + 10) = 50,
2L + 10 = 50,
2L = 40,
L = 20.
Substitute L = 20 into U = L + 10:
U = 20 + 10 = 30.
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The slant height of a cone is 26 cm and base diameter is 20 cm. Its height is
Explanation: The height (h) of a cone can be calculated using the Pythagorean theorem, as the slant height (l), radius (r), and height form a right triangle. The relationship is given by: l² = r² + h², where: - l is the slant height, - r is the radius of the base, - h is the height of the cone. FromRead more
Explanation:
The height (h) of a cone can be calculated using the Pythagorean theorem, as the slant height (l), radius (r), and height form a right triangle. The relationship is given by:
l² = r² + h²,
where:
– l is the slant height,
– r is the radius of the base,
– h is the height of the cone.
From the problem:
– The slant height (l) is 26 cm,
– The diameter of the base is 20 cm, so the radius (r) is:
r = Diameter / 2 = 20 / 2 = 10 cm.
Substitute the values of l = 26 cm and r = 10 cm into the formula:
l² = r² + h².
Rearrange to solve for h²:
h² = l² – r².
Substitute the values:
h² = 26² – 10²,
h² = 676 – 100,
h² = 576.
Take the square root of both sides:
h = √576,
h = 24 cm.
Thus, the height of the cone is 24 cm, which corresponds to option a) 24.
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The height of a cone is 16 cm and base radius is 12 cm. Its slant height is
Explanation: The slant height (l) of a cone can be calculated using the Pythagorean theorem, as the slant height forms the hypotenuse of a right triangle where: - The height (h) of the cone is one leg, - The radius (r) of the base is the other leg. The formula for the slant height is: l = √(r² + h²)Read more
Explanation:
The slant height (l) of a cone can be calculated using the Pythagorean theorem, as the slant height forms the hypotenuse of a right triangle where:
– The height (h) of the cone is one leg,
– The radius (r) of the base is the other leg.
The formula for the slant height is:
l = √(r² + h²).
From the problem:
– The height (h) of the cone is 16 cm,
– The radius (r) of the base is 12 cm.
Substitute the values of r = 12 cm and h = 16 cm into the formula:
l = √(12² + 16²).
Simplify step by step:
l = √(144 + 256),
l = √400,
l = 20 cm.
Thus, the slant height of the cone is 20 cm, which corresponds to option c) 20.
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The curved surface area of a right circular cone of slant height 10 cm and base radius 7 cm is
Explanation: The curved surface area (CSA) of a right circular cone is given by the formula: CSA = πrl, where: - r is the radius of the base, - l is the slant height of the cone. From the problem: - The radius (r) of the base is 7 cm, - The slant height (l) is 10 cm. Substitute the values of r = 7 cRead more
Explanation:
The curved surface area (CSA) of a right circular cone is given by the formula:
CSA = πrl,
where:
– r is the radius of the base,
– l is the slant height of the cone.
From the problem:
– The radius (r) of the base is 7 cm,
– The slant height (l) is 10 cm.
Substitute the values of r = 7 cm and l = 10 cm into the formula:
CSA = πrl.
Using π ≈ 22/7 for calculation:
CSA = (22/7) × 7 × 10.
Simplify step by step:
CSA = 22 × 10,
CSA = 220 cm².
Thus, the curved surface area of the cone is 220 cm², which corresponds to option b) 220.
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