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show that a norm on a vector space X is a sublinear functional on X
Pythagorean theorem Question

A hapless motorist is trying to find his friend's house, which is located 2.50 miles west of the intersection of State Street and First Avenue. He sets out from the intersection, and drives the same number of kilometers due south instead. How far in kilometers is he from his intended destination?
Table 1: Score
27 37 30 28 39 25 45 28
32 28 26 38 31 30 47 41

Based on Table 1, organize the data into a frequency distribution by taking 25 as the lowest boundary and 5 as the class width.

Construct a “less than or equal” ogive for the frequency distribution established in (a) and then approximate the number of candidates who scores below 35.
A tire manufacture dilutes a 25% sulfuric acid solution with a 10% sulfuric acid solution in order to produce 150 liters of 18% sulfuric acid solution. How much of the 10% and how much of the 25%must be used?
Suppose that a child's grade point average is directly proportional to that child's hours of outdoor play. Last semester, nine-year-old Jamie played outdoors an average of 20 hours per week, and a great point average was 3.25. So far this semester, she has only managed to play outdoors 12 hours/week. What grade point average for this produce?
Find the fourier series of f(x) of the given interval: f(x)= 1/2 x belongs to (-1,0)
-1/2 x belongs to (0,1)
Is the function above even or odd?
Please help differentiate this:

The height of a certain species 't' years after it was planted is given by
H=20ln(3t +2) +30cm
a) how tall was the shrub when it was planted
b) how long will it take for the shrub to reach a height of 1 metre
c)At what rate is the shrubs height changing
i) 3 years after being planted
ii) 10 years after being planted
How do I prove this statement using properties of numbers: If a < 0, b < 0, then √ab ≤ −(a+b)/2?
Find the slope of tangent to the curve y= √ (3x-8) at the point where x = 11