5. A cyclist leaves point A and rides 20 km [N] then makes a turn and then travels 25 km [E] and arrives at point B. What is the cyclist's average velocity if the entire trip from A to B takes 6 hours? Show all of your work

Being the owner of an ice cream company Jane wants to know about theexistence of any relation between customers’ ages and the amount of ice cream (gr.) bought byeach customer. In this regard, she uses past one year’s data on age and daily sales and selectrandomly chosen 100 agents. Jane separates selected number of agents into two parts according totheir ages i.e., those who are aged below 18 years and those above 18 years and wonders primarilywhether the customers who are aged above 18 years purchase more amount of ice cream or notusing simple probability theory. Please explain whether the classical approach to probability isappropriate to reach a correct probability value, if not, explain the alternative approach to achieveit.

What is the square root of 1023? (Hints: 10 is an integer number. Integer numbers are exact, they don't have any uncertainty. The result however is going to be a real number. Computers approximate real numbers using floating point numbers. Floating point numbers have a given number of significant figures or digits. LON-CAPA typically expects 3, 4 or 5 digits. 2 or 1 is not enough, 6 or more is too many. Very large or very small numbers are expressed in scientific or exponential notation like the number above. Numbers in scientific notation are entered to computer software - like LON- CAPA as 1.23E15 or 1.23e15, for example; and 1.23E-15 or 1.23e-15, if the exponent is negative. If both the number and the exponent are negative, then you type -1.23E- 15 or -1.23e-15. On calculators the button is usually labelled as 'EE', but 'E' or 'EEX' or 'Exp' are also possible.)

Find the ratio of the volume of the right circular cylinder of maximum volume to that of the circumscribing cone. Answer: 4/9

To get the density, then what is the volume?

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(a) Number i Units (b) Number i Units (c) (d) (e) > > > >

Let µ be the average of the random variable x. Then the quantities (xi − µ) are the deviations of x from its average. Show that the average of these deviations is zero. Hint: Remember that the sum of all the pi must equal 1.