# Examples for college students

- Derivation

Exists a function whose derivation is the same function? - Circular sector

I have a circular sector with a length 15 cm with an unknown central angle. It is inscribed by a circle with radius 5 cm. What is the central angle alpha in the circular sector? - Sales

From statistics of sales goods, item A buy 54% of people and item B buys 58% of people. What is the probability that from 3 people buy 2 item A and 1 item B? - Balls

We have n identical balls (numbered 1-n) is selected without replacement. Determine 1) The probability that at least one tensile strength number coincides with the number of balls? 2) Determine the mean and variance of the number of balls, which coincides. - TV fail

The TV has after 10,000 hours average 35 failures. Determine the probability of TV failure after 500 hours of operation. - Nuts, girl and boys

Milena collected fallen nuts and called a bunch of boys let them share. She took a condition: the first boy takes one nut and tenth of the rest, the second takes 2 nuts and tenth new rest, the third takes 3 nuts and tenth new rest and so on. Thus managed. - Fall

The body was thrown vertically upward at speed v_{0}= 46 m/s. Body height versus time describe equation ?. What is the maximum height body reach? - Goat and circles

What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which g - Statue

On the pedestal high 2.3 m is statue 3.3 m high. At what distance from the statue must observer stand to see it in maximum viewing angle? Distance from the eye of the observer from the ground is 1.5 m. - Goat

Meadow is a circle with radius r = 22 m. How long must a rope to tie a goat to the pin on the perimeter of the meadow to allow goat eat half of meadow? - Sails

We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail? - Paper box

Hard rectangular paper has dimensions of 60 cm and 28 cm. The corners are cut off equal squares and the residue was bent to form an open box. How long must be side of the squares to be the largest volume of the box? - SD - mean

Mean is 10 and standard deviation is 3.5. If the data set contains 40 data values, approximately how many of the data values will fall within the range 6.5 to 13.5? - Cone

Into rotating cone with dimensions r = 18 cm and h = 17 cm incribe cylinder with maximum volume so that the cylinder axis is perpendicular to the axis of the cone. Determine the dimensions of the cylinder. - Unknown number

I think number. If subtract from the twelfth square the ninth square I get a number 27 times greater than the intended number. What is this unknown number? - Distribution function

X 2 3 4 P 0.35 0.35 0.3 The data in this table do I calculate the distribution function F(x) and then probability p(2.5 - Area and two angles

Calculate the size of all sides and internal angles of a triangle ABC, if it is given by area S = 501.9; and two internal angles α = 15°28' and β = 45°. - Carpet

The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make rectangular cut of roll that piece of carpet will be longest possible and it fit into the room. How long is a piece of carpet? Note .: carpet will not be parallel with the diag - Jar

From the cylinder shaped jar after tilting spilled water so that the bottom of the jar reaches the water level accurately into half of the base. Height of jar h = 5 cm and a jar diameter D is 10 cm. How to calculate how much water remains in the jar? - Height of the arc - formula

Calculate the height of the arc if the length of the arc is 60 and chord length 39. Does exist a formula to solve this?

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