# Examples for college students

- TV fail

The TV has after 10,000 hours average 35 failures. Determine the probability of TV failure after 500 hours of operation. - 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 - 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? - Sphere and cone

Within the sphere of radius G = 26 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone? - 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? - 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

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? - 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. - 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 - Euclidean distance

Calculate the Euclidean distance between shops A, B and C, where: A 56 0.05 B 55 0.09 C 51 0.07 Wherein the first figure is the weight in grams of bread and second figure is price in USD. - Derivation

Exists a function whose derivation is the same function? - 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. - 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°. - Sails

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

Hot air balloon ascends 25 meters up for a minute after launch. Every minute ascends 75 percent of the height which climbed in the previous minute. a) how many meters ascends six minutes after takeoff? b) what is the overall height 10 minutes after launch - 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. - 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? - 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? - 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.

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