Examples for college students - page 2 of 5
Remember: Solve each problem thoughtfully and make sure to show your complete solution for every question.Number of problems found: 87
- Probability
In an election, 2,400,000 voters out of a total of 6,000,000 voted for party Z. Three voters are selected at random. Let the random variable ξ = {number of voters for party Z among the three selected}. Determine: a) the probability distribution, the distr - Applicant success
Of the 4,500 applicants, 2/9 were successful in the university entrance exams. How many applicants were successful? - Venn diagram
First-year university students choose a foreign language. Of 120 enrolled students, 75 chose English, 65 chose German, and 40 chose both English and German. Using a Venn diagram, determine: - how many students chose only English, - how many students chose - Convex lens
The convex lens consists of two spherical segments (dimensions given in mm). Calculate its weight if the density of the glass is 2.5 g/cm³. Dimensions: 60 mm in length and width of the upper part 5 mm, the width of the lower part 8 mm - Customer satisfaction probability Let the random variable ξ represent the number of satisfied customers. The probability of a satisfied customer for each of the four customers is 7/10. Specify: a) probability distribution, distribution function F(x) and P(-0.5 < ξ < 3.1) b) variance
- From MAN statistics A study determined how many points from homework assignments in statistics were received by randomly selected students from the MAN programme and the THK programme. The results were: MAN x: 17, 17, 15, 21, 29, 30, 16, 18, 15, 25, 16 THK y: 15, 18, 16, 22,
- Shopping malls
The chain of department stores plans to invest up to 24,000 euros in television advertising. Ads will place all commercials on a television station where the broadcast of a 30-second spot costs EUR 1,000 and is watched by 14,000 potential customers. Durin - Circle line probability
A rectangular grid consists of two mutually perpendicular systems of parallel lines with a distance of 2. We throw a circle with a diameter of 1 on this plane. Calculate the probability that this circle: a) overlaps one of the straight lines; b) do any of - Four equation system
Solve a system of equations with four unknowns: 2a + 2b-c + d = 4 4a + 3b-c + 2d = 6 8a + 5b-3c + 4d = 12 3a + 3b-2c + 2d = 6 - The university
At a certain university, 25% of students are in the business faculty. Of the students in the business faculty, 66% are males. However, only 52% of all students at the university are male. a. What is the probability that a student selected at random in the - Elections 3
From a randomised sample of 500 voters, 140 expressed that they consider the protection of the environment to be the most important task of society, and therefore they will vote for the political party which has in its programme the protection of the envi - Ball bearings One bearing is selected from the shipment of ball bearings. It is known from previous deliveries that the inner bearing radius can be considered a normal N distribution (µ = 0.400, σ2 = 25.10^−6). Calculate the probability that the selected radius will ex
- Linear system solving
Solve the linear system of equations by Gaussian elimination: 3x1 −2x2 −5x3 + x4 = 3 2x1 −3x2 + x3 + 5x4 = −3 x1 + 2x2 −4x4 = −3 x1 - x2 −4x3 + 9x4 = 22 - Counting hairs
Find out if two people in Bratislava have the same number of hairs on their heads. Instructions. Bratislava has about 420,000 inhabitants, and a person has less than 300,000 hairs on his head. - Molecule arrangement probability
What is the probability that ten molecules will arrange within the brown motion to be one molecule in the lower half and nine molecules in the upper half in one vessel? - Eq2 2
Solve the following equation with quadratic members and rational function: (x²+1)/(x-4) + (x²-1)/(x+3) = 23 - Probability of intersection
Three students have a probability of 0.7,0.5, and 0.4 to graduate from university, respectively. What is the probability that at least one of them will be graduated? - Cone Volume Surface Height
In the rotating cone = 100π S rotating cone = 90π v =? r =? - Flu probability
In the monitored group of people, 8% are ill with the flu. One hundred people from this group were examined. What is the probability that at most 5 of them will be sick with the flu? (round to 3 decimal places) - Drug liver elimination
The patient was given the drug, and the measured liver concentration was t hours after administration: c (t) = -0.025 t² + 1.8t. When will the liver product be eliminated entirely?
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