Examples for secondary school students - page 63 of 232
Number of problems found: 4622
- Centre of the hypotenuse
The interior angles of the triangle ABC, alpha, beta, and gamma are in a ratio of 1:2:3. The longest side of the AB triangle is 30 cm long. Calculate the perimeter of the triangle CBS if S is the center of the side AB. - Parallelogram diagonals
Find the area of a parallelogram if the diagonals u1 = 15 cm and u2 = 12 cm and the angle formed by them is 30 degrees. - Frequency of oscillation
A weight of 1 kg was suspended from the spring, and the spring was extended by 1.5 cm. Determine the frequency of the natural oscillation of the resulting oscillator. - Dynamometer
What is the volume of a body that stretches a dynamometer in air, on which a force of 2.5 N suspends it, and if it is immersed in alcohol with a density of 800 kg/m³, does it tension the dynamometer with a force of 1.3 N? - Function axis intersection
Where is the intersection of the function y = -3x + 5 with the coordinate axes x and y? (where they are on the x-axis and y-axis) - The profit
The profit made by a business in 2018 was triple that made in 2019. The profit in 2020 was R 3 million less than the profit in 2019. If the total profit in these three years was R 67 million, what was the profit made in 2020? - MIT 1869
You know the length of parts 9 and 16 of the hypotenuse, at which a right triangle's hypotenuse is divided by a height. The task is to find the lengths of the sides of the triangle and the length of line x. This assignment was part of the Massachusetts In - A professor
A professor in a typing class found out that the average performance of an expert typist is 85 words per minute. A random sample of 16 students took the typing test, and we obtained an average speed of 62 words per minute with a standard deviation of 8. C - Unemployment rate
Over the last 16 years, the country's unemployment rate has changed according to the following frequency table: years of unemployment: 2 5 2 3 3 1 unemployment rate: 0.5 1 1.5 2 2.5 3 in % (percent). Determine the two-sided confidence interval for the var - Intersection of functions
Draw a graph of the function given by the equation y = -2x +3, find its intersections with the coordinate axes, and complete the unknown coordinates A [3;? ], B [?; 8]. - Chi square
A phone battery manufacturer claims that his battery lives are approximately normally distributed with a standard deviation equal to 0.9 years. Suppose a random sample of 10 of these batteries has a standard deviation of 1.2 years. Do you think that the s - Confidence Interval The average grade of 50 senior students in a statistics class is 85, with a standard deviation of 10.2. In comparison, 60 senior students got an average of 80 with a standard deviation of 8.9. Can the difference in the mean grade be attributed to chance,
- Performance comparing
A standardized test was administered to thousands of students with a mean score of 85 and a standard deviation of 8. A random sample of 50 students was given the same test and showed an average score of 83.20. Is there evidence that this group performs le - Parallelogram - two sides
The parallelogram has the sides a = 25.3 b = 13.8, and the angle closed by the sides is a = 72°. Calculate the area of the parallelogram. - Steering wheel force
The steering wheel has a diameter of 40 cm. It is acted upon by a pair of forces with a torque of 27 Newton-meters. How much force does it exert on each side of the steering wheel? - Poisson distribution - daisies
The meadow behind FLD was divided into 100 equally large parts. Subsequently, it was found that there were no daisies in ten of these parts. Estimate the total number of daisies in the meadow. Assume that daisies are randomly distributed in the meadow. - Three sigma rule
The height of trees in a given stand is known to be a quantity with a normal probability distribution with a mean value of 15 m and a variance of 5 m². Determine the interval in which there will be tree heights in such a stand with a probability of 90% - Seedlings
The meadow was divided into 30 equally large parts, and then how many seedlings were in each part was calculated. It was found that there were no seedlings in six parts. Five parts contained one seedling, twelve parts two seedlings, and seven parts three - Corresponding Suppose that the country has had the following inflation rates over the past 14 years: 6.0; 6.7; 10.4; 11.9; 7.2;3.5; 8.4; 7.5; 2.8; 4.3; 1.9; 3.9; 0.9; 0.7. Use the χ² goodness-of-fit test to determine whether the random variable ξ corresponding to this
- The surface
The surface of the cylinder is 1570 cm²; its height is 15 cm. Find the volume and radius of the base.
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