Table of Contents

## Examples of test problem solving. It is known that England produces 12 vacuum **cleaners** and 8 televisions per hour, Spain produces 8 **vacuum cleaners** and 6 televisions per hour presentation

2 It is **known** that England produces 12 vacuum cleaners and 8 televisions per hour, Spain produces 8 **vacuum cleaners** and 6 televisions per hour. Which of the following relative for vacuum cleaners is possible with free and mutually beneficial trade between these countries: A. 1 **vacuum** cleaner = 1 TV. 1 vacuum cleaner = 2 TV sets C. 1 **vacuum** cleaner = 0.7 TV D. 1 vacuum cleaner = 1.6 televisions Relative price of a vacuum cleaner in England = absolute labor costs for vacuum **cleaners** (1/12)/ absolute labor costs for televisions (1/8) = 2/3 = 0.67 Relative price of a vacuum cleaner in Spain = absolute labor costs for vacuum cleaners (1/8)/ absolute labor costs for televisions (1/6) = 6/8 = 0.75 It is **known** that the world market relative price is between the relative of trading partners, therefore answer C

3 Country A produces 50 computers and 20 refrigerators in one hour; country B produces 100 computers and 25 refrigerators. What would be the total maximum output of computers (K) and refrigerators (X) in one hour in both countries under conditions of free trade and complete specialization according to the principle of comparative advantage: А. K = 150, X = 45 IN. K = 50, X = 20 S. K = 100, X = 25 D. K = 100, x = 20 Country A produces 50 computers and 20 refrigerators in one hour; country B produces 100 computers and 25 refrigerators. What would be the total maximum output of computers (K) and refrigerators (X) in one hour in both countries under free trade and full specialization, according to the principle of comparative advantage: А. K = 150, X = 45 IN. K = 50, X = 20 D. K = 100, X = 25 D. K = 100, X = 20 Let’s define comparative advantage in computers: Relative price in country A: 20/50 = 0,4 Relative price in country B: 25/100 = 0,25 Relative price in country B: 25/100 = 0,25 So, country B has comparative advantage in producing computers, country A. refrigerators. So country C produces only computers 100, country A only fridges 20. Answer D

4 The domestic demand and supply functions are: Qd = P and Qs = P. It is **known** that the world price has settled at Pw = 2. Determine the value of this country’s exports: A. 60 dena. ED. В. 100 dy. units. С. 80 den. units D. 40 dens. eu. At a price of Pw=2, the volume of demand is equal to: Qd = 60 At a price of Pw=2, the volume of supply is equal to: Qs = 100 Export volume in physical terms: = 40 Export volume in monetary terms: 402 = 80 den. unit. Answer C

5 The domestic demand and supply functions have the form: Qd = P and Qs =.100P. It is **known** that the world price is set at Pw = 250. Under free trade conditions, how will the volume of imports of a good into the country change if the demand for it decreases by 50%? А. will decrease by 50% B. will remain unchanged C. to decrease by 150 units. D. decrease by 300 units. Initial situation: Qd = 300, Qs = 150, imports = Qd. Qs = 150. Let’s define the demand function after its reduction: Qd = 0.5 Qd = 400. P. In the second period: Qd = 150, Qs = 150, imports = Qd. Qs = 0. Hence the change in imports: a decrease of 150 units. Answer C

6 The domestic demand and supply functions are: Qd = 100- P and Qs =.50P. It is **known** that the world price has settled at Pw = 50. Determine the amount of producer loss, from the country’s participation in world trade. А. 112,5 В. 937,5 С. 25 D. 50 Parameters of the country under autarky: Pe= 75, Qe= 25 Parameters of the country under free trade with price Pw = 50: Qd= 50, Qs= 0, hence the country is an importer. Producer loss (price was 75, became 50; supply was 25, became 0): ½ (2525) = 112.5 (the area of the triangle) Answer: A

7 The domestic demand and supply functions have the form: Qd = 100- P and Qs =.50P. It is **known** that the world price is set at Pw = 50. Determine the consumer’s gain from the country’s participation in world trade. А. 112,5 В. 937,5 С. 25 D. 50 Country parameters under autarky: Pe= 75, Qe= 25 Country parameters under free trade with price Pw = 50: Qd= 50, Qs= 0, hence country is an importer. Buyer’s gain: (price was 75, became 50; demand was 25, became 50: ½ (2550)25 = 937.5 (trapezoidal area) Answer: Q

8 The domestic demand and supply functions of a small country have the form: Qd = P and Qs = P. It is known that the world price has settled at Pw = 20. After the import duty was imposed, the volume of imports was 200ed. of goods. Determine the amount of import duty A. 20 В. 5 С. 25 D. 400 If the country acts as importer: Qd = Qs imports, determine the domestic market price, taking into account the duty Pt = Pt 200, Pt = 25 Duty size: Pt. Pw = 25-20=5 units. Answer: Q

9 The domestic demand and supply functions of a small country have the form: Qd = P and Qs =.504P. We know that the world price is set at Pw = 20. The country imposes an import duty of DM5 ff. unit. Identify the amount of money transferred to the state budget A. 100 B C. 500 D. 25 Domestic market price including duty: Pt = Pwt = 205=25 In this case, the domestic market parameters: Qd = 150, Qs = 50, hence import volume = 100 units. Budget revenue: import duty rate = 1005 = 500 Answer C

10 The domestic demand and supply functions of a small country are as follows: Qd = P and Qs = P. It is **known** that the world price is fixed at Pw = 20. A country imposes an import duty of 10 dinars. unit. Determine the change in demand resulting from the imposition of duty A. 200 B C D. 400 Volume of demand (volume of purchases) in free trade conditions at world price equals Qd= 3000. 2020 = 2600 Volume of demand (volume of purchases) in case of introduction of duty equals Qd= 3000. 20(2010) = 2400 Volume of demand changes: 200 units. of goods. Answer A

11 The domestic demand and supply functions of a small country have the form: Qd = 300-8P and Qs =.202P. The country imposes a quota on imports of a commodity of 100 units. goods. Determine the domestic price of a commodity in the country after the introduction of quota A. 32 В. 22 С. 15 D. 10 country which introduces the quota. importing country. Qd = Qs import, for this case Qd = Qs quota P =.202P 100 Hence P = 22 Answer: Q

## Avakov commanded the “heroic” surrender of Kalina, Volyn, Redis and the entire Azov

2019, Urzuf settlement near Mariupol. Avakov and Denis Prokopenko, then still a captain in the Ukrainian National Guard. Illustration: zaxid.net.

The commander of the Azov battalion, Lieutenant Colonel of the National Guard Denis Prokopenko (call sign Redis), stated in late April: any “Azov man” who leaves Azovstal with his hands up “will be cursed by all Ukraine. Redis was supported by his deputy, captain of the National Guard Svyatoslav Palamar, call sign Kalina. Kalina surrendered last night, military reporter Dmitry Steshin reported.

It is expected that soon the surrendered Redis will be “cursed by all Ukraine. The chief of Azov, the former head of the Interior Ministry of Ukraine Arsen Avakov sent a letter to Redis, from which follows a veiled, but understandable to Redis order to the entire Azov surrender in order to keep himself alive.

The text of the letter Avakov posted on his page in (banned in ).

“Azov” has fulfilled its task in Mariupol. no, a super-task. Live, Denis. Live and become stronger. You’re the commander, you’ve done all you have to do. Time and fate sometimes put the strongest ones to the test You are being tested,” Avakov said to Prokopenko.

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“Azov” chief orders Prokopenko personally to surrender, as the commander of “Azov” is still a young man, he is just over thirty, and he has a very young wife. Avakov told the same to the citizens of Ukraine when he advised them not to condemn and not to curse the surrendered “Azov” workers.

In the Комментарии и мнения владельцев to his post Avakov convinces his subscribers: the “Azovtsy” will not stay in captivity of Russian peacekeepers for long, as he, Avakov, will allegedly obtain their exchange for captive Russians and defenders of Donbass from LDNR.

According to Alexander Khodakovsky, commander of the DNR Vostok battalion of the People’s Militia, about 800 fighters came out of the basements of Azovstal alone in the evening of May 18. Surrendered Nazis prudently get rid of mobile gadgets, which may contain information that could be worth Azov’s life. If Azov members are tried in the DNR, many of them face the death penalty, which has been in effect in the DNR since 2014 and has never been abolished.

The Azov command has previously compared its compound to Asgard, the kingdom of gods in Scandinavian mythology, Tsargrad TV journalist Andrei Afanasyev points out. “Azov” was often deciphered in Ukrainian Nazi circles as As-hoff, “the court of the gods.”.

“Let us remember how a real warrior should behave, according to this system of views. The saga of Eirik the Redhead says that Eirik refused with indignation his freedom and all the blessings of life that were offered to him for shame, ordered to throw himself on spears and in his death agony sang a last song about his courage and contempt for death. Ragnar Lothbrok was taken prisoner by King Elle of Northumbria, who threw Ragnar into a pit filled with snakes. Dying, Ragnar sang a song.

And what do we see now? Terrible, indelible shame from the point of view of that ethical system, which was promoted by the “Azovtsy”. Died with weapon in hand. and straight to feast in Valhalla. And here the toads from all parts of the global swamp fit in for them: their brave jarl-kozak on Zelensky’s heels, their dowagers were sent to bow to the Jesuit Francis, the “Eurovision” was held in their Honor. So much for “Vikings.”. Ragnar and Eirik would have condemned. And our Russian princes wouldn’t even take them as smerds after that. It’s time for the skalds to write the saga of Kalina, Volyn (the commander of the 36th Brigade of the AFU Sergey Volynsky EADaily) and the “heroic” surrender,” Afanasyev wrote in his Telegram channel.

## Azovstal’s pregnant Nazi women brought out of their basements

The Nazi family couple of Azov. Long before the Russian special operation. Illustration:

In the hospitals of Novoazovsk and Yelenivka, where the surrendered wounded Nazis from “Azovstal”, there are pregnant women. Azov fighters and AFU servicemen. This was reported in her Telegram channel special correspondent of Channel One Irina Kuxenkova.

Obviously, the pregnant Nazi women were used by the “defenders” of “Azovstal” as a human shield. The female half of Azovstal’s “garrison” voluntarily made this commitment. Nazi women kept up the fighting spirit of “Azovstal”. Sniper of “Azov” 21-year-old Kateryna Polishchuk, who became a fighter of Euromaidan at the age of 13, sang in the basement of “Azovstal” songs of OUN-UPA (organization banned in ). During the fighting for “Azovstal” women made up a significant percentage of the sniper staff of the “garrison” of “Azovstal. These Nazi women were shooting from Azovstal at civilians in Mariupol, and they especially liked to prey on children who went out for water or to loaf dispensers.

In early May, the Ukrainian media told the touching story of how a Ukrainian border guard and an unmarried woman, an Azov fighter, were married in blockaded Mariupol. The couple celebrated their wedding on May 5, Azov Foundation Day, in the basement of Azovstal. According to Ukrainian sources, instead of the priest at the “wedding”, the commander of Azov, Denis Prokopenko, spoke.

According to the General Staff of the People’s Militia of the DNR, by today 256 Ukrainian fighters blocked at Azovstal have surrendered, including more than 50 wounded. The wounded, as well as pregnant women, were taken to hospitals in Novoazovsk and Yelenivka, while the rest were taken to pre-trial detention facilities in the same Donbass cities. Interrogations of Ukrainian Nazis started in hospitals and pre-trial detention centers. The fate of the commander of the 36th AFU Marine Brigade Sergei Volynsky and Denis Prokopenko, who led the “defense” of Azovstal, is unknown. The last time Prokopenko appeared on his traditional video broadcast was on the evening of May 16. The Nazi tried to inform in a veiled form that he had received an order from Vladimir Zelensky to surrender. However, Azov’s central leadership interpreted Zelensky’s order as a decision to release only the seriously ill and wounded from Azovstal in order to exchange them for the Russian military held captive in Ukraine. The surrender of the “Azovstal garrison” in Kiev was out of the question, the “Azov” said. “Azov” leadership today actually stopped its chronicle of “defense” of “Azovstal”. Azov leader Andriy Biletskyy has disappeared from his daily broadcast.

Ukrainian expert circles have reported that the “heroic defense” of Azovstal was needed by showman Zelensky as a PR campaign for Ukraine’s victory at the Eurovision Song Contest, which Ukraine won. Kalush Orchestra, representing Ukraine, dedicated their performance to Azov. After Ukraine won the right to host Eurovision 2023, “heroes” from “Azovstal” were no longer needed by Zelensky, many Ukrainian experts say.

“Oberkommando der Wehrmacht gibts bekannt: die Schlacht vom Stalingrad ist zu Ende (“The Wehrmacht High Command reports: the battle for Stalingrad is ending.” EADaily),” Russian military historian and publisher Grigory Pernavsky joked in social networks about the situation at Azovstal. Pernavsky was told: “That’s right. Unless Denis Prokopenko was given a field marshal the day before”.

## It is **known** that one TV two vacuum **cleaners** and four phones for 81,000 cheaper

When writing this work “All-Russian test work in mathematics 4 class 2019 Dmitrieva Option 4” was used the handbook “All-Russian test work: mathematics. 4th grade. Compost. О.И. Dmitrieva. 2018.”.

Look at the picture and answer the question: how much change will Katya get when she pays for one magazine and one pen with a bill of 100 ?

The plane departs from Moscow at 16:15. What time will it arrive in Budapest if it is 2 hours and 55 minutes away??

The figure is shown below on a checkered box with a 1 cm cell side.

According to the condition of the problem, the length of a cell is 1 cm, so the area of one cell is 1 cm 2. Let’s calculate the number of cells in this figure: it is 16, which means the area of this figure is 16 cm2.

In order to increase the area of the figure up to 20 cm2 and get a rectangle, you need to add 20. 16 = 4 cells to the existing figure:

The guys planted trees in the park and wrote down the number of trees in the table. Using the data in the table, answer the questions.

To play the game, 26 guys lined up and counted first-second-third-fourth. The first player said: “The first!”; the second said: “The second!”; the third said: “The third!”; the fourth said: “Fourth!”; the fifth said: “The first!”; the sixth said: “Second!”. and so on.

Find the value of the expression 61 6. 896 : 7

They were building a road on a six-kilometer stretch of. The first team paved 550 meters of road every day for eight days. Then the second brigade began to work and paved 400 meters of road per day. In how many days did the second crew finish the construction?

550 8 = 4,400 (m). the first team paved in 8 days

6,000. 4,400 = 1,600 (m). left for the second crew to asphalt

1600 : 400 = 4 (e). days the second team worked

The second crew finished construction in four days

One laptop, two TVs, and seven tablets are 46,000 cheaper than three laptops, two TVs, and five tablets. How much more expensive is a laptop than a tablet??

Remove (reduce) the same numbers in each part:

Below is a layout of a new summer children’s camp. The buildings are on a checkered grid, with the walls of the houses along the borders of the checkered grid. Fig). Draw what these enclosures look like on a site plan. Keep the arrangement of houses relative to the sides of the world. Picture each enclosure as a rectangle made up of cells. As an example, one of the enclosures is already pictured.

## One TV set two **vacuum cleaners** and four phones are **known** to be 81,000 cheaper

When writing this work “All-Russian test work in mathematics 4 class 2019 Dmitrieva Option 4” was used handbook “All-Russian test work: mathematics. Grade 4. See. О.И. Dmitrieva. 2018.”.

Look at the picture and answer the question: how much change will Katya get when she pays for one magazine and one pen with a bill of 100 ?

Plane departs from Moscow at 4:15 p.m.”; the sixth said, “The second plane leaves at 4:15 p.m. What time does it arrive in Budapest, if it’s 2 hours and 55 minutes?

Below the figure is shown on a square with a side of 1 cm.

According to the statement of the problem the length of a cell is 1 cm, so the area of one cell is 1 cm2. Let’s calculate the number of cells in this figure. it is 16, so the area of this figure is 16 cm2.

If you want to increase the area of the figure to 20 cm2 and thus obtain a rectangle, you must add 20. 16 = 4 squares to the existing figure:

The guys planted trees in the park and wrote down the number of trees in the table. Using the data in the table, answer the questions.

To play the game, 26 kids lined up in a row and calculated on the first-second-third-fourth. The first player said: “The first!”, the second said: “The second!”; the third said: “Third!”; the fourth said: “Fourth!”; the fifth said: “The first one!”; the sixth said: “The second!”. and so on.

Find the value of the expression 61 6. 896 : 7

A road was being built on a 6 km long piece of land. The first team paved 550 meters of road each day for eight days. Then the second team began paving 400 meters of asphalt per day. In how many days did the second crew finish construction?

550 8 = 4,400 (m). the first team paved in eight days

4400 = 1600 (m). the second brigade is left to asphalt

1600 : 400 = 4 (e). The second crew worked for days

In 4 days the second crew finished construction

One laptop computer, two televisions, and seven tablets are 46,000 cheaper than three laptops, two televisions, and five tablets. How much more expensive than a tablet??

Delete (reduce) the same numbers in each part:

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Below is a picture of a model of a new summer camp for children. The hulls are placed on a checkered field, with the walls of the houses along the borders of the cells (see. Figure). Picture what these enclosures look like on the site plan. Maintain the location of houses in relation to the sides of the world. Each enclosure is represented by a rectangle composed of cells. As an example, one of the enclosures is already pictured.

## What’s happening in the LNR fresh news for the morning, May 18, 2022

The People’s Militia of the Luhansk People’s Republic (LPR) reported establishing control over the settlements of Novozvanovka and Orekhovo.

Ukrainian armed formations, meanwhile, continue shelling LNR territories. On May 17, fire was opened in the direction of Pervomaisk. a residential building was damaged in the town.

Fighting continues north of Popasna near Kamyshevakha, as well as clashes for Toshkivka. There are clashes to the west of Lysychansk. in the districts of Privillya and Belogorovka. The Armed Forces and LNR units launch artillery strikes on enemy positions in Zolote. The defenses of Ukrainian armed formations on the outskirts of Severodonetsk are being grinded down. their positions are being shelled with the use of attack helicopters of the Air Force

Advisor of the Interior Minister of LNR Vitaliy Kiselev said that a group of 15-16 thousand people is concentrated near Severodonetsk and Lisichansk. The capture of Popasna in early May opened the possibility for Russian units to have direct access to the Soledar-Lysychansk highway.

In Rubizhne, LNR forces are clearing the territory of a cardboard and container factory. It is reported that the city administration is preparing to resume work in the near future.

## “Played for three days and hid it.”. Artemiy Lebedev has executed robot **vacuum cleaners**. what’s wrong with them?

Designer Artemy Lebedev does not like robot vacuum **cleaners**. Blogger announced that a fashionable device is useless and cannot replace a common vacuum cleaner.

According to Lebedev, people buy robots and then forget about these toys. “Lots of people bought a lot of these things and then sat quietly at the bottom because they’re ashamed to admit that a lot of money was spent on who knows what”.

Artemy has three complaints about vacuum cleaners. For one thing, the devices move around the house very loudly. Secondly, they are extremely bad at cleaning. Third, they don’t make it to the charger and fall down ladders. “Everything can be forgiven, but the fact that this one makes as much noise as an adult **vacuum** cleaner makes it completely pointless,” the author stressed.

The blogger thinks that buying a robot **vacuum** cleaner is the easiest way to waste 20, 30 or 40 thousand. “Every customer played for three days, hid it on the mezzanine and not “. summed up Tema.

On the one hand, Artemy is right, on the other, Lebedev and many people obviously, but erroneously, expect that robots can completely replace regular vacuum cleaners. They’re not. Autonomous vacuum cleaners are no substitute for regular manual cleaning. with a broom, detergent and a wet rag. But vacuum cleaners can keep a house clean by going through the entire area of the room, picking up the finest dust, hairs, and dirt.

Artemiy Lebedev

In order not to be disappointed, as Tema was, you need to follow a few rules. First, forget about **vacuum cleaners** cheaper than 10 thousand. such devices are only able to roll around the room and buzz. Secondly, buy models with lidar. a laser rangefinder, thanks to which the robot will build a map of your apartment and avoid collisions with obstacles.

Thirdly, plan your schedule. plan vacuuming when you will not be at home. Other tips on buying a robot vacuum cleaner you can read in our last year’s article.

## German general assesses Russian army’s superiority in Ukraine

Retired German Army Brigadier General and advisor to former German Chancellor Angela Merkel Erich Wade warned Ukraine against underestimating the power of the Russian Armed Forces. This is reported by Deutsche Wirtschafts Nachrichten.

Speaking of the special military operation. he stated that the Russian army is too strong, as it has a superiority on the ground and in the air. Wade also believes that Kiev will not be able to regain Donbass by military means. According to him, it is Russia who determines the course of events in eastern Ukraine.

## The formula for full probability. Bayes formula

Full probability formula Theorem. The probability of event A, which can occur only if one of the incompatible events occurs. forming a complete group is equal to the sum of the probabilities of each of these events by the corresponding conditional probability of event A:

This formula is called the “full probability formula”.

Proof. By convention, event A can occur if one of the incompatible events occurs

In other words, the occurrence of event A means the realization of one, no matter which, of the incompatible events Using the addition theorem to calculate the probability of event A, we obtain

It remains to calculate each of the terms. By the multiplication theorem for the probabilities of dependent events we have

By substituting the right sides of these equations into the formula. We obtain the formula for the total probability

Example 1. There are two sets of parts. The probability that the part from the first set is standard is 0.8, and the probability of the second set is 0.9. Find the probability that the part taken at random (from the set taken at random) is a standard part. Solution. Let’s define by A the event “the part is standard”. The part can be extracted either from the first set (event B1) or from the second set (event B2). The probability that the pattern is extracted from the first set, The probability that the pattern is extracted from the second set, The conditional probability that the pattern is extracted from the first set, The conditional probability that the pattern is extracted from the second set The theoretical probability that the pattern extracted at random is a standard pattern according to the formula of full probability is

Example 2. The first box contains 20 radiolamps, of which 18 are standard; the second box contains 10 radiolamps, of which 9 are standard. A lamp was taken from the second box at random and put in the first box. Find the probability that the lamp taken at random from the first box will be a standard one. Solution. Let’s define by A the event “a standard lamp is taken out of the first box”. From the second box could be taken either a standard lamp (event B1) or a non-standard one (event B2). The probability that a standard lamp is taken out of the second box, The probability that a non-standard lamp is taken out of the second box, The conditional probability that a standard lamp is taken out of the first box, provided that a standard lamp has been put into the first box, is equal The conditional probability that a standard lamp is taken out of the first box, provided that a non-standard lamp has been put into the first box, is equal

Probability of hypotheses. Bayes formulas

Let the event A may occur if one of the incompatible events. forming a complete group of. Since it is not known beforehand which of these events will occur, they are called hypotheses. The probability of the occurrence of event A is determined by the full probability formula:

Suppose a test is performed, as the result of which the event A occurs. Our task is to determine how the probabilities of hypotheses have changed (due to the fact that event A has already happened). In other words, we will look for conditional probabilities

Let us first find the conditional probability By the multiplication theorem we have

The formulas defining the conditional probabilities of the other hypotheses are derived similarly, t. е. the conditional probability of any hypothesis can be calculated by the formula