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Questions ( 1366 )
  • Melinda chooses a three-digit positive integer, subtracts it from 3000, and triples the result. What is the largest integer Melinda can get?  

  • A bookshelf is to hold 6 literature books, 3 geometry books and 7 algebra books, arranged in random order. What is the probability that the books are arranged so that the first book on the shelf is a math book? Express your answer as a common fraction.

  • A triangle with an area of 120 mm\(^2\) has a height of 10 mm. What is the area of a similar triangle with a height of 20 mm?

  • A bowl contains 50 grapes of different colors. If 20% of the grapes in the bowl are red, how many grapes are not red?

  • How many odd numbers are there between 20 and 158?

  • How many months are there in 35 years? 

  • A jar contains some number of pennies. When pennies are removed 2, 3, 4, 5, 6 or 8 at a time, one penny is left over. There are no pennies left over when they are removed 7 at a time. What is the least number of pennies that could be in the jar?

  • What is the result when Ellen starts with the integer 123,456 and performs the following sequence of operations: subtract 6, divide by 10, subtract 5, divide by 10, subtract 4, divide by 10, subtract 3, divide by 10, subtract 2, divide by 10? 

  • Kevin takes a bus from home to school. The bus travels 8 miles west, then turns and travels 8 miles north, then turns and travels 7 miles west to the school. If the bus were able to travel directly from Kevin’s house to the school, along a straight path, how much shorter would the trip be?

  • Harvey has a fair eight-sided die that has a different number from 1 to 8 on each side. If he rolls this die twice, what is the probability that the second number rolled is greater than or equal to the first number? Express your answer as a common fraction.

  • What is the absolute difference between \(\dfrac{1}{2}\) and \(\dfrac{1}{3}\) ? Express your answer as a common fraction.

  • What is the value of \(4:\dfrac{2}{3}-5\)?

  • The length of 5 small paper clips is equal to the length of 2 large paper clips. The length of 8 small paper clips is equivalent to the length of how many large paper clips? Express your answer as a mixed number.

  • A time capsule was sealed in 1940 and will be opened on the same date in 2017. How long will the capsule remain sealed? 

  • Here are the facts and hints for you to solve the 6 latest questions:

    (1) Lightning is the electrical discharge in a thunderstorm. It results in both a visible flash and the heating of air, causing a sonic boom commonly referred to as thunder. The speed of light is so fast that one may consider seeing the flash as instantaneous with the lightning. The speed of sound is slower, about 340 meters per second, or 1100 feet per second, so counting the seconds from the lightning flash to the lightning bang (thunder) gives the distance to the thunderstorm, based on 3 seconds per kilometer, or 5 seconds per mile.

    (2) Rotating atmospheric storm systems, called cyclones in general, have centers of lower pressure about which the air swirls. In the tropics, these are tropical cyclones. At middle latitudes, they are extra-tropical cyclones and are associated with fronts – boundaries of changing temperatures. Cyclones, tropical cyclones and extra-tropical cyclones are all three-dimensional flows of air with stronger horizontal winds but also upward motions that result in their cloud patterns.

    (3) Storms in the tropical regions do not have fronts and temperature changes. Instead they are organized thunderstorm masses about a center of lower air pressure. As these thunderstorm systems develop, they grow and are categorized by their associated wind speeds. When maximum sustained winds reach 37 km/h, the system is termed a tropical depression. Sustained winds of 63 km/h denote a tropical storm. A storm with maximum sustained winds reaching 119 km/h, by definition, is a hurricane (referred to as a typhoon in the western Pacific Ocean, or cyclone in the Indian Ocean and southern Pacific Ocean). Wind pressure is the force per unit area caused by air in motion. During a storm the factor by which the wind pressure increases is equal to the square of the factor by which the wind speed increases. 

    (4) The atmosphere can be arbitrarily divided into layers based on the vertical temperature pattern. The lowest layer is called the troposphere, where the temperature generally decreases with altitude from Earth’s surface up to about 11 km. 

    (5) Earth’s atmosphere consists mainly of nitrogen and oxygen. These gases do not react with most radiation, thus transmitting almost 100%. Some gases transmit some types of radiation, such as visible light, but absorb other portions, particularly infrared radiation. Gases that absorb infrared (heat) radiation from Earth outward to space, of which the atmosphere in turn can emit part back down to the surface, help warm the planet. This is called the greenhouse effect. Such gases are called greenhouse gases or GHG. The major GHG (although minor components of the atmosphere) are water vapor and carbon dioxide (CO2 ), as well as methane, nitrous oxide, chlorofluorocarbons and others. Rising concentrations of CO2 pose a problem in an enhanced greenhouse effect.

    (6) All objects including the Sun and Earth emit radiation. Depending on their temperature, the radiation has varying characteristics and differing names. Earth emits mainly infrared radiation (heat) outward to space. The Sun emits mostly visible light into space but also some ultraviolet and infrared, a small portion of which strikes Earth. Radiation that goes to Earth and encounters matter may be absorbed to become heat, may be reflected or scattered away, or may be transmitted to the Earth's surface without change. 

  • If 10 in of freshly fallen snow melts down to 1 in of liquid water, what is the liquid water equivalent depth of 30 cm of fresh snow? 

  • What is the density of snow if the ratio of snowfall depth to melted water depth is 3 to 1? Express your answer as a decimal to the nearest hundredth.

  • Suppose that a tropical depression with a maximum sustained wind speed of 50 km/h intensifies to hurricane strength with a maximum sustained wind speed of 150 km/h. By what factor does the wind pressure increase?

  • In a typical extra-tropical cyclone, the vertical motion of air is typically only 1% to 10% of the horizontal wind speed. If the horizontal wind in a cyclone is blowing at a rate of 20 km/h, what is the positive difference between the greatest and least typical values for the vertical air motion? Express your answer as a decimal to the nearest tenth.

  • Using the flash-to-bang method based on 5 sec/mi, what is the distance, in miles, to a thunderstorm if the time elapsed between the flash and the bang is 12 sec? Express your answer as a decimal to the nearest tenth.

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