Math Artifacts
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Problems 73
- The prime factorization of 242424 is 2a×3b×5c×7d2^a \times 3^b \times 5^c\times 7^d2a×3b×5c×7d for some nonnegative integers a,b,c,da,b,c,da,b,c,d. What is the sum of the expone…
- Alice's favorite number has the following properties: It has 888 distinct digits. The digits are decreasing when read from left to right. It is divisible by 180180180. What is A…
- What is 9.19.19.1 cubed? Choose the closest answer.
- A set S⊆NS \subseteq \mathbb{N}S⊆N satisfies the following conditions: (a) If x,y∈Sx, y \in Sx,y∈S (not necessarily distinct), then x+y∈S.x + y \in S.x+y∈S. (b) If xxx is an int…
- Let Q(x,y)Q(x,y)Q(x,y) be a polynomial with real coefficients such that xy−xy2=xy⋅Q(x,y)xy-xy^2 = xy\cdot Q(x,y)xy−xy2=xy⋅Q(x,y) for all real xxx and yyy when both xxx and yyy a…
- Q(x,y,z)Q(x,y,z)Q(x,y,z) is a polynomial and xy−xy2z=xy⋅Q(x,y,z)xy - xy^2z = xy\cdot Q(x, y, z)xy−xy2z=xy⋅Q(x,y,z) for all x,y,z∈Rx,y,z \in \mathbb{R}x,y,z∈R. What is the value …
- Compute 5÷(7÷(−4)).5\div(7\div(-4)).5÷(7÷(−4)).
- 16216^2162 is equal to which of the following?
- The speed of light is approximately 3.00×108 m/s.3.00\times 10^8\text{ m/s}.3.00×108 m/s. One light year is the distance light travels in a single calendar year. How many meters…
- An atom of carbon has a radius of 7×10−117\times 10^{-11}7×10−11 meters. If the diameter is on the order of 10N10^N10N meters, what is the value of NNN?
- True or False\text{True or False}True or False === We can consistently define 00=10^0 = 100=1.
- The expression 2x+3y+5xy−3x−6y+4xy2x+3y+5xy-3x-6y+4xy2x+3y+5xy−3x−6y+4xy can be rewritten as ax+by+cxyax+by+cxyax+by+cxy where a,ba,ba,b and ccc are integers. What is the value …
- True or False\text{True or False}True or False === 1x=y01^x=y^01x=y0 if y≠0y\neq0y=0
- There are 333 baseball teams with 999 players each. There are three available positions, and each team designates 333 of its players to each position. No player plays more than …
- You've been rolling fair dice for a game and you have made 212121 rolls so far. 888 of these rolls were divisible by 333 and 141414 rolls were divisible by 2.2.2. Is this possib…
- What is 6×104+5×10+2+10−56 \times 10^4 + 5 \times 10 + 2 + 10^{-5}6×104+5×10+2+10−5?
- How many different rankings of the players are possible?
- What is another way to write 1a×1b\frac{1}{a}\times \frac{1}{b}a1×b1 when a,ba,ba,b are nonzero real numbers? (Choose all that apply.)
- You are selling a product that is to be divided evenly among those who purchase it. Assuming everyone splits the cost of the product evenly, which of these would be the best sel…
- Which of the following, when divided by 23\frac{2}{3}32 results in an integer?
- If we have two numbers aaa and bbb, which factors will be multiplied to get the least common multiple of aaa and bbb?
- A three digit number is formed by rearranging the digits 333, 444, and 777. What is the probability that the number is divisible by 222?
- nnn is the smallest integer greater than 333 that leaves a remainder of 333 when divided by 444, 555, 666, and 777. Which two numbers is nnn between?
- Suppose you make a delicious blueberry pie to celebrate this holiday. It comes out to have a radius of 666 inches. You also decide to make a small pumpkin pie because let's be h…
- A set is "closed" under a given operation if for any two members of the set, the result of the operation is also in the set. Are negative numbers closed under any of the followi…
- Which of the following is equivalent to the inverse of ts+t\frac{t}{s+t}s+tt?
- Which of the following is equivalent to the inverse of ss2+st\frac{s}{s^2+st}s2+sts?
- Randy the Racecar Driver only has 12\frac{1}{2}21 of a mile left before he crosses the finish line. To beat his all-time record, he has to make it to the finish line in 303030 …
- Combine like terms in the following expression π+3−3π+27\pi+\sqrt{3}-3\pi+\sqrt{27}π+3−3π+27
- The speed of light is approximately 3.00×108 m/s3.00\times 10^8\;m/s3.00×108m/s. One light year is the distance light travels in a single calendar year. How far does light trave…
- The speed of light is approximately 3.00×108 m/s3.00\times 10^8\;m/s3.00×108m/s. One light year is the distance light travels in a single calendar year. How far does light trave…
- One light-year is approximately 5.9×10125.9\times 10^{12}5.9×1012 miles. Approximately how far is a light-second?
- The prime factors of a number YYY are 2x⋅5(x−2)⋅7(x−1)2^x\cdot5^{(x-2)}\cdot7^{(x-1)}2x⋅5(x−2)⋅7(x−1) If the sum of the exponents is 666. What is the number YYY?
- Choose the closest answer:
- You need to buy several hundred roses for a Valentine's Day party. In the flower district, there are several vendors selling roses in different-sized bundles. Each of the vendor…
- With today's commodity technology, we can easily achieve the angular resolution of the U-2 spy plane from the middle of last century! A modern press photographer at the red carp…
- You pedal your bicycle up a hill at 12 miles per hour, but you then go back down the same hill at 20 miles per hour. What is your average speed, in miles per hour?
- An Olympic sprinter runs the 100 meter dash in about 10 seconds. What is the minimum serve speed that guarantees your opponent will not be able to dash those 10 feet, even if he…
- From the back of your side of the court, you hit the ball all the way to the other side, landing right on your opponent's baseline, which is 100 mm100 \text{ mm}100 mm wide. You…
- What is the ratio of the speed upon impact when a durian falls 50 meters, to the speed when a durian falls 25 meters instead?
- According to Popular Mechanics, researchers have concluded that in order to run on water, you'd need to run roughly at the speed of a car on a highway (about 65 mph or 105 km/h)…
- In the United States, about half of all students take the bus to school. This results in about 252525 million students riding on a total of about 500,000500,000500,000 yellow sc…
- For simplicity, suppose that the price reduction from 700\700700 to 350\350350 was entirely due to the effect of reducing labor costs, and labor represents somewhere between 5−2…
- AnyTown has a population of 444 million people who use 666 major east-west freeways, each of which has 555 lanes of traffic in each direction. The freeway speed limit is 656565 …
- Of the options below, which is the longest length of time from now that you cannot measure exactly?
- Which of these is the smallest percentage of the popular vote that a winning candidate could have in a 2-candidate race?
- Assume that the thawing time estimate is correct for a typical 15 pound turkey. By about what factor off would the thawing time estimate be for the world's heaviest turkey, whic…
- The radio of the scale of this motor to a human cell is like the scale of your thumb to which of these objects?
- Who hears the broadcast first? People watching on TV, or throughout the stadium? \\ Keep in mind, the speed of light is 300,000,000 meters/second300{,}000{,}000\text{ meters/sec…
- Have you ever tried to walk in stiletto heels? Or worse yet, get your foot stepped on by stiletto heel? Which exerts more pressure on the ground? An elephant's foot or a stilett…
- The chart above shows the percentage of the total population of the United States who voted in each Presidential election. Can you tell which year women received the right to vote?
- You have two buckets, one holds exactly 242424 cups of liquid and one holds exactly 151515 cups. What is the smallest nonzero volume of water that you can measure out exactly us…
- The Sun produces about 400,000,000,000,000,000,000,000,000 watts of power. The Earth is about 150 billion meters from the Sun, and the Earth has radius of about 6000 kilometers.…
- The current U.S. population is, as of this moment, 325,424,421. If 1% of the U.S. population took action for Net Neutrality, how many people would this be? \\ Round answer to th…
- If I get 10\1010 for each hour worked, and you get 2\22 for each dollar I make, how much do you make if I work 555 hours?
- Are the number of fritters and blueberry scones proportional between Ada and Skye's boxes?
- What is the unit rate? In other words, how long does he take to make one portrait?
- The square root of xxx is between two consecutive positive integers. What can we say about these integers?
- Which is larger? ABx−1y−1\begin{array}{c|c} \text{A}&\text{B}\\ \hline x^{-1}&y^{-1} \end{array}Ax−1By−1
- The hardest ice hockey shot ever recorded at the NHL All Star Game is a 108.8 mph (175.1 km/h) slap shot by Zdeno Chara. The typical human blink is 200 milliseconds. How far doe…
- How dangerous is catching Pokémon near traffic? Suppose you spot an Aerodactyl, a Snorlax, and a Dragonite, 3 rare Pokémon in the middle of the highway. The highway has a speed …
- César Cielo set the world record for the 50 meter freestyle swim in April 2009, at 20.91 seconds, breaking the previous record by Frédérick Bousquet of 20.94 seconds. Cielo is 1…
- There are only two ways that you can vote for your favorite artist for the American Music Awards, via their site or on Twitter. Justin Bieber, who won 4 awards this year, has th…
- Every New Year's Eve, people gather in New York City's Times Square to watch the ball drop. In the last 60 seconds, the ball moves at a speed of 2.35 feet per second. The most e…
- We are delivering a full truck load worth of goods. What is the difference of carbon emission between delivering goods at half full and full? What is the difference in weight cl…
- 2x= ?2x =\,?2x=? (Select all that apply.)
- jjj and kkk are unknown constants. bbb and ccc are defined constants. What should be your next step? Assume all constants are integers.
- Suppose instead of parking your car in a drive-in theater, you travel along this road. Approximately, how fast would you have to drive to watch this billboard movie at the stand…
- Compute the following: πlog(x)15÷πlog(x)5\frac{\pi \log(x)}{15}\div \frac{\pi \log(x)}{5}15πlog(x)÷5πlog(x)
- Suppose the fraction ab\frac{a}{b}ba is written in simplest form. Which of the following statements must be false? (Note that 0b\frac{0}{b}b0 is not in simplest form because y…
- Every year, many people fill out brackets to predict who wins which games in the annual NCAA basketball championship, otherwise known as March Madness. In 2019, 0.9%0.9\%0.9% of…
- Every year, many people fill out brackets to predict who wins which games in the annual NCAA basketball championship, otherwise known as March Madness. In 2019, 8.4%8.4\%8.4% of…
- The Toronto Raptors are down to the Boston Celtics 102−111102-111102−111 with 222 minutes to go in the game! It takes the Raptors 666 seconds to run down the court and make a 33…