Question

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1. Andre, a physics undergraduate, enters a coffee shop that is holding a contest. Customers who guess the number of coffee beans inside of a closed, 16.0 f oz aluminum commuter mug get a free pastry and an espresso drink. Motivated by the prospect of free food and coffee, Andre puts his finely-tuned estimation skills to work. What should Andre submit as his estimate for the number of coffee beans in the mug? 2. How much methane was produced by the cows in Canada in 2017? 3. Hydro decides to revamp their computer systems and they find they can't use their old codes anymore, because the systems were so outdated. The new computer program uses units of mega-ergs. The meters, however, still read the same units as before. So they add a conversion factor to the meter readings in order to calculate the bills. Your bill last month was $114.32 but after the change it is $6,822.46. What is the likely error? 4. Homeopathic remedies frequently use serial dilution to create cures for common ailments This is the process of taking a substance and diluting it in pure water with a ratio of 1:-10 (1X) and then repeating the process by further diluting the diluted solution by a ratio of 1:10 (2x. For example, one treatment for poison ivy lists a potency of 30C which corresponds to 60X Assuming that the dilution of 1:10 means one molecule of substance for 10 molecules of water, calculate how many molecules of the curative substance remain in the solution. For comparison, an estimate of the number of grains of sand on all of earth's beaches is about 10 S. The two shorter sides of a right triangle have the same length. The area of the right triangle is 8.80 square meters. What is the length of the hypotenuse? 6. The lengths of the two sides of a triangle (not necessarily a right triangle) are 1.00 meters and 1.91 meters. The sine of the angle opposite the side of length 1.00 meters is 0.447. What is the sine of the angle opposite the side of length 1.91 meters? 7. Two of the interior angles of a triangle are equal. The third interior angle is 141 degrees. What are the other two interior angles? 8. A sphere and a cube have equal volumes. The length of one edge of the cube is 4.24 meters What is the radius of the sphere? 9. A partly-full paint can has 0.727 U.S gallons of paint left in it If all the remaining paint is used 12.7m), how thick is the layer of wet paint? to coat a wall evenly (wall area 10. How many unique values of x solve x,8x+ 12=0? 11. The depth of the ocean is sometimes measured in fathoms (1 fathom 6 feet). Distance on the surface of the ocean is sometimes measured in nautical miles (1 nautical mile s6076 feet) The water beneath a surface rectangle 3.90 nautical miles by 3.70 nautical miles has a depth of 16.0 fathoms. Find the volume of water (in cubic meters) beneath this rectangle. 12. Estimate the diameter of the earth

Answer 1

Solution: Consider, Length of each coffee bean is, 1 =1cm Thickness is considered to be half of its length. Thickness of each coffee bean is, t=0.5 cm Breadth of each coffee bean is, b=0.3 cm Volume of one coffee bean is, VCE =(lbt) =(1+0.5x0.3) cm = 0.15 cm = 0.15 mL Entire volume of the cup is. V =16 fl - oz = 473.176 mL There must be some volume lost due to air between the coffee beans. So let us assume that 20% is air and 80% is occupied by coffee beans. Volume occupied by the coffee bean is, V'=0.8( 473.176 mL) = 378.54 mL Number of coffee beans in the mug is, 1' 378.54mL-2523. 62524 VCE 0.15mL Number of coffee beans in the mug is 2524 Nu