Agrain of sand weighs approximately 0.011 grams. there are approximately 7.5 x grains of sand in the world. using scientific notation, calculate approximately how much all the grains of sand in the world weigh (in grams). answer in scientific notation and show or explain your work, rounding to the nearest hundredth. answer in a complete sentence.

Find the maximum value of p= 4x + 5y subject to the following constraints :

1. 2. ∠b and ∠y are right angles. 3.? 4.? which two statements are missing in steps 3 and 4? ∠x ≅ ∠c △abc ~ △zyx by the sas similarity theorem. ∠b ≅ ∠y △abc ~ △zyx by the sas similarity theorem. = 2 △abc ~ △zyx by the sss similarity theorem. = 2 △abc ~ △zyx by the sss similarity theorem.

1. an economy consists of three workers: larry, moe, and curly. each works 10 hours a day and can produce two services: mowing lawns and washing cars. in an hour, larry can either mow one lawn or wash one car; moe can either mow one lawn or wash two cars; and curly can either mow two lawns or wash one car. a. calculate how much of each service is produced under the following circumstances: a. all three spend all their time mowing lawns. b. all three spend all their time washing cars. c. all three spend half their time on each activity d. larry spends half of his time on each activity, while moe only washes cars and curly only mows lawns b. using your answers to part a, draw a production possibilities frontier and label points a, b, c, and d on your graph. explain why the production possibilities frontier has the shape it does. c. are any of the allocations calculated in part a inefficient? explain.