I need help to better understand these math problems please.

Question 12:

13. [-I4 Points] DETAILS SPRECALC7 10.1.069.Ml. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A chemist has two large containers of sulfuric acid solution, with different concentrations of acid in each container. Blending 200 mL of the first solution and 900 mL of the second gives a mixture that is 7% acid, whereas blending 100 mL of the first mixed with 300 mL of the second gives a 8 %% acid mixture. What are the concentrations of sulfuric acid in the original containers? first solution % :] second solution C] % Practice Another A chemist has two large containers of sulfuric acid solution, with different concentrations of acid in each container. Blending 400 mL of the first solution and 800 mL of the second gives a mixture that is 12% acid, whereas blending 100 mL of the first mixed with 300 mL of the second gives a 10 l% acid mixture. What are the concentrations of sulfuric acid in the original containers? first solution L] x z 24 % second solution [2] x 6 % 15. [I4 Points] DETAILS SPRECALC7 10.1.076.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the area of the triangle that lies in the first quadrant (with its base on the X-axis) and that is bounded by the given lines. _|._..|_.. 15 10 y=2x5 5 Need Help? 11. [/6 Points] DETAILS SPRECALC7 10.2.039. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Mark has $100,000 to invest. His financial consultant advises him to diversify his investment in three types of bonds: short-term, intermediate-term, and long-term. The short-term bonds pay 4%, the intermediateterm bonds pay 6%, and the longterm bonds pay 8% simple interest per year. Mark wishes to realize a total annual income of 5.9%, with equal amounts invested in short- and intermediate-term bonds. How much should he invest in each type of bond? shortterm $ intermediate-term $ long-term $ Need Help? _' 11. [-/6 Points] DETAILS SPRECALC7 10.2.039. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Practice Another X Mark has $100,000 to invest. His financial consultant advises him to diversify his investment in three types of bonds: short-term, intermediate-term, and long-term. The short-term bonds pay 3%, the intermediate-term bonds pay 5%, and the long-term bonds pay 6% simple interest per year. Mark wishes to realize a total annual income of 5.2%, with equal amounts invested in short- and intermediate-term bonds. How much should he invest in each type of bond? short-term $ X 20,000 intermediate-term to X 20,000 long-term to X 60,00012. [-/6 Points] DETAILS SPRECALC7 10.2.042. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A gas station sells three types of gas: Regular for $3.00 a gallon, Performance Plus for $3.20 a gallon, and Premium for $3.40 a gallon. On a particular day 4600 gallons of gas were sold for a total of $14,320. Three times as many gallons of Regular as Premium gas were sold. How many gallons of each type of gas were sold that day? Regular gallons Performance Plus gallons Premium gallons Need Help? _' A gas station sells three types of gas: Regular for $2.95 a gallon, Performance Plus for $3.20 a gallon, and Premium for $3.45 a gallon. On a particular day 4900 gallons of gas were sold for a total of $15,130. Three times as many gallons of Regular as Premium gas were sold. How many gallons of each type of gas were sold that day? ' Regular ' ix x 3300 gallons Performance Plus ' ix J 500 gallons Premium X J 1100 gallons 13. [-/6 Points] DETAILS SPRECALC7 10.2.045. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The Juice Company offers three kinds of smoothies: Midnight Mango, Tropical Torrent, and Pineapple Power. Each smoothie contains the amounts of juices shown in the table. On a particular day the Juice Company used 800 oz of mango juice, 710 oz of pineapple juice, and 450 oz of orange juice. How many smoothies of each kind were sold that day? Smoothie Mango Pineapple Orange juice (oz) juice (oz) juice (oz) Midnight Mango 8 u 3 Tropical Torrent 6 W UT Pineapple Power N 8 4 Midnight Mango smoothies Tropical Torrent smoothies Pineapple Power smoothies Need Help? Read It Watch ItThe Juice Company offers three kinds of smoothies: Midnight Mango, Tropical Torrent, and Pineapple Power. Each smoothie contains the amounts ofjuices shown in the table. On a particular day the Juice Company used 900 oz of mango juice, 720 oz of pineapple juice, and 480 oz of orange juice. How many smoothies of each kind were sold that day? Smoothie \"24:51:\" 32:23:: j::?%:) Midnight Mango 8 3 3 Tropical Torrent 6 5 3 Pineapple Power 2 8 4 Midnight Mango Tropical Torrent Pineapple Power X , 6O smoothies X 60 smoothies K 30 smoothies 14. [/6 Points] SPRECALC710.2.046. ASK YOUR TEACHER PRACTICE ANOTHER Kitchen Korner produces refrigerators, dishwashers, and stoves at three different factories. The table gives the number of each product produced at each factory per day. Kitchen Korner receives an order for 150 refrigerators, 178 dishwashers, and 152 ovens. How many days should each plant be scheduled to fill this order? Appliance Factory A Factory B Factory C Refrigerators 8 10 14 Dishwashers 16 12 10 Stoves 10 18 6 factory A days factory B daYS factory C days Need Help? _i' Kitchen Korner produces refrigerators, dishwashers, and stoves at three different factories. The table gives the number of each product produced at each factory per day. Kitchen Korner receives an order for 118 refrigerators, 166 dishwashers, and 124 ovens. How many days should each plant be scheduled to fill this order? factory A factory B factory C Appliance Factory A Factory 3 Factory C Refrigerators 8 10 14 Dishwashers 16 12 10 Stoves 10 18 6 x 7 days / 2 days i l x , 3 days 15. [-/6 Points] DETAILS SPRECALC7 10.2.048.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER By using Kirchhoff's Laws, it can be shown that the currents [1, I2, and I3 that pass through the three branches of the circuit in the figure satisfy the given linear system. Solve the system to find I1, 12, and I3. (Round your answers to three decimal places. Assume that V1 = 6 V and V2 = 3 V.) 11+ IZ- [3:0 1611812 =5 812 + 413 = 3 Need Help? _ By using Kirchhoff's Laws, it can be shown that the currents /1, 12, and 13 that pass through the three branches of the circuit in the figure satisfy the given linear system. Solve the system to find I1, 12, and 13. (Round your answers to three decimal places. Assume that V1 = 9 V and V2 = 5 V.) I1 + 12 - 13 = 0 1611 - 812 = 9 812 + 413 = 5 I1 = X 0.661 A 12 = X 0.196 A 13 = X 0.857 A 16 0 V2