Solve the system for each variable, and check your solutions. 20. x + y + z = 60 and x – z = y + 6 and y = 40 – x – 3z21. 2x + y + 4z = 3 and x + 2y = 2z -3 and 4z + 3y = 0 22. x + y + z = 1 and 2x – y + 3z = 4.5 and 4x -5y – 5z = -0.5Write a system of two equations for the following problem and solve. 23. A metal alloy that is made up of 15% aluminum is combined with a metal alloy that is 35% aluminum. If the result is 400 Kilograms of 27.5% of aluminum alloy, then how much of each alloy was used?Write a system with three equations for the following problem and solve. 24. If the digits of a three-digit number are reversed in order, then the sum of the new resulting number and the original number comes out to be 665. The difference of the two numbers is 297. The tens’ digit place is two times the hundreds’ place digit. What is the number?

Find the length of the diagonal of the rectangle. round your answer to the nearest tenth. || | | 8 m | | | | 11 m

The owner of the plant nursery where you were tells you to fill 350 ml bottles from a 30 l from a fertilizer

Listed below are time intervals (min) between eruptions of a geyser. assume that the "recent" times are within the past few years, the "past" times are from around 20 years ago, and that the two samples are independent simple random samples selected from normally distributed populations. do not assume that the population standard deviations are equal. does it appear that the mean time interval has changed? is the conclusion affected by whether the significance level is 0.10 or 0.01? recent 78 90 90 79 57 101 62 87 71 87 81 84 57 80 74 103 62 past 88 89 93 94 65 85 85 92 87 91 89 91 follow the steps of hypothesis testing, including identifying the alternative and null hypothesis, calculating the test statistic, finding the p-value, and making a conclusions about the null hypothesis and a final conclusion that addresses the original claim. use a significance level of 0.10. is the conclusion affected by whether the significance level is 0.10 or 0.01? answer choices below: a) yes, the conclusion is affected by the significance level because h0 is rejected when the significance level is 0.01 but is not rejected when the significance level is 0.10. b) no, the conclusion is not affected by the significance level because h0 is not rejected regardless of whether a significance level of 0.10 or 0.01 is used. c) yes, the conclusion is affected by the significance level because h0 is rejected when the significance level is 0.10 but is not rejected when the significance level is 0.01. d) no, the conclusion is not affected by the significance level because h0 is rejected regardless of whether a significance level of 0.10 or 0.01 is used.