Mathematics question(venn diagram) ; a final year maths student was given a project to identify which of 30 chemical substance contained the element iron, lead, and proporous in his project defence, he gave the following breakdown iron only (5), lead and phoporous (10), and the three elements (6), iron and lead (6), iron and proporous only (3). the number of substance that have only phoporous or only lead are equal assuming the elements are the only constituents; (a) how many substance have lead 0nly. (b) how many substance had at least two element

(60 points) explain this in detail

Astudent was asked to find the square of 7x+3. the student quickly wrote (7x+3)^3= 49x^2+9. identify the student's error and provide the correct answer.

Atechnician compares repair costs for two types of microwave ovens (type i and type ii). he believes that the repair cost for type i ovens is greater than the repair cost for type ii ovens. a sample of 6767 type i ovens has a mean repair cost of $79.79$⁢79.79. the population standard deviation for the repair of type i ovens is known to be $19.18$⁢19.18. a sample of 5555 type ii ovens has a mean repair cost of $75.24$⁢75.24. the population standard deviation for the repair of type ii ovens is known to be $21.40$⁢21.40. conduct a hypothesis test of the technician's claim at the 0.050.05 level of significance. let μ1μ1 be the true mean repair cost for type i ovens and μ2μ2 be the true mean repair cost for type ii ovens. step 2 of 4 : compute the value of the test statistic. round your answer to two decimal places.