The percentage y of mathematicians attending the annual conference “Math-ematics in Economics” can be modelled, as a function of the years t, byy = 50 − A e−at.Given that the percentage of participant mathematicians was 2 at the openingyear, and 5 after 2 years,(a) find the value of A and a, correct to 3 decimal places,(b) predict the percentage of mathematicians after 5 years, and(c) predict the percentage of mathematicians attending the conference inthe long run.

e percentage y of consulted books in a library specialized in literature aboutareonautics is modelled by the formulay = 100 − A e−at.Given that 1% of the books were consulted at the opening of the library, and50% after 1 year,(a) find the value of A and a, correct to 3 decimal places,(b) predict the percentage of consulted books after 5 years,(c) predict the percentage of consulted books in the long run

Seats for Mathematics, Physics and Biology in a school are in the ratio 5:7:8. There is a proposal to increase seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

In a school, 30 % of the students study math and science, 70 % of the students study science. What is the probability of students studying math, given that the student is already studying science.a42.8%42.8%b23.33%23.33%c40%40%d63.8%63.8%

What will be the percentage formula*3 points= Lectures attended / Lectures delivered) 100= D5*100/2=(D4/c4*)100=c4*d5/100

Refer to the previous exercise and perform the following tasks.a) Predict for the Director of the Department of Education in Queensland the mean mathematics test score at a school in the state where 50% of the teachers have at least one university degree in mathematics, their mean age is 43 years, and their mean annual income is $78,500. What is the corresponding approximate 95% prediction interval? Calculate the point prediction first manually and then with R, and the approximate 95% prediction interval manually only.b) Predict for the Director of the Department of Education in Queensland the mean mathematics test score at all schools in the state where 50% of the teachers have at least one university degree in mathematics, their mean age is 43 years, and their mean annual income is $78,500.c) Predict with 95% confidence the mean mathematics test score at a school in the state where 50% of the teachers have at least one university degree in mathematics, their mean age is 43 years, and their mean annual income is $78,500. How does this prediction interval compare to the approximate 95% prediction interval you obtained in part (a)? d) Estimate with 95% confidence the mean mathematics test score at schools in the state where 50% of the teachers have at least one university degree in mathematics, their mean age is 43 years, and their mean annual income is $78,500. How does this confidence interval compare to the prediction interval you obtained in part (c)?