If the universal set is all the digits from 0-9 a 23456 and

Question

Need help the following 10 questions in my statistics class, please snow work on how you received the answer.

1. If the universal set is ALL the digits from 0-9, A= {2,3,4,5,6} and B = {5,6,7,8, 9}, draw/shade a Venn diagram to represent the situation and find:

a) (A U B)

b) (A B)

c) (A U B)'

d) (A B)'

2. Evaluate: 2(3+4(7-10))²

3. Evaluate: 2(-3²+4-15÷3)³

4. Summerfest project managers expect that 100,000 people will visit in the summer of 2018 after all renovations are complete. They will be doing minor renovations each year and expect the number of Summerfest visitors to increase each year by 3,500 visitors as a result.

a) Write linear equation that models this situation. Be sure to define your variables.  

b) Use your equation to determine the total number of Summerfest visitors expected in 2027. 

5. Solve the following system of equations:

y= 5x - 1

2y= 3x + 12

6. An estimate from two landscaping companies: Company A gave an estimate of $220 for materials and equipment rental plus $65 per hour for labor; Company B gave an estimate of $300 for materials and equipment rental plus $55 per hour for labor. 

a) Write equations to represent the total costs for each company.

b) Determine how many hours of labor will be required for the two companies to cost the same. 

7. Simplify completely: 

1. (2x³ - 4x² + 2x) + (x⁵ - 4x³ + 3x² - 4x +10)
2. (2x³ - 4x² + 2x) - (x⁵ - 4x³ + 3x² - 4x +10)

8. Solve by factoring: x² - x - 6 = 0

9. Solve (either by factoring of quadratic formula): 2x² - 21x + 25 = -15

10. A mean score of 90 for 5 exams is needed for a final grade of A. Paul's first 4 exam grades are 79, 89, 97, and 95. Determine the grade needed on the fifth exam to get an A in the course?