Cathy found a part time job for the summer. Each week , when she works up to 10 hours she earns a regular hourly wage if she works more than 10 hours each week , she earns more money per hour for overtime hours. She worked 14.5 hour during the first week. Her paycheck before taxes and deduction was $93.75. The second week she worked 12 hours and her paycheck before taxes and deduction was $75.00. Cathy boo had told her what her hourly and overtime rates were but cathy was so excited to get the job that she couldn't remember what she was told. Write a system of equations for Cathys hourly and overtime pay rates.

(a) (8%) compute the probability of an even integer among the 100 integers 1! , 2! , 3! , until 100! (here n! is n factorial or n*(n-1)*(n-2) *… 1) (b) (16%) compute the probability of an even integer among the 100 integers: 1, 1+2, 1+2+3, 1+2+3+4, …., 1+2+3+… + 99, and 1+2+3+… + 100

In need of in the diagram, ∠abc is a right angle. ∠dbc = 30°27'40". find the measure of ∠abd.

Statement reason 1. δabc is similar to δced. given 2. 3. definition of slope 4. slope of slope of definition of slope 5. slope of × slope of multiplying the slopes 6. slope of × slope of substitution property of equality 7. slope of × slope of simplifying the right side the table contains the proof of the relationship between the slopes of two perpendicular lines. what is the reason for statement 2? a. parallel line segments that meet a common perpendicular line are proportional in length. b. the lengths of vertical and horizontal sides in congruent triangles are in a common ratio. c. trigonometric identities determine the lengths of the legs in a right triangle. d. corresponding side lengths in similar triangles are proportional in length.