MAT 1100 – Mathematics FundamentalsMath as Languagedue Friday 4/12 at the beginning of classFor the following problems,1. choose a variable/symbol/letter (different for each problem) and write an equationthat represents the scenario;2. use algebra to solve the equation for your variable, showing all your work;3. have each answer checked for correctness and completeness by another member ofthe class.In the last step, have them sign (digitally, if necessary) each of the problems that theyhave checked. If they find an error in your work, please submit the original work and thecorrected work.1. A bicycle and a bicycle helmet cost 240 dollars. How much did each cost, if the bicyclecost 5 times as much as the helmet?2. Jamal and Moshe began a business with a capital of 7500 dollars. If Jamal providedhalf as much capital as Moshe, how much did each provide?3. A book is currently on sale, and the original price was 25% higher than the price now.If the original price was 6 dollars more than the sale price, what is the sale price?4. An electrician cuts a 30 ft piece of wire into two pieces. One piece is 2 ft longer thanthe other. How long are the pieces?5. A ten foot long ribbon is cut into three pieces. One piece is 4 feet longer than another,and 4 times longer than the third piece. How long are the pieces?

For the following problems,1. choose a variable/symbol/letter (different for each problem) and write an equationthat represents the scenario;2. use algebra to solve the equation for your variable, showing all your work;3. have each answer checked for correctness and completeness by another member ofthe class.In the last step, have them sign (digitally, if necessary) each of the problems that theyhave checked. If they find an error in your work, please submit the original work and thecorrected work.1. A bicycle and a bicycle helmet cost 240 dollars. How much did each cost, if the bicyclecost 5 times as much as the helmet?2. Jamal and Moshe began a business with a capital of 7500 dollars. If Jamal providedhalf as much capital as Moshe, how much did each provide?3. A book is currently on sale, and the original price was 25% higher than the price now.If the original price was 6 dollars more than the sale price, what is the sale price?4. An electrician cuts a 30 ft piece of wire into two pieces. One piece is 2 ft longer thanthe other. How long are the pieces?5. A ten foot long ribbon is cut into three pieces. One piece is 4 feet longer than another,and 4 times longer than the third piece. How long are the pieces?

11. This is the part where you will be assigning your variables.*1 pointStep 1: Understand the problemStep 2: Devise a planStep 3: Carry out the plan (solve)Step 4: Look back (check and interpret

Sasikumar is a mathematics teacher, and he is preparing a question paper of his own. He needs to calculate the answers to the questions he prepared without any errors. As he is busy with his work, he has no time to make it.Write the program and trace the output for the following expressions:a) x = a + b * 5 / 4 + c% 3 * 5, where a, b, and c are variables.b) y = u > v, u and v being variables (inputs).c) z = ++i && ++j && ++k; where i, j, and k are variables (inputs).Input format :The first line consists of three integers for the first expression, separated by a space.The second line consists of two integers for the second expression, separated by a space.The third line consists of three integers for the third expression, separated by a space.Output format :The output consists of the answers for the equations after substituting their corresponding values.Refer to the sample input and output for formatting specifications.Sample test cases :Input 1 :5 3 142 4-5 6 0Output 1 :x = 18y = 4z = 1Input 2 :99 84 274 574738 85 -382Output 2 :x = 204y = 574z = 1

Mathematical programming,

he figure shows the flow of traffic (in vehicles per hour) through a network of streets.(a) Solve this system for xi, i = 1, 2, . . . , 5.   (b) Find the traffic flow when x3 = 0 and x5 = 100.(c) Find the traffic flow when x3 = x5 = 100.