The list of ingredients for chocolate brownies given at right will make 16 brownies. Use the list to decide how much of each ingredient is needed to make 12 brownies. |:| cup(s) of butter is needed. 1 cup butter 6 ounces unsweetened chocolate 2 cups sugar 1 25 teaspoons vanilla 4 eggs 1 5 Ccup flour (Simplify your answer. Type an integer, simplified fraction, or mixed number.) |:| ounce(s) of chocolate are needed (Simplify your answer. Type an integer, simplified fraction, or mixed number.) |:| cup(s) of sugar are needed. (Simplify your answer. Type an integer, simplified fraction, or mixed number.) |:| teaspoon(s) of vanilla are needed. (Simplify your answer. Type an integer, simplified fraction, or mixed number.) |:| egg(s) are needed. (Simplify your answer. Type an integer, simplified fraction, or mixed number.) |:| cup(s) of flour is needed. (Simplify your answer. Type an integer, simplified fraction, or mixed number.) Shown in the figure is an 8-hour clock and the table for clock addition in the 8-hour clock system. a. How can you tell that the set {0,1,2,3,4,5,6,7} is closed under the operation of Complete parts (a) through (e). clock addition? (O A. Whenever clock addition is being applied, the elements can be grouped in any order and the answer is unchanged. (O B. The order of the elements does not matter when applying clock addition to any number of elements in the set. (O C. The set has an identity element. (O D. Applying the operation of clock addition to any two elements in the set results in a number that is also in the set. b. Verify the associative property for the following equation. (506)P3 = 3D (6D5) Both sides of the equation are equal to oN|[o(a|~|w(NN i c. What is the identity element in the 8-hour clock system? N[=|Oo|N[o(a(d|w|w The identity element is d. Find the inverse of each element in the 8-hour clock system. The inverse of 0 is The inverse of 1 is The inverse of 2 is The inverse of 3 is The inverse of 4 is The inverse of 5 is The inverse of 6is | |. e, [0 d. Find the inverse of each element in the 8-hour clock systen The inverse of 0 is |:| The inverse of 1 is I:I The inverse of 2 is |:| The inverse of 3 is |:| The inverse of 4 is |:| The inverse of 5 is I:I The inverse of 6 is |:| The inverse of 7 is |:| e. Verify two cases of the commutative property. 201 =1@2=| | 660 =06 =] | In 20186, to help pay for college, you worked part-time at a local restaurant, earning $24,000 in wages and tips. Use the following information to complete parts (a) through (c) below. For people who are not self-employed, the 2016 Marginal Tax Rates, 2016 FICA tax rates were as follows: Standard Deductions, and 7.65% on the first $118,500 from wages Exemptions and tips [ ToxRate [Snge | 1.45% on income in excess of $118,500 up to $9275 [Taxpayers are not permitted to $9276 to $37,650 subtract adjustments, exemptions, or Standard Deduction | $6300 deductions when determining FICA taxes. Exemptions (per person)| $4050 a. Calculate your FICA taxes. The FICA taxes are $D. (Type an integer or a decimal. Round to two decimal places as needed.) b. Calculate your income tax. Assume you are single with no dependents, have no adjustments or tax credit, and you take the standard deduction. The income tax is $|:. (Type an integer or a decimal. Round to two decimal places as needed.) c. Including both FICA and income tax, what percentage of your gross income are your federal taxes? Federal taxes are | |%. (Type an integer or a decimal. Round to one decimal place as needed.) Determine whether the figure shown exhibits self-similarity. Does the figure shown exhibit self-similarity? O yes O noA graph is given to the right. a. Determine whether the graph has an Euler path, an Euler circuit, or neither. b. If the graph has an Euler path or circuit, use trial and error or Fleury's Algorithm to find one. This graph has an Euler circuit. | This graph has an Euler path (but not an Euler circuit). | The graph has neither an Euler path nor an Euler circuit. |D | F| A/ B| G C E Drag the correct answers into the boxes below. If an Euler path or an Euler circuit exists, drag the vertex labels to the appropriate locations in the path. If no path or circuit exists, leave the boxes in part (b) blank. a. Does the graph have an Euler path, an Euler circuit or neither? b. If the graph has an Euler path or an Euler circuit, use trial and error or Fleury's Algorithm to find one whose first vertex is G and third vertex is A. Complete parts (a) through (d) using the graph to the right. A B D E Which of the following edges need to be added'? Select all that apply. A. CD B. AE C. BE D. AB E. AD OF. DE G. BD OH. BC I. CE J. AC Determine the number of Hamilton circuits for the modified graph. The number of Hamilton circuits for the modified graph is (Type a whole number.) b. Give two Hamilton circuits for the modified graph in part (a). Find a possible Hamilton circuit starting with vertices D and B. Fill in the remaining vertices. One possible Hamilton circuit is D,B, ,D. (Use a comma to separate vertices as needed.) Find another possible Hamilton circuit starting with vertices D and C. Fill in the remaining vertices. Another possible Hamilton circuit is D,C, ,D. outing(Use a comma to separate vertices as needed.) Find another possible Hamilton circuit starting with vertices D and C. Fill in the remaining vertices. Another possible Hamilton circuit is D,C, ,D. (Use a comma to separate vertices as needed.) c. Modify the given graph by removing the least number of edges so that the resulting graph has an Euler circuit. Which of the following edges need to be removed? Select all that apply. A. AC B. BD " c. CD and BD D. DE and BD E. AD and AB OF. AB G. BE OH. CE and BE I. AE and AB J. BC d. Find an Euler circuit for the modified graph in part (c). Start with vertex C and fill in the remaining vertices. One possible Euler circuit is C, ,c. (Use a comma to separate vertices as needed.)Use Kruskal's Algorithm to find the minimum spanning tree for the weighted graph. Give the total weight of the minimum spanning tree. Which of the following trees matches the shape of the minimum spanning tree? O A O B. Oc. N7 L