**Understanding Dice Probability: Calculating Sums**This table represents all possible outcomes when rolling two dice: a Red Die and a Green Die. The outcomes are shown as ordered pairs, where the first number represents the Red Die and the second number represents the Green Die. There are a total of 36 possible outcomes, as each die has 6 sides.**Table of Possible Outcomes:**- **Green Die (Columns):** 1, 2, 3, 4, 5, 6- **Red Die (Rows):** 1, 2, 3, 4, 5, 6**Outcomes:**| | *1* | *2* | *3* | *4* | *5* | *6* ||-----------|---------|---------|---------|---------|---------|---------|| **1** | (1,1) | (1,2) | (1,3) | (1,4) | (1,5) | (1,6) || **2** | (2,1) | (2,2) | (2,3) | (2,4) | (2,5) | (2,6) || **3** | (3,1) | (3,2) | (3,3) | (3,4) | (3,5) | (3,6) || **4** | (4,1) | (4,2) | (4,3) | (4,4) | (4,5) | (4,6) || **5** | (5,1) | (5,2) | (5,3) | (5,4) | (5,5) | (5,6) || **6** | (6,1) | (6,2) | (6,3) | (6,4) | (6,5) | (6,6) |### Objective:Determine how many ways the sum of the two dice is 4.**Solutions with Sum = 4:**1. In this geometry problem, you are given two parallel lines, \( l_1 \) and \( l_2 \), intersected by a transversal. Your task is to determine the measures of angles \( \angle 1 \) through \( \angle 12 \).**Diagram Explanation:**- The two parallel lines, \( l_1 \) and \( l_2 \), are horizontally aligned, with arrows indicating their parallel nature.- A diagonal line traverses these parallel lines, creating a set of angles at each intersection point.- The known angles in the diagram are: - \( \angle 5 = 62^\circ \) - \( \angle 10 = 68^\circ \)Given this setup, apply the knowledge of angles formed by parallel lines and a transversal to find the measures of the remaining angles. Use concepts such as corresponding angles, alternate interior angles, and the fact that angles on a straight line sum to \( 180^\circ \).At the bottom of the prompt, it asks for the measure of \( \angle 7 \). Enter your answer in the provided box and click "Check Answer" to see if it's correct.**Instructions:**Type your responses into the answer box for each angle as you solve, ensuring to follow through with checking your work for correctness as you proceed through each angle measurement from \( \angle 1 \) to \( \angle 12 \). There are 11 parts remaining after finding the first answer.

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Of the 36 possible outcomes in the table below, determine the number for which the sum (for both dice) is 4. Green Die 1 2 3 4 6. (1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1) (1, 2) (2, 2) (3, 2) (4.2) (5, 2) (6, 2) 1 (1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6,3) (1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4) (1, 5) (2, 5) (3, 5) (4, 5) (5,5) (6, 5) (1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6) Red Die 4 6. In how many ways can you roll 4? ways 23

Of the 36 possible outcomes in the table below, determine the number for which the sum (for both dice) is 4. Green Die 1 2 3 4 6. (1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1) (1, 2) (2, 2) (3, 2) (4.2) (5, 2) (6, 2) 1 (1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6,3) (1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4) (1, 5) (2, 5) (3, 5) (4, 5) (5,5) (6, 5) (1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6) Red Die 4 6. In how many ways can you roll 4? ways 23

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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