Step-by-step explanation: GIVEN: Two digit number means we will have to choose from numbers 0-9 for the second digit and 1-9 for the first digit. (since zero can't be in the tens place) Formula: We will use m x n. That is, m is the number of elements we can use for the first digit and n will be the number of elements we can use for the second digit. Sample Space: To get the probability, we must find the sample space or all the outcomes. m - 9 elements (1-9) m - 9 elements (1-9)n - 10 elements (0-9) m x n = 9x10 =90 90 is our sample space. A. An odd number Conditions: For an odd number, the second number will determine whether or not it is an odd number. For the first digit, we can use 1-9. Elements: m - 9 elements (1-9) m - 9 elements (1-9)n - 5 elements (1,3,5,7,9) m x n=9x5=45 SOLVE (probability) Probability= possible outcomes/sample space P=45/90 P=1/2 B. Larger than 75. Conditions: The first digit could be equal to 7 or greater. But n will only be greater than 5 if and only if m=7 and n could be any number if m>7. Elements 1: m - 1 element (7) m - 1 element (7)n - 4 elements (6,7,8,9) m - 1 element (7)n - 4 elements (6,7,8,9)m x n=1x4=4 Elements 2: m - 2 elements (8,9) m - 2 elements (8,9)n - 10 elements (0,1,2,3,4,5,6,7,8,9,) m - 2 elements (8,9)n - 10 elements (0,1,2,3,4,5,6,7,8,9,)mxn=2x10=20 TOTAL: 4+20=24 SOLVE (PROBABILITY) Probability= possible outcomes/sample space P=24/90 P=4/15 C. multiple of 5 Condition: the second digit must be either 0 or 5 and the first digit could be any digit. Elements: m - 9 elements (1-9) m - 9 elements (1-9)n - 2 elements (0,5) m x n =9x2=18 SOLVE (PROBABILITY) P=18/90 P=1/5 D. An even number smaller than 40 Condition: The first digit could be equal to 4 but the second digit must be even (excluding zero). Another situation is the first digit would be greater than 4 and the second digit would be any even number. Elements 1: m - 1 element (4) n - 4 elements (2,4,6,8) m x n = 1x4=4 Elements 2: m - 5 elements (5,6,7,8,9) n - 5 elements (0,2,4,6,8) mxn=5x5=25 TOTAL: 25+4=29 SOLVE: Probability P=29/90
Step-by-step explanation: The two lines have the same solution where both lines intersect. So, if you look at the point on the graph where the two lines intersect, and count the tick marks on the number lines, the point is clearly located at (-2, 3).
