<span>If set X is made up of the possible ways five students, represented by A, B, C, D, and E, can be formed into groups of three, then the set X consists of such triples {ABC, ABD, ABE, ACD, ACE, ADE, BCD, BCE, BDE, CDE} (note that triple ABC is the same as triple ACB, or BCA, or BAC, or CAB, or CBA). The set X totally contains 10 elements (triples). The first statement is true.
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<span>If set
Y is made up of the possible ways five students can be formed into
groups of three if student A must be in all possible groups, then </span><span>the set Y consists of such triples {ABC, ABD, ABE, ACD, ACE, ADE} and contains 6 elements. The second statement is also true.
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<span>If person E must be in each group, then there can be only one group is false statement, because you can see from the set X that triples which contains E are 6.
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<span>There are three ways to form a group if persons A and C must be in it. This statement is true and these groups are ABC, ACD, ACE.</span>
Answer:
5/8
Step-by-step explanation:
There are 5 people when 3 more join for a total of 8 people
5 candy bars divided by 8 people
Take the candy bars and divide by the people
5/8
So in these problems, we're dealing with absolute value. Absolute value is the real amount of the number, or it's real place value without a negative sign.
Part A: if the absolute value of X was 17, then X could equal -17 or 17.
Part B: |x+9|=15. We know that 6+9=15, so X could equal -6 or 6.
Part C: |x-10| ≤ 13. We know that 23-10 is 13. So 23 would be the greatest value of X. Then, for the smallest value of X, if we insert -3 in the equation to take the place of the variable, we get |-3-10|=13. So -3 would be the smallest value of the equation. X≤ 23 and X≥-3.
Answer:
X = -1/3, 1/3
Step-by-step explanation:
6x^2 - x = 1
(subtract 1 from both sides)
6x^2 - x - 1 = 0
(factor)
(6x - 3) (6x + 2)
(simplify)
(2x - 1) (3x + 1)
(Solve for x in each parentheses)
2x-1= 0 and 3x+1=0
X= -1/2 X= -1/3
Answer:
20
Step-by-step explanation:
2, 5, 9, 14, ?, 27.
2,5 the number added is 3
5,9 the number added is 4
9,14 the number added is 5
14,20 the number added is 6
20 , 27 the number added is 7
