A game is played as follows: a die numbered 1 to 6 is rolled. If the number 1 comes up, you get nothing. If the number 2, 3, or
1 answer:
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Answer:
The number of students who took English and History, but not Math is 143.
Step-by-step explanation:
Denote the subject choices as follows:
<em>M</em> = a students was taking Math
<em>E</em> = a students was taking English
<em>H</em> = a students was taking History
The data provided is as follows:
N (M) = 257
N (E) = 282
N (H) = 323
n (M ∩ E) = 154
n (M ∩ H) = 171
n (E ∩ H) = 143
n (M ∩ E ∩ H) = 80
Consider the Venn diagram below.
From the provided data and the Venn diagram the value of the set E and H minus M is 143.
Thus, the number of students who took English and History, but not Math is 143.
Answer:
The completed proof is presented as follows;
The two column proof is presented as follows;
Statements Reason
1. ║
, J is the midpoint of
1. Given
2. ∠IHJ ≅ ∠JLK 2. Alternate angles are congruent
3. ∠IJH ≅ ∠KJL 3. Vertically opposite angles
4. ≅
4. Definition of midpoint
5. ΔHIJ ≅ ΔLKJ 5. By ASA rule of congruency
Step-by-step explanation:
Alternate angles formed by the crossing of the two parallel lines and
, by the transversal
are equal
Vertically opposite angles formed by the crossing of two straight lines and
are always equal
A midpoint divides a line into two equal halves
Angle-Side-Angle, ASA rule of congruency states that two triangles ΔHIJ and ΔLKJ, that have two congruent angles, ∠IHJ in ΔHIJ ≅ ∠JLK in ΔLKJ and ∠IJH in ΔHIJ ≅ ∠KJL in ΔLKJ, and that the included sides between the two congruent angles is also congruent
≅
, then the two triangles are congruent, ΔHIJ ≅ ΔLKJ.