To help plan the number of meals to be prepared in a college cafeteria, a survey was conducted, and the following data were obtained. 130 students ate breakfast.
175 students ate lunch.
279 students ate dinner.
63 students ate breakfast and lunch.
114 students ate breakfast and dinner.
89 students ate lunch and dinner.
51 students ate all three meals.
How many students ate
(a) At least one meal in the cafeteria?
students

(b) Exactly one meal in the cafeteria?
students

(c) Only dinner in the cafeteria?
students

(d) Exactly two meals in the cafeteria?
students

Given: ad¯¯¯¯¯ is an altitude. prove: ab2+ac2=cb2 right triangle a b c with right angle a. point d lies on side b c and segment a d is drawn. angle a d c is a right angle. drag and drop a reason into each box to correctly complete the two-column proof. statement reason ad¯¯¯¯¯ is an altitude, and ∠bac is a right angle. given ∠adb and ∠adc are right angles. definition of altitude ∠bac≅∠bda ? ∠bac≅∠adc ? ∠b≅∠b ? ∠c≅∠c reflexive property of congruence △abc∼△dba ? △abc∼△dac aa similarity postulate abbd=cbab ? ab2=(cb)(bd) cross multiply and simplify. acdc=cbac polygon similarity postulate ac2=(cb)(dc) cross multiply and simplify. ab2+ac2=ab2+(cb)(dc) addition property of equality ab2+ac2=(cb)(bd)+(cb)(dc) substitution property of equality ab2+ac2=(cb)(bd+dc) ? bd+dc=cb segment addition postulate ab2+ac2=cb2 substitution property of equality