If Bonny has $$ 4 $$ different shirts, how many unique sets of $$ 2 $$ shirts can she choose?
This kind of question can be done by simply list out all the possible combinations: Say we label the $$ 4 $$ shirts $$ A, B, C, D $$, we can list all the unique pairs: $$ AB, AC, AD, BC, BD, CD = 6$$ pairs
How many ATP molecules are produced through the oxidation of $$ 1 $$ molecule of glucose?
It takes approximately $$ 4 $$ protons to generate $$ 1 $$ ATP molecule. Each $$ NADH $$ molecule pumps $$ 10 $$ protons across the mitochondrial membrane. Each $$ FADH_2 $$ molecule pumps $$ 6 $$ protons across the mitochondrial membrane. We can calculate the total number of ATP molecules produced by each electron carrier to be: $$ NADH = 10/4 = 2.5 $$ ATP $$ FADH_2 = 6/4 = 1.5 $$ ATP Now we can sum the total ATP produced for each phase of cellular respiration: Glycolysis: $$ 2 $$ ATP $$ 2 $$ $$ NADH = 2*2.5 = 5$$ ATP Pyruvate Oxidation: $$ 2 $$ $$ NADH = 2*2.5 = 5$$ ATP Krebs/TCA Cycle: $$ 2 $$ ATP $$ 6 $$ $$ NADH = 6*2.5 = 15$$ ATP $$ 2 $$ $$ FADH_2 = 2*1.5 = 3$$ ATP Adding together the ATP molecules produced at each phase yields of total of $$ 32 $$ ATP!
Solve for the roots of $$ x^2+5x+7 = 1 $$
Subtract $$ 1 $$ from both sides to set the equation equal to $$ 0 $$... $$ x^2+5x+6 $$ At this point the roots can be found by graphing, factoring, or the quadratic formula. Since this equation is factorable, we can find the roots without a calculator... $$ (x+2)(x+3) = 0 $$ Hence, the roots are $$ -2, -3 $$.