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question:Solve for x in the equation: (x-2)/4+3=5
answer:#"subtract 3 from both sides of the equation"# #(x-2)/4cancel(+3)cancel(-3)=5-3# #rArr(x-2)/4=2# #"multiply both sides by 4 to eliminate the fraction"# #cancel(4)xx(x-2)/cancel(4)=4xx2# #rArrx-2=8# #"add 2 to both sides to solve for x"# #xcancel(-2)cancel(+2)=8+2# #"which gives us"# #x=10" as the solution"#
question:Janelle Heinke, the owner of Ha'Peppas!, is considering two oven options for baking her signature vegetarian pizzas. Oven A has a capacity of 24 pizzas/hour, fixed costs of 25,000, and variable costs of 2.00 per pizza. Oven B can bake 42 pizzas/hour, with fixed costs of 35,000 and variable costs of 1.50 per pizza. Each pizza is sold for 15.00. 1) Calculate the break-even point in unit sales for each oven: For Oven A: For Oven B: 2) If Janelle expects to sell 9,000 pizzas, which oven should she choose? A) Oven A B) Oven A or B (Equal Profit) C) Oven B 3) If Janelle anticipates selling 13,000 pizzas, which oven should she select? A) Oven A or B (Equal Profit) B) Oven A C) Oven B 4) What is the volume at which the total costs for Oven A and Oven B are equal (crossover point)?
answer:1) For Oven A, the break-even point (Q) can be calculated as: {eq}begin{array}{l} Q = frac{{Fixed;Costs}}{{Selling;Price;-;Variable;Costs}} Q = frac{{25000}}{{15 - 2}} Q approx 1923 end{array} {/eq} For Oven B: {eq}begin{array}{l} Q = frac{{Fixed;Costs}}{{Selling;Price;-;Variable;Costs}} Q = frac{{35000}}{{15 - 1.5}} Q approx 2593 end{array} {/eq} 2) Janelle should choose Oven A (Option A). With 9,000 pizzas: - Oven A: Profit = 9,000 × (15 - 2) - 25,000 = 92,000 - Oven B: Profit = 9,000 × (15 - 1.5) - 35,000 = 86,500 3) Janelle should choose Oven A (Option B). With 13,000 pizzas: - Oven A: Profit = 13,000 × (15 - 2) - 25,000 = 144,000 - Oven B: Profit = 13,000 × (15 - 1.5) - 35,000 = 140,500 4) The crossover point occurs when the total costs for both ovens are equal: Total Costs for Oven A = Fixed Costs + (Variable Costs × Volume) Total Costs for Oven B = Fixed Costs + (Variable Costs × Volume) Let V be the crossover volume: {eq}begin{array}{l} 25000 + 2V = 35000 + 1.5V 0.5V = 10,000 V = 20,000 end{array} {/eq} So, the crossover point is 20,000 pizzas.
question:A yacht race has a normally distributed completion time with a mean of 2 hours and a standard deviation of 30 minutes. a) What percentage of boats complete the race in one hour or less? b) What percentage of boats will take between two and a half hours to three hours to finish the race? c) If the maximum time limit is three and a half hours, what percentage of boats will not have finished the race when the time expires?
answer:a) To find the percentage of boats that complete the race in one hour or less, we calculate the probability: {eq}P(X ≤ 1) = Pleft(frac{X - mu}{sigma} ≤ frac{1 - 2}{0.5}right) = P(Z ≤ -2) = 0.0228{/eq} Therefore, approximately 2.28% of boats complete the race in one hour or less. b) To find the percentage of boats that will take between two and a half hours to three hours to finish the race, we calculate the probability: {eq}P(2.5 ≤ X ≤ 3) = Pleft(frac{2.5 - 2}{0.5} ≤ frac{X - mu}{sigma} ≤ frac{3 - 2}{0.5}right) = P(1 ≤ Z ≤ 2) = 0.1359{/eq} Therefore, approximately 13.59% of boats will take between two and a half hours to three hours to finish the race. c) To find the percentage of boats that will not have finished the race when the time limit expires, we calculate the probability: {eq}P(X > 3.5) = 1 - P(X ≤ 3.5) = 1 - Pleft(frac{X - mu}{sigma} ≤ frac{3.5 - 2}{0.5}right) = 1 - P(Z ≤ 3) = 0.0013{/eq} Therefore, approximately 0.13% of boats will not have finished the race when the time limit expires.
question:Which pair of molecules does not have a polar bond?
answer:D) O-O Explanation: A polar bond is formed when two atoms have a significant difference in electronegativity, which is the ability of an atom to attract electrons towards itself. In the case of O-O, both oxygen atoms have the same electronegativity, so the bond between them is nonpolar. In contrast, the other three pairs of molecules (N-O, C-O, and O-H) have polar bonds because the electronegativity of one atom is greater than the other.