A restaurant made 200 pizzas, some of which had no toppings, while the others had at least one of three toppings -- mushrooms, onions, and peppers -- as summarized in the table above. No pizza had all three toppings. How many of the pizzas had no toppings?
Answer(s): A
Adding the single-topping counts and then subtracting the double-topping overlaps (no pizza has all three toppings) gives the number with at least one topping:80 + 100 + 90 - (28 + 23 + 25) = 194.Since 200 pizzas were made, 200 - 194 = 6 had no toppings.
The 6 temperatures, in degrees Celsius, t1, t2, t3, t4, t5, t6 have a standard deviation of 2.14. Which of the following lists of temperatures, in degrees Celsius, must also have a standard deviation of 2.14?Indicate all such distributions.
Answer(s): A,B
The two lists -t1, -t2, -t3, -t4, -t5, -t6 and t1 + 4, t2 + 4, t3 + 4, t4 + 4, t5 + 4, t6 + 4 each have the same standard deviation of 2.14, because multiplying every value by -1 or adding the same constant to every value does not change a distribution's standard deviation.
If w, x, y, and z are consecutive positive integers, where w < x < y < z, which of the following statements must be true?Indicate all such statements.
Let the integers be w = n, x = n + 1, y = n + 2, z = n + 3.When any three consecutive integers are taken (here w, x, y), exactly one of them is divisible by 3, so their product wxy must be divisible by 3.
Answer(s): D
During a sale, a store is selling all of its chairs at 30 percent to 50 percent off the regular price.Quantity AThe sale price of a chair that regularly sells for $300Quantity BThe sale price of a chair that regularly sells for $400
$300 chair· Highest possible sale price: 300 × 0.70 = $210· Lowest possible sale price: 300 × 0.50 = $150$400 chair· Highest possible sale price: 400 × 0.70 = $280· Lowest possible sale price: 400 × 0.50 = $200Because the exact discount on each chair is not specified, either chair could end up with the higher sale price (for example, 30 % off the $300 chair vs. 50 % off the $400 chair, or vice versa).
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