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question:a tanning salon , customers are charged 10 for their first visit in a calendar month and 8 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ?
answer:Let's calculate the revenue from each type of visit: 1. Revenue from first visits: Since every customer is charged 10 for their first visit, and there were 100 customers, the revenue from first visits is: 100 customers * 10/first visit = 1000 2. Revenue from second visits: 30 customers made a second visit, and each second visit costs 8, so the revenue from second visits is: 30 customers * 8/second visit = 240 3. Revenue from third visits: 10 customers made a third visit, and each third visit also costs 8, so the revenue from third visits is: 10 customers * 8/third visit = 80 Now, let's add up the revenue from all visits to get the total revenue for the last calendar month: Total revenue = Revenue from first visits + Revenue from second visits + Revenue from third visits Total revenue = 1000 + 240 + 80 Total revenue = 1320 The revenue for the last calendar month at the salon was boxed{1320} .
question:From the set {1, 2, 3, ldots, 8}, two different numbers are chosen. What is the probability that their greatest common divisor is one? Express your answer as a fraction.
answer:1. **Calculate the total number of two-element subsets**: The set {1, 2, 3, ldots, 8} contains 8 elements, so the number of different pairs we can choose is given by: {8 choose 2} = frac{8 times 7}{2} = 28. 2. **Identify non-coprime pairs**: We need to find the pairs (a, b) where text{gcd}(a, b) neq 1: - Pairs involving 4 and another multiple of 2 (except each other): (2, 4), (4, 6), (4, 8). - Pairs involving 6 and another multiple of 2 (except itself and pairs with 4 which we’ve included above): (2, 6). - Pair involving 8 and another multiple of 2 (less than it, except pairs with 4 which are included): (2, 8). This gives us 5 non-coprime pairs. 3. **Calculate the probability**: Subtracting the fraction of non-coprime pairs from 1, the probability that a randomly selected pair is relatively prime is: 1 - frac{5}{28} = frac{23}{28}. The resulting probability is boxed{frac{23}{28}}.
question:The motion equation of an object is s = 1 t + t^2, where the unit of s is meters (m), and the unit of t is seconds (s). What is the instantaneous velocity of the object at the end of 3 seconds?
answer:To find the instantaneous velocity, we need to differentiate the motion equation with respect to time t. The derivative of s with respect to t is s'(t) = 2t - 1. Then, to find the instantaneous velocity at t = 3 seconds, we substitute 3 into the derivative: s'(3) = 2 times 3 - 1 = 5. Therefore, the instantaneous velocity of the object at the end of 3 seconds is boxed{5 , text{m/s}}.
question:f AB=2, what is the perimeter of parallelogram ABCD?
answer:Given that AB=2, we aim to find the perimeter of parallelogram ABCD. First, we are given the equation 4-2m+2=0 when x=2. To solve for m, we rearrange the equation: [ 4 - 2m + 2 = 0 6 - 2m = 0 2m = 6 m = 3 ] With m=3, we substitute this value into the quadratic equation {x}^{2}-3x+2=0 to find the values of x. This gives us: [ x^2 - 3x + 2 = 0 ] Solving this quadratic equation, we find the roots to be {x}_{1}=2 and {x}_{2}=1. To find the perimeter of the parallelogram, we note that the lengths of the sides are given by the values of x. Since a parallelogram has two pairs of equal sides, its perimeter can be calculated as 2 times (x_1 + x_2), where x_1 and x_2 are the lengths of the sides. Substituting the values of x_1 and x_2 we found: [ text{Perimeter} = 2 times (2 + 1) = 2 times 3 = 6 ] Therefore, the perimeter of parallelogram ABCD is boxed{6}.