For each x-y table given, copy the table, find the pattern and fill in the missing entries. Then write the rule for the pattern in words. IN (x) OUT (y) a. b. IN (x) OUT (y) с. IN (x) OUT (y), 23 1 8 4 -2 -4 -2 -5 4 8. 26 -7.5 -20 -9 -10 302 27.5 1 1.5 -4 -10 -2.5 Rule: Rule: Rule: 3.
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- A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. y p(x, y) 0 1 2 x 0 0.10 0.03 0.02 1 0.07 0.20 0.08 2 0.05 0.14 0.31 (a) Given that X = 1, determine the conditional pmf of Y—i.e., pY|X(0|1), pY|X(1|1), pY|X(2|1). (Round your answers to four decimal places.) y 0 1 2 pY|X(y|1) (b) Given that two hoses are in use at the self-service island, what is the conditional pmf of the number of hoses in use on the full-service island? (Round your answers to four decimal places.) y 0 1 2 pY|X(y|2) (d) Given that two hoses are in use at the…A service station has both self-service and full-service islands. On each island, there is a single regular unleaded pump with two hoses. Let X denote the number of hoses being used on the self-service island at a particular time, and let Y denote the number of hoses on the full-service island in use at that time. The joint pmf of X and Y appears in the accompanying tabulation. y p(x, y) 0 1 2 x 0 0.10 0.05 0.01 1 0.07 0.20 0.08 2 0.05 0.14 0.30 (d) Compute the marginal pmf of X. x 0 1 2 pX(x) Compute the marginal pmf of Y. y 0 1 2 pY(y) Using pX(x), what is P(X ≤ 1)? P(X ≤ 1) =Considerthreemappingsα,β,γ:Z→Zdefined by α(n)=2n−1, β(n)=(n−1)^2, γ(n)=(n−1)^3
- homogenous DE 3udv-vdv-udu-vdu=0max z = x1 + 3x2 s.t. x1 + 2x2 ≥ 6 2x1 + x2 ≤ 8 x1, x2 ≥ 0 For the LP above, which of the following is its standard form? max z = x1 + 3x2 s.t. x1 + 2x2 + s1 = 6 2x1 + x2 + s2 = 8 x1, x2, s1, s2 ≥ 0 max z = x1 + 3x2 s.t. x1 + 2x2 – e1 = 6 2x1 + x2 – e2 = 8 x1, x2, e1, e2 ≥ 0 max z = x1 + 3x2 s.t. x1 + 2x2 + s1 = 6 2x1 + x2 – e2 = 8 x1, x2, s1, e2 ≥ 0 max z = x1 + 3x2 s.t. x1 + 2x2 – e1 = 6 2x1 + x2 + s2 = 8 x1, x2, e1, s2 ≥ 0In Figure, which of graphs (A), (B), and (C) is not the graph of an antiderivative of y = f (x)? Explain.
- considering the nonhomogenous 2ndorder ode y'' + 4y = 10sin(9pi x t)2. Find the linearization of √x at a = 49. Then use your linearization to approximate √56.A cup of water at an initial temperature of 81°C is placed in a room at a constant temperature of 24°C. The temperature of the water is measured every 5 minutes during a half-hour period. The results are recorded as ordered pairs of the form (t, T), where t is the time (in minutes) and T is the temperature (in degrees Celsius). (0, 81.0°), (5, 69.0°), (10, 60.5°), (15, 54.2°), (20, 49.3°), (25, 45.4°), (30, 42.6°) (a) Subtract the room temperature from each of the temperatures in the ordered pairs. Use a graphing utility to plot the data points (t, T) and (t, T − 24). (b) An exponential model for the data (t, T − 24) is T − 24 = 54.4(0.964)t. Solve for T and graph the model. Compare the result with the plot of the original data. (c) Use a graphing utility to plot the points (t, ln(T − 24)) and observe that the points appear to be linear. Use the regression feature of the graphing utility to fit a line to these data. This resulting line has the form ln(T − 24) = at + b, which is…