21. Each day you buy exactly one of the following items: tape (costing $1), a ruler (costing $1), pens (costing $2), pencils (costing $2), paper (costing $2), or a loose-leaf binder (costing $3). Write a recurrence relation and initial conditions for the number s, of different sequences in which you can spend exactly n dollars (n 1) 22. Suppose that you have a large supply of 2-, 3-, and 5-cent stamps. Write a recurrence relation and initial conditions for the number sn of different ways in which n cents worth of postage.can be attached to an envelope 9.1 Recurrence Relations 469 if the order in which the stamps are attached matters. (Thus a 2-cent stamp followed by a 3-cent stamp is different froma 3-cent stamp followed by a 2-cent stamp.) 23. Write a recurrence relation and initial conditions for an, the number of arrangements of the integers1, 2, ...,n. 24. Write a recurrence relation and initial conditions for s, the number of subsets of a set with n elements. 25. Write a recurrence relation and initial conditions for s, the number of two-element subsets of a set with n elements. 26. Write a recurrence relation and initial conditions for the number sn of n-bit strings having no two consecutive 27. Write a recurrence relation and initial conditions for the number s of sequences of nickels, dimes, and quarters that can be inserted into a vending machine to purchase a soft drink costing 5n cents. How many sequences zeros. Compute s6. a recurrencerelation and initial conditions for pn, the number of L-shaped pieces needed to cover a 6 x for the number Cn of different ways to group 2n people int are there for a drink costing 50 cents? 28. For n 2, a 6 x n checkerboard can be covered by L-shaped pieces of the type shown in Figure 2.20. Write its natu

Q: $ 438 200 115 2 215 433 380 193 45

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A: We have to solve the given expression for y. The expression is 24=3+y.

Q: Let Mbe as in Equation (3.14) and let X = [1, 0, ½]¹. Show that the entries of Y=MX sum to 1.

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Q: 1. For what values of a does the function f have a local (relative) maximum on (0,8)? Answer…

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Q: limx→2 f(x) = lim, ¹x→−1+ f(x) =

A: Given graph of the function fx is   1. Find :  limx→2 fx. 2. Find :limx→-1+ fx.

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.