3. A 6 inch personal pizza has 610 calories, with 240 of those from fat. A 16 inch pizza is cut into 8 slices. Estimate the number of calories in one slice of a 16 inch pizza. ____Calories

Which of the following statements are true and which are false?

(a) Assume that we are implementing AES or a similar system on an RFID tag. When calculating the ASIC cost, one of the things we need to take into account is the key.

(b) Assume that we are implementing AES or a similar system on an RFID tag. When calculating the ASIC cost, one of the things we need to take into account is the internal state. (c) Assume that we are implementing AES or a similar system on an RFID tag. When calculating the ASIC cost, one of the things we need to take into account is the cryptographic signature.

(d) When studying how hard it is to break a cryptosystem, average-case complexity is more important than worst-case complexity. (e) The function n −5 is negligible.

(f) The function 5−n is negligible.

(g) The function log n is negligible.

(h) The function n − log n is negligible.

Problem 4. Consider ϕ : (Z100, +100) → (Z100, +100) defined by ϕ([x]100) = [41x + 19]100. a.) Show that ϕ is well-defined. b.) Use the fact that 61 · 41 = 2501 to argue that the function ϕ is one-to-one. c.) Is ϕ onto? Why or why not. Suppose that y is in the image of ϕ, find an element x so that ϕ(x) = y. [The answer will be dependent on the value of y.] Then prove that the found element works. d.) Is ϕ a homomorphism?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume the carrying capacity of the earth is

15

billion. Use the 1960s peak annual growth rate of

2.1​%

and population of

3

billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of

6.8

billion. How does the predicted growth rate compare to the actual growth rate of about

1.2​%

per​ year?

What is the base growth​ rate?

Assume you have a balance of ​$1400 on a credit card with an APR of 18​%, or 1.5​% per month. You start making monthly payments of​ $200, but at the same time you charge an additional ​$ 60 per month to the credit card.

Assume that interest for a given month is based on the balance for the previous month.

The following table shows how you can calculate your monthly balance. Complete and extend the table to show the balance at the end of each month until the debt is paid off. How long does it take to pay off the credit card​ debt?

Fill out the table row by​ row, and continue until the last full payment. ​(Round to the nearest cent as​ needed.)

Month Payment    Expenses Interest    New Balance

0 ​- ​-        ​ -    ​$ 1400

1    ​$200       ​$60      ​$ 1400 −​$200 plus +​$ 60 +​$ 21.00 =​$ 1281.00   2    ​$200       ​$60   ​    $ ?

A probability density function on R is a function f :R -> R satisfying (i) f(x)≥0 or all x e R and (ii) \int_(-\infty )^(\infty ) f(x)dx = 1. For which value(s) of k e R is the function

f(x)= e^(-x^(2))\root(3)(k^(5)) a probability density function? Explain.

Let X = ( X1, X2, X3, ,,,, Xn ) is iid,

f(x, a, b) = 1/ab * (x/a)^{(1-b)/b} 0 <= x <= a ,,,,, b < 1

then, find a two dimensional sufficient statistic for (a, b)

Suppose that you pick a bit string from the set of all bit strings of length ten. Find the probability that

1. the bit string has exactly two 1s;
2. the bit string begins and ends with 0;
3. the bit string has the sum of its digits equal to seven;
4. the bit string has more 0s than 1s;
5. the bit string has exactly two 1s, given that the string begins with a 1.

Given a complicated lim x → af (x), how do you quickly determine which items are

significant and which items are negligible —¿ quick guess in 5 seconds? Degree (or order) of largeness. How to convert your QuickGuess to an air tight high quality argument?

Problem 3Consider the following definitions for sets of characters:•Digits ={0,1,2,3,4,5,6,7,8,9}•Letters ={a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}•Special characters ={∗,&,$,#}Compute the number of passwords that satisfy the given constraints

.(i) Strings of length 7. Characters can be special characters, digits, or letters ,with no repeated characters

.(ii) Strings of length 6. Characters can be special characters, digits, or letters ,with no repeated characters. The first character can not be a special char-acter.

Determine whether the following two planes x + 4y − z = 7 and 5x − 3y −7z = 11 are parallel, orthogonal, coincident (that is, the same) or none of these.

please show full working for learning purposes

Use the technique developed in this section to solve the minimization problem.

The minimum is C =

at (x, y, z) = .