4. Is it more likely that Harper will pick 2 French books or 2 English books? Use the following information to answer questions 5-8. Round each answer to the nearest thousandth. Michael chooses 1 pair of socks and 1 pair of sneakers randomly each morning. The table below lists the colors and number of pairs of socks and sneakers he owns. Number of pairs by color Item White Gray Black Blue Orange Socks 2 1 2 Sneakers 1 2 5. What is the probability that Michael selects both white socks and white sneakers? 6. What is the probability that his socks are black and his sneakers are white?

Q: Evaluate 10!/4!(10-4) Type an integer or a simplified fraction

A: It is needed to evaluated 10!/4!(10-4)!.

Q: How to write 0.014 (014 recurring) in the form p/q.  (Where p,q are elements of real numbers.)

A:

Q: Simply the expression to a sum of 2 terms and then factor the result to obtain the product of sums:…

A: The complete solution is in given below

Q: Using the result you proved in the question above, find a list of 200 consecutive composite…

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Q: For a natural number n, we define n! = 1-2-3 (n − 1). n. - For example: 2! = 1-2, 3! = 1-2-3 = 6,…

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Q: How many ways can you get we get a 2 digit passcode if zeros are not allowed?

A: If zero is not allowed, The number of available digits is 9 (1,2,3,4,5,6,7,8,9)

Q: The sum of the squares of the first 5 fibonacci terms, check and prove

A: Fibonnaci Sequence is: 1,1,2,3,5,8,13,21,34,55,89,... (That is, each term of the sequence is the sum…

Q: Part A. Ranional & Irational Numbers 1. For each number, state if the number is rational or…

A: Kindly keep a note in step 1️⃣ stating that as per our guidelines we are supposed to answer only 1️⃣…

Q: Use any method, list all the three digit numbers from the set {3,4,5,6} where there are no repeating…

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Q: Prove that (n!)! is divisible by (n!)

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Q: Rum: sum o fust n natural To werify the Am :- numbers usarg the fermula and equare grid Precedure: -…

A: To verify the formula for sum of n natural numbers using the square grid.

Q: For the number 70260.011000 What is the number of significant digits and what are the significant…

A: Number of  Significant digits = 11

Q: How do we proof that 2logn = n?

A:

Q: Using direct proof method, prove the following. If n is an even integer then n²+ 13 is odd.

A: n is even, so take n=2k and put on the expression.

Q: Factorial Is n! same as n+1? If I have n+1 in an equation, can I put n! instead?

A: Since n! = n (n-1)! e.g:- Let n=3  Then n+1 = 4 but n! = n(n-1)! Then 3! = 3×2×1 =6

Q: To prove that: n²= 5k or 5k+1 or 5k+4 we use the following method: Division into cases. We need 3…

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Q: For all integers n, if 6 | n, then 9 | ((n^2) + 21n/2)

A:

Q: 5. Consider the subtraction problem "6 - "13. a. Show how to represent the problem on a number line…

A: 6a)

Q: 1. How many elements are in the set {49, 51, 53,..., 177}? >

A:

Q: Prove this statement Discrete Math There exists a prime number l so that l^2 − l + 11 is also…

A: We have to prove that, "there exists a prime number I so that I2-I+11 is prime". We know the set of…

Q: how do you proof part a with a formal proof

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Q: integers a and b, if a^2+b^2 is odd, then a or b is odd.    use indirect or direct proofs…

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Q: 1) Show all your work in proper mathematical form to receive full marks. An answer with little or no…

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Q: Using direct proof method, prove the following. If n is an even integer then n2 + 13 is odd.

A: Direct proof

Q: The product of two numbers are 12 and there Least Common Multipleis 6 then Greatest Common Divisor…

A: Given,  Product of two numbers = 12 and Least common Multiple = 6 To find the greatest common…

Q: • Show that if m divides 3, then m divides 9. (We say a divides b if there exists an integer k such…

A: Let  m divides 3 .  Then there exists an integer k such that 3 = mk. Now, 9 can be written as…

Q: 1 2/7 * (-2 2/3) / 1 3/7 + 1 1/3

A: We will reduce the fractions of possible and then perform the required addition, multiplication and…

Q: Odd numbers between 0 and 48 that are multiples of 5.

A: The number that are not divisible by 2 are referred as odd numbers. The odd numbers between 0 and 48…

Q: Question:  a) prove that 100 can not be written as sum of an odd integer and two even integers.…

A: a) To prove that 100 cannot be written as sum of an odd integer and two even integer. Even integer…

Q: Prove that when you select n +1 numbers from {1,2, ... 2n} two of them must be consecutive (that is,…

A: Use inductive argument and Pigeon hole principles

Q: m = q192 ··•¶s – P192··· ¶s %3D .. =n – pi(q2 .qs) - = P1P2•• · Pr – P192 ··•92 .. = P1(P2 .· Pr –…

A:

Q: Use a direct proof to show that if n² is an odd integer, then n* is also an odd integer.

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Q: How many numbers of four digits can be formed with the digits 0, 1, 2, 3 (repetition of digits is…

A: The digits given are 0,1,2 and 3.Here the repetition of digits is not allowed.We need to find the…

Q: (a) Prove the following statement about natural numbers from the axioms N1 to N13. Apart from the…

A: Given:  a<b and b<c, ∀a, b, c∈ℕ To prove : a+1<c

Q: summary of direct proofs

A:

Q: Using c++

A: Correcting the code:To fix the code, we need to replace the incorrect condition with a logical…