4. (10 points) Prove that if A is not connected, then A is not an interval. 5. (10 points) Use only the definition of a compact set to prove the interval [0, o0) is not compact. 6. (10 points) Let {an} be a sequence in R with rn a. Use the definition of a compact set to prove the set {Tn :n € N}U {a} is compact. 7. (10 points) Let K be a nonempty compact subset of R. Prove every sequence in K has a convergent subsequence that converges in K.

Q: Number 27

A:

Q: 25+2=

A: First we calculate 2^5.2^5= 2x2x2x2x2=32

Q: The number of guest represented is not 85

A: Min  = 15Q1 = 30Median = 45Q2 = 55Max = 100

Q: Number 9 was not answered. I ask for 5 and 9 not 5 and 6. Thank you.

A: We find linear function using table and then find f(0).

Q: Number 28

A:

Q: ust do number 27.

A: 27) To sketch the contour map and graph of the function:

Q: to 48x

A: Given expression is:

Q: Please answer D

A: (a) Given that the percentage of stadiums have just built in the past 20 years is, P=15%=15/100=0.15…

Q: I wanted help with 22 not 21

A: 22)

Q: answer just letter d  , please

A: Solution:

Q: 3&4 please

A: (3) Given that, the normal distribution has a population mean is, μ=50 The expected value of the…

Q: — 33 > 5а + 2

A:

Q: Can number 9 be completed please.

A: Given a 1211220021112347451112 b 1202231110240000

Q: 66 to the nearest 100

A: Find 66 to the nearest 100

Q: Number 284

A: Given revenue function: R(x)=-x2+8x

Q: :N N amd 9: N-oN are functions such that f is not onto but f+9 is onto Prove that 9 is onto or give…

A: Suppose that f:ℕ→ℕ and g:ℕ→ℕ are functions such that f is not onto but f+g is onto. To prove that g…

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 14x – 60x? – læ + 3)dx…

A: Since you have posted a multiple question according to guildlines I will solve first  question for…

Average

In mathematics, everyone must have heard the term average in one place or other. Almost all types of calculation require taking out an average. In everyday life, the term is used for denoting a certain amount that can be said to be a typical quantity for multiple people or objects. In other words, if a group of people possesses a certain object, then the average gives us an idea regarding the quantity of the object possessed by each person. However, this is solely based on mathematical calculation. It is important to note that most people will not strictly have the average value in a group.