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Neporo4naja [7]
3 years ago
14

(1) In Section 1.4 we used the Axiom of Completeness (AoC) to prove the Archimedean Property of R (Theorem 1.4.2). Show that the

Monotone Convergence Theorem can also be used to prove the Archimedean Property without making any use of AoC.
(2) Use the Monotone Convergence Theorem to supply a proof for the Nested Interval Property (Theore 1.4.1) that doesn't make use of AoC. These two results suggest that we could have used the Monotone Con- vergence Theorem in place of AoC as our starting axiom for building a proper theory of the real numbers

Mathematics
1 answer:
serious [3.7K]3 years ago
3 0

Answer:

Both Answers are in the following attachment (a) and (b)

Step-by-step explanation:

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The number of accidents that occur at a busy intersection is Poisson distributed with a mean of 4.5 per week. Find the probabili
Mariana [72]

Answer:

a) 0.01111

b) 0.4679

c) 0.33747

Step-by-step explanation:

We are given the following in the question:

The number of accidents per week can be treated as a Poisson distribution.

Mean number of accidents per week = 4.5

\lambda= 4.5

Formula:

P(X =k) = \displaystyle\frac{\lambda^k e^{-\lambda}}{k!}\\\\ \lambda \text{ is the mean of the distribution}

a) No accidents occur in one week.

P(x =0)\\\\= \displaystyle\frac{4.5^0 e^{-4.5}}{0!}= 0.01111

b) 5 or more accidents occur in a week.

P( x \geq 5) = 1-\displaystyle \sum P(x

c) One accident occurs today.

The mean number of accidents per day is given by

\lambda = \dfrac{4.5}{7} = 0.64

P(x =1)\\\\= \displaystyle\frac{0.64^1 e^{-0.64}}{1!}= 0.33747

5 0
3 years ago
overnight a pipe cracked and started to leak into a basement. the graph shows the depth of the water in relation to time. how ma
Shkiper50 [21]

Answer:

if a water pipe bursts over night depends on the pressure of the water but i will say a foot or more an hour

Step-by-step explanation:

3 0
3 years ago
the first group of students consists of 10 and their average age was 13 years old the next group consisted of 30 students and th
Kazeer [188]

Answer: The average was 9 years old find the average age of both groups is 10 years old.

Step-by-step explanation:

Formula foe average : \text{Average} =\dfrac{\text{Sum of all observations}}{\text{Number of observations}}

Given : The first group of students consists of 10 and their average age was 13 years old.

i.e. 13=\dfrac{\text{Sum of ages of students of first group}}{10}\\\\\Rightarrow\ \text{Sum of ages of students of first group}=13\times10=130      (1)

The next group consisted of 30 students and their average was 9 years old.

i.e. 9=\dfrac{\text{Sum of ages of students of next group}}{30}\\\\\Rightarrow\ \text{Sum of ages of students of nextgroup}=9\times30=270      (2)

Then from (1) and (2) , the sum of both groups (first group and next group )students = 130+270 =400

Combined students of both groups (first and next group )= 10+30=40

Now , the average of both groups =\dfrac{\text{Sum of combined students}}{\text{combined students}}

=\dfrac{400}{40}=10

Hence, the average was 9 years old find the average age of both groups is 10 years old.

4 0
3 years ago
What is the rule of a function of the form f(t)= a sin (bt+c) +d whose graph appears to be identical to the given graph?
olasank [31]

Answer:

Option A.

f(x) = -4*sin((1/3)*t + (π/6))  + 3

Step-by-step explanation:

We can easily solve this problem by using a graphing calculator or plotting tool.

The function is

f(t) = a*sin (b*t +c) + d

Please, see attached picture below.

By looking at the picture with all the possible cases, we can tell that the correct option is A.

The function has a period of T = 6π

Max . Amplitude = 7

Min . Amplitude = -1

7 0
3 years ago
Read 2 more answers
Use the equation 5x + (–7) = –8x + 6 to determine which statements are true. Check all that apply. The terms 5x and –8x are like
Aleks [24]

5x and -8x are like terms. 6 is not a variable. 5 is the coefficient of the term 5x. X is not the constant.

3 0
3 years ago
Read 2 more answers
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