Factor completely. 9 x 2 + 6 x + 1

Exercise 2.2.5. Let [[x]] be the greatest integer less than or equal to x. For example, [[π]] = 3 and [[3]] = 3. For each sequen

Debora [2.8K]

Answer:

a) $\lim_{n\rightarrow \infty}a_n=0$

b) The limit is [[4/3]]=1, that is, $\lim_{n\rightarrow \infty}a_n=1$

Step-by-step explanation:

The definition of the limit of a sequence (an) is as follows:

$\lim_{n\rightarrow \infty}a_n=L$ (the sequence (an) converges to L) means that given $\epsilon>0$ , there exists some natural number N such that if n≥N, then $|a_n-L|$

We will use that [[x]] is a increasing function. That is, if x≤y then [[x]]≤[[y]]

a) For all $\epsilon>0$ , take N≥6. Then 1/N ≤1/6 and 5/N ≤ 5/6 < 1. We have that 0<5/N<1, therefore [[5/N]]=0 (0 is the biggest integer less than or equal than x, for any x on the interval 0<x<1)

For n≥N, we have that 1/n ≤ 1/N, hence 0< 5/n ≤ 5/N < 1 . As we discussed above, [[5/n]]=0. Then |a_n|=0, therefore $|a_n-0|=|a_n|=0$

b) For all $\epsilon>0$ , take N≥3/4 (any N will do). Then 1/N ≤ 4/3 and 1/4N ≤ 1/3. Note that a_n=[[(12 + 4n)/3n]]=[[1/4n + 4/3]]

For n≥N, we have that 1/4n ≤ 1/4N, hence 1< 4/3< 1/4n +4/3 ≤ 1/4N+4/3 ≤ 5/3 <2.If 1<x<2 then [[x]]=1 , hence a_n=[[1/4n +4/3]]=1

Then |a_n-1|=|1-1|=0, therefore $|a_n-1|=0$

4 0

4 years ago

Abigail is using her mother's pancake recipe, but she wants to make 60% more pancakes than the recipe usually prepares. If her m

Volgvan

Answer:

1 and 1/4 cup of flour

Step-by-step explanation:

Abigail needs to use 3/4 cup more flour

3 0

3 years ago

I will give you thanks and :)<br> Please help

avanturin [10]

Answer:

Scale factor = 2, x = 3 cm

Step-by-step explanation:

The scale factor is 2 because you can see that in the second figure you multiply the sides from the first one by 2.

Using the scale factor 2, you can multiply 1.5 * 2 = 3 for x.

3 0

3 years ago

A bank is reviewing its risk management policies with regards to mortgages. To minimize the risk of lending, the bank wants to c

agasfer [191]

1. μ = 306,500

2.σ = 24,500

3. n = 150

4. μ $_x$ = $306,500

5. σ $_x$ = $2000

<h3>What is Standard deviation?</h3>

The standard deviation serves as a gauge for the degree of variation or dispersion among a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the mean of the collection.

With a standard deviation of $24,500 and an average mortgage debt of $306,500, Americans have a median mortgage debt.

<h3>According to the given information:</h3>

The population's average is

μ = 306,500

Standard deviation for the general population is

σ = 24500

Imagine 150 Americans are chosen at random for the sample.

n= 150

The sample mean is roughly normally distributed as a result of the high sample size, which is supported by the central limit theorem.

The population mean and sample mean would be the same,

μ $_n$ = μ =306,500

Here is how to calculate the sample standard deviation:

$\sigma_{x}=\frac{\sigma}{\sqrt{n}}$

the sample size is n, and is the population standard deviation.

$\begin{aligned}&\sigma_{x}=\frac{24,500}{\sqrt{150}} \\&\sigma_{x}=\$ 2,000\end{aligned}$

The necessary conditions are thus:

1. μ = 306,500

2.σ = 24,500

3. n = 150

4. μ $_x$ = $306,500

5. σ $_x$ = $2000

To know more about Standard deviation visit:

brainly.com/question/16965372

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I understand that the question you are looking for is :

A bank is reviewing its risk management policies with regards to mortgages. To minimize the risk of lending, the bank wants to compare the typical mortgage owed by their clients against other homebuyers. The average mortgage owed by Americans is $306,500, with a standard deviation of $24,500. Suppose a random sample of 150 Americans is selected. Identify each of the following, rounding your answers to the nearest cent when appropriate:

1. $1. $mu=?\\2. $sigma=?\\3. $=n=$\\4. $mu_{overlinex}=$x=?\\5. $sigma_{overlinex}=$x=?$

4 0

2 years ago

Cherie accepted a job through an employment agency. The job pays $1,100 a week. The agency charges 30% of her first 4 weeks pay.

Leto [7]

If this job pays 1100 a week, in four weeks Cherie would make 4400. If she’s giving a 30% cut to the agency for four weeks, she’d be giving 330 of every weeks paycheck. At the end of those four weeks, she’d end up giving $1,320 to the agency.

5 0

3 years ago

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