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3 years ago

Convergence in mathematics

Mathematics

2 answers:

nexus9112 [7]3 years ago

7 0

Answer:

Converges to $\frac{\sqrt{\pi }}{2}$

Step-by-step explanation:

$\int _0^{\infty \:}e^{-x^2}dx$ = $\lim_{b \to \infty}$ $\int _0^{b \:}e^{-x^2}dx$ = $\frac{\sqrt{\pi }}{2}$

steps:

write improper integral as a limit

solve integral

apply limit

If limit exists and this number is finite, the improper integral converges

Rashid [163]3 years ago

3 0

Answer:

that looks so complicated im dropping out

Step-by-step explanation:

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Jim and Jackie are married with three children at home and a mortgage. Jim’s net pay per year is $67,000 and Jackie does not hav

rodikova [14]

The correct option is that they should work on their plan for managing income.

<h3>How to illustrate the information?</h3>

Given that Jim and Jackie are married with three children and have a home at mortgage.

The net pay per year of Jim is $67,000 and Jackie do not earn at all. The mortgage expenses and monthly expenses are

$(2,800+2,700) = $5,500, not much as compared to the total income.

Also, Jim contributes 15% of his income , i.e., $10050 into the retirement fund and also they have savings of $5,000.

In addition, there is a $500,000 life insurance policy on Jim and a $100,000 policy on Jackie.

Therefore, looking at all of these, it can be concluded that the net income of Jim per year is not bad at all to manage the expenses, they just have to work on it little more to run the family smoothly.

Thus, the correct option is that they should work on their plan for managing income.

Learn more about income on:

brainly.com/question/25745683

#SPJ1

Complete question:

Jim and Jackie are married with three children at home and a mortgage. Jim’s net pay per year is $67,000 and Jackie does not have income. Their mortgage payment of $2,800 includes insurance on their home. They have additional monthly expenses of $2,700. Jim contributes 15% of his earnings to a retirement fund and they have $5,000 in savings. There is a $500,000 life insurance policy on Jim and a $100,000 policy on Jackie. As their financial advisor, what part of Jim and Jackie’s financial plan would you encourage them to work on? a. They should work on their plan for managing income. b. They should work on their plan for managing their liquidity. c. They should work on their plan for protecting their assets. d. They should work on their plan for protecting their income.

3 0

2 years ago

A random sample of 500 of these people is drawn, of whom 194 turn out to be currently enrolled in college. Estimate the percenta

Rzqust [24]

Answer:

$0.388 - 2.00\sqrt{\frac{0.388(1-0.388)}{500}}=0.344$

$0.388 + 2.00\sqrt{\frac{0.388(1-0.388)}{500}}=0.432$

The 95.5% confidence interval would be given by (0.344;0.432)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

The estimated proportion on this case is given by:

$p = \frac{X}{n}= \frac{194}{500}=0.388$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95.5% of confidence, our significance level would be given by $\alpha=1-0.955=0.045$ and $\alpha/2 =0.0225$ . And the critical value would be given by:

$z_{\alpha/2}=-2.00, z_{1-\alpha/2}=2.00$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.388 - 2.00\sqrt{\frac{0.388(1-0.388)}{500}}=0.344$

$0.388 + 2.00\sqrt{\frac{0.388(1-0.388)}{500}}=0.432$

The 95.5% confidence interval would be given by (0.344;0.432)

4 0

3 years ago

Graph the function f(x)=x3-5x2+6

Ilia_Sergeevich [38]

x 1 2 3 4 5

y 6 0 -4 0 18

7 0

3 years ago

598 x 3 =? Show your work

emmasim [6.3K]

Answer:

1794

Step-by-step explanation:

598

× 3

-------

1794

5 0

3 years ago

On a vacation to Puerto Rico Rose jumped off a cliff into a river in Elion forest preserve her height as a function of time to b

ioda

To solve for t, you will use the equation given: -16t^2 + 16t + 480 = 0. First, simplify the equation by dividing everything by 16: -t^2 + t + 30 = 0. Then complete reverse FOIL: (-t + 6)(t + 5) = 0. Next, set each of these equations to 0 separately, and solve for t. You will get t = 6, and t = -5. Since time can't be negative (Rose can't have hit the water after a negative number of seconds), the answer is 6.

3 0

3 years ago

Convergence in mathematics ​

Convergence in mathematics