Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→[infinity] ln(5x) 5x Step 1 As x → [infinity], ln(5x) → and 5x → .

Answers

Answer 1

Answer:

[tex]\lim_{x \to \infty} \frac{ln(5x)}{5x} = \lim_{x \to \infty} \frac{1/x}{5} = \lim_{x \to \infty} \frac{1}{5x} = 0[/tex]

Step-by-step explanation:

L'Hopital's rule says that, if both numerator and denominator diverge, then we can look at the limit of the derivates.

Here we have:

[tex]\lim_{x \to \infty} \frac{ln(5x)}{5x}[/tex]

The numerator is ln(5x) and when x tends to infinity, this goes to infinity

the denominator is 5x, and when x tends to infinity, this goes to inifinity

So both numerator and denominator diverge to infinity when x tends to infinity.

Then we can use L'Hopithal's rule.

The numerator is:

f(x) = Ln(5x)

then:

f'(x) = df(x)/dx = 1/x

and the denominator is:

g(x) = 5*x

then:

g'(x) = 5

So, if we use L'Hopithal's rule we get:

[tex]\lim_{x \to \infty} \frac{ln(5x)}{5x} = \lim_{x \to \infty} \frac{1/x}{5} = \lim_{x \to \infty} \frac{1}{5x} = 0[/tex]


Related Questions

A random sample of n1 = 296 voters registered in the state of California showed that 146 voted in the last general election. A random sample of n2 = 215 registered voters in the state of Colorado showed that 127 voted in the most recent general election. Do these data indicate that the population proportion of voter turnout in Colorado is higher than that in California? Use a 5% level of significance.

Answers

Answer:

The p-value of the test is 0.0139 < 0.05, which means that these data indicates that the population proportion of voter turnout in Colorado is higher than that in California.

Step-by-step explanation:

Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

California:

Sample of 296 voters, 146 voted. This means that:

[tex]p_{Ca} = \frac{146}{296} = 0.4932[/tex]

[tex]s_{Ca} = \sqrt{\frac{0.4932*0.5068}{296}} = 0.0291[/tex]

Colorado:

Sample of 215 voters, 127 voted. This means that:

[tex]p_{Co} = \frac{127}{215} = 0.5907[/tex]

[tex]s_{Co} = \sqrt{\frac{0.5907*0.4093}{215}} = 0.0335[/tex]

Test if the population proportion of voter turnout in Colorado is higher than that in California:

At the null hypothesis, we test if it is not higher, that is, the subtraction of the proportions is at most 0. So

[tex]H_0: p_{Co} - p_{Ca} \leq 0[/tex]

At the alternative hypothesis, we test if it is higher, that is, the subtraction of the proportions is greater than 0. So

[tex]H_1: p_{Co} - p_{Ca} > 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the two samples:

[tex]X = p_{Co} - p_{Ca} = 0.5907 - 0.4932 =  0.0975[/tex]

[tex]s = \sqrt{s_{Co}^2+s_{Ca}^2} = \sqrt{0.0291^2+0.0335^2} = 0.0444[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{0.0975 - 0}{0.0444}[/tex]

[tex]z = 2.2[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a difference above 0.0975, which is 1 subtracted by the p-value of z = 2.2.

Looking at the z-table, z = 2.2 has a p-value of 0.9861.

1 - 0.9861 = 0.0139.

The p-value of the test is 0.0139 < 0.05, which means that these data indicates that the population proportion of voter turnout in Colorado is higher than that in California.

Determine if the table represents a linear function. If so, what's the rate of change?


A) Yes; rate of change = 3


B) No; a nonlinear function


C) Yes; rate of change = 2


D) Yes; rate of change = –4

Answers

The answer of this question is C. Because the different on y value is increasing by 2 so it’s linear

Eight students are running for three positions in
the student council: president, vice president,
and secretary. Which represents the total
number of ways that three students can be
selected if each student can be elected to only
one position?

Answers

Answer:

Step-by-step explanation:

Total number of outcome are  

1320

.

Explanation:

It is apparent that there are  

12

ways in which the post of President can be filled. Once President's post is filled, there are  

11

ways to fill the post of Vice President and then  

10

ways to fill the post of Secretary,

Hence a total of  

12

11

10

or  

1320

ways or outcomes.

Answer:

1320

Step-by-step explanation:


Hey guys today you could help that would be great

Answers

Answer: the answer is b

6,10,16,24,34 find an expression for the nth term in this sequence ​

Answers

Answer:

Answer

Step-by-step explanation:

please like and mark brainlist

Cow gives two fifths of liters of milk each day. How many liters of milk can the cow give in the second month of 2016?

Answers

Step-by-step explanation:

ex : Cow Produce Milk 2.5 Litters/day

1 Month = 30 days(Assume in 30 days )

for second Months

2.5 litters/day x 30 days

= 75 Litters/Month

Eco-Cook rice cooker has a mean time before failure of 38 months with a standard deviation of 6 months, and the failure times are normally distributed. What should be the warranty period, in months, so that the manufacturer will not have more than 8% of the rice cookers returned

Answers

Answer:

The warranty period should be of 30 months.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Eco-Cook rice cooker has a mean time before failure of 38 months with a standard deviation of 6 months.

This means that [tex]\mu = 38, \sigma = 6[/tex]

What should be the warranty period, in months, so that the manufacturer will not have more than 8% of the rice cookers returned?

The warranty period should be the 8th percentile, which is X when Z has a p-value of 0.08, so X when Z = -1.405.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.405 = \frac{X - 38}{6}[/tex]

[tex]X - 38 = -1.405*6[/tex]

[tex]X = 30[/tex]

The warranty period should be of 30 months.

I need two examples of division of decimal to the thousandths place by one to the hundredths place. SHOW ALL WORK!!!!!!!!

Answers

Answer:

i think you need to work on your decimals mate

Step-by-step explanation:

Bill works for a large food service company. In one hour he can make 19 sandwiches or he can make 40 salads. Bill works 7 hours per day. If Bill needs to make 30 sandwiches then how many salads can he make

Answers

Answer:

[tex]x=216 salads[/tex]

Step-by-step explanation:

One Hour:

Salad=40

Sandwich=19

Total work time[tex]T=7[/tex]

Generally

Time to make 30 sandwiches is

[tex]T_s=\frac{30}{19}[/tex]

[tex]T-s=1.6hours[/tex]

Therefore

Bill has 7-1.6 hours to make salads and can make x about of salads in

[tex]x=(7-1.6)*40[/tex]

[tex]x=5.4*40[/tex]

[tex]x=216 salads[/tex]

The perimeter of rectangle is 36 cm.If it's breadth is half of it's breadth is half of it's length then find it's dimension.And explain it.​

Answers

Answer: 12 x 6

Step-by-step explanation:

36/2=18

3x=18

x equal 6

6x2=12 as it is two times

If a quadrilateral is a square, then all sides are the same. What part is the conclusion

Answers

All squares are rhombuses, but not all rhombuses are squares. The opposite interior angles of rhombuses are congruent. Diagonals of a rhombus always bisect each other at right angles. Hope this helped

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.02 level that the medicine relieves pain in more than 384 seconds. For a sample of 41 patients, the mean time in which the medicine relieved pain was 387 seconds. Assume the population standard deviation is 23. Find the P-value of the test statistic.

Answers

Answer:

The p-value of the test statistic is 0.2019.

Step-by-step explanation:

Test if there is evidence at the 0.02 level that the medicine relieves pain in more than 384 seconds.

At the null hypothesis, we test if it relieves pain in at most 384 seconds, that is:

[tex]H_0: \mu \leq 384[/tex]

At the alternative hypothesis, we test if it relieves pain in more than 384 seconds, that is:

[tex]H_1: \mu > 384[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

384 is tested at the null hypothesis:

This means that [tex]\mu = 384[/tex]

For a sample of 41 patients, the mean time in which the medicine relieved pain was 387 seconds. Assume the population standard deviation is 23.

This means that [tex]n = 41, X = 387, \sigma = 23[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{387 - 384}{\frac{23}{\sqrt{41}}}[/tex]

[tex]z = 0.835[/tex]

P-value of the test:

The p-value of the test is the probability of finding a sample mean above 387, which is 1 subtracted by the p-value of z = 0.835.

Looking at the z-table, z = 0.835 has a p-value of 0.7981.

1 - 0.7981 = 0.2019

The p-value of the test statistic is 0.2019.

Can someone help me find the answer to this question ?

Answers

Answer:

  B.  x ≤ 1 or x > 6

Step-by-step explanation:

Subtract 8 and divide by 2. (Same steps for both inequalities.)

  2x +8 ≤ 10

  2x ≤ 2

  x ≤ 1

__

  2x +8 > 20

  2x > 12

  x > 6

The solution is x ≤ 1 or x > 6.

whats the correct answer?

Answers

Answer:

its the 4 one

Step-by-step explanation:

what is the ratio of the two values and what new value do they produce? $280 in 7m
what is the ratio of the two values and what new value do they produce? 105 miles in 2 hours
what is the ratio of the two values and what new value do they produce? $33 for 5lb
what is the ratio of the two values and what new value do they produce? 50 pages in 2 hours

Answers

Answer:

The ratio between two values A and B is just the quotient between these two values:

ratio = A/B

a) $280 in 7m

Here the ratio is:

$280/7m = $40/m

This also can be read as:

$40 per meter.

b) 105 miles in 2 hours

Here the ratio is:

105mi/2h = 52.5 mi/h

This also can be read as:

52.5 miles per hour

c) $33 for 5lb

The ratio is:

$33/5lb = $6.6/lb

This can be read as:

$6.6 per pound.

d) 50 pages in 2 hours

the ratio is:

(50 pages)/2h = 25 pages/h

this can be read as:

25 pages per hour.

In how many ways can a committee of 3 men and 4 boys be chosen from 7 men and 6 boys so as not to include the youngest boy if the eldest man is serving?

Answers

Answer:

There are 75 ways to form the committee.

Step-by-step explanation:

The order in which the people are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

Considering the eldest has to be there, 2 men from a set of 6 and 4 boys from a set of 5(excluding the youngest), so:

[tex]T = C_{6,2}C_{5,4} = \frac{6!}{2!4!} \times \frac{5!}{1!4!} = 3*5*5 = 75[/tex]

There are 75 ways to form the committee.

Which number produces an irrational number when added to
ON
O A. 2/7
O B. -0.4
O C. 15
D. 0.555...

Answers

Answer: 0.555

Step-by-step explanation:

Can I have help I am stuck on this problem It would mean the world if u helped me and tysm!! =-)

Answers

Answer:

1. >

2. <

3. =

4. <

Step-by-step explanation:

23.197 > 23.179

3 2/10 which is the same as,

3.2 < 3.243

30.423 = 30 423/1000

18.546 < 18 56/100

Which column represents the correct method for the proof of the following statement?
If two angles form a linear pair, then they share a common ray.
Column A
1. Assume the angles do not form a
linear pair
2. If the angles do not form a linear
pair, then they are not adjacent
Column B
1. Assume the angles do not share a
common ray
2. If the angles do not share a
common ray, then they are not
adjacent
3. If two angles are not adjacent, then
they cannot form a linear pair
4. If two angles do not share a
common ray, then they do not form
a linear pair
3. If two angles are not adjacent then
they do not have a common ray
4. If two angles do not form a linear
pair, then they do not have a
common ray
A column A
B. column B
C. both column A and column B
D. neither column A nor column B

Answers

Answer:

90

Step-by-step explanation:

the colums add up to angle 1, which make angle 2 adjacent.

9-9=0

According to records from a large public university, 88% of students who graduate from the university successfully find employment in their chosen field within three months of graduation. What is the probability that of nine randomly selected students who have graduated from this university, at least six of them find employment in their chosen field within three months

Answers

Answer:

0.9842 = 98.42% probability that at least six of them find employment in their chosen field within three months.

Step-by-step explanation:

For each student, there are only two possible outcomes. Either they found employment, or they did not. The probability of a student finding employment is independent of any other student, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

88% of students who graduate from the university successfully find employment in their chosen field within three months of graduation.

This means that [tex]p = 0.88[/tex]

Nine randomly selected students

This means that [tex]n = 9[/tex]

What is the probability that of nine randomly selected students who have graduated from this university, at least six of them find employment in their chosen field within three months?

This is:

[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 6) = C_{9,6}.(0.88)^{6}.(0.12)^{3} = 0.0674[/tex]

[tex]P(X = 7) = C_{9,7}.(0.88)^{7}.(0.12)^{2} = 0.2119[/tex]

[tex]P(X = 8) = C_{9,8}.(0.88)^{8}.(0.12)^{1} = 0.3884[/tex]

[tex]P(X = 9) = C_{9,9}.(0.88)^{9}.(0.12)^{0} = 0.3165[/tex]

Then

[tex]P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) = 0.0674 + 0.2119 + 0.3884 + 0.3165 = 0.9842[/tex]

0.9842 = 98.42% probability that at least six of them find employment in their chosen field within three months.



Suppose 50.7 liters of water came out of a faucet today. If 2.6 liters of water come out each minute, for how many minutes was the faucet on?

Answers

I believe the answer is 19.5 (or 19m 30s), 50.7/2.6=19.5, 2.6x19.5=50.7

Which of the following is correct based on this picture?
A. tan D=31/24
B. sin D=31/24
C. tan K=31/24
D. cos K=31/24

Answers

Answer:

C. tan K=31/24

Step-by-step explanation:

Relations in right triangles:

The sine of an angle is the length of the opposite side to the angle divided by the length of the hypotenuse.

The cosine of an angle is the length of the adjacent side of the angle divided by the length of the hypotenuse.

The tangent of an angle is the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

In this question:

Sides 24 and 31.

Side opposite to K: 31

Side adjacent to K: 24

Then

tan K=31/24

And the correct answer is given by option D.

From past experience, a company has found that in cartons of transistors, 92% contain no defective transistors, 3% contain one defective transistor, 3% contain two defective transistors, and 2% contain three defective transistors. About how many extra transistors per day would the company need to replace the defective ones if it used 10 cartons per day?

Answers

Answer:

Ungrouped data refers to the data that is first gathered from a study, it is a raw data that is, i.e it has not sorted into categories or grouped. To calculate the mean of ungrouped data we use the formula

Step-by-step explanation:

A vegetable garden and a surrounding as a shaped like a square that together a 11 ft wide. The path is 2 feet wide. If one bag of gravel covers 10 square feet, how many bags are needed to cover the path? Round your answer to the nearest tenth. NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW. ​

Answers

Answer:

[tex] \displaystyle 4[/tex]

Step-by-step explanation:

we are given that A vegetable garden and a surrounding as a shaped like a square that together a 11 ft wide. The path is 2 feet wide.since together the width of Vegetable garden and path is 11 ft, the width of the vegetables garden will be the difference between the total width and the width of path Thus,

[tex] \displaystyle \rm W _{ garden} = 11 - 2[/tex]

simplify substraction:

[tex] \displaystyle \rm W _{ garden} = 9[/tex]

recall that, every single side of a square is equal to each other therefore the the area of the garden will be

[tex] \displaystyle {9}^{2} [/tex]

simplify square:

[tex] \displaystyle 81[/tex]

together the garden and path makes a square of every side length 11 ft saying that the area will be:

[tex] \displaystyle {11}^{2} [/tex]

simplify square:

[tex] \displaystyle 121[/tex]

the area of path will be the difference between the total area and the garden area therefore,

[tex] \displaystyle 121 - 81[/tex]

simplify addition:

[tex] \displaystyle 40[/tex]

to figure out how many bags are needed to cover the path. we just need to divide the area of the path by the area of a bag of gravel and that yields:

[tex] \displaystyle \frac{40}{10} [/tex]

simplify division:

[tex] \displaystyle \boxed{\rm4}[/tex]

hence,

4 bags are needed to cover the path.

Select the correct statement about what data scientists do during the Data Preparation stage.

a. During the Data Preparation stage, data scientists define the variables to be used in the model.
b. During the Data Preparation stage, data scientists determine the timing of events.
c. During the Data Preparation stage, data scientists aggregate the data and merge them from different sources.
d. During the Data Preparation stage, data scientists identify missing data.
e. All of the above statements are correct.

Answers

Answer:

e. All of the above statements are correct.

Option e is correct. All of the above statements are correct.

What is Data science?

Data science is an interdisciplinary academic field that uses statistics, scientific computing, scientific methods, processes, algorithms and systems to extract or extrapolate knowledge and insights from noisy, structured and unstructured data

Data Scientist makes value out of data, he is expert in various tools and technologies like machine learning, deep learning, artificial intelligence and he solve business problems by presenting a model to predict business future.

During data preparation, data scientists and DBAs aggregate the data and merge them from different sources. During data preparation, data scientists and DBAs define the variables to be used in the model.

Hence, All of the above statements are correct, Option e is correct.

To learn more on Data science click:

https://brainly.com/question/20815848

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Two classes have a total of 50 students. One of the classes has 6 more students than the other. How many students are in the larger class.
14
19
28
31

Answers

Answer:

28 are in the larger class.

Step-by-step explanation:

50/2 = 25 xy

25+ 3 = 28 larger

25-3 = 22 smaller

x = 28

The larger class has 28 students, and the correct option is 28.

Let's assume the number of students in one class is x.

According to the given information, the other class has 6 more students than this class, which means the number of students in the other class is x + 6.

To find the total number of students, we add the number of students in both classes: x + (x + 6) = 50.

Combining like terms, we have: 2x + 6 = 50.

Next, we subtract 6 from both sides of the equation: 2x = 44.

Finally, we divide both sides of the equation by 2 to solve for x: x = 22.

So, there are 22 students in one class, and the other class has 22 + 6 = 28 students.

Therefore, the larger class has 28 students, and the correct option is 28.

To know more about equation:

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Find the measure of the indicated angle. (Round to 2 decimal places if necessary)
9
?
21

Answers

To answer this, since the hypotenuse is given, whichever side 9 is you will square it and take it away so c^2-a^2=b^2 9 squared + 21 squared = 360 the square root of 360 would be 18.9 which you can round to 19 hope this helps!

The following chart summarizes the selling price of homes sold last month in the Sarasota, Florida, area. a. What is the chart called? multiple choice Pie chart Histogram Cumulative frequency polygon Frequency polygon b. How many homes were sold during the last month? c. What is the class interval? d. About 75% of the houses sold for less than what amount? (Enter your answer in thousands.) e. One hundred seventy-five of the homes sold for less than what amount? (Enter your answer in thousands.)

Answers

Answer:

Following are the solution to the given points:

Step-by-step explanation:

For question a:

The chart is called a cumulative frequency polygon.

For question b:

The total number of sold homes in last month= 250

For question c:

The class intervels are:

[tex]\to 100-50 = 50[/tex]

For question d:

[tex]\to[/tex] 240000 (75% of houses)

For question e:

[tex]\to[/tex] 230000

Select the correct answer. Solve the equation using the method of completing the square. 2r2 + 16r - 8 = 0​

Answers

Answer:

r=-4+2[tex]\sqrt{5}[/tex], r=-4-2[tex]\sqrt{5}[/tex]

Answer:

r=-4+2[tex]\sqrt{5}[/tex], r=-4-2[tex]\sqrt{5}[/tex]

Step-by-step explanation:

It was right for me

solve -3x+2y=-6 -2x+y=6 using substitution

Answers

Answer:

See below

Step-by-step explanation:

-3x+2y = -6 [1]

-2x + y = 6 [2]

For [1], solve for X.

-3x + 2y = -6

-3x = -6 - 2y

3x = 6 + 2y

x = 2 + (2/3)y

Plug x into [2]

-2(2+(2/3)y) + y = 6

-4 - 4/3y + y= 6

-4/3y + y= 10

-1/3y = 10

y = -30

9514 1404 393

Answer:

  (x, y) = (-18, -30)

Step-by-step explanation:

When choosing to solve by substitution, it is convenient if one of the variables has a coefficient of 1 or -1. Here, y has a coefficient of 1 in the second equation, making it easy to rearrange that equation to give an expression for y:

  y = 2x +6 . . . . . add 2x to the second equation

Using this expression, we can substitute for y in the first equation:

  -3x +2(2x +6) = -6

  x + 12 = -6 . . . . . . . . . simplify

  x = -18 . . . . . . . . . . . subtract 12

  y = 2(-18) +6 = -30 . . . . substitute into the equation for y

The solution is (x, y) = (-18, -30).

Other Questions
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