Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.
y = x5, y =
square root of x
; about the x-axis

Answers

Answer 1

Rotating the area bounded by the given curves around the designated line yields the solid's volume as \(V = \frac{9}{22}\pi\)

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere. Different forms have various volumes.

The amount

of space that a solid occupies is measured by its volume. The amount of unit cubes required to completely fill the solid serves as the measurement. The capacity of an object to hold matter is generally thought of as its volume in three dimensions.
The functions provided are,

\(`y = f(x) = \sqrt{x}``y = g(x) = x^5`\)

By rotating the area around the x-axis, the solid's volume is given by (using washer method)
\(V = \pi int_a^b [f^2(x)-g^2(x)]dx\)
evaluate the integral, limit the plugins, and
\(V = \pi int_0^1 [(\sqrt{x})^2-(x^5)^2]dx\\\\V= \pi int_0^1 [x-x^10]dx V = \pi [\frac{x^2}{2}-\frac{x^11}{11}]_0^1 V = \pi [\frac{1^2}{2}-\frac{1^11}{11}]. V = \pi [\frac{1}{2}-\frac{1}{11}] = \frac{9}{22}\pi\)

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Related Questions

Use the terms quality of life, poverty, equality, and inequality to write a statement that describes your living conditions.

Answers

Promoting equality and addressing poverty and inequality are crucial for creating a society that values the wellbeing of all inequality and supports their pursuit of a good quality of life.

Description of our living conditions:

The general statement that highlights the importance of quality of life, poverty, equality, and inequality for individuals and societies.

Access to basic needs such as food, shelter, healthcare, education, and opportunities for personal and professional growth are fundamental aspects of a good quality of life. Poverty, on the other hand, restricts access to these resources and can negatively impact physical and mental health, social mobility, and overall wellbeing.

Equality means that everyone has an equal opportunity to achieve their potential and enjoy a good quality of life, regardless of their background or circumstances. In contrast, inequality can lead to disparities in access to resources, opportunities, and power, creating a system that benefits some while disadvantaging others.

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Given triangle MAT is an isosceles triangle and point H is the midpoint if MT. Prove triangle MHA is congruent to triangle THA

Answers

Answer:

There is everything in the image

Given triangle MAT is an isosceles triangle and point H is the midpoint if MT. Prove triangle MHA is

The Side-Angle-Side postulate is satisfied. Then the triangle ΔMHA and ΔTHA are congruent with each other.

What is the triangle?

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

In an isosceles triangle, the two legs of the triangle are congruent and their opposite angles too.

A triangle MAT is an isosceles triangle and point H is the midpoint of MT.

In triangle ΔMHA and ΔTHA, we have

AH = AH (Common sides)

MH = HT (H is the midpoint of MT)

∠AMH = ∠ATH (Isosceles angles)

The Side-Angle-Side postulate is satisfied. Then the triangle ΔMHA and ΔTHA are congruent with each other.

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In January 2020 oil price was $1283 but in April 2020 the price was $1351. What is the percent increase or decrease

Answers

Answer:

5.3%

Step-by-step explanation:

% Increase = Increase / Original Number × 100.

68/1283 * 100

= 5.3%

Which value is a solution to the inequality x < 4?

A. 3
B. 6
C. 5
D. 4.5

Answers

The answer is x > 4.5.

Explanation:

-24 > -6(x - 0.5)

-24 > -6x + 3

6x > 3 + 24

6x > 27

x > 27/6

x > 4.5

Hope this helps :)

Please help me with this :)

Please help me with this :)

Answers

A and D
A and D
A and D

Last question I need help with an answer not a link

Last question I need help with an answer not a link

Answers

Answer:

it's toooo complicated

y=mx+b
answer fast, please!

y=mx+banswer fast, please!

Answers

Answer: y = -1x + 3

Step-by-step explanation:

it's going through the y intercept ( 3 )

and down ( negative by 1 )

you can also write the answer as y = -x + 3

either one, its the same.

y=-1x + 3 is the answer

Ming bought 40 pencils and Catherine bought 24. If each package of pencils sold at the store contain the same number of pencils, what is the largest possible number of pencils in a package?

Answers

Answer:

8 pencils.

Step-by-step explanation:

This is a common, GCF question and the question becomes, what number is the GCF of 40 and 24.

40= 2x2x2x5

24=2x2x2x3

Both share 2x2x2, which is 8 so the largest number of pencils in each pack is 8.

Answer:

8

Step-by-step explanation:

To solve this you need to find the largest common factor. The way I did it was by listing out all of the factors of each number, then going through all of them and finding the largest common factor which was 8.

the product of 9 and the sum of a number x and 12

Answers

Answer:

X * 12 = 9

Step-by-step explanation:

The required model of the given situation is given as y = 9 (x + 12).

What are equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
the product of 9 and the sum of the number x and 12 is given as
Let the product is equal to y
y = 9 (x + 12)

Thus, the required model of the given situation is given as y = 9 (x + 12).

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can yall help me??? it would be awsome and i will give brainleist

can yall help me??? it would be awsome and i will give brainleist

Answers

Answer:

Its eather 2a or -18

Step-by-step explanation:

I think its one of those two

Could i have a heart and branliest please.

a^2=18
Replace a with 10
(10)^2 = 18
10 squared is 100 so
100=18
subtract 18 from 100
100-18=82
82 Hope this is correct and helps !!

Can I please get some help I’ve been stuck on this question for a while!

Can I please get some help Ive been stuck on this question for a while!

Answers

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

How many minutes of the ride are spent higher than 28 meters above the ground?

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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I need help please look at the picture and tell me what x equals thank you.

I need help please look at the picture and tell me what x equals thank you.

Answers

Answer:

X= 72

Step-by-step explanation:

(x-2)+ (x-2)+(x-2) = 180°

or, 3x - 36 = 180°

or, 3x = 180+36

or, 3x = 216

or, x =216/3

or, x = 72°

which of the following demonstrates how the first 21 on the left side of the triangle is calculated using the combination pattern?

which of the following demonstrates how the first 21 on the left side of the triangle is calculated using

Answers

Answer:

d

Step-by-step explanation:

In two half-lives, how much of a 400-gram sample of a radioactive element will remain un-decayed?

Answers

Answer:

100 grams

Step-by-step explanation:

1/2 * 1/2 = (1/2)² = 1/4

1/4 * 400 = 100

Round nine in 7,297 please do it fast

Answers

Answer:

7300 is the write answer

The ratio of dogs to cats at the
pet store is 2:5. If there are 6 more
cats than dogs, how many dogs are
at the pet store?

Answers

The ratio of dogs to cats at the

pet store is 2:5. If there are 6 more

cats than dogs, how many dogs are

at the pet store?

Dogs : 2

Cats : 5

Answer :

-1

5 - 2 = 3,

-1, 0, 1, 2, 3, 4, 5

1 - 5 will give us a 6

d i need help on this ​

d i need help on this

Answers

Step-by-step explanation:

Yes, they are similar because if you convert both of the measurements to fractions, which will be 2/3 and 8/12, you can see that if you simplify 8/12, you will get 2/3. That is why they are similar.

Every evening for the months of September and October, the following eight Gry ndor students, Harry, Ron, Hermione, Ginny, Fred, George, Seamus, and Dean will play a game of Exploding Snap. Let's suppose that each night, exactly three of them play one game. Can there be a game of Exploding Snap every evening throughout September and October without having the same three Gry ndors play a game twice

Answers

Answer:

Yes.  There can be 56 games (92%) of Exploding Snap every evening throughout September and October that can be played without having the same three Gry ndors play a game twice.

Step-by-step explanation:

This is a combination game without repetition.

The formula for combination without repetition is:

n! /r! (n - r)!

where n = 8 and r = 3

Therefore, n! /r! (n - r)!

= 8! / 3! (8 -3)!

= 40,320 / 6 (120)

= 40,320 / 720

= 56

There are 30 nights in September and 31 nights in October, totaling 61 nights

This implies that 56/61 games can be played in these two months without repeating the same three gamers.

56/61 = 0.918

= 92%

Divide: 7 5/6 ÷ 2/3 need help

Answers

To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction and then multiply it by the reciprocal of the fraction.

Step 1: Convert the mixed number to an improper fraction:

7 5/6 = (6 * 7 + 5) / 6 = 47/6

Step 2: Multiply the improper fraction by the reciprocal of the fraction:

47/6 ÷ 2/3 = 47/6 * 3/2

Step 3: Simplify the fraction if possible:

47/6 * 3/2 = (47 * 3) / (6 * 2) = 141/12

Step 4: Simplify the fraction further, if necessary:

141/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3:

141/12 = (141 ÷ 3) / (12 ÷ 3) = 47/4

Therefore, 7 5/6 ÷ 2/3 is equal to 47/4 or 11 3/4.

If I earn $15/hour and work for 20 hours/week, how much would I earn in one
week?

A.) $35

B.)$300

C.)$150

D.)$30

Answers

Answer:

B.) $300

Step-by-step explanation:

just multiply 15 by how many hours you have

On average, Nathaniel drinks
4/5 of a 10-ounce glass of water in
2 2/5​
hours. How many glasses of water does he drink in one hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.

Answers

Nathaniel drinks 3 glasses of water in one hour.

To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.

In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.

Let's convert the mixed number of hours to an improper fraction:

\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)

\(=\frac{12}{5}\)

Now, we can set up a proportion to find his drinking rate per hour.

We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.

Let's assign "x" as the number of glasses he drinks in one hour.

The proportion is then

\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)

Cross-multiplying gives us

\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)

Simplifying, we get

\(\frac{12}{5} =\frac{4}{5}\times x\)

Dividing both sides by \(\frac{4}{5}\), we find x:

\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)

\(x=\frac{12}{4}\)

\(x = 3.\)

Therefore, Nathaniel drinks 3 glasses of water in one hour.

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elect all equations that represent the number of subscribers, , in terms of months since the beginning of the year (when she had 150 subscribers).

Answers

There are no equations provided in the question, so I am unable to select equations that represent the number of subscribers in terms of months since the beginning of the year. Please provide me with the equations to choose from.

Ken jumps 1 1/5 metres and Steve jumps 1.5 metres. How much more does Steve jump?

Answers

Answer: 0.3 meters.

Step-by-step explanation:

First we need to turn one of those into a fraction or decimal to make things easier for us. Lets turn \(1 \frac{1}{5}\) into a decimal.

1 1/5 as a decimal is 1.2.

Now we compare the two

\(1.5 > 1.2\)

Now we need to subtract 1.5 by 1.2 to see how much more he jumps by.

\(1.5 - 1.2 = 0.3\)

Steve jumps more by 0.3 meters.

Answer:

3/10 or .3 meters

Step-by-step explanation:

1 1/5 = 1.2

1.5 - 1.2 = 0.3

3. What percentage of an average household's expenses would you consider needs as compared to
wants?

Answers

According to the 50-30-20 budget rule shown in the image, an average household should aim to allocate 50% of their income towards needs, 30% towards wants, and 20% towards savings.

A broad rule of thumb that may be used to gauge the proportion of necessities to desires in the average household budget is included in the image you provided. A typical household should seek to allocate 50% of its income towards requirements, 30% towards desires, and 20% towards savings, according to the 50-30-20 budget guideline seen in the graphic. Of fact, given that everyone's circumstances and objectives are unique, this rule might not apply to everyone.

But for those who want to make a budget or better control their spending, it can be a helpful place to start. In the end, a multitude of variables, such as income, family size, geography, and personal preferences, will determine how much of an average household's costs are spent on necessities vs desires. It's crucial to create a budget that works for your specific situation and allows you to achieve your financial goals.

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Your question is incomplete. The complete question is:

What percentage of an average household's expenses would you consider needs as compared to wants in the image attached?

3. What percentage of an average household's expenses would you consider needs as compared towants?

ill give brainiest if ur correct :)

ill give brainiest if ur correct :)

Answers

Answer:

Step-by-step explanation:

rate  of car per minutes = 39/60 = 13/20 = 0.65 mil/min

distance travelled in 2 minutes = 13/20*2 = 1.3 miles

Hope you will give brainliest to reach genius

Marco wants to know how much the other students in his mathematics class study. He recorded the data he collected in
the following table.
Time spent studying per week (in hours)
2.0
5.0
1.0
2.5
2.5
3.5
0.0
4.5
2.5
4.0
3.5
3.0
2.0
1.5
4.0
2.0
0.5
3.0
1.0
3.0
3.5
1.5

1. Construct a histogram for the data.

Marco wants to know how much the other students in his mathematics class study. He recorded the data

Answers

Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

7. The Taylor Rule states that the central bank should set the short-term nominal interest rate (i)
based on the inflation gap [the difference between inflation (3.14) and desired inflation (3.14*)] and the
output gap (the percentage difference between real GDP (Y) and potential GDP (Y*) An
example of a Taylor Rule would be the formula
i - 3.14 = 1.5 +0.5(3.14-3.14*) +0.5 (Y-Y*/Y*)
The term on the left-hand side is the real interest rate. Consider the following table

Inflation rate (3.14), %
Target inflation rate (3.14*), %
Output gap, %
Real interest rate
Nominal interest rate
Base Scenario Scenario B Scenario C
4.0
20
2.0
20
0.0
20
20
20
00
a. Fill in the real and nominal interest rates chosen by the policy maker in the base scenano
b. How does scenario B differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move the inflation rate toward its target?
c. How does scenario C differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move output toward the potential level?
d. Suppose a new chair of the central bank is appointed and she switches to a new policy rule of
the form given in the next equation. Recalculate the real and nominal interest rates for the
three scenarios. What has been the effect of the change in weights?
i-3.14=1.5 +0.75(3.14-3.14*) +0.25(Y-Y*/Y*)

Answers

The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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Find the value of n for which the division of x^2n-1 by x+3 leave remainder of -80.​

Answers

The value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

To find the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80, we can use polynomial long division. Let's perform the division step by step:

Write the dividend and divisor in polynomial long division format:

_________________________

x + 3 │ x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ...

Divide the leading term of the dividend (x^(2n-1)) by the leading term of the divisor (x). The result is x^(2n-1)/x = x^(2n-2).

Multiply the divisor (x + 3) by the quotient obtained in the previous step (x^(2n-2)). The result is x^(2n-2) * (x + 3) = x^(2n-1) + 3x^(2n-2).

Subtract the result obtained in step 3 from the original dividend:

x^(2n-1) + 0x^(2n-2) + 0x^(2n-3) + ... - (x^(2n-1) + 3x^(2n-2)) = -3x^(2n-2) + 0x^(2n-3) + ...

Bring down the next term of the dividend (which is 0x^(2n-3)) and repeat steps 2-4 until the remainder is constant.

Since we are given that the remainder is -80, we can set the remainder equal to -80 and solve for 'n'.

-3x^(2n-2) + 0x^(2n-3) + ... = -80

Since the remainder is constant (-80), it means that all the terms with x have been canceled out in the division process. Therefore, we can deduce that the highest power of x in the divisor (x + 3) is 0.

This implies that x^(2n-2) = 0, and for any value of 'n', the exponent 2n-2 should be equal to zero. Solving this equation:

2n-2 = 0

2n = 2

n = 1

Therefore, the value of 'n' for which the division of x^(2n-1) by x + 3 leaves a remainder of -80 is n = 1.

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the respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes

Answers

The standard deviation of the response time is 1.53 minutes.

What is the standard deviation of the response time?

To get standard deviation, we will determine z-scores corresponding to the given percentiles and use them to calculate the standard deviation.

Z-score = z = (x - μ) / σ

For the lower bound of 10 minutes:

z = (10 - 13) / σ

For the upper bound of 16 minutes:

z = (16 - 13) / σ

As normal distribution is symmetric, the z-score corresponding to the lower tail of 2.5% is -1.96, and the z-score corresponding to the upper tail of 2.5% is 1.96.

Using z-scores, we set up  equations:

(10 - 13) / σ = -1.96

(16 - 13) / σ = 1.96

Solving the first equation:

-3 / σ = -1.96

σ = -3 / -1.96

Solving the second equation:

3 / σ = 1.96

σ = 3 / 1.96

Dividing both sides by 1.96:

-3 / 1.96 = σ

1.53 = σ

Full question:

The respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes. What is S.D. of the response time.

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15 is what percentage of 30?

Answers

Answer:

50%

Step-by-step explanation:

It is half of 30

Hey there!

QUESTION:

“15 is what percentage of 30?”

SIDE NOTE(S):

We will label “x” as the unknown number until we find what the actual number is.

⚠️Remember⚠️

PERCENTAGES RUNS OUT OF 100

SOLVING YOUR QUESTION:

15 = x% of 30

x% of 30 = 15

x% * 30 = 15

x/100 * 30 = 15

3/10 * x = 15

x * 3/10 = 15

MULTIPLY 10/3 to BOTH SIDES

x * 3/10 * 10/3 = 15 * 10/3

CANCEL out: 3/10 * 10/3 because it gives you 1

KEEP: 15 * 10/3 because it helps solve for the x-value (to find out what the actual percentage number is)

NEW EQUATION: x = 10/3 * 15

SIMPLIFY IT!

x = 50

ANSWER:

Therefore, your answer should be about [50%]

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

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Not everyone was in favor of the changes that occurred during the Great Awakening. Why would a minister or person be against religious changes in the colonies?4. The Great Awakening prepared people for the revolution during the 1770s. How were people prepared, and why did this happen in the colonies? What are the effects of cystic fibrosis genetic mutations? If c = 13 and A = 73, find a. Round to the nearest tenth. somone tlk to meeeeeeee problem: report error now suppose that not only must sir lancelot and sir gawain be diametrically opposite, but sir galahad and sir percival also demand to be diametrically opposite. how many seatings of the $10$ knights are possible? How do I find the rule of a linear table ? what president made armistice day veterans day The wholesale price for a desk is $195 A certain furniture store marks up the wholesale price by 30% . Find the price of the desk in the furniture store. The percent of the U.S. population that shares math pupper-doggo memes can be described by p= 1.19x + 58.0 where x is the number of years after 1990. (a) Find the slope m and the p-intercept of the graph of this equation. slope = ___p-intercept = ___ (b) Write a sentence that interprets the meaning of the slope as a rate of change. a. The U.S. population that shares math pupper-doggo memes is decreasing by -m percentage points each year. b. The U.S. population that shares math pupper-doggo memes is decreasing by multiplying 1 m percent each year. c. The U.S. population that shares math pupper-doggo memes does not change each year. d. The U.S. population that shares math pupper-doggo memes is increasing by multiplying m percent each year. e. The U.S. population that shares math pupper-doggo memes is increasing by an additional m percentage points each year. Drew is single and files using the head of household filing status. His agi is $95,000. He has two qualifying children: sage, age 5, and peppa, age 17. What is the amount of drew's 2022 child tax credit? $2,000 $3,600 $4,000 $6,600. What is the value of w?w+12w+45w-23 I need help on the equation for this PLEASE PLEASE PLEASE HELP!!with the meselson and stahl DNA replication experiment, how did identifying and analyzing alternative hypotheses help scientists design and analyze experiments? Describe a business buyer for FedEx brand. For instance, Suave Shampoo might sell to a hotel chain. Briefly discuss how serving that buyer would be different from selling to consumers. What would change about each of the four Ps (Product, Price, Promotion and Place, if anything? which functions domain consist of all real numbers except -2A) f(x)=1/x+2B)f(x)=2xC)f(x)=2x-2D)f(x)=1/x+2 The firt time larry play a video game, he i knocked out in 30 econd. The next time he play 30 econd longer than the econd. Larry i able to play 30 econd longer each game. It cot him 25 cent to play each game. How much will it cot Larry to lat 4 minute before he i knocked out?