a farmer wants to fence an area of 3750 square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. what should the lengths of the sides of the rectangular field be so as to minimize the amount of fencing needed?

Answers

Answer 1

The lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 30 feet by 20 feet

Let x represent the length of the fence and y represent the width of the fence.

Since the area is 3750, hence:

Area = length * width = x * y

3750 = xy

y = 3750/x

A fence divide the field in half and is parallel to one of the sides of the rectangle. Hence:

Amount of fencing needed (P) = x + x + y + y  + y = 2x + 3y

Amount of fencing needed (P) = 2x + 3(3750/x) = 2x + 1800/x

To minimize the amount of fencing needed, dP/dx = 0, hence:

dP/dx = 2 - 1800/x²

2 - 1800/x² = 0

2 = 1800/x²

2x² = 1800

x² = 900

x = 30 feet

y = 600/x = 600/30 = 20 feet

Hence, the lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 30 feet by 20 feet

learn more about of area here

brainly.com/question/15719559

#SPJ4


Related Questions

(d) is it possible for this curve to have a horizontal tangent at points where it intersects the x-axis? explain your reasoning.

Answers

No, there cannot be a horizontal tangent at the point where the curve intersects the x-axis.

What is a curve on the graph?

A smooth-drawn figure or line with a bend or turn is referred to as a curve.

A circle is an illustration of a curved shape.

The path, also known as the topological arc, is the name of the curve (or just arc).

If a curve is the continuous injective image of an interval or a circle, it is considered simple.

If a curve is determined by a continuous function, in other words.

So, it possible for the curve to have a horizontal tangent:

On the curve, horizontal tangents appear where:

x = -1 and y ≠ -1

y = 0 where the curve crosses the x-axis.

-1² + 2(-1) + 0⁴ + 4.0 ≠ 5

No, the point where the curve crosses the x-axis cannot have a horizontal tangent.

Therefore, no, there cannot be a horizontal tangent at the point where the curve intersects the x-axis.

Know more about the curve on the graph here:

https://brainly.com/question/27887527

#SPJ4

Complete question:

Consider the closed curve in the xy-plane given by : x²+2x+y⁴=4y = 5

Is it possible for this curve to have a horizontal tangent at points where it intersects the x-axis? explain your reasoning.

the second angle of a triangle is 28 more than the first angle. the third angle is two times the first. find the three angles.

Answers

Let the first angle be h
h+h+28+2xh =180
h+h+2h+28=180
4h+28=180
4h=152
h=38

First angle is 38
Second angle is 66
Third angle is 76

Hope this helps

write a equivalent expression ( x + 3) +4y

Answers

The expression equivalent to the given expression will be x+y+3(1+y).

What is an expression?

It is defined as the combination of constants and variables with mathematical operators.

It is given that the expression is,( x + 3) +4y

We have to write the equivalent expression for the given expression,

Expressions that function identically despite having different appearances are called equivalent expressions. If two algebraic expressions are equivalent, then they both have the same result when the same value of the variable is entered.

=( x + 3) +4y

=x+3+4y

=x+3+y+3y

=x+y+3+3y

=x+y+3(1+y)

Thus, the expression equivalent to the given expression will be x+y+3(1+y).

Learn more about the expression here:

brainly.com/question/14083225

#SPJ1

A random number generator is used to create a list of 150 single-digit numbers. of those 150 numbers, 72 are odd and 78 are even. the number 9 was generated 15 times to the nearest whole percent, what is the experimental probability of an odd number other than 9 being generated? o 38% 0 48% o 52% o 79% 20°f sunny 'o

Answers

The experimental probability of an odd number other than 9 being generated is 38%.

Explain the term experimental probability?A probability that has been established by a series of tests is called an experimental probability. To ascertain their possibility, a random experiment is initiated and iterated over a number of times; each iteration is referred to as a trial. The goal of the experiment is to predict the likelihood that an event will occur or not.

For the stated question-

150 numbers altogether.Odd numbers in total: 72There are 15 nines.

Other odd numbers outside nine are as follows: 72 - 15 = 57

Probability =  (number of odd numbers except nine)]/(total number)

Probability = 57/150

Probability = 0.38.

Thus, the experimental probability of an odd number other than 9 being generated is 38%.

To know more about the experimental probability, here

https://brainly.com/question/8652467

#SPJ4

A house on the market was valued at 376,000. After several years, the value decreased by 9%. By how much did the house value decrease in dollars. What is the current value of the house?

Answers

Answer:

Step-by-step explanation:

The price decreases by $288,000*(0.19)=$54,720

The current value is then $233,280.

What is 8640 minutes, in days? (remember, there are 60 minutes in an hour and 24 hours in a day. ).

Answers

As there are 60 minutes in an hour and 24 hours in a day, there are 6 days as well as 144 days in 8640 minutes.

What is division?

A number is split in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of things being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.

Here,

There are 60 minutes in an hour,

=8640/60

=144 hours

There are 24 hours in a day,

=144/24

= 6 days

There is 6 days as well as 144 days in 8640 minutes as there are 60 minutes in an hour and 24 hours in a day.

To know more about division,

https://brainly.com/question/3315095

#SPJ4

Practice #3
Tell whether each table represents a function.

Answers

a. The table represents a function.

b. The domain is given as follows: {1, 2, .., 12 AM, 1, 2, ... , 12 PM).

c. The range is given as follows: {1, 2, 3, ..., 24}.

Is this a function? What are the domain and the range?

To obtain whether a relation represents a function, we need to observe if each input is mapped to only one output.

This table gives the conversion of hours in the AM-PM format to hours in the military format. Each hour in the AM-PM format has only one equivalent hour in the military format, that is, each input is mapped to a single output, hence the table in fact represents a function.

The domain of a function is the set that contains all the input values of the function, hence for this problem the domain is the set of hours in the AM-PM format.

The range of a function is the set that contains all the output values of the function, hence for this problem the range is the set of hours in the military format.

More can be learned about domain and range of functions at https://brainly.com/question/2264373

#SPJ1

Find the roots of the equation

Answers

Answer: There are not any roots for that equation.

Angles a and b are supplementary. determine the measure of angle a if the measure of angle b is 115.2°. 244.8° 64.8° 25.2° 11.5°

Answers

The measure of angle 'a' is 64.8°.

What is supplementary angles?

Two angles are considered to be supplementary if their sums total 180 degrees.

For instance, angle 130° and angle 50° are supplementary angles since the sum of these two angles is 180°.

The given angle is a = 115.2°.

We have to find the angle 'b' supplementary to the angle 115.2°.

Since, sum of supplementary angles is 180 degrees.

⇒ a + b = 180°

115.2 + b = 180°

Subtract 115.2° from both sides,

b = 180° = 115.2°

b = 64.8°

Hence, the measure of angle 'b' which is supplementary to angle 'a' is 64.8°.

To know more about supplementary angles, click on the link

https://brainly.com/question/12919120

#SPJ4

henry scored 85, 76, 84, and 69 on four exams. what must he make on the fifth exam to have an average of 80?

Answers

Henry must have to score 86 marks in the fifth exam to make an average of 80 marks.

What is the average?

This is the arithmetic mean and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

Henry scored 85, 76, 84, and 69, and let's suppose he scored 'x' marks in the fifth exam.

Average = sum of all marks/total number of exams

  80 =(85 + 76 + 84 + 69 + x)/5

 80 = 314 + x/5

 80 * 5 = 314 + x

 400 = 314 + x

  x = 400 - 314

  x = 86

Hence, Henry must have to score 86 marks in the fifth exam to make an average of 80 marks.

To learn more about average in mathematics, visit:

https://brainly.com/question/20118982

#SPJ4

An article in the Washington Post on March 16, 1993 stated that nearly 45 percent of all Americans have brown eyes. A random sample of n=55 C of I students found 11 with brown eyes. Give the numerical value of the statistic p^(P HAT)=

Answers

The numerical value of the statistic ^p or sample proportion (p-hat) is 0.2.

^p = X/N where X denotes the number of successes and N denotes the size of the sample. Here, X=55 and N=11.

Sample Proportion (p-hat) of the data:

The sample proportion is a random variable which varies from sample to sample which is not predicted with certainty.Sample proportion is given by the ratio of number of successes in a sample to the size of that sample. It is symbolised as p-hat.the mean of p-hat is exactly (p).Standard Deviation of sample proportion is  [tex]\sqrt{[p(1-p)/n]}[/tex].

To know more about Sample proportion:

https://brainly.com/question/24232216

#SPJ4

6 yellow balls and 8 red balls are placed in an urn. two balls are then drawn in succession without replacement. what is the probability that the first ball drawn is a red ball if the second ball drawn is yellow?

Answers

The probability that the first ball drawn is a red is 8/14

the probability that the first ball drawn is a yellow is 6/13

Let A = getting a red ball

B= getting a yellow ball given that first was red ball

P( A ) = 8/14

P( B  ) = 6/ 13 (since 1 red ball is out)

A(A ∩ B)= 6/13 x 8/14 =

48/182

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.

Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

To learn more about probability

https://brainly.com/question/4651868

#SPJ4

Myesha has a coin collection. She keeps 4 of the coins in her box, which is 5% of the collection. How many total coins are in her collection? Multiply/scale up to solve.

Answers

Answer:

There are 80 coins in her collection.

Step-by-step explanation:

We can find out how many coins are in her coin collection by first converting 5% into a fraction by moving the decimal place to the left twice. Which then we get 0.05. Then, we can set up this equation:

4 ÷ 0.05 = 80

Now, let's check our answer:

0.05 x 80 = 4.

Yep! It checks out!

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 2 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Use point-slope form to write the equation of a line that passes through the point
(-12, 15) with slope - 1.

Answers

Answer:

y=-1x+3

Step-by-step explanation:

Find the equation of a line given the slope m = -1 and the point P = (-12 , 15)

Now, the y-intercept is b=y1−m⋅x1

b = 15 - (-1) ⋅ (-12) = 3

Finally, the equation of the line can be written in the form y=mx+b.

y = -1x + 3

Slope-intercept form is:

y = -1x + 3

Point-slope form is:

y - (15) = -1 ⋅ ( x - (-12))

If you want to check if right then:

Input the point given it should give you the y output if the equation of the line is correct.

-1x-(12)=12 and then add 3 and you get 15. It is therefore correct (-12,15).

I hope this helps!^^

outside temperature over a day can be modeled as a sinusoidal function. suppose you know the temperature is 65 degrees at midnight and the high and low temperature during the day are 76 and 54 degrees, respectively. assuming t is the number of hours since midnight, find an equation for the temperature, d, in terms of t.

Answers

Outside temperature over a day can be modeled as a sinusoidal function. suppose you know the temperature is 65 degrees at midnight and the high and low temperature during the day are 76 and 54 degrees, respectively. assuming t is the number of hours since midnight, the temperature, d, in terms of t. The Equation is :

                                    D = - 11 sin(π/12) + 65

The range is 76 - 54 = 22

so, a = 11

we know that the period is 24 hours

So, 2π/k=24

  ⇒ 24k = 2π

⇒ k = π/12

So far we have:

D = 11 sin(π/12)(t) + 65

Giving us a range from 76 to 54

But obviously the temp after midnight would decrease, whereas our function has it increasing to 76 when t = 6 (6:00 am)

We could do a phase shift, or more simply, just flip the function to

D = -11sin(π/12)t + 76

Checking some values

t = 0 , D = -11sin0 + 65 = 65

t=6 , (6:00 am) D = -11 sin (π/2) + 65 = 54

t = 12 (noon), D = -11 sin π + 65 = 65

t = 18 , (6:00 pm) , D = -11sin 3π/2 + 65 = 76

Learn more about Temperature:

https://brainly.com/question/11464844

#SPJ4

Tanya has read 3/4 of a book, which is 36 pages. How many pages are in the entire book?​

Answers

Answer:

There are 48 pages in the whole book.

Step-by-step explanation:

We know that 36 is 3/4 of the book. To find the total number of pages, we have to divide 36 by 3. We know that is 12. Then, we have to multiply 12 by 4 to get the answer, 48.

Use a tape diagram to model this problem. The whole tape is the number of pages. Divide it into fourths. 3 of those fourths equals 36, so one of the fourths is 12 pages. (36 divided between the 3 boxes of the tape diagram). Four fourths is therefore 4x12, or 48 total pages in the book. Peace!

consider a function z(x, y) and its partial derivative (∂z/∂y)x. under what conditions is this partial derivative equal to the total derivative dz/dy?

Answers

When the (∂z/∂x) is 0, the partial derivative (∂z/∂y) will be equal to the total derivative dz/dy.

What is Total Derivative?

The overall change in the dependent variable as a result of changes in all the independent variables is known as the total derivative of a function of multiple variables.

Given that,

A function z(x, y)and its partial derivative (∂z/∂y) is x.

We know that,

total derivative (dz) = (∂z/∂x) dx + (∂z/∂y) dy

here, (∂z/∂y) = x

So, The dz will be equal to (∂z/∂y) dy only if  (∂z/∂x) dx = 0.

hence, (∂z/∂x) should be 0.

Learn more about Total Derivative from the link given below :

https://brainly.com/question/28376218

#SPJ4

                               

water is leaking out of an inverted conical tank at a rate of 8 , 900 8,900 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. the tank has height 11 11 meters and the diameter at the top is 5.5 5.5 meters. if the water level is rising at a rate of 24 24 centimeters per minute when the height of the water is 3 3 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.

Answers

the rate at which water is being pumped into the tank in cubic centimeters per minute. is 1508527.582 cm³/min

The net rate of flow dV/dt = flow rate in - flow rate out

Let flow rate in = k. Since flow rate out = 8900 cm³/min,

dV/dt = k - 8900

Now, the volume of a cone V = πr²h/3 where r = radius of cone and h = height of cone

dV/dt = d(πr²h/3)/dt = (πr²dh/dt)/3 + 2πrhdr/dt (since dr/dt is not given we assume it is zero)

So, dV/dt = (πr²dh/dt)/3

Let h = height of tank = 11 m, r = radius of tank = diameter/2 = 3/2 = 1.5 m, h' = height when water level is rising at a rate of 21 cm/min = 3.5 m and r' = radius when water level is rising at a rate of 21 cm/min

Now, by similar triangles, h/r = h'/r'

r' = h'r/h = 3.5 m × 1.5 m/12 m = 5.25 m²/12 m = 2.625 m = 262.5 cm

Since the rate at which the water level is rising is dh/dt = 21 cm/min, and the radius at that point is r' = 262.5 cm.

The net rate of increase of water is dV/dt = (πr'²dh/dt)/3

dV/dt = (π(262.5 cm)² × 21 cm/min)/3

dV/dt = (π(68906.25 cm²) × 21 cm/min)/3

dV/dt = 1447031.25π/3 cm³

dV/dt = 4545982.745/3 cm³

dV/dt = 1515327.582 cm³/min

Since dV/dt = k - 6800 cm³/min

k = dV/dt - 6800 cm³/min

k = 1515327.582 cm³/min - 6800 cm³/min

k = 1508527.582 cm³/min

So, the rate at which water is pumped in is 1508527.582 cm³/min

learn more about of radius here

https://brainly.com/question/24319549

#SPJ4

Select all of the relations that ARE functions.
Select 2 correct answer(s)

Answers

Answer:

the first one at the top . but can you put up a better picture ?

Step-by-step explanation:

A new Community Wellness Complex is being built in Del Rio. The perimeter of the rectangular playing field is 414 yards. The length of the field is 9 yards less than triple the width What are the dimensions of the playing field?

Answers

Answer:

Length=153 yards

Width=54 yards

Hope this helps! :)

Step-by-step explanation: (153*=306, 54*2=108, 306+108=414)

P=2l+2w                                              

P=414

L=3w-9

W=w

414=2(3w-9)+2w

414=6w-18+2w

414=8w-18

+18      +18

432=8w

/8

54=w

L=3(54)-9

L=162-9

L=153

a sample of 1200 computer chips revealed that 37% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature claimed that more than 34% do not fail in the first 1000 hours of their use. is there sufficient evidence at the 0.05 level to support the company's claim? state the null and alternative hypotheses for the above scenario.

Answers

As per the question the required hypothesis are

Null Hypothesis, H0: p=0.72

Alternate Hypothesis, H1 : p ≠ 0.72

The null hypothesis reflects that there will be no observed effect in our experiment. In a mathematical formulation of the null hypothesis, there will typically be an equal sign. This hypothesis is denoted by H0.

The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample.

Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample. It’s critical for your research to write strong hypotheses.

To learn more about hypothesis

brainly.com/question/15980493

#SPJ4

a national business magazine reports that the mean age of retirement for women executives is 63.2. a women’s rights organization believes that this value does not accurately depict the current trend in retirement. to test this, the group polled a simple random sample of 78 recently retired women executives and found that they had a mean age of retirement of 64.2. assuming the population standard deviation is 4.4 years, is there sufficient evidence to support the organization’s belief at the 0.02 level of significance?

Answers

The calculated value |Z| = |-2.00722 | = 2.00722 > 2.054 at 0.02 level of significance. So their claim is wrong.

Given that the mean age of retirement for women, executives is 63.2

Given that the size of the sample 'n' = 78

Given that the mean of sample x⁻ = 64.2

Given that the standard deviation  'σ' = 4.4 years

Null hypothesis: H₀: μ ≠ 63.2

Alternative Hypothesis: H₁: μ = 63.2

Test statistic

Z =  -2.00722

|Z| =  2.00722 > 2.054 at 0.02 level of significance

The calculated value |Z| = 2.00722 > 2.054 at 0.02 level of significance

Therefore, we reject the hypothesis.

Statistics is the study of research and surveys on numerical data in mathematics. In order to conduct surveys, the hypothesis must be established. There are typically two different kinds of hypotheses. A null hypothesis is one that holds true, whereas an alternate hypothesis is another.

The null hypothesis is a broad assertion or default stance that there is zero happening or nothing happening in probability and statistics. For instance, there is no association between two measured events or a connection between groups.

To learn more about hypothesis

https://brainly.com/question/23094732

#SPJ4

Pls help
, I really need an answer for this rn

Answers

Answer:

Step-by-step explanation:

A health researcher conducted a survey and recorded the percentage of body fat of 20 randomly selected men from two different towns.

Answer: 7 hrs and 15 minutes

Step-by-step explanation: because 15 - 8 = 7 45 - 30 = 15

Jacob knows that 120 means “1 divided by 20.” He uses this to find the decimal equivalent for 120. Enter a digit into each box to complete his work.

Answers

The value of the decimal equivalent for 120 will be;

⇒ 0.05

What is Decimal number?

A decimal number is a number that consists of a whole and a fractional part.

Given that;

Jacob knows that 120 means “1 divided by 20.”

Now,

Since, Jacob knows that 120 means “1 divided by 20.”

Hence, The value of 120 by using this will be;

⇒ 1/20 = 0.05

Thus, The value of the decimal equivalent for 120 will be;

⇒ 0.05

Learn more about the decimal number visit:

https://brainly.com/question/24342270

#SPJ1

How many solutions does the equation 5n + 1 = 1 + 4n have

Answers

Short Answer:

The given equation has one solution; [tex]n=0[/tex].

Further Explanation:

______________________________________________________

"How Can You Determine Whether An Equation Has One Solution, Infinite Solutions, or No Solution?"

One Solution - Some equations have exactly one solution. In these equations, there is only one value for the variable that makes the equation true. You can tell that an equation has one solution if you solve the equation and get a variable equal to a number.

Infinite Solutions - Some equations have infinitely many solutions. In these equations, any value for the variable makes the equation true. You can tell that an equation has infinitely many solutions if you try to solve the equation and get a variable or a number equal to itself.

No Solution - If a linear equation has the same variable term but different constant values on opposite sides of the equation, it has no solutions.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This being said, lets now go back to the given scenario and determine the amount of solutions it has, if any.

1. We are given the following to solve:

[tex]5n+1=1+4n[/tex]

2. First, subtract 1 from both sides.

[tex]5n+1-1=1+4n-1[/tex]

3. Simplify.

[tex]5n=4n[/tex]

4. Move 4n to the left side, leaving us with our final solution.

[tex]n=0[/tex] ← Final Solution

____________________________________________________

Hope this helps!

What is the value of 13(a • b + a2) + 4 if a = 5 and b = −3?

308
134
−74
−126

Answers

The value of the expression, 13(a • b + a²) + 4, when a = 5 and b = -3 is: B. 134.

How to Find the Value of an Expression?

To find the value of an expression, we have to plug in the respective values for each of the variables given in the expression, then simplify.

Given the expression, 13(a • b + a²) + 4, where:

a = 5

b = -3

To find the value, substitute a = 5 and b = -3 into the expression:

13(5 • -3 + 5²) + 4

13(-15 + 25) + 4

13(10) + 4

= 130 + 4

= 134

The value is: B. 134.

Learn more about the value of expression on:

https://brainly.com/question/625174

#SPJ1

David has a bank account which pays interest at the rate of 1.5% per year, compounded annually. determine what amount david must have in the bank, given that he would like to draw an annual salary of $32,635.15 from his account at the end of each year for 30 years. round to the nearest cent. a. $783,760.48 b. $979,054.50 c. $1,225,080.50 d. $795,516.88 please select the best answer from the choices provided a b c d

Answers

If David wants to withdraw $32,635.15 every year from his account at the end if each year for 30 years, he has to have $783243.6 in the bank account .

Define the term present annuity?The amount of money that would be required today to finance a series consecutive future annuity payments is referred to as the annuity's present value. sum of money received now is worth more than a similar sum at a later time due to the time value of money.

We would use the equation for calculating present annuity.

It is written as

PV = R[1 - (1 + r)^- n]

In which.

The investment's present value is represented by PV.R stands for the consistent payments made (also weekly, monthly)The expression r stands for interest rate/interval payments.A total number of repayments is indicated by the number n.

Considering the data provided,

r = 1.5/100 = 0.015

n = 30 years

R = $32,635.15

Put the values in the formula,

PV = 32635.15[1 - (1 + 0.015)⁻³⁰]/0.015

PV = 32635.15[1 - (1.015)⁻³⁰]/0.015

PV = 32635.15(1 - 0.64)/0.015

PV = 32635.15 × 24

PV = $783243.6

Thus, amount David must have in the bank presently is  $783243.6.

To know more about the present annuity, here

https://brainly.com/question/14000207

#SPJ4

write the general antiderivative. (use c for the constant of integration. remember to use absolute values where appropriate.) 1 8 x 1 8x 1 8 x dx

Answers

The general antiderivative is; (x²/16) + 1/8 ln |x| - 1 / (3 ln × 2 × 8ˣ) + C

Given,

f (x) = x/8 + 1/8x + (1/8)ˣ

We have to find the antiderivative;

Antiderivative;-

In calculus, a differentiable perform F whose spinoff is sufficient to the initial perform f could be an antiderivative, inverse derivative, primitive perform, primitive integral, or integral of a perform f. Symbolically, this could be expressed as F' = f.

Here,

To find antiderivative, we have to integrate the function first;

Then,

∫ f(x) + g(x) dx = ∫ f(x) dx + g(x) dx

∫ f(x/8) dx = x² / 16

∫ f(1/8 x) dx = 1/8 ln |x|

∫ f(1/8ˣ) dx = -1/ (3 ln × 2 × 8ˣ)

That is,

∫ x/8 + 1/8x + 1/8ˣ dx = (x²/16) + 1/8 ln |x| - 1 / (3 ln × 2 × 8ˣ) + C

Therefore,

(x²/16) + 1/8 ln |x| - 1 / (3 ln × 2 × 8ˣ) + C will  be the antiderivative.

Learn more about antiderivative here;

https://brainly.com/question/29654274

#SPJ4

what is the variance of the number of times a 6 appears when a fair die is rolled 12 times? (enter the final answer in decimal format and round to three decimal places.)

Answers

The variance of the number of occasions a 6 appears when a fair die is thrown 12 times is 0.156.

It determines the likelihood of achieving a specific number of successes over a specific number of trials with a consistent success rate using the binomial distribution.

With a 1/6 likelihood of success for each trial, the number of successes in this example is equal to the number of 6s that occur.

The probability of each conceivable value of the quantity of 6s that appear may be calculated using the binomial formula. The likelihood of receiving exactly 0 number of 6s is (12 choose 0) ×[tex](\frac{1}{6})^0[/tex] × [tex](\frac{5}{6}) ^{12}[/tex] = 0.1680. The probability of getting exactly 1 number of 6 is (12 choose 1) × [tex](\frac{1}{6})^1[/tex] × [tex](\frac{5}{6})^{11}[/tex] = 0.4401. The probability of getting exactly 2 numbers of 6s is (12 choose 2) × [tex](\frac{1}{6})^2[/tex] × [tex](\frac{5}{6})^{10}[/tex] = 0.3744. And so on.

The likelihood of receiving 0 6s, for instance, multiplied by the square of the 0's divergence from 2 is 0.1680 × (0 - 2)² = 0.7056. The likelihood of receiving 1 6 when multiplied by the square of the difference between 1 and 2 is 0.4401 × (1 - 2)² = 0.4401. And so on.

To get the anticipated value of the squared departure of the number of 6s that occur from 2, we may finally total up all of these probabilities.

This predicted value is equal to 1.8801 by adding 0.7056, 0.4401, 0.3744, 0.1596, 0.0368, and 0.0036.

The range in the number of 6s that appear after tossing a fair die 12 times is thus 1.8801.

To express the variation in decimal notation, divide the difference by the total number of rolls (12), then round the output to the closest three decimals.

As a consequence, we obtain a variance of 0.1567. The variance in the number of occasions a 6 appears when a fair dice is rolled 12 times is thus 0.1567.

Learn more about probability at

https://brainly.com/question/29098847?referrer=searchResults

#SPJ4

Factor 24cd − 36c2d.

A: 12c2d(2 − 6)
B: 12cd(2 − 36c2d)
C: 6cd(4 − 36c2d)
D: 4cd(6 − 9c)

Answers

Answer:

D

Step-by-step explanation:

24cd-36c²d = (4×6)c×d-(4×9)c×c×d

Then we take the common numbers and variables

4cd(6-9c) and to check our answer we can distribute 4cd to get:

4cd×6-(4cd×9c)

24cd-36c²d

Other Questions
What pair of features is relevant when buying a cell phone? A. servicio de mensajes escritos y conexin inalmbrica B. memoria del disco duro y servicio de mensajes escritos C. servicio de mensajes escritos y precio del plan D. ancho de banda y conexin inalmbrica help me with math pls im almost done with it for the week................... according to federal guidelines, hospices may provide no more than what percentage of the aggregate annual patient-days at the inpatient level? 20 POINTS!!! HELP QUICKLY PLEASE Genre, :Science: Homeostasis is a ________ of an internal environment in an organism's body to remain in a ________ and balanced condition.ResponsesA.maintenance, stableB.repair, higherC.maintenance, higherD.repair, stable the statement a kodak all-in-one printer may cost a little more, but you'll pay far less for replacement ink than you will with other printers . a. gains attention by describing a problem b. builds interest in a product c. motivates action d. reduces resistance a brass cube, 10 cm on a side, is raised in temperature by 200oc. the coefficient of volume expansion of brass is 57x10-6/oc. by what percentage does its volume increase? Which two women won their elections to fill two of alaskas three seats in congress?. Question 1 of 10What are two examples of stem cells working in adult animals?A. Cells divide to form the blastocyst and then the gastrula.B. New nerve cells are produced to repair nervous tissue.C. Germ layers develop into specialized cells and tissues.D. Bone marrow produces new blood cells to fight disease. What is the range of this relation? this proposal is not without its critics, however. generally, what might be some of the concerns of this type of engineering strategy? check all that apply. which of the following does not lead to an increase in phytoplankton reproduction? a. increased nutrient availability b. increased sunlight c. increased oxygen levels d. increased levels of carbon dioxide Jack took Diane out to dinner to celebrate her birthday. The total bill for the dinner was $62.80. Jack wants to tip the waiter exactly 15%. How much will Jack tip the waiter? chemist carries out this reaction and obtains 11.4 g of tungsten. if the percent yield is 89.4%, what mass of wo3 was used? Nos How many atoms are in 11010 g Au? to compute cash flows from financing activities, accountants normally analyze changes in all of the following accounts except: Kaleb deleted 20 songs from his MP3 player. If the ratio of songs he deleted to songs hekept was 10:3, how many songs did he originally have on his MP3 player? a community health nurse is concerned about poor compliance with recommended immunization schedules for infants (birth to 2 years). after surveying some of the parents, it is determined there are many variables inhibiting compliance, such as limited clinic hours, difficulty making appointments through an automatic system, and no reminder call/email or follow-up intervention. when meeting with staff, managers, and physicians to resolve the issues, it is revealed there are many underlying issues that must be addressed, such as an insufficient number of providers available to treat this demographic. this nurse is acting in what capacity? thththththththththththththththt WRITE: PAPER #4 -->350-400 words, double-spaced...on YOUR CHOICE: a. Singer Solution to World Poverty, b. UKRAINE, or c. Whether we should give money to beggars on the street. -- ** The final paper is a "synthesis" paper where we read several sources addressing giving money directly to the homeless from different angles and then synthesize the material into our own take or angle on the topic.