A gardener uses a roller to flatten a bowling green of length 29 m. The roller has a diameter of 1.3 m. The gardener says the roller makes 8 full turns in travelling the length of the green. Is the gardener correct? Explain your answer.​

As per the given demand function and equilibrium point, the consumers' surplus is 852.072.

What is consumer surplus?

Consumer advantages from market competition are measured economically as consumer surplus. When customers pay less for a good or service than they are willing to, this is known as a consumer surplus.

Given demand function,

[tex]D(q) = \frac{3000}{(3q+1)^2}[/tex]

at q = 4

putting value of q in function,

[tex]q' = \frac{3000}{(3(4)+1)^2}[/tex]

[tex]q' = \frac{3000}{169}[/tex]

Finding Consumer Surplus

[tex]CS = \int\limits^q_0 {D(q) - q'} \, dq[/tex]

[tex]CS = \int\limits^4_0 {\frac{3000}{(3q+1)^2} - \frac{3000}{169} } \, dq[/tex]

[tex]CS = [-\frac{1000}{3q+1} - \frac{3000q}{169}]^4_0[/tex]

CS = [-(76.923)-(71.005)] - [-1000]

CS = -147.928+1000

CS = 852.072

Therefore, consumers' surplus is 852.072.

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Complete Question

Find the consumers surplus if the demand function for a particular beverage is given by D(q)=(3000)/((3q+1)^(2)) and if the supply and demand are in equilibrium at q=4

The sixth term of an arithmetic sequence is 3/2 and the twelfth term is 5/2. The common difference is 1/6.

A common difference in an arithmetic series is one between any term and its predecessor, and it is typically denoted by the letter "d". So, subtract the first term from the second term, the second term from the third term, etc. to find the common difference of an arithmetic sequence. The common difference is the difference that exists between every pair of phrases that follow one another in a series. For instance, the number 3 is a common difference in the series 4, 7, 10, 13, etc. An arithmetic progression is a series of differences.

Given,

a₆ = 3/2

a₁₂ = 5/2

Arithmetic sequence:

a₇ = a₆ + d

a₈ = a₇ + d

a₈ = a₆ + 2d

a₉ = a₈ + d

a₉ = a₆ + 3d

...

a₁₂ = a₁₁ + d

a₁₂ = a₆ + 6d

As given,

a₆ = 3/2

a₁₂ = 5/2

Equating,

5/2 = 3/2 + 6d

6d = 1

d = 1/6

The sixth term of an arithmetic sequence is 3/2 and the twelfth term is 5/2. The common difference is 1/6.

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Answer:

[tex]\dfrac{1}{6}[/tex]

Step-by-step explanation:

General form of an arithmetic sequence:

[tex]\boxed{a_n=a+(n-1)d}[/tex]

Where:

Given terms:

  [tex]a_6=\dfrac{3}{2}[/tex]

  [tex]a_{12}=\dfrac{5}{2}[/tex]

Substitute the given terms into the formula to create two equations for a:

Equation 1

[tex]\begin{aligned}a_6=a+(6-1)d&=\dfrac{3}{2}\\\\a+5d&=\dfrac{3}{2}\\\\a&=\dfrac{3}{2}-5d\end{aligned}[/tex]

Equation 2

[tex]\begin{aligned}a_{12}=a+(12-1)d&=\dfrac{5}{2}\\\\a+11d&=\dfrac{5}{2}\\\\a&=\dfrac{5}{2}-11d\end{aligned}[/tex]

Substitute the second equation into the first equation and solve for d:

[tex]\begin{aligned}\implies \dfrac{5}{2}-11d&=\dfrac{3}{2}-5d\\\\\dfrac{5}{2}-11d-\dfrac{3}{2}&=\dfrac{3}{2}-5d-\dfrac{3}{2}\\\\\dfrac{2}{2}-11d&=-5d\\\\1-11d&=-5d\\\\1-11d+11d&=-5d+11d\\\\1&=6d\\\\\dfrac{1}{6}&=\dfrac{6d}{6}\\\\\dfrac{1}{6}&=d\end{aligned}[/tex]

Therefore, the common difference of the arithmetic sequence is ¹/₆.

Answer:

1/2

Step-by-step explanation:

The equation given is put in slope intercept form

y = mx + b

where m = slope and b = y intercept

In the equation y = 1/2x + 3/2,
"1/2" takes the spot of "m" meaning that the slope of the equation is 1/2

A 95​% confidence interval for the population proportion is ( 0.297, 0.335 ).

What is confidence interval?

A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The parameter's true value, for instance, should be present in 95% of all intervals computed at the 95% level.

Given that,

Point estimate = sample proportion = p' = x / n = 738 / 2336 = 0.316

 1 - p' = 1 - 0.316 = 0.684  

 Z(α/2) = Z(0.025)  = 1.96

A 95% confidence interval for population proportion p is ,

p' ±  E

= 0.316  ± 0.019

= ( 0.297, 0.335 )

With 95% confidence, it can be said that the population proportion of adults who believe in UFO's is between the endpoints of the given confidence interval  

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The expression -9z - 21y - 2.4 ​when -3 is factored out is -3(3z + 7y + 0.8)

From the question, we have the following expression that can be used in our computation:

-9z - 21y - 2.4 ​

The common factor is given as

-3

So, we divide -9z - 21y - 2.4 ​ by 3

The results of these divisions are

-9z/3 = -3z

- 21y/3 = -7y

- 2.4 /3 = -0.8

So, we have the following results

-9z - 21y - 2.4 ​ = -3(3z + 7y + 0.8)

Hence, the factored expression is -3(3z + 7y + 0.8)

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The $28,000 investment will earn $696 more than the $16,000 investment if both make a 5.8% (APY) annual percentage yield for a year.

APY means annual percental yield.

Annual Percentage Yield describes the real interest rate earned on an investment in a year.

The Annual Percentage Yield refers to the interest an investment, saving, and loan attracts for the time value of money and inflationary effects.

The Annual Percentage Yield is applied to the investment amount for a year to calculate the interest earned.

                                 Plan A         Plan B

Investments            $28,000     $16,000

Interest earned         $1,624           $928 ($16,000 x 5.8%)

The difference in interest earned = $696 ($1,624 - $928)

Thus, when an investor puts $28,000 in a savings account at 5.8%, they earn $696 more than investing $16,000 at the same APY.

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The parabola's graph leads us to deduce that the quadratic equation is

x² + 5x + 1.

An algebraic expression with variables and constants is known as a quadratic equation.

Since the degree of a quadratic equation is two, it has two roots.

We are aware that the roots of a quadratic equation can be found at the vertex of a parabola, which is the graph of a quadratic function.

Given, The roots of the equation are x = - 4 and x = - 1, and the quadratic expression is, as the vertex of the parabola is at (-4, -1),

(x + 4)(x + 1).

= x² + x + 4x + 1.

= x² + 5x + 1.

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Answer:

y=-2/5x+4/5

Step-by-step explanation:

it’s parallel so it will have the same slope

2=-2/5(-3)+4

2=6/5+4

2=1 1/5+4

2=5 1/5

5 1/5-2=3 1/5

We know this is 3 1/5 to big so we subtract it from y intercept

4-3 1/5

4/5 is the new y intercept

2=-2/5(-3)+4/5

2=6/5+4/5

2=10/5

2=2

So now the equation is true

Hopes this helps

Answer: x = 5

Step-by-step explanation:

3x + 6 = 21

3x = 21 - 6

3x = 15

x = 15/3

x = 5

Answer: X =5

Step-by-step explanation:  Subtract both sides by 6 to isolate 3x:

3x+6-6=21-6

3x=15

Divide both side by 3 to come up with x:

X=5.

A shortcut method but it does not follow the correct rules of math but if you're in a hurry it works:

3x+6=21

transfer +6 converting the sign to a -6

3x-=21-6

Subtract 3x=15

Divide by the number with x (3)

x=5

Answer:

See below

Step-by-step explanation:

Amount of water in pool = 14 000 -  .5 x       where x is in minutes

1.5 hr = 90 minutes

amount of water in pool =  14 000 - .5(90) = 13 955 gal

Answer:

==============================

Slope-intercept form:

Find the value of b:

The line is:

Answer:

y = (-5/4)x + 13

Step-by-step explanation:

Formula we use,

→ y = mx + b

Now the value of b will be,

→ 3 = (-5/4)8 + b

→ 3 = -40/4 + b

→ 3 = -10 + b

→ 3 + 10 = b

→ [ b = 13 ]

Then the equation will be,

→ y = mx + b

→ 3 = (-5/4)8 + 13

→ y = (-5/4)x + 13

Thus, answer is y = (-5/4)x + 13.

The area of the sector is 8800cm²

What is an area of the sector?

The area of the sector refers to the area encircled by a circle's sector. A sector always originates from the center of the circle.

What is curved surface area?

The area with just curved surfaces, leaving the circular top and base, is referred to as the curved surface area. Total Surface Area: This is the combined area of the bases and the curved surface.

Here, we have

Radius = 28cm,  Height = 96cm

L² = 96² + 28²

= 9216 + 784

= 10000

L = √10000

= 100cm

curved surface area = πrl

= 22/7×28×100

= 8800cm²

area of cone = area of sector

area of sector = 8800cm2

Hence, the area of the sector is 8800cm²

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A savings account with a set term and interest rate is known as a certificate of deposit (CD). While CDs often provide greater rates than traditional savings accounts, you can't get to your money right away until the term is over.

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Answer:

Parent function:

f(x) = √x

Add a number to the value of the function, such as k:

f(x) = (√x) + k

If k is positive, the function moves up. If k is negative, the function moves down.

The rocket's maximum height is therefore 2704 feet, its maximum height is reached in 3 seconds, and the rocket reaches the ground at time t=16 seconds.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.

Given,

A rocket is fired upward from some initial distance above the ground. Its height (in feet), h, above the ground t seconds after it is fired is given by h ( t ) = − 16 t 2 + 80 t + 384

Following is our relationship between height and time:

h ( t ) = − 16 t 2 + 80 t + 384

The vertex of the equation above is as follows because it is a parabola equation.

In this case, a = -16, b = 96, and c = 2560.

The highest point at:

= -96/(2×(-16)

= 96/32

= 3 sec.

Maximum height at three seconds later:

h = -16 ×3² + 96 × 3 + 2560

h = 2704 feet

The rocket reaches the ground at y = 0, adding the following value to the parabolic equation:

0 = 16t² + 96t + 2560

Once we've solved it, we'll get:

t = 16 or

t = -10

Time cannot be negative, so we will choose t = 16 seconds.

The rocket's maximum height is therefore 2704 feet, its maximum height is reached in 3 seconds, and the rocket reaches the ground at time t=16 seconds.

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Answer:

Step-by-step explanation: xxxdadyxxx12 snap

y

Answer:

Step-by-step explanation:

c

Answer:

It's A

Step-by-step explanation:

I=Prt

I=$660(3.5%)5

I=23.1(5)

I=$115.50

Answer

314

Step-by-step explanation:

hope this helps ya

Answer: 68.61/6 = 11.435

Answer:

  t(r) = log(r)/log(5) = log₅(r)

Step-by-step explanation:

You want the inverse of r(t)=5^t.

An exponential function is solved using logarithms.

  [tex]r = 5^t\qquad\text{given}\\\\\log(r)=t\cdot\log(5)\qquad\text{take logarithms}\\\\\boxed{t(r)=\dfrac{\log(r)}{\log(5)}}\qquad\text{divide by the coefficient of t}[/tex]

The change of base formula can be used to simplify this a bit.

  [tex]\boxed{t(r)=\log_5(r)}[/tex]

__

Additional comment

The latter form of the inverse function can be found directly at the first step by taking logarithms base 5.

The notation here is slightly different from the usual "inverse function" notation, where we designate the inverse of f(x) using f⁻¹(x). The notation we have used recognizes that the function r(t) generates ordered pairs (t, r), and the inverse function t(r) generates ordered pairs (r, t).

You are welcome to make use of whatever inverse function notation will satisfy your grader.

Answer:

So you see what happened there

the sides are not equal so there is no answer

the answer that is the closest is 8 = 0

Step-by-step explanation:

Add x to both sides

2 - x + 6 + x = -x + x

simplify

2 + 6 = 0

simplify 2 + 6: 8

8 = 0

The both fractional parts of an English ton are each of these fish.

The English ton, also known as the long ton, is equivalent to 2,240 pounds. Therefore, the fractional parts, of each of the two fish, of the English ton are:

Fish caught in region A weights = 279 lb

Therefore, fish caught in region A

A = 279 ÷ 2240

Fish caught in region B weights = 619 lb

Therefore, fish caught in region B

B = 619 ÷ 2240

Both fractions are irreducible.

So, both fractional parts of an English ton are each of these fish.

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1.  The rewritten form of the equation is (x + 2)² = -6

2. The solutions to the equation are 0.45 and -4.45

Given,

The equation;  

0=x^2+4x+10

1. We have to rewrite the equation;

x² + 4x + 10 = 0

x² + 4x = -10

Add the square of the half of coefficient of x to both sides

4/2 = 2

x² + 4x  + 2² = -10 + 2²

x² + 4x + 4 = -6

(x + 2)² = -6

Therefore,

The rewritten form of the equation is (x + 2)² = -6

2. Calculate the value of x

(x + 2)² = -6

Square root both sides

√(x + 2)² = ±√6

x + 2 = ±2.45

x= ±2.45 - 2

x = 2.45 - 2 and -2.45 - 2

x = 0.45 and -4.45

Hence the solutions to the equation are 0.45 and -4.45

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Answer:

0=x²+4x+1

3=(x+2)²

x=−2± [tex]\sqrt{3}[/tex]

Step-by-step explanation:

We conclude that 80% of patients stop smoking when given sustained care.

Given,

The number of patients given sustained care = 175

Patients who were no longer smoking after one month = 82.3%

Significance level = 0.05

We have to claim that 80% of patients stop smoking when given sustained care.

Let p = percentage of patients stop smoking when given sustained care.

So, Null Hypothesis, H₀ : p = 80%     {means that 80% of patients stop smoking when given sustained care}

Alternate Hypothesis, Hₐ : p  80%     {means that different from 80% of patients stop smoking when given sustained care}

The test statistics that would be used here One-sample z test for proportions;  

                      T.S. =  [tex]\frac{p_{0} -p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~ N(0,1)

where,  p₀ = sample proportion of patients who stop smoking when given sustained care = 82.3%

n = sample of patients = 175

So, the test statistics  =  [tex]\frac{0.823-0.80}{\sqrt{\frac{0.823(1-0.823)}{175} } }[/tex]

                                    =  0.80

The value of z test statistics is 0.80

Also, P-value of the test statistics is given by the following formula;

 P-value = P(Z > 0.80) = 1 - P(Z  > 0.80)

  = 1 - 0.21185 = 0.78815

Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that 80% of patients stop smoking when given sustained care.

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The required derivatives of the given hyperbolic functions are

d/dx(sinh3x) = 3cosh3x, d/dx(cosh7x) = 7sinh7x, d/dx(tanh6x) = 6sech²6x, d/dx(coth5x) = −5csch²5x, d/dx(sech3x) = −3sech3xtanh3x, and d/dx(csch7x) = −7csch7xcoth7x.

The differentiation formulas for the hyperbolic functions are below as

d/dx(sinhx) = coshx

d/dx(coshx) = sinhx

d/dx(tanhx) = sech²x

d/dx(cothx) = −csch²x

d/dx(sechx) = −sechxtanhx

d/dx(cschx) = −cschxcothx

As per the given question,

⇒ d/dx(sinh3x)

Using formula d/dx(sinhx) = coshx,

⇒ cosh3x × (d/dx(3x))

⇒ cosh3x (3)

⇒ 3cosh3x

⇒ d/dx(tanh6x) = 6sech²6x

⇒ d/dx(coth5x) = −5csch²5x

⇒ d/dx(sech3x) = −3sech3xtanh3x

⇒ d/dx(csch7x) = −7csch7xcoth7x

Thus, the required derivatives of the given hyperbolic functions are

d/dx(sinh3x) = 3cosh3x, d/dx(cosh7x) = 7sinh7x, d/dx(tanh6x) = 6sech²6x, d/dx(coth5x) = −5csch²5x, d/dx(sech3x) = −3sech3xtanh3x, and d/dx(csch7x) = −7csch7xcoth7x.

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Rotation is represented by a table fan, Dilation enlargement by flowers, reflection by ducks building a heart, and translation by a window picture.

Compared to translation, reflection, and rotation, what is a dilation?

Dilation:

Translation:

Reflection:

Rotation:

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The value of the scale on the map is 18 cm 1 mi

Knowing the distance between two places on the map and measuring that distance on the map will yield the scale. Additionally, if a map has division lines, they are normally spaced apart by a mile. Example 4: On the map, the separation between points A and B is 6 inches

The ratio between a distance on a map and its corresponding distance on the ground is referred to as the "map scale."

People can accurately visualise how the distances mentioned on the map are plotted by using map scales. This is helpful in figuring out how to get from one place to another, especially if one travels or works in a profession that requires similar knowledge.

Given,

Model cm/actual miles

12/2/3

= 12/1,3/2

=18/1

=18:1

Therefore the value of the scale on the map is 18 cm 1 mi

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Answer:

-0.6, -0.2, 0, 0.5, 0.7

Step-by-step explanation:

To find out this answer, we know first that negatives are the least. And -0.6 is farther away from 0 than -0.2, so we can have -0.6, -0.2 as our last numbers.

Then, 0.5 and 0.7 are greater than 0, so, then we have -0.6, -0.2, 0.

Then, 0.7 is greater than 0.5, so we can arrange the final numbers:

-0.6, -0.2, 0, 0.5, 0.7

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Answer: -0.6,-0.2, 0, 0.5, 0.7

Step-by-step explanation: Use a number line

The slope of the line T will be 1 and the y-intercept will be (0,4) in the given coordinate plane.

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. In the case of the equation y = 3x - 7, the slope is 3 and the y-intercept is (0, 7). And b is the value of b in the point that is the y-intercept (0, b). By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.

Here,

The slope of line D=1

y-intercept=(0,0)

factor=2

coordinate=(3,4)

The slope will not change that will be 1.

y-intercept=0+4

=4

y-intercept=(0,4)

In the given coordinate plane, the y-intercept of line T will be (0,4) and its slope will be 1.

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The volume of the right circular cylinder is 3141592.65 centimeter cube  and the surface area is 125663.70 centimeter square

The diameter of the right circular cylinder = 200 cm

The radius = 200/2

= 100 cm

The height of the right circular cylinder = 100 cm

The volume of the right circular cylinder = π × [tex]r^2[/tex] × h

Where r is the radius

h is the height

Substitute the values in the equation

The volume = π × [tex]100^2[/tex] × 100

= 3141592.65 centimeter cube

The Surface area = 2πrh + 2π[tex]r^2[/tex]

Substitute the values in the equation

= 2×π×100×100 + 2×π×[tex]100^2[/tex]

= 62831.85 + 62831.85

= 125663.70 centimeter square

Hence, the volume of the right circular cylinder is 3141592.65 centimeter cube  and the surface area is 125663.70 centimeter square

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