Please help!! a company sells widgets. the amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit. y=-30x^2+1325x-8569

Answers

Answer 1

The widgets should be sold for $22.08 for the company to make the maximum profit.

To maximize a function, y = f(x), we differentiate it with respect to x, to get y' = f'(x). Equate it to zero to get the points on inflections.

Differentiate y' = f'(x) again with respect to x, to get y'' = f''(x), and put in the points of inflections to check whether y'' is greater than or less than zero. If it is greater than zero, then we have a minimum, and if it is less than zero, then we have a maximum.

In the question, we are given a profit function y, with respect to the sale price of each widget x. We are asked to find the sale price that maximizes the profit.

The function given is:

y = -30x² + 1325x - 8569.

Differentiating this with respect to x, we get:

y' = -60x + 1325.

To find the point of inflection, we equate this to zero, to get:

0 = -60x+ 1325,

or, x = 1325/60 = 22.0833

Now, we differentiate, y' = -60x + 1325, with respect to x, to get:

y'' = -60 < 0, thus we have a maximum at x = 22.0833.

Thus, the widgets should be sold for $22.08 for the company to make the maximum profit.

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Related Questions

Which description best compares the graphs of the two functions below?

Answers

A description which best compares the graphs of the two functions above include the following: B. The line for function A is steeper.

How to compare the two functions?

In order to compare the two functions, we would have to find the slope of function B based on the data points contained in the table by using the slope formula.

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Substituting the given points into the slope formula, we have the following;

Slope, m = (-1 - (-2))/(3 - 0)

Slope, m = (-1 + 2)/3

Slope, m =1/3

From function A y = 3x - 2, the slope is equal to 3. Consequently, we can logically deduce that the line representing function A is steeper than the line representing function B because its slope is bigger i.e 3 > 1/3.

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The sum of two numbers is 27. The difference between the two numbers is 5. What are the two numbers?

Answers

Answer:

x = 16

y = 11

Step-by-step explanation:

x+y = 27

x-y = 5

__________

2x = 27+5

2x = 32 /:2

x = 16

16+y = 27

y = 27-16

y = 11

Select the reason why these triangles are
similar. If they are not, select "Not similar."
A. AA
C. SAS
60°
/60°
B. SSS
D. Not similar

Answers

The reason why these triangles are similar is A. AA.

What is similar triangle?

A similar triangle is a triangle in which the corresponding angles are congruent (equal in measure) and the corresponding sides are in proportion. This means that the corresponding sides of two similar triangles are in the same ratio, but the triangles may be different sizes.

What is triangle?

A triangle is a three-sided polygon. It is defined by three points in a plane, called its vertices, and the straight lines connecting each pair of these points, called its sides. The three angles of a triangle always add up to 180 degrees.

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help me its due today

Answers

Answer:

(1,-1)

Step-by-step explanation:

my guy, are you good? dude this question is so easy l m a o

anyways, heres the explanation

where there is an "x," replace it with a 1

so: -4-9y = 5

-9y = 9

y = -1

and the question already gives you what x is so:

(x,y)

(1,-1)

SOMEONE HELP ME PLEASE DUE TONIGHT

Answers

HI is 7 because all sides are equal. K is 100 because J is 40 and L is also 40 because they are equal. All triangles are equal to 180. 40+40+100=180

Hi, please help with this circle geometry question (image attached)! It would be helpful if you show your working out/proof. You also need to use tangent properties of circles.
Thank you!

Answers

Given that ABC is a right-angled triangle and that AB, BC, and CA are tangents to the circle, the value of x is 2 cm.

what is triangle ?

Since a triangle has three parts and three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to one triangle that has vertex shader A, B, and C. When the three principles are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sections and three corners. The points where the sides meet are known as the triangle's corners.

given

To find : radius 'r' of the incircle.

ABC is a right angled triangle

=100

⇒ BC= 100 =10cm

Since area of right anged triangle = 1/2×base×height

⇒ Area of △ABC= 1/2×6×8

=3×8=24cm 2

⇒ Area of △ABC=24cm 2 ....(1)

Also, Area of △ABC= area of △OAC+ area of △OBC+ area of △OBA

= 1/2 ×r×8+ 1/2 ×r×10+ 1/2 ×6×r= 1/2* r(8+10+6)= 1/2r(24)=12r....(2)

Equating (1) and (2) 12r=24

⇒ r= 12/24 =2cm

Given that ABC is a right-angled triangle and that AB, BC, and CA are tangents to the circle, the value of x is 2 cm.

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The complete question :- In fig. 4 triangle ABC is a right triangle with AB=6 cm, AC=8 cm and ∠A=90∘ . A circle with center O is inscribed inside the triangle. Find the radius 'r'

I'LL GIVE BRAINIEST TO WHOEVER ANSWERS THIS CORRECTLY
3. The function represents the number of specialty items produced at the old factory w weeks after a change in management. The graph represents the number of specialty items produced at the new factory during the same time period.



(a) During Week 0, how many more specialty items were produced at the old factory than at the new factory? Explain.
(b) Find and compare the growth rates in the weekly number of specialty items produced at each factory. Show your work.
(c) When does the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory? Explain.

Answers

Answer:

The correct answer is A

I hope that helped.

Step-by-step explanation:

The balance on a credit card, that charges a 10.5% APR interest rate, over a 1 month period is given in the following table:

Days 1-3: $200 (initial balance)

Days 4-20: $300 ($100 purchase)

Days 21-30: $150 ($150 payment)

What is the finance charge, on the average daily balance, for this card over this 1 month period?

finance charge = $[?]

Round to the nearest hundredth.​

Answers

The finance charge on the average daily balance for the one month is $2.07.

What is the finance charge?

The finance charge is the interest and other fees charged on a credit facility.

To compute the finance charge, we apply the annual percentage rate (APR) on the Average Daily Balance, multiplied by the number of days in the billing cycle, and divided by 365.

Days 1-3: $200 (initial balance)            $600 ($200 x 3)

Days 4-20: $300 ($100 purchase)    $5,100 ($300 x 17)

Days 21-30: $150 ($150 payment)    $1,500 ($150 x 10)

Total = $7,200

Average Daily Balance = $240 ($7,200/30)

APR interest rate = 10.5%

MPR interest rate = 0.875% (10.5%/12)

Finance Charge = $2.07 ($240 x 10.5% x 30/365)

Or $ ($240 x 0.875%)

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PLEASE HELP
calculate (30m) (2.01m). Use the correct number of significant digits in the answer

Answers

The expression 30m × 2.01m will be 60.3m²

How to illustrate the expression?

In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The value of the expression will be:

= 30m × 2.01m

= 60.3m²

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Help Please! I need to find the value of x in the quadrilateral
I know the sum of the exterior angles and interior angles is 360 and I know I need to do something with substitution but I have no idea where to start. Please explain it step by step so I understand.

Answers

The value of x in the quadrilateral is 23.

How to find the angles of a quadrilateral?

A quadrilateral is a polygon with 4 sides. The sum of interior angles in a quadrilateral is 360 degrees.

The sum of exterior angles in a quadrilateral is 360 degrees.

Therefore, let's find the value of x in the quadrilateral.

Hence,

6x + 5x + x + 16 + 3x - 1 = 360

combine like terms

6x + 5x + x + 3x + 16 - 1 = 360

15x + 15 = 360

subtract 15 from both sides of the equation

15x = 360 - 15

15x = 345

divide both sides by 15

x = 345 / 15

x = 23

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Which expression renames 3/4−7/10 using common denominators?

Answers

3/4 and 9/10 using the least common denominator is 15/20 and 18/20.

What is LCM?

LCM of two or more than two given numbers is the smallest common multiple that is divisible by two or more than two given numbers.

Given, are two fractions 3/4 and 7/10 we know the LCM of 4 and 10 is 20.

∴ (3×5)/(4×5) and (7×2)/(10×2).    

(we have to multiply same constant to the fraction to retain it's original value).

So,  3/4 and 4/10 using the least common denominator is 15/20 and 14/20.

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Find the length of the indicated
side of the similar figure.
12
X
x = [?]
X
8
4

Answers

The length of the side indicated in the similar figure can be found using the concept of similarity.

Find the length of the indicated side?The length of the side indicated in the similar figure can be found using the concept of similarity.When two figures are similar, the corresponding sides are proportional.In this case, the side indicated in the figure is 8, and the side we are looking for is X.To find the length of X, we can set up a proportion and solve for X. The proportion would be 8/X = 12/8, which simplifies to X = 12.Therefore, the length of the side indicated in the similar figure is 12.The length of the indicated side of the similar figure is 4.This is because the two figures are similar, meaning they have the same shape and ratio of sides.This means that if one side is 8, the other will be 4, since 8/4 = 2.This theory is called the Proportionality Rule and states that if two figures are similar, the corresponding sides are proportional.

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2) A normal distribution has mean 700 and standard deviation 50. The probability is 0.6 that a randomly
selected term from this distribution is above x. What is x?

Answers

According to the normal distribution data given the value for x is obtained as 687.5.

What is normal distribution?

One of the families of continuous distributions, the standard normal distribution has a mean of zero and a standard deviation of one. Since most observations are grouped around the mean and mean=median=mode, the distribution is symmetric at the mean zero.

The value for mean is μ = 700.

The value for standard deviation is σ = 50.

The probability value is 0.6.

Use z score formula to solve for value of x -

P (X>x) = 0.6

0.6 = 1 - P (X>x)

0.4 = P[{(X-μ)/σ} ≤ {(x-700)/50}]

z0.4 = (x-700)/50

-0.25 = (x-700)/50

x = (-0.25 × 50) + 700

x = -12.5 + 700

x = 687.5

Therefore, the value for x is 687.5.

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1. Which polygon or polygons are regular? (2 points)

Answers

Answer:

the first and the third

Step-by-step explanation:

Shawn has 22 boxes of golf balls. Each box has three golf balls.

Look at each equation below. Decide if it can be used to find the total number of golf balls?

(SCREENSHOT BELOW)

Answers

Answer:

1) can 2) can’t 3) can’t 4) can

Step-by-step explanation:

There are 66 golf balls in total 1 and 4 are the only equations that equal 66

Triangle D has been dilated to create triangle D′. Use the image to answer the question.

Answers

Answer:
D’ -> D uses scale factor of 3
D -> D’ uses scale factor of 1/3
x = 0.9

Explanation:
Since the triangles are dilations of each other, than means the scaling factor is constant, meaning the angles of the triangle stay the same while the edges increase or decrease by a scalar value.

To find the scalar value, simply choose one side of D and one did of D’ and divide them to find the scalar. We can verify that we have the correct scalar by performing this division on each related edge. Below I will do D to D’ represented like D/D’:

4.8 / 1.6 = 3
4.2 / 1.4 = 3
2.7 / x = 3

Knowing that the scaling for each edge is 3, we can solve for x.

2.7 / 3 = x
0.9 = x

So we know the edges for D are 4.8, 4.2, and 2.7 respectively to D’ scaled by 1/3. So we can determine that the edges for D’ are 1.6, 1.4, and 0.9 respectively to D scaled by 3.

So if we go D’ to D, we scale by 3. If we go D to D’, we scale by 1/3.

Cheers.

Answer: It is C I got it right on the exam

Step-by-step explanation:

1. Which of the following is 60% in fraction form?A. 25B. 35C. 45

Answers

Answer:

I think 35

Step-by-step explanation:

Is it possible to construct a triangle whose sides are 3.5 cm 9.2 cm and 5.3 cm Why or why not?

Answers

We cannot construct a triangle with side lengths 3.5 cm, 9.2 cm and 5.3 cm. So it is not possible to construct a triangle whose sides are 3.5 cm 9.2 cm and 5.3 cm. This is because these lengths does not follow triangle inequality theorem.

It is not possible to construct a triangle using the given side lengths of 3.5 cm, 9.2 cm, and 5.3 cm. This is because of the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, if we take 3.5 cm and 5.3 cm as two sides, the sum of their lengths is 8.8 cm. But the length of the third side (9.2 cm) is greater than 8.8 cm, so these three side lengths cannot form a triangle.

It is important to note that this theorem applies to any triangle, whether it is acute, right or obtuse-angled triangle.

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By which postulate or theorem is ∠3 ≅ ∠6?

Answers

Answer:

B) Alternate Interior Angles Theorem

Step-by-step explanation:

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. In the above diagram, m∠3 ≅ m∠6

What is an exponential function called?

Answers

An exponential function is a function in which the variable appears in an exponent.

The most common form of an exponential function is f(x) = aˣ, where a is a positive constant, known as the base of the function, and x is the variable. The variable x is called the exponent of the function.

The base, a, determines the growth rate of the function. If the base is greater than 1, the function will increase rapidly as x increases. If the base is between 0 and 1, the function will decrease rapidly as x increases.

Exponential functions can also be written in the form y = a×bˣ, where a and b are constants, b is the base and x is the exponent. In this form, a represents the y-intercept of the function, which is the point where the function crosses the y-axis.

An exponential function can be recognize by the presence of the variable in an exponent and the graph of an exponential function is a curve that goes up and to the right if the base is greater than 1, and goes down and to the right if the base is between 0 and 1.

In conclusion, an exponential function is a function in which the variable appears in an exponent and is defined as f(x) = aˣ or y = a×bˣ, where a is the base of the function and x is the exponent.

The base determines the growth rate of the function and the graph of an exponential function is a curve that goes up and to the right if the base is greater than 1, and goes down and to the right if the base is between 0 and 1.

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Five Smithtown High School students are saving up to buy their first cars. They all have after-school jobs, and their weekly sala-ries are listed in the table. (Table: Emily $110, Sam $145, Danielle $130, Katie $160, Stephanie $400)
a. What is the mean weekly salary for these students?
b. What is the median salary?
c. Whose salary would you consider to be an outlier?
d. Which number do you think is better representative of the data, the mean or the median?
e. Explain your answer to part d.

Answers

Answer:

A. $189.

B. $130.

C. Stephanie's.

D. The Mean.

E. The mean is the average of the data. The Median is just the middle number which doesn't reveal all that much about the data.

Answer:

A.) $189

B.) $145✔️ | *(not $130❌)*

C.) Stephanie's

D.) Median✔️ | *(not "mean"❌)

E.) Because there is an outlier, the median is better representative than the mean.

what is the slope of the graph?

Answers

The slope of the line is -4.

What is slope?A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x). The slope is calculated as the ratio of the rise, which is the vertical change between two points, to the run, which is the horizontal change between those same two sites. A line's steepness is indicated by its slope. The slope's steepness increases with its size. The slope flattens out as it grows smaller. Slope also reveals whether a line is horizontal or vertical, or if it is going up or down. The slope in mathematics is a measure of how steep a line is. The gradient is another name for it. The slope equations.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

From the diagram, the graph passes through point ( 0,2) and (1,-2)

Point 1( 0.2 )

x₁ = 0

y₁ = 2

Point 2( 1,-2 )

x₂ = 1

y₂ = -2

To determine the slope of the line, plug the coordinates into the above slope formula.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( -2 - 2 )/( 1 - 0 )

Slope m = ( -4 )/( 1  )

Slope m = -4/1

Slope m = -4

Therefore, the slope of the line is -4.

Option A is the correct answer.

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Lance ay that 2,376 ÷10 by the power of 2 i the ame a 2,376 x 0. 1 i he correct ? Why or why not

Answers

It is possible that Lance ay that 2,376 ÷10 by the power of 2 i the ame a 2,376 x 0. 1 i he correct

The power (or exponent) of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. In this example the little "2" says to use 8 two times in a multiplication: 82 = 8 × 8 = 64.

What are powers?

A power is the product of multiplying a number by itself. Usually, a power is represented with a base number and an exponent. The base number tells what number is being multiplied. The exponent, a small number written above and to the right of the base number, tells how many times the base number is being multiplied.

Since 2376÷10

It will give us

237.6

So to convert to standard form it will be

2376×10^-1

How

Since the point has been shifted to the right side

And it will definitely give us 2376.0

But the point zero is not necessary

10^1 also means 0.1

So it is possible

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Which graph represents the inequality y is less than negative one-third times x plus 1?

Answers

A graph which represents the inequality y is less than negative one-third times x plus 1 is shown in the image below.

What is an inequality?

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Less than or equal to (≤).Greater than (>).Greater than or equal to (≥).Less than (<).

How to determine the graph which represents the inequality?

In order to determine and plot the graph which represents the inequality, we would first of all translate the word problem into an algebraic equation as follows;

y is less than or equal to one-third times x plus 1 ⇒ y < x/3 + 1.

Next, we would use an online graphing calculator to graphically solve the given inequality.

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Answer:

B

Step-by-step explanation:

The graph shows the answer accurately

Solve for x round to the nearest tenth 33 27

Answers

54.90
sinx =opp/adj
sinx= 27/33
x=sin^-1(9/11)

Eric ran 3 kilometers in 20 minutes.
Taylor ran 2,550 meters in 17 minutes. Was one person faster than the other or were they running at the same rate?

Answers

Answer:It is not possible to answer this question without knowing the rate at which the other person was running.

Step-by-step explanation:

(THIS IS DUE TMRW!!)

Explain how to get the Unit Rate for Amount of Miles Ran per Minute for #18. Jaime ran 6 miles in 60 minutes. How far does Jaime run (in miles) per minute? Show all work and then write an explanation.

Answers

A mile is 5,280 feet long and an hour is 3,600 seconds long, thus 60 miles per hour is 60 x 5,280 / 3,600 = 88 feet per second.

What is the unit rate formula?

How Do I Determine the Unit Rate? The denominator of a unit rate is always 1. To calculate the unit rate, divide the denominator by the numerator so that the denominator equals 1. For example, if 50 kilometers are reached in 5.5 hours, the unit rate is 50 kilometers/5.5 hours = 9.09 kilometers per hour.

Miles per hour is a relatively typical example of a unit rate that we face on a daily basis. This rate is a unit rate since it describes the number of miles in one hour.

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i cant figure this out

Answers

Answer:

4^2 or 16

Step by step explanation:

4^5 = 4x4x4x4x4

4^3 = 4x4x4

4^5 ÷ 4^3 = 4x4x4x4x4 ÷ 4x4x4 = 4x4

4x4 = 4^2 = 16

Select the correct answer!!!

Answers

The correct answer is a: k=3

Select all the equations that are equivalent to y - 4 = (x - 1).

Answers

It's important to note that equation y = x - 1 + 4 and y = x + 3 are in slope-intercept form, which is a common way to write linear equations.

How to determine the equivalent equation?

To determine if two equations are equivalent, you can check if they represent the same line in the cartesian plane. The following methods can be used to determine equivalent equations:

Graph the equations: You can graph the equations on the same coordinate plane and see if they produce the same line. If they do, the equations are equivalent.Check for the same slope and y-intercept: You can check if the equations have the same slope and y-intercept. If they do, the equations are equivalent.Solving for y: You can put the equation in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, if the slope and y-intercept are the same for both equations, the equations are equivalent.

The following equations are equivalent to y - 4 = (x - 1):

y = x - 1 + 4

y = x + 3

y - 4 = x - 1 + 4

y - 4 = x + 3 - 4

(y - 4) + 4 = (x - 1) + 4

y = x - 1 + 4

All of the above equations have the same slope and y-intercept, which means they represent the same line in the cartesian plane.

It's important to note that equation y = x - 1 + 4 and y = x + 3 are in slope-intercept form, which is a common way to write linear equations.

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PQ-18. What is the pH of a 0.400 M sodium formate (NaCHO,) solution? K (HCHO,)-1.8x104 (A) 2.07 (B) 5.33 (C) 8.67 (D) 11.93 Give a teaser about the book 1984 by George Orwell without spoiling the ending. (not a summary of the plot) THANK YOU Which of the following is FALSE regarding Gause's (1934) experiment on competition in Paramecium? A. Competition was strong between these two species because these species overlapped in resource use. B. Results showed that both species were able to co-exist, though one species limited its realized niche. C. When the two species were grown separately, each population exhibited logistic growth. D> When grown together, one species caused the other population to go extinct. Please help me answer all questions. I will give points. Thank youuuu many cells store lipids in droplets of varying sizes. these droplets Do you think alliances help prevent or fuel conflict? Ground your answer with at least one historical circumstance that you have learned in this lesson. retained earnings represent the cumulative total of all earnings, net of dividends, that have been retained and reinvested in the firm since its inception.T/F u.s. workers will see increased competition in the future due to: a short-term capital loss carryover to the current year retains its character as short-term and is combined with the short-term items of the current year. the total thermal resistance of a system is 36.7 k/w and the area of heat transfer is 1.02 m2. calculate the overall heat transfer coefficient for the system. 1. The lessee can purchase the leased asset for a minimal $5 payment at the end of the lease and the lease term is for a major part of the asset's remaining economic life. The lease term is 5% of the leased asset's useful life and there is no option for the lessee to purchase the asset. 2. 3. The lessor retains title to the asset, and the lease term is 3 years on an asset that has a 10-year useful life. Government spending influences the economy by:A. setting the salaries for employees in all private industries.B. influencing the brands of products the country is allowed toproduce.C. deciding on the prices for goods available to consumers.OD. determining which government programs get the most funding. In two factor ANOVA, an F ratio is calculated for each differentsum of squares.mean square.factor.null hypothesis. an area of land has been planted with christmas trees. on december 1, twelve years from now, the trees will be ready for harvest. at that time, the standing christmas trees can be sold for $2,000 per acre. the land, after the trees have been removed, will be worth $400 per acre. there are no taxes or operating expenses, but also no revenue from this land until the trees are harvested. the interest rate is 11%. 1) what can we expect the market price of the land to be? 2) suppose that the christmas trees do not have to be sold after 10 years, but could be sold in any year. their value if they are cut before they are 10 years old is zero. after the trees are 10 years old, an acre of trees is worth $2,000 and its value will increase by $100 per year for the next 30 years. after the trees are cut, the land on which the trees stood can always be sold for $400 an acre. when should the trees be cut to maximize the present value of the payments received for trees and land? what would be the market price of the acre of the land? 3) will your reply on the second question change if the rate becomes 15%? 8%? How to connect wireless router to laptop in cisco packet tracer? People tend to use emotion-focused, rather than problem-focused, coping strategies in which situation? Starting with 100.0 grams of carbon and an excess of silicon dioxide and calcium phosphate, howmany moles of phosphorus will be produced?2 Caz(PO4)2 +6 SIO, 100 - 6 Casioz + PA+ 10 CO If 36. 7 mL of 3M MgCl2 is used what is the mass of Mg(OH)2 produced? recall the role of tropymyosin in regulating keletal muscle contraction. will a mutant form of tm that can bind to the actin filaments but is uable to bind the troponin complex function in a dominant-negative fashion to affect muscle contraction?A. No, because the mutant TM and troponin will bind to actin filaments independentlyB. No, beacuse the mutant TM cannot bind to the action filamentsC. No, beacuse the mutant TM will be displaced easily from the actin filamentsD. No, beacuse the mutant TM can never be displaced from the actin filamentsE. No, beacuse the mutant TM can still bind strongly to calcium ions calculate the hydronium ion concentration and the ph of the solution that results when 75.0 ml of 0.405 m ch3cooh is mixed with 104 ml of 0.210 m naoh. acetic acid's ka is 1.70 105