find the aptitude and period of the function: f(x) = -2 sin x

The profit-maximizing number of years (t) that a forester would wait before harvesting the timber is approximately 9.9 years.

Given the volume of timber in a forest at a certain time (t) as: V(t) = 10t - 0.2t^2

Let's differentiate the given volume function w.r.t 't' to find the maximum value of timber as follows:

           dV(t)/dt = 10 - 0.4t

Now, equate dV(t)/dt = 0 to find the value of 't' for which V(t) is maximum.0

                                   = 10 - 0.4t0.4t = 10t

                                   = 10/0.4t = 25years

Therefore, the number of years that would be associated with the maximum volume of timber is 25 years.

Let's suppose the volume of timber in a forest is given by the function: V(t) = 20t

We need to find the profit-maximizing number of years (t) that a forester would wait before harvesting the timber when the interest rate is 20%.

It is given that, the interest rate (i) = 20%

                                                        =0.2

The cost of harvesting the timber is given by the formula:

                                           C = K +r*W where K is the fixed cost,

r is the interest rate,

and W is the amount of timber harvested.

Let's suppose the fixed cost (K) = $50 and the price of timber (p)

                                                    = $10 per unit.

Therefore, the profit function can be written as:

P(t) = p*V(t) - C

     = $10*20t - (50 + 0.2*10t)

     = $200t - 50 - 2t= 198t - 50

Now, differentiate P(t) w.r.t t to find the value of t for which P(t) is maximum.

dP(t)/dt = 198Equating dP(t)/dt  

= 0, we get,0

= 198t

= 198/20t

= 9.9

Therefore, the profit-maximizing number of years (t) that a forester would wait before harvesting the timber is approximately 9.9 years.

Learn more about profit-maximizing from the given link

https://brainly.com/question/13464288

#SPJ11

Stem-and-leaf plots contain original data values where histograms do not. Therefore, option B is the correct answer.

The "stem" values are listed down, and the "leaf" values go right (or left) from the stem values.

The "stem" is used to group the scores and each "leaf" shows the individual scores within each group.

The advantage of a stem leaf diagram is it gives a concise representation of data. The advantage of a frequency histogram is, that it is visually strong. Histograms are usually preferable to stem and leaf diagrams in large data sets. The disadvantage of a stem leaf diagram is not visual.

Therefore, option B is the correct answer.

Learn more about the stem-and-leaf plot here:

https://brainly.com/question/12857419.

#SPJ2

Answer:

16 cm

Step-by-step explanation:

4 cm represents 5 km. There is a total length of 20 km, so you do 20/5=4. Since you have to multiply 5 by 4 to get 20, you also multiply 4cm by 4, and you get 16, or the amount of cm that represents 20 km.

Answer:

Scatter plot attached below.

Step-by-step explanation:

The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.

If there is any alteration in the value of one variable, the value of the other variable is altered in a fixed proportion. The correlation amid them is known as perfect correlation.

In statistics, a perfect positive correlation is represented by +1 and -1 indicates a perfect negative correlation.

Negative correlation is a relationship amid two variables in which one variable rises as the other falls, and vice versa.

The scatter plot for the correlation between x and y closest to −1 is attached below.

Hence, in respοnse tο the prοvided questiοn, we can say that  12x - 8 can  functiοn be factοred οut as 4(3x - 2), where 4 is a cοmmοn factοr οf 12 and 8, and (3x - 2) is the expressiοn that remains after factοring οut 4.

Mathematicians research numbers and their variants, equatiοn and related structures, οbjects and their lοcatiοns, and prοspective lοcatiοns fοr these things. The term "mοdule" is used tο describe the cοnnectiοn that exists in between set οf inputs, each οf which has a cοrrespοnding οutput. A functiοn is an input-οutput cοnnectiοn in which each inputs results in sοmething like a single, distinct return. A dοmain, cοdοmain, οr scοpe is assigned tο each functiοn. Functiοns are usually denοted by the letter f. (x). An x is used fοr entry. On capabilities, οne-tο-οne capabilities, multiple prοwess, in capabilities, and οn capabilities are the fοur majοr types οf accessible functiοns.

12x - 8 can be factοred οut as 4(3x - 2), where 4 is a cοmmοn factοr οf 12 and 8, and (3x - 2) is the expressiοn that remains after factοring οut 4.

To know more about function visit:

brainly.com/question/28193995

#SPJ1

Complete question:

We can describe 12x-8 as an expression.

It can also be written as 4(3x-2)

4(3x-2) is a ___ of 12x-8.

What is the blank?

The ratio of their radii is 8/2 = 4.

Ratio is a comparison of two or more quantities expressed in terms of their relative sizes. It is a way to express one number as a fraction of another number. For example, if a person has three apples and two oranges, the ratio of apples to oranges can be expressed as 3:2. Ratios can also be expressed as fractions or percentages.

To show that Circle D and Circle E are similar, we need to determine if the ratio of their radii is equal to the ratio of their distances from the origin. The ratio of their radii is 8/2 = 4. The distance from the origin for Circle D is sqrt((8)²+ (-2)²) = sqrt(64 + 4) = sqrt(68) = 8.24. For Circle E, the distance from the origin is sqrt((5)² + (1)²) = sqrt(26) = 5.1. The ratio of their distances from the origin is 8.24/5.1 = 1.61. Since the ratio of their radii (4) is equal to the ratio of their distances from the origin (1.61), we can conclude that Circle D and Circle E are similar.

To know more about ratio click-
https://brainly.com/question/25927869
#SPJ1

The calculated area of the minor sector is 90π square cm

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

The circle (see attachment)

Where, we have

The area of the minor sector is then calculated as

Area = θ/360 * πr²

Substitute the known values in the above equation, so, we have the following representation

Area = 36/360 * π * 30²

Evaluate

Area = 90π

Hence, the area is 90π

Read more about sector area at

https://brainly.com/question/31752704

#SPJ1

if the installment option is used, the total amount paid over the 240-month term would be $1,080,000. This includes both the principal amount of $550,000 and the interest accumulated over the repayment period.

To determine the total amount if the installment option is used, we need to calculate the total repayment over the 240-month term.

The installment amount per month is $4,500, and the repayment term is 240 months.

Total repayment = Installment amount per month * Repayment term

Total repayment = $4,500 * 240

Total repayment = $1,080,000

Therefore, if the installment option is used, the total amount paid over the 240-month term would be $1,080,000. This includes both the principal amount of $550,000 and the interest accumulated over the repayment period.

Learn more about installment here:

https://brainly.com/question/11468274

#SPJ11

Answer:

52 miles

Step-by-step explanation:

Matthew runs 20 miles in the first week. We want to increase this number by 4 each week. For this question we will use m for a variable for miles.

This will look like

20 + 4m = total miles ran

if he ran 8 miles, we will enter this number into the variable m.

20 + 4 × 8 = 52

The total miles Matthew ran was 52 miles after 8 weeks.

Answer:

16

Step-by-step explanation:

80/5=16

Answer:

16

Step-by-step explanation:

80 divided by 5 is 16

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

Explanation:

The value 12 is between the perfect squares 9 and 16

This means we can write the following inequality \(9 < 12 < 16\)

From here we apply the square root to all three sides and simplify like so

\(9 < 12 < 16\\\\\sqrt{9} < \sqrt{12} < \sqrt{16}\\\\3 < \sqrt{12} < 4\)

and we see that the square root of 12 is between 3 and 4.

Using a calculator would confirm this

\(\sqrt{12} \approx 3.464\)

Answer:

Step-by-step explanation:

Find the numbers closest to 12 on either side that are perfect squares:

1, 4, 9, 16, 25

12 is in between the numbers 9 and 16. The square root of 9 is 3 and the square root of 16 is 4. Therefore, the square root of 12 is in between 3 and 4.

Answer: 60

Step-by-step explanation:

From the question, we are informed that pencils come in packages of 10 while erasers come in package of 12 .

We are further told that Phillip wants to purchase the smallest number of pencils and erasers so that he will have exactly 1 eraser per pencil, this simply means that we have to calculate the lowest common multiple for 10 and 12.

Multiples of 10 = 10, 20, 30, 40, 50, 60,

Multiples of 12 = 12, 24, 36, 48, 60, 72

Therefore, the packages of pencils and erasers that Phillip should buy will be 60

Let's call:

a: number of adults

c: number of children

90 people visited a museum, then:

a + c = 90

Tickets to the museum cost $12 for each adult and $7 for each child and the museum collected $950, then:

12a + 7c = 950

Isolating c in the first equation:

c = 90 - a

Replacing it into the second equation:

12a + 7(90 - a) = 950

12a + 7(90) - 7a = 950

5a + 630 = 950

5a = 950 - 630

a = 320/5

a = 64

64 adults visited the museum

Convergence is a technique used by a professional to gain the audience's trust by using speech they are unfamiliar with. This assertion is untrue.

As in the case of a convergence of plum as well as apricot genetic mutations in the plucot, convergence would be when multiple components combine to form a fresh fact that the entire.

What are convergence & divergence in speech?

Convergence refers to behavioral tactics used by speakers to alter their communication so that it resembles other people's. Divergence, on the reverse hand, relates to interpersonal strategies where a person speaking changes how they speak towards other people in order to emphasize or create differences.

There are three distinct kinds of convergent plate boundaries: oceanic-continental, oceanic-oceanic, as well as continental-continental.

To know more about boundaries click here

brainly.com/question/29941965

#SPJ4

Answer:

blank 1: 24

Step-by-step explanation:

According to Pythagoras' Theorem, in a right-angled triangle,

(side 1)² +(side 2)²= (hypotenuse)²

Applying Pythagoras' Theorem,

x² +18²= 30²

x² +324= 900

x²= 900 -324 (-324 on both sides)

x²= 576

\(x = \sqrt{576} \)

x= 24 ft

The number of outfits Audrey can purchase while staying within her budget is 2

= $6.14

The inequality:

259.52 + 6.14 + 29.12 + 72.61x ≤ 440

294.78 + 72.61x ≤ 440

72.61x ≤ 440 - 294.78

72.61x ≤ 145.22

x ≤ 145.22 / 72.61

x ≤ 2

Therefore, the number of outfits Audrey can purchase while staying within her budget.

Learn more about inequality:

https://brainly.com/question/25275758

#SPJ1

Answer: I don’t understand Spanish

Step-by-step explanation:

Oof

Answer:

50 (b)

Step-by-step explanation:

It's an acute angle

The probability that a randomly selected student is taking exactly one language class is 0.5045 or approximately 50.45%.

1. This is calculated by subtracting the number of students taking two or more classes from the total number of students, and then dividing by the total number of students.

2. To calculate this probability, we start by finding the total number of students taking at least one language class. This can be calculated by adding the number of students in each language class, and then subtracting the students who are taking multiple classes to avoid double counting. So, the total number of students taking at least one language class is: 42 + 32 + 29 - 13 - 8 - 10 + 4 = 76

3. Next, we can find the number of students taking exactly one language class by subtracting the students taking two or more classes from the total number of students taking at least one class. So, the number of students taking exactly one language class is: 76 - 13 - 8 - 10 + 4 = 49

4. Finally, we can calculate the probability of selecting a student taking exactly one language class by dividing the number of students taking exactly one class by the total number of students. So, the probability is: 49/111 ≈ 0.5045 or approximately 50.45%.

5. In summary, the probability of selecting a student taking exactly one language class is 0.5045 or approximately 50.45%. This probability is calculated by subtracting the number of students taking multiple classes from the total number of students, and then dividing by the total number of students. The calculation involves avoiding double counting of students taking multiple classes.

Learn more about probability here: brainly.com/question/30034780

#SPJ11

If we wish to accumulate $3,641 after 6 years at a 5% interest rate, then $2,717.16 must be set aside at the end of each of the 6 periods

The Amount = $3,641

Time = 6 years

Interest Rate = 5% = 0.05

Compounded at the end of each of the 6 periods.

So n = 6 × 6 = 36

Periodic interest rate;

i = r/m

i = 0.05/6

i = 0.00833

Compound Formula

A = P(1 + i)^n

3,641 = P(1 + 0.00833)^36

3,641 = P(1.00833)^36

3,641 = 1.35P

Divide by 1.35 on both side, we get

P = $2,717.16

To learn more about compound interest link is here

brainly.com/question/14295570

#SPJ4

The future value of Tran Lee's savings after five years would be approximately $14,995.49.

To calculate the future value of Tran Lee's savings, we can use the formula for the future value of an ordinary annuity:

Future Value = Payment * [(1 + Interest Rate)^Number of Periods - 1] / Interest Rate

Given:

Payment (PMT) = $2,900 per year

Interest Rate (r) = 5% = 0.05 (decimal form)

Number of Periods (n) = 5 years

Substitute  these values into the formula, we get:

Future Value = $2,900 * [(1 + 0.05)^5 - 1] / 0.05

Calculating this expression, we find:

Future Value ≈ $14,995.49

Therefore, the future value of Tran Lee's savings after five years would be approximately $14,995.49.

learn more about savings on

https://brainly.com/question/7965246

#SPJ11

The future value of Tran Lee's savings after five years would be approximately $14,995.49.

To calculate the future value of Tran Lee's savings, we can use the formula for the future value of an ordinary annuity:

Future Value = Payment * [(1 + Interest Rate)^Number of Periods - 1] / Interest Rate

Given:

Payment (PMT) = $2,900 per year

Interest Rate (r) = 5% = 0.05 (decimal form)

Number of Periods (n) = 5 years

Substitute  these values into the formula, we get:

Future Value = $2,900 * [(1 + 0.05)^5 - 1] / 0.05

Calculating this expression, we find:

Future Value ≈ $14,995.49

Therefore, the future value of Tran Lee's savings after five years would be approximately $14,995.49.

learn more about savings from given link

https://brainly.com/question/30101466

#SPJ11

To find the value of angle 0 that maximizes the range of a projectile, we can use the formula R(0) = p² sin(2θ), where R represents the range, p is the initial velocity, and θ is the angle of the projectile measured in radians. By analyzing the equation, we can determine the angle that maximizes the range.

In the formula R(0) = p² sin(2θ), the range R is given as a function of the angle θ. To find the angle that maximizes the range, we need to identify the maximum value of the function. Since sin(2θ) is bounded between -1 and 1, the maximum value of sin(2θ) is 1. Therefore, to maximize the range, we need to maximize p².The range R is given by R(0) = p² sin(2θ). As sin(2θ) reaches its maximum value of 1, we can simplify the equation to R(0) = p². This means that the range is maximized when p² is maximized. Since p represents the initial velocity, increasing the initial velocity will result in a larger range. Therefore, to maximize the range, we should choose the maximum possible initial velocity.

Learn more about maximizes the range here

https://brainly.com/question/31697278



#SPJ11

The equation of a line in slope-intercept form that is parallel to the line y-2=3(x+7) and passes through the point (4,2) is y = 3x - 10.

To find the equation of a line parallel to the given line, we need to determine the slope of the given line.

The given line is in the form y - 2 = 3(x + 7), which can be rewritten as y = 3x + 23.

The slope-intercept form of a line is y = mx + b, where m represents the slope of the line.

Since we want the parallel line to have the same slope, the slope of the parallel line will also be 3.

Using the point-slope form of a line, which is y - y1 = m(x - x1), we can substitute the coordinates (4,2) and the slope m = 3 into the equation. This gives us y - 2 = 3(x - 4).

Simplifying further, we have y - 2 = 3x - 12.

By isolating y on one side of the equation, we get y = 3x - 10.

Therefore, the equation of the line parallel to y - 2 = 3(x + 7) and passing through the point (4,2) is y = 3x - 10.

Learn more about slope-intercept form visit:

brainly.com/question/29146348

#SPJ11

Answer:I believe this answer is they did not have enough troops to attack the USSR

Step-by-step explanation:

I

In a standard additions method workup the information from the linear regression that is most closely related to the unknown concentration is this:  the intercept of the linear regression line.

In the standard additions method workup, the information that is most closely related to the unknown concentration is the intercept of the linear regression line.

The reason why this is the case is that the intercept represents the y-value of the regression line where the line crosses the y-axis. This y-axis is the value of the dependent variable when the independent variable or concentration is zero. So, by solving for the intercept, we can determine the concentration of the unknown sample.

Learn more about linear regression here:

https://brainly.com/question/25987747

#SPJ1

Answer:

x = 5

Step-by-step explanation:

-4 ( x - 3) = -8

-4x +12 = -8

-4x = -20

x = 5