30 POINTS AND BRANLIEST
Mahek owns a holiday tree farm. There are currently 800 trees on the property. Each year 20% of the trees are harvested and sold, and 200 seedlings are planted. Write a recursive definition for the number of trees on the farm at the beginning of the nth year.

Angle x's cosine is doubled in 2cosx, which ranges from [-2, 2]. The cosine of the angle 2x, or two times the angle x, is called cos 2x, and it lies between [-1, 1].

Trigonometric function cos 2 x is a cosine of angle that is twice as large as angle, whereas trigonometric function 2 cos x is twice as large as angle.

Due to the fact that they contain an angle that is twice as large as the angle in their formulas, the identities and formulas of sin 2x, cos 2x, tan 2x, cot 2x, sec 2x, and cosec 2x are referred to as double angle formulas. 2sinxcosx is the sin 2x formula.

2•cos²(x) + cos(x) - 1 = 0

Factoring gives;

(2•cos(x) - 1)•(cos(x) + 1) = 0

2•cos(x) - 1 = 0

cos(x) = 1/2

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By alternating internal angles, angles 1 and 2 are equivalent.

What does the triangle's angle sum property entail?

According to the triangle's "angle sum property," the inner angles of a triangle add up to 180 degrees.

1. Angles 1 and 2 complement one another. Angles 2 and 3 compliment one another.

These angles are linear, hence their sum is 180 degrees.

2.m angle

Angle 1 + m2 Equals 90° Angle m2 + m3 = 90°

Equals makes a straight angle

3. m angle1 plus m angle2 equals m angle2 plus m angle3

= 180 degrees when the total of the two sides

4. m angle2 equals m angle

= The total of the two sides is equal

5. m angle1 = m angle3

= The total of the two sides is equal

6.Angle1 and Angle3 are congruent.

Alternate interior angles are what they are.

Angle 1 and Angle 3 are therefore equivalent based on the triangle's characteristics.

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The probability of selecting all bottles of the same variety is P(A) = 6/46656 = 0.00013.

The probability of selecting two bottles of each variety when randomly selecting 6 bottles can be calculated using the formula P(A) = n(A) / n(S), where n(A) is the number of possible ways to select two bottles of each variety and n(S) is the total number of possible ways to select 6 bottles. In this case, n(A) is equal to 6! / (2!2!2!) = 90 and n(S) is equal to 6^6 = 46656. So, the probability of selecting two bottles of each variety is P(A) = 90/46656 = 0.0019.

The probability of selecting all bottles of the same variety when randomly selecting 6 bottles can be calculated using the same formula. In this case, n(A) is equal to 6, which is the number of ways to select 6 bottles of the same variety, and n(S) is equal to 46656. So, the probability of selecting all bottles of the same variety is P(A) = 6/46656 = 0.00013.

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Answer:

below

Step-by-step explanation:

The upper and lower horizontal lines are parallel

 so y = 71°      alternate angles with transverse line

then z = 180 - 71 - 65 = 44°     ( interior angles of a triangle sum to 180 °)

The measure of 2D is five-halves the measure of ZY, the measure of each angle of the deck.

D and R are opposite sides & G and Y are also opposite sides.

So, we have:

∠D = ∠R = 5/2 ∠Y

and

∠G = ∠Y

The sum of angles is given as:

∠D + ∠G + ∠Y + ∠R = 360

Substitute values for ∠D, ∠G, ∠R

5/2 ∠Y + 5/2 ∠Y + ∠Y + ∠Y = 360

Multiply both sides by 2/14,

∠Y = 51.43

So:

∠G , ∠Y = 51.43

∠D = 5/2 ∠Y

∠D = 128.57

Therefore, measure of angle m∠D = 128.57°, m∠G = 51.43°, m∠R = 128.57°, m∠Y = 51.43°.

A parallelogram is a two-dimensional flat shape with four angles. The internal angles on either side are equal. The transversal's angles on the same side are supplementary, which means they sum to 180 degrees. As a result, a parallelogram's internal angles add up to 360 degrees.

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On solving the provided question, we can say that angle a = 113

;angle b = 57;

angle c = 57  

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that converge at a center point known as the angle's vertex.

Two rays can create an angle in the plane where they are arranged. Additionally, when two planes collide, an angle is created. Dihedral angles are what they are called. An angle is a possible shape for two rays or lines with a common termination in planar geometry. The English term "angle" derives from the Latin word "angulus," which meaning "horn." The vertex is the common endpoint of the two rays, also known as the sides of the angle.

from the 3rd figure, we have -

angle a = 113 ( vertical opposite angle)

angle b = 180 - a    (Corresponding angles)

180 - 113 = 57

b = 57

angle c = 57  ( vertical opposite angle)

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The value of the expression (1/5)r + 9/20 when r = 1/4 is 1/2.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(1/5)r + 9/20

For r = 1/4,

(1/5) x 1/4 + 9/20

= 1/20 + 9/20

= 10/20

= 1/2

Thus,

The value of the expression is 1/2.

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Variability around the mean or nominal dimension is a measure of quality because it helps to quantify the spread of data and the degree to which it deviates from the expected value.

By considering variability, manufacturers and designers can identify areas for improvement, determine tolerances for product specifications, and ensure consistency in production. Additionally, it helps to identify outliers and inconsistencies in the data which can be indicative of defects or issues in the production process. Furthermore, considering variability helps to assess the risk of non-conformance and predict the performance of a product in real-world scenarios. In short, considering variability helps to improve the overall quality of products and ensure they meet customer expectations.

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The required pressure for the given information is 55.6 N/m².

Pressure is defined as the force exerted per unit area. It can be calculated by dividing the force by the area over which it is spread. In this case, the force is 506 N and the area is 9.1 m², so the pressure can be calculated as follows:

pressure = force / area

= 506 N / 9.1 m²

= 55.6 N/m².

The unit of pressure is N/m² or Pascal (Pa). Therefore, the pressure in this case is 55.6 Pa. This means that for every square meter of area, there is a force of 55.6 N acting on it. The pressure can be used to determine the force required to cause deformation of an object, the amount of gas in a container, and many other physical phenomena.

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Since, Ian worked 25 hours at the grocery store last week and 36 hours this week. Therefore, the percent of change is a decrease  of 44% in work efficiency.

Given that:

Last week working hour of Ian is 25 hours.

Current week working hour of Ian is 36 hours.

Now,

First, subtract to find the amount of change:

36 - 25 = 11.

Therefore, The decrease is 25.

Next, divide the amount of change by the original amount:

11 ÷ 25 = 0.44

Now, to change the decimal to a percent, multiply the number by 100:

0.44 x 100 = 44%

The answer is 16.7%.

Therefore,  the percent of change, a decrease of 44% in working efficiency.

Complete Question:

Lan worked 25 hours at the grocery store last week and 36 hours this week.

What is the percent change?

O 44% Increase

O 44% Decrease

O 31% Increase

O 31% Decrease

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The algebraic expression that represents the amount that Sohail got is given as follows:

[10(x - 8)]².

His break lasted x days and he was out of station for 8 days, hence the number of days that Sohail worked is given as follows:

x - 8 days.

Each day he earned Rs 10, hence the total amount earned can be modeled as follows:

10(x - 8).

After the amount was squared, the expression is given as follows:

[10(x - 8)]².

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The solutions to the quadratic equation x² - 10x + 25 = 17 are x = -√17 + 5 and x = √17 + 5.

The quadratic equation in its standard form is;

ax² + bx + c = 0

Where x is the unknown .

To find x, we use the quadratic formula;

x = (-b±√(b² - 4ac)) / (2a)

Given the quadratic equation in the question.

x² - 10x + 25 = 17

First, we rearrange in standard form

x² - 10x + 8 = 0

Plug these values into the quadratic formula above and solve for x.

x = (-b±√(b² - 4ac)) / (2a)

x = ( -(-10) ±√( (-10)² - 4×1×8)) / (2×1)

x = ( 10 ±√( 100 - 32 )) / 2

x = ( 10 ±2√17 ) / 2

x = 10/2 ± (2√17)/2

x = 5 ± √17

x = ±√17 + 5

x = -√17 + 5 and x = √17 + 5

Therefore, the solutions are x = -√17 + 5 and x = √17 + 5.

Option (B) and (F) are the correct answer.

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Answer:

200 seconds

Step-by-step explanation:

1 km = 1000m

3 km = 3000m

How long would it take to travel 3 km at a speed of 15 m/s?

The equation to solve this is:

Time = Distance / Rate

D = 3km or 3000m

R = 15 m/s

3000 divided by 15 = 200 seconds

So, it would take 200 seconds to travel 3 km at a speed of 15 m/s

Answer:

Below

Step-by-step explanation:

You need to have consistent units

  3 km = 3000 m

Distance / rate = time

 3000 m / 15 m/s = 200 seconds

To sell 80% of a total of 1400 units, the salesman must sell 1120 units, and he must sell 520 units from his next shipment of 600 units.

To solve this problem, we need to find out how many units the salesman must sell in order to have sold 80% of the 1400 units in total (800 units from the first shipment and 600 units from the next shipment).

The 80% of the total number of units is calculated as:

To find out how many units from the next shipment the salesman must sell, we subtract the number of units from the first shipment (800 units) from the total number of units that need to be sold (1120 units), which results in:

Finally, we subtract the number of units the salesman has already sold from the next shipment (600 units) from the number of units he still needs to sell (320 units), which results in:

However, since the number of units sold cannot be negative, we must instead calculate the number of units the salesman must sell from the next shipment, which is:

Hence, the salesman must sell 520 units from his next shipment of 600 units.

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Answer:

No se puede determinar la edad de cada hijo con la información proporcionada.

Step-by-step explanation:

The CPA selected the probability-proportional-to-size (PPS) sampling technique because it enables the selection of items in a population in proportion to the items' sizes. This technique yields a more accurate audit by precisely measuring the population of accounts receivable balances.

CPAs frequently employ the probability-proportional-to-size (PPS) sampling technique, also known as dollar-unit sampling, when examining the receivables balances of their clients. With this approach, it is possible to choose population members based on how big they are. The CPA can precisely gauge the population of accounts receivable amounts as a result, which is advantageous. A more accurate audit is made possible by the fact that the larger items in the population are more likely to be chosen than the smaller ones. Additionally, when the sample size grows, the audit's accuracy rises as well, which is another reason CPAs like to employ PPS sampling in their audits. This approach is advantageous because it ensures that the CPA is assessing the population of accounts receivable balances precisely and that the audit is carried out in a precise and trustworthy manner.

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The differentiation of the function would yield -e^-x.

Differentiation is the process of finding the derivative of a function. It measures the rate of change of a function at a given point. The derivative of a function can be found using the power rule, product rule, quotient rule, and chain rule. The derivative of a function can also be represented using the notation f'(x), where f'(x) represents the derivative of the function f(x) with respect to x.

For the exponential function that we have, the standard form of the derivative is that; dy/dx of e^nx = ne^nx.

Thus we have that the result is -e^-x

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The expression that represents the amount of money after t years when $10,000 is compounded quarterly at 12% interest is C. $10,000 (1 + 0.12)^4t.

The compound interest formula or equation for finding the final amount after some years of the principal compounded at an interest rate is given as follows:

Formula for the Final Amount:

A = P(1 + r/n)^{nt}

Where:

A = The Final amount

P = The initial principal

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Thus, the correct expression for finding the final amount after t years under the compound interest system is given by Option C.

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The ratio of the area of the two similar figures is 9 : 16.

Based on the question above, by comparing side shape 1 with side shape 2.

6 : (6+2)

6 : 8

3 : 4

For the ratio of area between the two figures, you can square each one.

3 : 4 = 3² : 4² = 9 : 16

Similar polygons have the same angles and proportional sides. "Proportional" means that the lengths occur in equal proportions (e.g., if the base of triangle 1 is twice the length of the shortest side of triangle 1, then the base of triangle 2 is the length of triangle 2). twice the length of the shortest side).

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The value of x is 20 degrees.

Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two two angles are two pairs of supplementary angles. Meaning that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.

a ║ b, m∠3 = 5x + 10, and m∠5 = 3x + 10.

Thus interior angles are supplementary;

m∠3+ m∠5 = 180°

5x+ 10 + 3x + 10 = 180°

8x + 20 = 180

8x = 160

x= 160/8

x= 20°

Hence, the value of x is 20 degrees.

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The x-coordinate of the solution to the system of equations is 3.

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

Two lines are labeled on x-y coordinate y = - x + 5 and y = x - 1.

Now, Adding these two equations we have,

2y = 4.    (x and - x cancells).

y = 2.

Now, Putting the value of 'y' in any of the equations we have,

2 = - x + 5.

x = 5 - 2.

x = 3.

so, The x-coordinate of the solution is 3.

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$75 is the total money would Ethan have after 5 weeks of saving.

An expression is combination of variables, numbers and operators.

Given that Ethan is saving up to buy a new jacket.

He already has $45 and can save an additional $6 per week using money from his after school job

45+6x is the expression for total money.

Now let us find the total money for 5 weeks.

45+6(5)

45+30

$75

Hence, $75 is the total money would Ethan have after 5 weeks of saving.

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Answer:

20 students went to college.

Step-by-step explanation:

In order to find a percent of a number you must do the number multiplied by the percent divided by 100. For example, the formula is (x*%) divided by 100. 25*80 = 2000. 2000/100 = 20 students. Hope I helped!

Answer:

80% of 25 students

80÷100 × 25 = 20

therefore , 20 students went to college.

The probability 7C3 = 35 possible ways to place 7 identical balls into 3 identical boxes.

The number of ways to place 7 identical balls into 3 identical boxes can be calculated by using the combination formula. The formula for combinations is nCr = n! / (r! (n-r)!), where n represents the total number of items and r represents the number of items being chosen. In this case, n = 7 and r = 3, so the formula becomes 7C3 = 7! / (3! (7-3)!). This simplifies to 7C3 = 7! / (3!4!) = 35. Therefore, there are 35 possible ways to place 7 identical balls into 3 identical boxes.

In each case, the balls can be placed into one box, two boxes, or three boxes, depending on how many balls are placed in each box. If one ball is placed in each box, then the remaining four balls can be placed in any of the boxes, giving four possibilities. If two balls are placed in each box, then the remaining one ball can be placed in any of the boxes, giving three possibilities. Finally, if all seven balls are placed in one box, then there is only one possibility. When the combinations of each scenario are added together, the total number of possible ways to place 7 identical balls into 3 identical boxes is 35.

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Answer:

156.8

Step-by-step explanation:

1.6 * 98

The linear model that could be used to determine which plan would be less expensive based on the number of visits he makes is given as follows:

Second graph (top right graph, where the two lines intersect).

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For the plan with the set price, we have that:

Hence it costs less for a lower number of visits.

For the plan with the set price plus the fee, we have that:

Hence it costs less for a higher number of visits.

Meaning that the second graph is the correct graph in this problem.

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Answer:

2

Explanation:

you need to find the common denominators. Looking at the problem, there are 3 different denominators. 8, 16, and 4. To tell the difference, here they are bolder and italicized to see the difference.

1 3/8+13/16-3/16+2/8-1/4

We can combine the common denominators, leaving us with this:

1 5/8+10/16-1/4

Then you need to make the denominators the same, and since 4 times 2 is 8, you can multiply the numerator and denominator by 2 so the denominator is 8. Then since you can divide 16 by 2 and it equals 8, and the numerator is even, you can divide the numerator and denomorator by 2 so the denominator is also 8. This ends up looking like this:

1 5/8+5/8-2/8

Then you need to combine the common denominators again, leaving you with this:

1 8/8

You can simplify that to simply “2”

(From the start you can also take the 1 and make the original operation into 11/8+13/16 etc., but for this equation it was possible to leave it out until the end and only write it as a placeholder and reminder until the very end. Then at the end I added back in.)

A positive correlation indicates that: the value of one variable increases, the value of the other increases.

There are many instances in daily life where we employ related variables, such as height and weight. Ice cream sales rise in tandem with rising temperatures. Therefore, we refer to two variables as being correlated when they are connected. There are 4 different kinds. i.e., a perfect correlation, a perfect correlation, a negative correlation, and no correlation.

The supplied two variables move in the same direction when there is a positive correlation (i.e increasing together o decreasing together). So, in this case, the correlation coefficient is positive. We may claim that as one variable rises, the other variable likewise increases since they are going in the same direction.

The necessary response is,

As the values of one variable increase, the values of the other variable also tend to increase.

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Complete question: Two variables have a positive association when

a. the values of one variable tend to increase as the values of the other variable increase.

b. the values of one variable tend to decrease as the values of the other variable increase.

c. the values of one variable tend to increase regardless of how the values of the other variable change.

d. the values of both variables are always positive

Answer:

It has no solution.

Step-by-step explanation:

5(x - 2) = 8 + 5x

5x - 10 = 8 + 5x

5x = 18 + 5x

0 = 18

The variable cancels out, so there is no solution to substitute it for.