A biologist is studying a certain species of tree in a forest. The tree density for this species in this forest is about 50 trees per acre. The forest is 93 hectares in area; one hectare is equal to 2.47 acres. What is the approximate density of this species in trees per hectare?

sin(x) is a mathematical function that calculates the sine of angle x, where x is in radians.

In mathematics, angles are measured in radians or degrees. The symbol π represents the mathematical constant pi, which is approximately equal to 3.14159.

When we say π/2, it means half of the circumference of a circle, which corresponds to 90 degrees.

The inequality "π/2 < 0" suggests that π/2 is less than zero, implying that the angle of 90 degrees is negative. However, this is incorrect.

In the standard coordinate system, angles are measured counterclockwise from the positive x-axis.

Thus, π/2 or 90 degrees lies in the positive direction. The correct relationship should be "π/2 > 0" to indicate that the angle is greater than zero.

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Answer:

(x-20) (x+3)

Step-by-step explanation:

x^2 - 17x - 60

What two numbers multiply to -60 and add to -17

-20 * 3 = -60

-20 +3 = -17

(x-20) (x+3)

Answer:

option A is correct

Step-by-step explanation:

x^2 - 17 - 60

using middle term break method

x^2 - (20 - 3)x - 60

x^2 - 20x + 3x - 60

x(x - 20) + 3(x - 20)

(x + 3)(x - 20)

The algebraic expression for 8 less than a number is x - 8

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations

Let the number be x.

The algebraic expression for 8 less than a number will be:

x - 8.

The expression is x - 8.

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Answer:

15pi/7 - 13 pi/7

Step-by-step explanation:

to find a positive and negative coterminal angle

● add and subtract 2pi to the given angle

pi/7+2pi=pi/7+14pi/7=15pi/7 positive

pi/7-2pi=pi/7-14pi/7= -13pi/7 negative

Answer:

A

Step-by-step explanation:

2pi radians = 2*pi*9 = 18 pi

That's the circumference. Now you want to take pi/6 part of the circumference.

pi / 6 part of the circumference / 2pi is what you are looking for.

(pi / 6 // 2 pi) * 18 pi = 1/12 * 18 pi = 3/2 pi

Step-by-step explanation:

Reduce = Deduct = Subtract

7y + 2y^2 - 7 - (3 - 4y)

distribute the negative sign outside 3-4y.

7y+2y^2-7 - 3 + 4y

collect like terms, meaning try to make similar components of the equation together at one place.

7y & 4y are like terms in this case.

7y + 4y + 2y^2 - 7 - 3

11y + 2y^2 - 10

rewrite 2y^2 infront of the equation because it has the highest degree which is 2.

2y^2 + 11y - 10

Answer:Reduce = Deduct = Subtract

7y + 2y^2 - 7 - (3 - 4y)

distribute the negative sign outside 3-4y.

7y+2y^2-7 - 3 + 4y

collect like terms, meaning try to make similar components of the equation together at one place.

7y & 4y are like terms in this case.

7y + 4y + 2y^2 - 7 - 3

11y + 2y^2 - 10

rewrite 2y^2 infront of the equation because it has the highest degree which is 2.

2y^2 + 11y - 10

Step-by-step explanation:

thats the estimate

Answer:

im pretty sure that the answer is -50.5 feet.

Step-by-step explanation:

Answer:

$75.65

Step-by-step explanation:

1 - .15 = .85 = 85% of the price is what you pay

89 • .85 = $75.65

Answer:

\(\frac{d}{dt} [sec(\frac{t}{2} )] = \frac{1}{2} sec(\frac{t}{2} )tan(\frac{t}{2} )\)

General Formulas and Concepts:

Calculus

Step-by-step explanation:

Step 1: Define

\(\frac{d}{dt} [sec(\frac{t}{2} )]\)

Step 2: Differentiate

Margin of error for the given standard deviation is  m = 3.77 , 4.21.

What is standard deviation?

Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.

Main body:

Consider the given data, the sample of 84 announcements of upcoming engineering conferences were randomly selected. Here, sample mean = 3.94 days and sample standard deviation s = 1.28 days. The population standard deviation is unknown.

C.I . = 95% = 0.95

value of 0.95 in z-table = 1.96

m(margin of error ) = x - bar ±z*σ/√n

m = 3.94 ± 1.96*1.28/√84

m = 3.94±0.27

m = 3.77 , 4.21

Hence margin of error is m = 3.77 , 4.21

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Answer:

X = 15

Step-by-step explanation:

Since these lines are parallel, this means that Angle 2 is equal to angles 5 and 3.

Since it is equal to 3, this means angle 2 + angle 4 = 180

2x+10+4x+80=180

6x+90=180

6x=90

x=15

A=200,201,202.........,2000

Here, it forms an AP with common difference 1

Let the number of terms in the set be n

\( T_{n} = a+(n-1)d \\\\ 2000= 200+(n-1) \\\\ 200+n-1= 2000 \\\\ => n=2000-199= 1801\)

Hence,n(A)=1801

Answer:

(1) -4, (2) 4,(3) -9.6, (4) 9.6

Step-by-step explanation:

A point has 1 measurement. In geometry, a factor is a simple element that is used to define other shapes and figures. Therefore option 1 is correct.

It's far a location in space that has no length or dimensions, and consequently simplest calls for one dimension to be fully described. This size may be in any path, as a point has no defined orientation.

Points are typically represented on a graph or diagram as a dot, and are often categorized with a letter or image for easy reference. at the same time as a point may appear like a easy idea, it's far essential to many different geometric ideas and serves as a building block for shapes, lines, and angles.

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The number A(t) of pounds of salt in the tank at time t is, \(A(t) = 1200(1-e^-^0^.^0^1^t)\).

What is pounds and gallons?

The name of a unit of currency is pound. Both presently and in the past, it was employed in many different nations.

A gallon, which is equal to eight pints or 4.564 liters, is a unit of measurement for liquids.

Let A(t) be the number of pounds of salts at time t.

Input rate = (4 Ib/gal)(3 gal/min) = 12 Ib/min

Output rate = ((a/300) Ib/gal )(3 gal/min) = 0.01a Ib/min

\(\frac{dA}{dt} = 12 - 0.01A\\ \frac{dA}{dt} + 0.01A = 12\\\)

\(I.F = e^\int\limits^{0.01}\, ^d^t = e^0^.^0^1^t\)

Solution:

\(A(e^0^.^0^1^t)=\int\limits{12(e^0^.^0^1^tdt+c}\\= 12(\frac{e^0^.^0^1^t}{0.01} +c\\Ae^0^.^0^1^t = 1200 e^0^.^0^1^t + c\\A = 1200 + ce^-^0^.^0^1^t\\\\A(0) = 0\\So,\\0 = 1200 + c\\c = -1200\\A(t) = 1200 - 1200e^-^0^.^0^1^t\\A(t) = 1200(1-e^-^0^.^0^1^t)\)

This is the number of pounds of salt in the tank at time t.

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Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Answer:

1/5 or 1 out of 5 chances he would not catch the pitch. also could be said .2 or 20 percent

Answer:

20%

Step-by-step explanation:

Answer:

Step-by-step explanation:

7 no

113+12x+7+90+90=360

300+12x=2=360

12x=360-300

x=60/12

x=5

9 no

10x-6+109+79+20x-2=360

30x+180=360

30x=360-180

x=180/30

x=6

Answer: $634.99

Step-by-step explanation:
Regular price, R - Discount, D = S

subtract discount from regular price

Answer: $634.99

Step-by-step explanation:

$828.15 - 193.16 would equal 634.99

so the discounted price would be $634.99

The equation `sin(x) - ln(x) = 0` has a solution in the interval `(0, π/2)` based on the behavior of the function.

To show that the equation `f(x) = sin(x) - ln(x)` has a solution on the interval `(0, π/2)`, we need to demonstrate the existence of a point where the function crosses the x-axis.

Let's analyze the behavior of `f(x)` on the interval `(0, π/2)`:

1. Boundary conditions:

  - At `x = 0`, `f(0) = sin(0) - ln(0)` is undefined since the natural logarithm of 0 is undefined.

  - At `x = π/2`, `f(π/2) = sin(π/2) - ln(π/2)` is a negative value since the sine function is positive while the natural logarithm of a value greater than 1 is positive.

2. Derivative of `f(x)`:

  Taking the derivative of `f(x)`, we have `f'(x) = cos(x) - 1/x`.

3. Behavior of the derivative:

  - At `x = 0`, `f'(0) = cos(0) - 1/0` is undefined since division by zero is undefined.

  - As `x` approaches 0 from the right side (small positive values), `f'(x)` approaches `-∞`. This indicates a vertical asymptote.

  - As `x` approaches infinity, `f'(x)` approaches 0. This indicates a horizontal asymptote.

4. Analyzing the intervals:

  - When `x` is small and positive, the value of `f(x)` is negative since `sin(x)` is positive and `ln(x)` is increasing at a slower rate.

  - As `x` increases, `f(x)` starts to approach zero as `ln(x)` dominates over `sin(x)`.

  - Eventually, `f(x)` becomes positive as `ln(x)` grows faster than `sin(x)`, and it continues to increase.

  - At `x = π/2`, `f(x)` is negative.

Based on the above analysis, we can conclude that `f(x)` starts as a negative value, crosses the x-axis at some point in the interval `(0, π/2)`, and becomes positive afterward. Therefore, there is at least one solution to the equation `sin(x) - ln(x) = 0` on the interval `(0, π/2)`.

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Answer:

2430 is the answer to 2.43 ×1000

Answer:

2.43 × 1,000= 2,430

Answer:

38 degrees

Step-by-step explanation:

corresponding angles are equal

Answer:

BC= 9.04

AC= 15.0

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Answer:

  BC ≈ 9

  AC ≈ 15

Step-by-step explanation:

The side adjacent to the given angle is the one whose length is known, so the relevant trig relations are ...

  Cos = Adjacent/Hypotenuse   ⇒   cos(37°) = AB/AC

  Tan = Opposite/Adjacent   ⇒   tan(37°) = BC/AB

Then the unknown sides are ...

  AC = AB/cos(37°) = 12/cos(37°) ≈ 15

  BC = AB·tan(37°) = 12·tan(37°) ≈ 9

__

Additional comment

Rounded to the nearest degree, angles 37° and 53° are the acute angles found in a 3-4-5 right triangle. Since the given side is adjacent to the smallest acute angle (not the hypotenuse), it will correspond to "4" in the 3-4-5 triangle. That means the scale factor is 12/4 = 3, and the other two sides are 3·3 = 9 and 3·5 = 15.

The numbers work out this way only by rounding to tenths or integers.

The transformation of System A into System B is:

Equation [A2]+ Equation [A 1] → Equation [B 1]"

The correct answer choice is option D

How can we transform System A into System B?

To transform System A into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

System A:

-3x + 4y = -23 [A1]

7x - 2y = -5 [A2]

Multiply equation [A2] by 2

14x - 4y = -10

Add the equation to equation [A1]

14x - 4y = -10

-3x + 4y = -23 [A1]

11x = -33 [B1]

Multiply equation [A2] by 1

7x - 2y = -5 ....[B2]

So therefore, it can be deduced from the step-by-step explanation above that System A is ultimately transformed into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

The complete image is attached.

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Answer: Number six should be 14/18.

Step-by-step explanation:

The simplified answer is 7/9.

Answer:

80

Step-by-step explanation:

First move like terms to one side:

x/2=25+15

Notice that the sign (+ or -) changes when we switch it to the opposite side

x/2=40

Multiply both sides by 2...

x=80

Answer:

x = 80

Step-by-step explanation:

\(\frac{x}{2}\) - 15 = 25 ( add 15 to both sides )

\(\frac{x}{2}\) = 40 ( multiply both sides by 2 to clear the fraction )

x = 40 × 2 = 80