Suppose that a forest on a flat terrain has perimeter 200 kilometers, but there is no information on the shape of the forest. What shape will give the largest possible area for the forest? what is this area?

The percentage of gold will be equal to 39.7%

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %.

1. First find the density of your chain

Density = mass / volume

Volume = displaced water volume

                     = Volume of Final level of water - initial level of water

                     = 20 ml - 15 ml = 5 ml

Mass = 66.7 g

Density = 66.7g / 5 ml = 13.34 g/ml

2. Second, write the density of the chain as the weighted average of the densities of the other metals:

Mass of gold x density of gold + mass of other metals x density of other metals, all divided by the mass of the chain.

Calling x the amount of gold, then the amount of other metals is 66.7 - x:

[(19.3x+(9.7)(66.7-x)] / 66.7 = 13.34

19.3x + 635.66 - 9.7x = 889.778

9.6x = 254.118

x = 26.47

Then, there are 26.47 grams of gold in 66.7 grams of chain, which yields a percentage of:

(26.47 / 66.7) x 100 = 39.7%

Therefore the percentage of gold will be equal to 39.7%

To know more about percentages follow

https://brainly.com/question/24304697

#SPJ1

The option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

Let x be the number.

According to the problem.

50% of x = 10

x = 10 ÷ 50%

= 10×(50/100)

= (50÷5)/(100÷5) = 10/20

Thus, the option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.

Learn more about the percentage here:

brainly.com/question/8011401

#SPJ1

Answer:

28n+24

Step-by-step explanation:

3 ( 7 n + 5 n + 8 ) - 8 n

combine 7n and 5n to get 12n

3 ( 12n + 8 ) - 8

distribute 3 to 12n +8

36n+24-8n

combine like terms

28n+24

since ypu cant simply any more it stays like thats

*by the way there is an app that helps with equation and explains the process, its Microsoft Math Solver. hope it helped

Answer:

[tex]2261.9cm^{2}[/tex]

Step-by-step explanation:

Total Surface Area of Cylinder = [tex]2\pi rh+2\pi r^{2}[/tex]

Note: Do not get tricked by the 24cm (taking 24cm as the radius), that is the diameter.

To find r, radius = [tex]\frac{1}{2} d[/tex]

                          =[tex]\frac{1}{2} (24)\\[/tex]

                          = 12cm

Now we know r = 12cm, h = 18cm

Now we substitute r and h into the formula to find the total surface area.

Total Surface Area of Cylinder = [tex]2\pi (12)(18)+2\pi (12)^{2} \\=432\pi +288\pi \\=720\pi cm^{2} \\=2261.9cm^{2}[/tex]

The option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

Let x be the number.

According to the problem.

50% of x = 10

x = 10 ÷ 50%

= 10×(50/100)

= (50÷5)/(100÷5) = 10/20

Thus, the option fourth StartFraction 50 divided by 5 Over 100 divided by 5 EndFraction = StartFraction 10 Over 20 EndFraction is correct.

Learn more about the percentage here:

brainly.com/question/8011401

#SPJ1

Answer:

294pi

Step-by-step explanation:

1/3*pi*r^2*h=V

1/3*pi*49*18=V

V=294pi

Using a trigonometric identity, it is found that the sine of the angle is given as follows:

[tex]\sin{\theta} = -\frac{4}{5}[/tex].

Considering an angle [tex]\theta[/tex], the identity is given as follows:

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

In this problem, the cosine is given as follows:

[tex]\cos{\theta} = \frac{3}{5}[/tex]

Hence the sine is found as follows:

[tex]\sin^2{\theta} + \cos^2{\theta} = 1[/tex]

[tex]\sin^2{\theta} + \left(\frac{3}{5}\right)^2{\theta} = 1[/tex]

[tex]\sin^2{\theta} + \frac{9}{25} = 1[/tex]

[tex]\sin^2{\theta} = \frac{16}{25}[/tex]

[tex]\sin{\theta} = \pm \sqrt{\frac{16}{25}}[/tex]

In quadrant IV, the sine is negative, hence:

[tex]\sin{\theta} = -\frac{4}{5}[/tex].

More can be learned about trigonometric identities at https://brainly.com/question/7331447

#SPJ1

Answer:

y = (-4/5)x - 7/5

Step-by-step explanation:

The general equation of the line is slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept. You have been given the value of the slope (m = -4/5). To find the y-intercept, use the slope and values from the Point (2,-3) to isolate "b".

y = mx + b                                   <----- Slope-intercept form

y = (-4/5)x + b                             <------ Plug -4/5 in "m"

-3 = (-4/5)(2) + b                         <----- Plug in "x" and "y" values from Point

-3 = -8/5 + b                               <------ Multiply -4/5 and 2

-15/5 = -8/5 + b                          <----- Assign common denominator

-7/5 = b                                      <----- Add 8/5 to both sides

Now that you have the slope and y-intercept, you can construct the equation.

y = (-4/5)x - 7/5

The magnitude of the resultant vector is 22.6 m and the direction is 56.8⁰.

Ax = A cosθ

Ay = A sinθ

Ax = 7.7 x cos(27.8)

Ax = 6.81 m

Ay = 7.7 x sin(27.8)

Ay = 3.59 m

Bx = B cosθ

By = B sinθ

θ with respect to x - axis = 90 - 20 = 70⁰

Bx = 16.3 m x cos(70)

Bx = 5.575 m

By = 16.3 m x sin(70)

By = 15.32 m

Vx = Ax + Bx

Vx = 6.81 m + 5.575 m = 12.385 m

Vy = Ay + By

Vy = 3.59 m + 15.32 m = 18.91 m

V = √(Vy² + Vx²)

V = √(18.91² + 12.385²)

V = 22.6 m

tan θ = Vy/Vx

tan θ = (18.91)/(12.385)

tan θ = 1.527

θ = arc tan (1.527)

θ = 56.8⁰

Thus, the magnitude of the resultant vector is 22.6 m and the direction is 56.8⁰.

Learn more about vectors here: https://brainly.com/question/25811261

#SPJ1

The equation which represent number of days is 87 ÷ n = 3

It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.

Here,

total hour practicing = 87 hours

Daily hours for practicing = 3 hours

total number of days = n days

Now, according to question;

n X 3 = 87

87 ÷ n = 3

Thus, the equation which represent number of days is 87 ÷ n = 3.

Learn more about Division from:

https://brainly.com/question/21416852

#SPJ1

Two or more triangles are said to be congruent if their length of sides and measure of angles are equal. Thus, the required proof expected in the question is option D. <R ≅ <U

When the length of sides or measure of angles of two or more figures is equal, then we say the figures are congruent.

From the given question, the following can be deduced:

RT ≅ US (given: opposite sides are equal)

and TS is a common side for the two triangles.

<TRS  ≅  <RSU (alternate angle property)

<RTS  ≅ <UST (right angle property)

<RTU  ≅  <SUT (alternate angle property)

Therefore it can be observed that the necessary condition to prove that ΔRST ≅ ΔUTS is option D. <R  ≅ <U.

For more clarifications on  ≅ congruent properties of triangles, visit: https://brainly.com/question/1619927

#SPJ1

Answer:

Step-by-step explanation:

The product (a+b)(a-2b) is a^2 - ab - 2b^2

The product expression is given as:

(a+b)(a-2b)

Expand the bracket

a * a - a * 2b + b * a - b * 2b

Evaluate the product

a^2 - 2ab + ab - 2b^2

Evaluate the like terms

a^2 - ab - 2b^2

Hence, the product (a+b)(a-2b) is a^2 - ab - 2b^2

Read more about products at:

https://brainly.com/question/10873737

#SPJ1

Answer:

6(q + 9)

Step-by-step explanation:

The amount you should put is 3846

The given parameters are:

Amount, A = 4000

Rate, r = 8%

Time = 0.5 year i.e. 6 months

The amount on simple interest is calculated as:

A = P(1 + RT)

This gives

4000 = P * (1 + 8% * 0.5)

Evaluate the product

4000 = P * (1 + 0.04)

Evaluate the sum

4000 = P * (1.04)

Divide both sides by 1.04

P= 3846

Hence, the amount you should put is 3846

Read more about simple interest at:

https://brainly.com/question/20690803

#SPJ1

Answer:

0.25 or 1/4

Step-by-step explanation:

P(coin is flipped as head) = 0.5 or 1/2 (one of 2 sides)

P(coin is flipped as head twice) = P(coin is flipped as head) x P(coin is flipped as head)

= 0.5 x 0.5

= 0.25 or 1/4

Answer

sum of all 3 digit even number = 247050

The series is 100 + 102 + 104 + .... + 998

which by using formula Sn = N/2 ( a + an)

where N = number of terms

a = first term = 100

an = last term = 998

Answer:

D

Step-by-step explanation:

Answer:

1/16

Step-by-step explanation:

To evaluate the function f(-4), we let x =4 in f(x) = [tex]2^{x}[/tex]

f(-4) = [tex]2^{-4}[/tex]

     = 1/[tex]2^{4}[/tex]

     =1/16

Answer:

$33.915 for the cd

Step-by-step explanation:

70% of 19.95 = 13.965

19.95 + 13.965= 33.91

Answer:

6^4 * 6^3

Step-by-step explanation:

Here is conversion chart

1 day=24hr

so the equation to solve this would look like this

(24*11)+7

Therefore the answer is 271 hr

Answer:

9x^3-15x

Step-by-step explanation:

The ice cube tray can make 200.96 cubic centimeters of ice.

For a sphere of radius R, the volume is:

[tex]V = \frac{4}{3}*3.14*R^3[/tex]

In this case, we have 6 spheres, each one with a radius of 2cm.

Then the total volume of ice that the ice cube tray can make at one time is:

[tex]volume = 6*V = 6*(\frac{4}{3} *3.14*(2cm)^3) = 200.96cm^3[/tex]

The ice cube tray can make 200.96 cubic centimeters of ice.

If you want to learn more about volumes:

https://brainly.com/question/1972490

#SPJ1

Answer:

[tex]\dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

Increase the power by 1, then divide by the new power.

Given indefinite integral:

[tex]\displaystyle \int x \ln x \:\: \text{d}x[/tex]

To integrate the given integral, use Integration by Parts:

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]

[tex]\text{Let }u=\ln x \implies \dfrac{\text{d}u}{\text{d}x}=\dfrac{1}{x}[/tex]

[tex]\text{Let }\dfrac{\text{d}v}{\text{d}x}=x \implies v=\dfrac{1}{2}x^2[/tex]

Therefore:

[tex]\begin{aligned}\displaystyle \int u \dfrac{dv}{dx}\:dx & =uv-\int v\: \dfrac{du}{dx}\:dx\\\\\implies \displaystyle \int x \ln x\:\:\text{d}x & = \ln x \cdot \dfrac{1}{2}x^2-\int \dfrac{1}{2}x^2 \cdot \dfrac{1}{x}\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x -\int \dfrac{1}{2}x\:\:dx\\\\& = \dfrac{1}{2}x^2\ln x - \dfrac{1}{4}x^2+\text{C}\end{aligned}[/tex]

Learn more about integration here:

https://brainly.com/question/27805589

https://brainly.com/question/27983581

https://brainly.com/question/27759474

Explanation:

There are 7 ways to pick the first place position, then 6 ways for second place, 5 for third, and so on. We count down until we get to 1

7,6,5,4,3,2,1

Multiply out those values to get the final answer. On many calculators this can be done using the factorial button, indicated as an exclamation mark

7! = 7*6*5*4*3*2*1 = 5040

Answer:

1. Colouring Pencil 2. Notebook 3. Pencil Case

Step-by-step explanation:

Duplicate don't answer!

I assume you meant [tex]g(x)=4^x -1[/tex].

The graph is shown in the attached image.

The two points on the graph are (0,0) and (1, 3).

The asymptote is y = -1.

The domain is (-∞,∞)

The range is (-1,∞)

Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be written as 2 2 2 2=25 for the number 32. This phrase should be understood as "two to the fifth power."

The two points on the graph are (0,0) and (1, 3).

The asymptote is y = -1.

The domain is (-∞,∞)

The range is (-1,∞)

The graph of the function is attached with the answer.

To know more about an exponential expression follow

brainly.com/question/2456547

#SPJ2

Answer:

Step-by-step explanation:

[tex]\sqrt{- i} =\sqrt{(-1)i} =\sqrt{i^2i} =i\sqrt{i}[/tex]

Answer:

Step-by-step explanation:

|√2-y|=|y-√2|

√2-y=±(y-√2)

when √2-y=y-√2

y+y=√2+√2

2y=2√2

y=√2

when √2-y=-(y-√2)

√2-y=-y+√2

or 0=0

it gives no value of y.

so only possible value is y=√2

The express elevator will go 4 floors per seconds.

We have to find the rate of the express elevator before we can find how many floors one can go in one seconds.

time = 12 3 / 4  = 51 / 4 seconds

number of floor = 51 floors

rate = 51 / 51 / 4

rate = 51 × 4 / 51

rate = 4 floors per seconds

Therefore, the elevator will go 4 floors per seconds.

learn more on rate here: https://brainly.com/question/8891579

#SPJ1