Which property of real numbers is shown below?
3+ ((-5) + 6) = (3 + (-5)) + 6
commutative property of addition
identity property of multiplication
associative property of addition
commutative property of multiplication

The population of an island in 1950 was 2 million. The population grew exponentially for 63 years and reached 6.5 million in 2013. The carrying capacity of the island is estimated to be 10 million.

If the population growth rate in the future is similar to the last 50 years, what will the population be in 2050

The population is given to be increasing exponentially, which means it will follow the equation:

\($P(t) = P_0 e^{rt}$\)Here,\($P(t)$\) is the population after a period of time \($t$, $P_0$\) is the initial population, $r$ is the annual growth rate (which we are given is the same as the growth rate of the last 50 years), and \($t$\) is the time.

We can find the annual growth rate $r$ using the formula:\($$r = \frac{\ln{\frac{P(t)}{P_0}}}{t}$$\)
We know\($P_0 = 2$ million, $P(t) = 6.5$ million, and $t = 63$\) years. Substituting these values, we get:

\($r = \frac{\ln{\frac{6.5}{2}}}{63} = 0.032$\) (rounded to 3 decimal places)

Since the carrying capacity of the island is 10 million, we know that the population will not exceed this limit.

Therefore, we can use the logistic model to find the population growth over time. The logistic growth model is:

\($$\frac{dP}{dt} = r P \left(1 - \frac{P}{K}\right)$$\)

where $K$ is the carrying capacity of the environment. This can be solved to give:\($P(t) = \frac{K}{1 + A e^{-rt}}$\)

where \($A = \frac{K-P_0}{P_0}$. We know $K = 10$ million, $P_0 = 2$ million, and $r = 0.032$\). Substituting these values, we get:\($A = \frac{10-2}{2} = 4$\)

Therefore, the equation for the population of the island is:\($P(t) = \frac{10}{1 + 4 e^{-0.032t}}$\)

To find the population in 2050, we substitute\($t = 100$\) (since 63 years have already passed and we want to find the population in 2050, which is 100 years after 1950):

\($P(100) = \frac{10}{1 + 4 e^{-0.032 \times 100}} \approx \boxed{8.76}$ million\)
Therefore, the estimated population of the island in 2050, assuming constant carrying capacity and consumption per capita, is approximately 8.76 million.

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Answer:

Step-by-step explanation:

The area of a rectangle is length time width.

A=LW

In this case,

A=32x^2+12

W=4x

Solve for L

L=A/W

Substitute

L=(32x^2+12)/4x

L=(8x^2+3)/x

Answer:

Step-by-step explanation:

Below, I have attached the slope formula. Inserting the numbers into the formula, we get 9/3=3

a 21.8 g sample of osmium would occupy a volume of approximately 0.9646 cm³.

To calculate the volume occupied by a sample of osmium, we can use the formula:

Volume = Mass / Density

Given:

Mass = 21.8 g

Density = 22.6 g/cm³

Substituting these values into the formula:

Volume = 21.8 g / 22.6 g/cm³

Simplifying:

Volume = 0.9646 cm³

what is volume?

Volume is a measure of the amount of space occupied by a three-dimensional object or substance. It quantifies the extent or capacity of an object or substance in terms of how much space it occupies.

In mathematical terms, volume is typically measured in cubic units (such as cubic meters, cubic centimeters, or cubic inches). It is calculated by multiplying together the three dimensions of the object (length, width, and height) or by using specific formulas depending on the shape of the object.

For example, the volume of a rectangular box can be calculated by multiplying its length, width, and height. The volume of a cylinder can be calculated using the formula πr²h, where r is the radius of the base and h is the height.

Volume is an essential measurement in various fields such as physics, engineering, chemistry, and everyday life. It helps determine capacities, quantities, displacements, and the amount of space occupied by objects or substances.

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Answer:

Alternate Interior Angles

The trip from Rochester to New York City is a distance of 330 miles, and Ben is driving at a rate of 65 miles per hour.

To determine the approximate duration of the trip, we can divide the distance by the speed. Therefore, the trip will take approximately 5.1 hours.

To calculate the time it takes for the trip, we divide the distance (330 miles) by the rate of travel (65 miles per hour). The formula for calculating time is time = distance / rate. In this case, the distance is 330 miles and the rate is 65 miles per hour.

Dividing 330 by 65 gives us 5.07692307692, which can be rounded to the nearest tenth of an hour as 5.1. Therefore, the trip will take approximately 5.1 hours.

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To simplify the trigonometric expression

cos(3π/4)cos(π/8) - sin(3π/4)sin(π/8)cos(7π/8)sin(7π/8) - sin(7π/8)(-cos(7π/8))

we can use the addition/subtraction formula for cosine and sine.

The addition/subtraction formula for cosine is:

cos(a ± b) = cos(a)cos(b) - sin(a)sin(b)

And the addition/subtraction formula for sine is:

sin(a ± b) = sin(a)cos(b) ± cos(a)sin(b)

Using these formulas, let's simplify the given expression step by step:

cos(3π/4)cos(π/8) - sin(3π/4)sin(π/8)cos(7π/8)sin(7π/8) - sin(7π/8)(-cos(7π/8))

Applying the cosine addition formula to the first two terms:

= cos(3π/4 + π/8) - sin(3π/4 + π/8)cos(7π/8)sin(7π/8) - sin(7π/8)(-cos(7π/8))

Simplifying the first two terms using the sine addition formula:

= cos(11π/8) - sin(11π/8)cos(7π/8)sin(7π/8) - sin(7π/8)(-cos(7π/8))

Applying the sine subtraction formula to the last two terms:

= cos(11π/8) - sin(11π/8)cos(7π/8)sin(7π/8) + sin(7π/8)cos(7π/8)

Since sin(7π/8)cos(7π/8) = 1/2 sin(14π/8), we can simplify further:

= cos(11π/8) - sin(11π/8)cos(7π/8)sin(7π/8) + 1/2 sin(14π/8)

Simplifying the expression sin(7π/8)cos(7π/8) using the sine addition formula:

= cos(11π/8) - sin(11π/8)(1/2) + 1/2 sin(14π/8)

Now, cos(11π/8) = cos(π - 3π/8) = -cos(3π/8) and sin(11π/8) = -sin(3π/8), so we can substitute these values:

= -cos(3π/8) + sin(3π/8)(1/2) + 1/2 sin(14π/8)

Finally, sin(14π/8) = sin(7π/4) = √2/2, so we can substitute this value as well:

= -cos(3π/8) + sin(3π/8)(1/2) + 1/2 (√2/2)

Therefore, the simplified expression is:

- cos(3π/8) + (1/2)sin(3π/8) + (1/2)√2/2

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Answer:

2

Step-by-step explanation:

Option A. AA Similarity Postulate. The AA Similarity Postulate is a geometric principle that states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

This means that their corresponding sides are in proportion, and the triangles have the same shape, but not necessarily the same size. This postulate is one of the ways to prove the similarity of two triangles. In the case of the given question, if we know that two angles of one triangle are congruent to the two angles of another triangle, then we can use the AA Similarity Postulate to prove that the triangles are similar. This principle is widely used in geometry and helps to establish relationships between different shapes and figures.

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Lines e and f are parallel because their alternate exterior angle is congruent. Option C is correct.

Find the diagram attached;

The point where two lines meet is known as an angle.

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Answer: Option 3 or C. Lines e and f are parallel because their alternate exterior angles are congruent.

Step-by-step explanation: The correct answer is C.  

I got it right on the Edge 2022 quiz. Trust me the proof is shown below.

Answer:

  x = 117

Step-by-step explanation:

The sum of the interior angles of a pentagon is 180°(5 -2) = 540°. This means ...

  x +59 +138 +140 +86 = 540

  x +423 = 540 . . . simplify

  x = 117 . . . . . . . . subtract 117

Answer:

Yes

Step-by-step explanation:

The two objects are plotted at different points in graph and one gets the difference of points y coordinates (change in y) and change in x too.

Then one can look for distance as hypotenous and change in y as height and change in x as the base of our imaginery triangle.

Therefore, from Pythagoras Theoreom:

hyptenous² = height² + base²

Distance² = change in y² + change in x²

Distance = √change in y² + change in x²

Answer:

1. 8000mm is the same as 8 metres. So 8km is greater than 8000mm

2. 5000m is the same as 5 km. So 50 km is greater than 5000m

3. 100cm is the same as 1 m. So 10m is greater than 100cm

4. 40 cm is the same as 400mm. So 4mm is less than 40cm.

The length of the ladder is approximately 17.4 feet.

Let's call the length of the ladder "L". We can use the Pythagorean theorem to solve for L.

We know that the ladder is leaning against a vertical wall at a slope of 9/4, which means that for every 9 units the ladder goes up, it goes 4 units away from the wall. We can use this to set up a right triangle with the ladder as the hypotenuse:

To know the sides use pythagorean theorem. The vertical distance from the ground to the tip of the ladder is 13.7 feet, so the length of the side opposite the angle θ (the angle between the ladder and the ground) is 13.7. The length of the side adjacent to θ (the distance from the wall to the base of the ladder) is (9/4) times the length of the opposite side.

Using the Pythagorean theorem, we have:

L² = (9/4 * 13.7)² + (13.7)²

L² = 114.96 + 187.69

L² = 302.65

L = √(302.65)

L ≈ 17.4

Therefore, the length of the ladder is approximately 17.4 feet.

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Answer:27.78% ; Twi; 1/3

Step-by-step explanation:

Given the data :

Language - - - - - - - Number of students

Nzema - - - - - - - - - - - 5

Ga - - - - - - - - - - - - - - - 20

Twi - - - - - - - - - - - - - - - 30

Ewe - - - - - - - - - - - - - - - 25

Fante - - - - - - - - - - - - - - 10

1.) To prepare pie chart:

Total number of students :

(5 + 20 + 30 + 25 + 10) = 90 students

Nzema: (5/90) × 360 = 20

Ga : (20/90) × 360 = 79.99 = 80

Twi : (30/90) × 360 = 119.99 = 120

Ewe : (25/90) × 360 = 79.99 = 100

Fante : (10/90) × 360 = 39.99 = 40

Total = 360

Pie chart is attached in the picture below

2)Percentage students that speak Ewe = (25/90) * 100 = 27.78%

Or (100/360) * 100 = 27.78%

3.) Modal language : This is the language spoken by majority of the students = Twi

4.) Fraction of student that speak either GA or Fante :

(GA or Fante) = (20 + 10) / 90 = 30/90 = 1/3

The car will need 6 gallons of gasoline to travel 102 miles

Given that the car travels 442 miles on 26 gallons of gasoline.

Because the more the distance, the more the volume of gasoline used, this is a direct proportion.

So, we have:

It will need 6 gallons.

We can expect to observe 14 complete interference fringes within the central diffraction peak.

The act of bending light around corners such that it spreads out and illuminates regions where a shadow is anticipated is known as diffraction of light. In general, since both occur simultaneously, it is challenging to distinguish between diffraction and interference.

The number of complete interference fringes within the central diffraction peak depends on the specific experimental setup, such as the distance between the slits and the screen, the distance between the slits, and the wavelength of the light being used.

However, we can use the following equation to calculate the number of interference fringes within the central diffraction peak:

N = (2d/a)(L/λ)

where N is the number of interference fringes, d is the distance between the slits, a is the width of the slits, L is the distance between the slits and the screen, and λ is the wavelength of the light being used.

Assuming that we have a double-slit setup and the distance between the slits and the screen is much larger than the slit width, we can simplify the equation to:

N = 2d/a

Given that d/a = 7, we can substitute this value into the equation to get:

N = 2(7) = 14

Therefore, we can expect to observe 14 complete interference fringes within the central diffraction peak.

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Answer:

Option b

Step-by-step explanation:

To represent this proportion using fractions, let the numerators be the number of waffles sold and denominator, the number of sugar cones.

Thus, the proportion that can be used to represent the cone sales is

14/6 = 7/3

Answer:

BBBBBB

Step-by-step explanation:

Answer:

\(y=-\frac{3}{2} +3\)

Step-by-step explanation:

Start at the y-intercept, and go down until you see an even intersection (down 3 over 2).

Answer: length = 27 cm

Step-by-step explanation:

Perimeter = 2(l + w)

86 = 2(l + 16)

86 = 2l + 32

86 - 32 = 2l

l = 54/2 = 27 cm.

Step-by-step explanation:

3.14 is rounded to the nearest 100th    (4 is the hundredth position)

Answer:

1/36

Step-by-step explanation:

P(rolling a 3) and P(rolling a 4)

= 1/6 and 1/6

=(1/6)(1/6)

=1/36

Answer:

2.5 is the answer

Step-by-step explanation:

∑(17-4n) is the summation formula represents the series 13 + 9 + 5 + 1.

A series is the cumulative sum of a given sequence of terms.

The given expression is 13 + 9 + 5 + 1

The terms of this series are 13,9,5,1

It is an AP. Here, first term is 13 and common ratio is -4.

The nth term of an AP is

aₙ=a+(n-1)d

=13+(n-1)(-4)

=13-4n+4

=17-4n

The summation formula of an Arithmetic progression is

∑aₙ

The value of n is 4 because the number of term is 4. So, the summation formula is

∑(17-4n)

Hence ∑(17-4n) is the summation formula represents the series

13 + 9 + 5 + 1.

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Answer:

2

Step-by-step explanation:

One property of a triangle is that the sum of any two sides of a triangle is greater than the third side. Therefore, if the third side was represented by x, this would mean that :

17 + x > 16

16 + x > 17

17 + 16 > x

Since 17 is already greater than 16, there is no limit on x there. However, because 16 is 1 less than 17, x must be greater than 1. Furthermore, since 17+16 is 33, x must be less than 33. Therefore, the smallest whole number that fits these conditions is 2.

Answer:

okie

Step-by-step explanation:

Answer:

Ok

Step-by-step expl

Answer:

\(m=\frac{-1}{2}\)

Step-by-step explanation:

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Simply plug in the 2 coordinates into the slope formula to find slope m:

\(m=\frac{-3-(-1)}{2-(-2)}\)

\(m=\frac{-3+1}{2+2}\)

\(m=\frac{-2}{4}\)

\(m=\frac{-1}{2}\)

During the winter season, a family sets up a hot chocolate stand near a local ice skating rink. They sell cups of hot chocolate for $1.50 each and typically sell 50 cups per day.

However, due to changes in weather conditions and customer preferences, the family decides to conduct a market experiment by varying the price of hot chocolate to assess the impact on sales volume. The experiment involves increasing the price to $2.00 per cup and monitoring the resulting sales.

By increasing the price of hot chocolate from $1.50 to $2.00 per cup, the family aims to observe how the change in price affects the demand for their product. The experiment helps them understand the price elasticity of demand, which measures the responsiveness of quantity demanded to changes in price. If the increase in price leads to a significant decrease in sales volume, it suggests that the demand for hot chocolate is elastic, meaning consumers are sensitive to price changes. Conversely, if sales remain relatively stable despite the price increase, it indicates that the demand is inelastic, indicating that consumers are less sensitive to price changes. The family can analyze the results of this experiment to make informed pricing decisions and optimize their profitability during the winter season.

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Herberto travelled through Amusement Park (AP), City Park (P), Landmark (L), High School (HS), City Hall (CH).

Herberto can take the following path to travel from the amusement park (AP) to the city hall (CH):

Amusement Park (AP) -> City Park (P) -> Landmark (L) -> High School (HS) -> City Hall (CH)

This path takes him through the city park, then to the landmark, followed by the high school, and finally to the city hall.

Please note that without a specific map or layout of Knappville, there could be multiple valid paths from the amusement park to the city hall. The path provided above is just one example.

When Herberto travels from the amusement park to the city hall, he can choose various paths depending on the specific layout of Knappville. The path mentioned earlier is just one example, but the actual paths could differ based on the town's infrastructure and the locations of the landmarks.

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Answer:

b. 0.75 kg

Step-by-step explanation:

1 kilogram is 1000 grams