Please help!find x and y

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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Read the link attached.

I have written it down on the word doc

A stem-and-leaf diagram separates each value of a data set into two parts: the stem and the leaf.

The stem is the first part of the number, typically the largest place value, and it is used to group similar values together. The leaves are the last part of the number, typically the smallest place value, and they provide the specific values within each group.

For example, consider a data set with the values 15, 19, 10, 11, 15. In a stem-and-leaf diagram, the stem for these values would be 1 and the leaves would be 5, 9, 0, 1, and 5, respectively.

The stem-and-leaf diagram would then look something like this:

This format allows for a quick visualization of the distribution of the data and can be useful for identifying patterns and relationships within the data set.

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Answer:

16384

Step-by-step explanation:

=4^4*4^3

=(4*4*4*4)*(4*4*4)

=4*4*4*4*4*4*4

=4^7

The probability that the sum is strictly larger than 21 is P = 0.46

We already have a 10 and a 4, so: 10 + 4 = 14

To sum more than 21, we need to draw at least an 8.

On the deck there are:

So, 23 out of 50 cards meet our requirements. So the probability will be:

P = 23/50 = 0.46

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Answer:

7. 2 6/7

8. -2 1/12

9. -12 4/5

10. 16/9

11. 53/15

12. -29/12

Given:

solution :

so answer is 75.

Answer:

75

Step-by-step explanation:

Answer:

71

Step-by-step explanation:

64+3×5-8

64+15-8

79-8

71

Answer:

71

Step-by-step explanation:

4^3 = 64 + 15 = 79 - 8 = 71

Give me my brainllest

Answer:

Dylan mislabeled opposite and adjacent, and 19.95.

Step-by-step explanation:

Dylan mixed up his labeling of opposite and adjacent so if we switch them we get y= 47tan23 = 19.95

Answer: 27/ D8

Step-by-step explanation: Don’t know if you still need the answer and Hope this helps and have a good day

My friend consumed 8 donuts in one sitting. 8 donuts is a lower bound on how many donuts he is physically capable of eating in one sitting option A.

An element of K that is bigger than or equal to each member of S is referred to as an upper limit or majorant of a subset S of some preordered set (K, ) in mathematics, notably in order theory. In addition, each element of K that is smaller than or equal to each element of S is characterised as a lower limit or minorant of S.

A set that has an upper (or lower) bound is referred to as being majorized (or minorized), bounded from above, or minorized by that bound. In the mathematical literature, sets that have upper (or lower, respectively) limits are referred to as being bounded above (or below).

Friend consumed 8 doughnuts. So it is

lower bound on how can eat in a sitting.

Many donuts he lower bound is the lowest quantity in a set, as in our.

example, we definitely know he can eat 8 of them. We don't know how many more can be eat (upper bound) or is it exact amount be can eat.

Hence option (a) is correct.

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The value of angle Z= 39°, line XY= 21.9 and line XZ= 34.7

A right-angled triangle is a type of triangle which as one of it's sides equal to 90°. Since angle Y is 90°, then ∆ABC is a right-angled triangle

angle Z = 180-(90+51)

angle Z= 180- 141= 39°

using trigonometry ratio

tan51 = 27/XY

XY= 27/tan51

XY= 27/1.2

XY= 21.9

using Pythagoras theorem

XZ²= 21.9²+27²

XZ²= 1208.6

XZ= √1208.6

XZ= 34.7

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The third side of the triangle whose two sides are 11 cm and 19 cm can be between 9 and 29.

A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.

The sum of the angles of a triangle is always 180°

Given that,

The sides of triangles are 11 cm and 19 cm,

Let the third side of the triangle is x,

Since, a side of a triangle is greater than the difference of two sides and less than the sum of two sides,

implies that,

19-11<x<19+11

8 < x < 30

The possible range of third side is (9,29).  

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Answer:

8cm < x < 30cm

Step-by-step explanation:

To find the range of lengths for the third side of a triangle when two side lengths are known, first, assign a variable for the length of the third side.

Let x be the length of the unknown side.

Use the Triangle Inequality Theorem to write the three inequalities.

x + 11x > 19

x + 19 > 11

11 + 19 > x

Solve each inequality.

x > 8

x > -8

30 > x

Now find the range of values that satisfies all three inequalities.

The range between 8 and 30 satisfies all 3 inequalities. Therefore, this triangle's third side lengths range is 8cm < x < 30cm.

The required slopes are:

(a) slope = 4

(b) slope = 6/7

(c) slope =  -3

(d) slope = 4

(e) slope = -5/2

We know that,

When a line passing through (x₁, y₁) and (x₂, y₂)

Then  the slope of the line be,

slope (m) = (y₂ - y₁) / (x₂ - x₁)

Using this formula, calculate the slope for each given points

a. (9, 10) and (7, 2)

⇒ slope (m) = (2 - 10) / (7 - 9)

                    = -8/-2 = 4

So, the slope is 4.

b. (-8, -11) and (-1, -5)

⇒ slope (m) = (-5 - (-11)) / (-1 - (-8))

                    = 6/7

So, the slope is 6/7.

c. (5, -6) and (2, 3)

⇒ slope (m) = (3 - (-6)) / (2 - 5)

                    = 9/-3

                    = -3

So, the slope is -3.

d. (6, 3) and (5, -1)

⇒ slope (m) = (-1 - 3) / (5 - 6)

                    = -4/-1

                    = 4

So, the slope is 4.

e. (4, 7) and (6, 2)

⇒ slope (m) = (2 - 7) / (6 - 4)

                    = -5/2

So, the slope is -5/2.

Therefore, the slope of the line that joins (-8, -11) and (-1, -5) is 6/7.

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Answer:

x < \(\frac{15-3a}{a-4}\); a > 4

a < \(\frac{4x+15}{x+3}\)

Step-by-step explanation:

ax+3a < 4x + 15

ax - 4x < 15 - 3a

x( a -4) < 15 - 3a

x < \(\frac{15-3a}{a-4}\)

ax + 3a < 5x + 15 -x

ax + 3a < 4x + 15

a( x + 3) < 4x + 15

a < \(\frac{4x+15}{x+3}\)

Answer:

x <  (15 - 3a) / (a - 4). ( only true if a > 4)

a < (x + 15)/x

Step-by-step explanation:

a(x + 3) < 5x + 15 - x

ax + 3a < 5x + 15 - x

ax  - 5x + x < 15 - 3a

ax - 4x < 15 - 3a

x(a - 4) < 15 - 3a

Dividing both sides by (a - 4):

x <  (15 - 3a) / (a - 4)

a < (x + 15)/x

A checking account is used for daily basis transaction and a debt and is usually associated with it.Saving accounts is just used for saving money.It has a time limit then you can withdraw your money.It is not on daily basis.

A bank account that allow the user to withdraw the money ,pay bill,transfer money to other person or make a purchase anything by writing checks.Check accounts typically don't earn interest.By checking accounts we can easily deposit and withdraw money for daily transaction.

Saving accounts are intended for storing your money which you don't plan to use daily.saving accounts earns interest at your money.saving account is designed for the accumulation of money in a safe place for future use.saving accounts offer easy access to your money in any emergency.so keeping your money in a saving account means that your money is safe for your future use.

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Thus, the value of the line segment GE for the given tangent on circle is found as: GE = 12.

The slope of a curve at a certain point's line is known as the tangent. It is the line that contacts the curve at any specific point and follows the curve in that location. In other words, the tangent line would be the line that would result if the curve at that point stopped obeying the function and instead went straight.

The slope of the curve is determined at the point where the tangent almost touches the curve.

Given that:

We know that the tangent drawn from the same external points are equal.

So,

GH = GF

x - 1 = 6

x = 6 + 1

x = 7

GE = GF + FE

GE = 7 + 5

GE = 12

Thus, the value of the line segment GE for the given tangent on circle is found as: GE = 12.

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Complete question-

Find the measure of the line segment indicated, assume that lines which appear tangent are tangent.

find GE

Possible answers —>

A. 12

B. 10

C. 17

D. 4

E. 12

Answer:

I got you

Step-by-step explanation:

they would like bass boosted music and music with deep meaning

To find the inverse function of F(x) = 2x - 3, we replace F(x) with y, swap the positions of x and y, and solve for y. The inverse function is f⁻¹(x) = (x+3)/2.

To find the inverse function of F(x) = 2x - 3, follow these steps

Replace F(x) with y. The equation now becomes y = 2x - 3.

Switch the positions of x and y, so the equation becomes x = 2y - 3.

Solve for y in terms of x. Add 3 to both sides: x + 3 = 2y.

Divide both sides by 2 (x + 3)/2 = y.

Replace y with the notation for the inverse function, f⁻¹(x): f⁻¹(x) = (x + 3)/2.

So, the inverse function of F(x) = 2x - 3 is f⁻¹(x) = (x + 3)/2.

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--The given question is incomplete, the complete question is given

" How do I find the inverse function of F(x) = 2x - 3"--

The full set is;

(x + 7) (3x + 1) = 3x² + 22x + 7

This question introduces the concept of polynomial long division.

This is what we are

Given: (3x² + 22x + 7) ÷ (x + 7) = 3x + 1

Now, from the concept of polynomial long division, we can see that:

if, f (x) ÷ g (x) = h (x),

This means that we can write:

f (x) = g (x) × h (x)

Applying the same concept to the question, we can also say:

(3x² + 22x + 7) ÷ (x + 7) = 3x + 1,

Next; (x + 7) (3x + 1) = 3x² + 22x + 7

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The correct formula to calculate the number of tires, t, needed for c cars per day is t = c/4, which is option b).


The formula that shows how to calculate the number of tires, t, needed for c cars per day is option b) t = c/4.

To understand this formula, let's break it down step by step:

1. Each car needs four regular tires and one spare tire for the trunk. So, the total number of tires needed for one car is 4 + 1 = 5.

2. If we want to calculate the total number of tires needed for c cars, we can multiply the number of cars by the number of tires needed per car, which is 5. So, the formula becomes t = 5c.

3. However, we need to find the number of tires needed, which is represented by t. Since we have t on the left side of the equation, we can rearrange the formula by dividing both sides by 5: t/5 = c.

4. Now, we have the number of tires needed (t) expressed in terms of the number of cars (c), but we want to find the number of cars needed given the number of tires (t).


To do this, we can rearrange the formula again by dividing both sides by 4: t/4 = c/4.

Therefore, the correct formula to calculate the number of tires, t, needed for c cars per day is t = c/4, which is option b).

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The standard deviation of the salaries for the company's 80 employees is calculated to be X, where X represents the numerical value of the standard deviation.

The standard deviation measures the dispersion or variability of a set of data points. In order to calculate the standard deviation, we need to first find the mean (average) of the salaries. Then, for each salary, we calculate the difference between the salary and the mean, square that difference, and sum up all the squared differences. Next, we divide the sum by the total number of salaries (80 in this case) minus 1 to obtain the variance. Finally, the standard deviation is obtained by taking the square root of the variance. This accounts for the fact that the squared differences are in squared units, while the standard deviation should be in the original units (currency in this case).

By following this process, we can find the standard deviation of the salaries for the 80 employees in the company. This value represents the measure of variability or spread in the salary distribution, providing insights into how salaries deviate from the mean.

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A statistic is, 4.13%.

Given that;

On Feb. 19th, 2010, 4.13% of the randomly selected spots had potamogeton (a type of seagrass)

Since, A parameter is a value that is determined from all of the data, whereas a statistic is a value that is produced from a sample of the data.

Here, The percentage of spots containing portamento in this instance was solely determined from a randomly chosen sample, making it a statistic.

Hence, It would be a parameter if the percentage was determined using the whole population of spots.

Thus, 4.13% is a statistic.

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Using identity :

therefore, the correct choice is :

\(( \sqrt{5} + \sqrt{2} {)}^{2} \\ \)

\(by \: \: \: using \: \: \: the \: \: \: formula \: \: (a + b) ^{2} = {a}^{2} + 2ab \: + {b}^{2} \: \: we \: \: \: get \\ ( \sqrt{5} {)}^{2} + 2( \sqrt{5}) \: (\sqrt{{2)}} + ( \sqrt{2) }^{2} \\ = \sqrt{5} \times \sqrt{5} + 2 \sqrt{5 \times 2} + \sqrt{2} \times \sqrt{2} \\ = 5 + 2 \sqrt{10} + 2 \\ = 7 + 2 \sqrt{10} \)\)

(C) 7+2√10

Answer:

x + 2y = -15

Step-by-step explanation:

simplify -3x - 6y = 12 by dividing a -3 from each term to get:

x + 2y = -4

now put into slope-intercept form to get:

2y = -x - 4

y = -1x/2 - 2

parallel lines have the same slope so we know our answer must have a slope of -1/2

now we can plug (1,-8) into y=mx + b to get the 'y-intercept', or 'b'

-8 = 1(-1/2) + b

-8 = -1/2 + b

b = -7 1/2 or -15/2

we now know the slope and the y-intercept so our answer is:

y = -x/2 - 15/2

re-write in standard form, which is ax + by = c

multiply each term by  2 to get:

2y = -x - 15

add 'x' to each side to get:

2y + x = -15

x + 2y = -15

Population refers to the entire group of individuals or items that share a common characteristic and are of interest to the researcher. It is the complete set of individuals or items from which data is collected and analyzed. For example, if we are studying the average height of all students in a school, the population would include every student enrolled in that school.

Sample, on the other hand, refers to a subset of the population that is selected to represent the whole population. It is a smaller group of individuals or items that are chosen from the population to provide information about the entire population. Using the same example, if we randomly select 100 students from the school to measure their height, those 100 students would be considered the sample.

Here are a few key differences between population and sample:

1. Size: The population is typically larger than the sample. It includes all the individuals or items of interest, while the sample is a smaller representation of the population.

2. Data Collection: It is often more practical and feasible to collect data from a sample rather than the entire population. Gathering data from a large population can be time-consuming, costly, and sometimes even impossible.

3. Representativeness: The sample should ideally be representative of the population. This means that the characteristics and attributes of the sample should closely mirror those of the population. This ensures that the findings from the sample can be generalized to the larger population.

4. Precision: The larger the sample size, the more precise and accurate the estimates are likely to be. A larger sample size reduces the impact of random variability and increases the reliability of the results.

In conclusion, the population refers to the entire group of individuals or items of interest, while the sample is a smaller subset of the population that is chosen to represent the whole. The choice between using a population or a sample depends on various factors such as feasibility, time, resources, and the research objectives.

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Answer:

1/6 of the bread

Step-by-step explanation:

Given data

Let the amount of the loaf of bread be 1

But they are expected to share half

hence the amount to be shared is= 1/2 bread

The number of children is 3

Hence

=1/2/3

=1/2*1/3

=1/6 bread

Hence each child will get 1/6 of the bread

Answer:

a.

t=11

A=210-14(11)

A=210-154

A=56

$56 left

b.

A=0

0=210-14t

14t=210

t=210/14

t=15

in 15 trips he'd be broke

Answer:

x = 103

Step-by-step explanation:

Using the far right intersection, we can figure out that in inner angle is 32 degrees.

32 + 34 = 66 which is the angle of the left side of the middle cross.

x = 37 + 66 = 103

Answer:

YesTheorem 8.3: If two angles are complementary to the same angle, then these two angles are congruent.

A and B are complementary, and C and B are complementary.