explain how finding the square root of a number is different from finding the cube root

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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The variable y represents the cost of the gym for x months and the varible x represents the number of months of membership for the gym.

So the meaning of the y-value for x = 1 is the cost a person will need to pay in order to use the gym for 1 month.

A. In the alternate universe, the p subshell would have 5 orbitals.

B. In the alternate universe, the d subshell would have 10 orbitals.

In the alternate universe where the possible values of mℓ range from -l-1 to l+1, the number of orbitals in each subshell can be determined.

A. For the p subshell, the value of l is 1. Therefore, the range of mℓ would be -1, 0, and 1. Including the additional values of -2 and 2 from the alternate universe, the total number of orbitals in the p subshell would be 5 (mℓ = -2, -1, 0, 1, 2).

B. For the d subshell, the value of l is 2. In the conventional universe, the range of mℓ would be -2, -1, 0, 1, and 2, resulting in 5 orbitals. However, in the alternate universe, the range would extend to -3 and 3. Including these additional values, the total number of orbitals in the d subshell would be 10 (mℓ = -3, -2, -1, 0, 1, 2, 3).

Therefore, in the alternate universe, the p subshell would have 5 orbitals, and the d subshell would have 10 orbitals.

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Let's start by representing the two consecutive even numbers as x and x+2. Then, the difference between their squares can be expressed as:

(x+2)^2 - x^2

Expanding the squares and simplifying, we get:

(x^2 + 4x + 4) - x^2

Which simplifies further to:

4x + 4

Factoring out 4, we get:

4(x + 1)                

This shows that the difference between the squares of consecutive even numbers is always a multiple of 4. Therefore, we have proven algebraically that the statement is true for all even numbers.          

Answer:

See below for proof.

Step-by-step explanation:

An even number is an integer (a whole number that can be either positive, negative, or zero) that is divisible by 2 without leaving a remainder. Therefore:

Consecutive even numbers are a sequence of even numbers that increase by 2 with each successive number. Therefore:

The difference between the squares of consecutive even numbers can be written algebraically as:

\((2n + 2)^2 - (2n)^2\)

Use algebraic manipulation to rewrite the expression:

\(\begin{aligned}(2n + 2)^2 - (2n)^2&=(2n+2)(2n+2)-(2n)(2n)\\&=4n^2+4n+4n+4-4n^2\\&=4n^2-4n^2+4n+4n+4\\&=8n+4\\&=4(2n+1)\end{aligned}\)

As the common factor of 4 can be factored out of the expression, this proves that the difference between the squares of consecutive even numbers is always a multiple of 4.

Answer:

B

Step-by-step explanation:

For example, if i gave u 28

The digit two stands for 20, and the digit 8 stands for 8, therefore u call it 28

Each spot has it own name

For example if i gave u the number 12345

5 is in the first spot, therefore 5 x 1 =5

4 is in the tenth spot, therefor 4 x 10 = 40

3 is in the hundred spot, therefore 3 x 100 =300

2 is in the thousand spot, therefore 2 x 1000=2000

1 is in the ten thousand spot, therefore 1 x 10000

=100000

So if u add all these numbers together u will get

12345

OK, so for your question, the 6 in 558672, is in the hundred spot, so 6 x 100 =600

The 3 in 74139 is in the ten spot, so 3 x 10=30

So the product is to multiply them together

600 x 30 =18000

Answer:

(2,-4)

Step-by-step explanation:

y = -9x + 14
-9x + y = -22
the first equation is set equal to y, so you can plug it in
-9x + (-9x + 14) = -22
-9x + -9x + 14 = -22
-18x + 14 = -22
-18x = -36
x = 2
now take one of the equations and plug x in
y = -9x + 14
y = -9(2) + 14
y = -18 + 14
y = -4

(2,-4)

Answer:

Amy still owes her mother $38.

Step-by-step explanation:

76 - 14 - 24

76 - 14 = 62

62 - 24 = 38

Answer 6.2 minutes

Step-by-step explanation:

convert it into a decimal

Answer:

A sample is a subset of the population.

Answer:

Domain:  { x ∈ R | x ≠ -2, 3 }

Step-by-step explanation:

\(f(x)=\dfrac{(x+2)(x-1)}{(x-3)(x+2)}\)

The domain (x-values) of a rational function is all real numbers of x with the exception of those for which the denominator is 0.   Therefore, to find the values of x that need to be excluded from the domain, equate the denominator to zero and solve for x.

The denominator for the given function is \((x - 3)(x + 2)\)

\(\implies (x - 3)(x + 2)=0\)

\(\implies (x - 3)=0\implies x=3\)

\(\implies (x + 2)=0 \implies x=-2\)

There will be a hole at x = -2 and an asymptote at x = 3.

So the values of x that need to be excluded from the domain are:

x = 3 and x = -2

Therefore, the domain of the given rational function is:  { x ∈ R | x ≠ -2, 3 }

The value of z-stat is -0.6721.

What is z stat?

The relationship between a value and the mean of a group of values is quantified by a Z-stat. The Z-stat is calculated using standard deviations from the mean. When a data point's Z-stat is 0, it means that it has the same score as the mean.

One standard deviation from the mean would be indicated by a Z-stat of 1.0. Z-stats can be positive or negative; a positive value means the score is above the mean, while a negative value means it is below the mean.

Solution Explained:

We use the formula,

\(z = \frac{P - \pi }{\sqrt{\frac{\pi (1-\pi )}{200} }}\), where P is the observed proportion, π is the hypothesized proportion

Therefore, P = 42/200 = 0.21 & π = 23/100 = 0.23

Putting the values in

\(z = \frac{0.21 - 0.23 }{\sqrt{\frac{0.23 (1-0.23)}{200} }}\)

After calculating, z-stat is therefore equal to -0.6721

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Answer:

-32

Step-by-step explanation:

Answer:

-32

Step-by-step explanation:

(7x(6))-(5x(-2))=-32

If Mateo jogged 25 9/10 miles last week and jogged the same course all 7 days, then he jogged an average of (25 9/10) / 7 = 3 11/14 miles per day.

To convert this mixed number to an improper fraction, we can multiply the whole number by the denominator of the fraction and add the numerator, then place the result over the denominator:

3 * 14 + 11 = 53

53/14

So, Mateo jogged an average of 53/14 miles per day last week

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Answer:

it's the third one. x=47/3

Step-by-step explanation:

if needed in decimal form: 15.666

mixed number form: 15 2/3

The effect of this change on the function's values and the graph is the same.

Given `f(x) = x²` after performing the following transformations shift upward 40 units and shift 83 units to the right, the new function `g(x)` is: `g(x) = (x - 83)² + 40`

To understand the given problem statement, we need to know about the different transformations that can be performed on a function. Transformations of the function refer to changing the function's position or size without altering its shape. The following are the three main transformations of the function:

Translation: The graph of a function may be shifted up, down, right, or left using the translation method. We replace `x` by `(x-h)` in the equation to translate `h` units left and by `(x+h)` to translate `h` units right.Change in `x`:

The graph of a function may be stretched or compressed horizontally using the change in `x`. The new equation can be found by replacing `x` with `(x/a)`, where `a` is the stretch or compression factor.Change in `y`: The graph of a function may be stretched or compressed vertically using the change in `y`. The new equation can be found by multiplying the entire equation by the stretch or compression factor.In the given problem statement, the given function `f(x) = x²` is shifted 83 units to the right and 40 units upward, and the new function is `g(x) = (x - 83)² + 40`.

Therefore, g(x) = (x - 83)² + 40 is the new function after the given transformations.If the formula `y=x³` is changed by adding four (shown in red below), the new function will be `f(x) = x³ + 4`.

The addition of four in the function will cause the graph of the function to shift upward by four units.

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The answer is , new function would be: y = x³ + 4 , and The graph of the function is a shifted version of the original graph upward by 4 units.

Given f(x) = x² and after performing the following transformations:

shift upward 40 units and shift 83 units to the right, the new function

g(x) = g(x)

= (x - 83)² + 40.

If the formula y = x³ is changed by adding four (shown in red below), then the effect would be an upward shift of 4 units for the function's values.

The new function would be:

y = x³ + 4

The graph of the function would shift upward by 4 units as shown below:

Explanation:

The transformation of f(x) = x², after shifting 83 units to the right and upward 40 units can be shown below:

f(x) = x²g(x)

= (x - 83)² + 40

Note that g(x) is a parabola with vertex at (83, 40).

The transformation of y = x³ by adding four can be shown below:

y = x³ + 4

The graph of the function is a shifted version of the original graph upward by 4 units.

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The margin of error for a 90% confidence interval for the proportion of all employees dissatisfied with their jobs, based on a survey of 200 employees where 44% reported dissatisfaction, is  0.068.

We can use the formula for the margin of error for a proportion:

ME = zsqrt((p_hat(1-p_hat))/n)

where z is the z-score associated with the desired level of confidence (90% in this case), p_hat is the sample proportion (0.44), n is the sample size (200), and sqrt is the square root.

From a standard normal distribution table, the z-score for a 90% confidence level is approximately 1.645.

Plugging in the values, we get:

ME = 1.645sqrt((0.44(1-0.44))/200)

ME ≈ 0.068

So the margin of error for a 90% confidence interval is approximately 0.068 or 0.068/1= 0.068 = 0.068 = 6.8% (rounded to 3 decimal places).

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

"A human resources consulting firm conducted a survey of 200 employees to determine how dissatisfed they were with their jobs. 44% of the employees said they were dissatisfied, what is the margin of error for a 90% confidence interval for the proportion of all employees that are dissatisfied with their jobs? Answer to 3 decimal places"--

(1) To find the area of the surface obtained by rotating the curve x = (1/3)*(y^2 + 2)^(3/2) about the x-axis, we use the formula: A = 2π∫[a,b] f(x)√(1 + (f'(x))^2) dx. Answer : A = (π/36)∫[37,145] u

where f(x) is the function to be rotated and a and b are the limits of integration. In this case, we need to express the function in terms of y and find the derivative with respect to y.

x = (1/3)*(y^2 + 2)^(3/2)

Differentiating with respect to y:

dx/dy = (1/2)*(1/3)*(y^2 + 2)^(1/2)*2y = (1/3)*y*(y^2 + 2)^(1/2)

Using this in the formula for the surface area:

A = 2π∫[1,2] [(1/3)*(y^2 + 2)^(3/2)]√[1 + ((1/3)*y*(y^2 + 2)^(1/2))^2] dy

Simplifying the expression under the square root:

A = 2π∫[1,2] [(1/3)*(y^2 + 2)^(3/2)]√[(y^4 + 4y^2 + 4)/(9*(y^2 + 2))] dy

Simplifying further:

A = (2π/3)∫[1,2] (y^2 + 2)^(3/2) dy

Let u = y^2 + 2, then du/dy = 2y and the limits of integration change:

A = (2π/3)∫[3,6] u^(3/2) (1/2u) du

Simplifying:

A = (π/9)[u^(5/2)]_[3,6] = (π/9)[(6^5/2 - 3^5/2)] = (π/9)(1339) (exact answer)

Therefore, the exact area of the surface obtained by rotating the curve x = (1/3)*(y^2 + 2)^(3/2) about the x-axis is (π/9)(1339).

(2) To find the area of the surface obtained by rotating the curve x = 1 + 3y^2 about the x-axis, we again use the formula:

A = 2π∫[a,b] f(x)√(1 + (f'(x))^2) dx

where f(x) is the function to be rotated and a and b are the limits of integration. In this case, we need to express the function in terms of y and find the derivative with respect to y.

x = 1 + 3y^2

Differentiating with respect to y:

dx/dy = 6y

Using this in the formula for the surface area:

A = 2π∫[1,2] (1 + 3y^2)√[1 + (6y)^2] dy

Simplifying:

A = 2π∫[1,2] (1 + 3y^2)√[1 + 36y^2] dy

Let u = 1 + 36y^2, then du/dy = 72y and the limits of integration change:

A = (π/36)∫[37,145] u

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Answer:

-2x - 9

Step-by-step explanation:

Answer:

−2x−9

I hope this helps

Answer:

Jamie's string is 3ft and 9in

Step-by-step explanation:

10ft 1in

-6ft 4in

=3ft 9in

Answer:

3ft 9 in

Step-by-step explanation:

So, in each foot there's 12 inches. Knowing that, the operation you use is subtraction. So you do 10 ft 1 in - 6 ft 4 in. If you do that operation knowing that 12 inches=1 foot, then you should get 3 ft 9 in.

Please let me know if there is still any confusion.

Answer:

\(length = x\)

\(width = 2x - 3\)

\(perimeter = 2(x + (2x - 3))\)

\(51 = 2(3x - 3)\)

\(51 = 6(x - 1)\)

\(x - 1 = 8.5\)

\(x = 9.5cm\)

\(length = 9.5\)

\(width = 2x - 3 = 2(9.5) - 3 = 16cm\)

Answer:

433345344 Answer

Step-by-step explanation:

SOLUTION

Given the question, the following are the solution steps to answer the question.

The course of Bear Creek is entirely contained within San Bernardino County, and primarily within the San Bernardino National Forest. It rises near the community of Woodlands, and flows north into Baldwin Lake in the eastern Big Bear Valley.

Hence, the answer is Baldwin Lake.

Answer:

Step-by-step explanation:

as you see the difference between terms is 7

6,13,20,27,34,41,48,55

Previous Balance: $120

Finance Charge: $15

New Purchases: $200

Payments: $300

Recall this is a Credit Card Statement.

To find the new balance we must subtract the payments and add the charges:

New Balance = $120 - $300 + $15 + $200

New Balance = $35

Answer: A. $35.00

Answer:

-7/3 or -2.3

Step-by-step explanation:

1. y2-y1 divided by x2-x1 which would be y2-y1/x2-x1

2. plug in : -2-19/3-(-6)

4. Solution ( -7.3 or -2.3 )

Answer:

\(y = -\dfrac{7}{3}x +5\)

Step-by-step explanation:

The general equation of a line in slope-intercept form is

y = mx + b

where m = slope and b = y-intercept is rise over run

\(m = \dfrac {(y_{2} - y_{1})} {(x_{2} - x_{1})}\)

where (x₁, y₁) and (x₂, y₂) are any two points on the line

For the line passing through (-6, 19) and (3, -2) , the slope

\(m = \dfrac{-2 - 19}{3 - (-6)}\\\\\)

\(\\\\m= \dfrac{-21}{9}\)

\(m = -\dfrac{7}{3}\)

So slope-intercept form is
\(y = -\dfrac{7}{3}x +b\\\\\)

To compute y-intercept, b,  plug in any of the two points into the above equation and solve for b

Let's choose point (3, -2)

Plugging x = 3 and y = -2 gives

\(-2 = -\dfrac{7}{3}\cdot 3 +b\\\\\\\\-2 = -7 + b\\\\\)

So equation of line is
\(y = -\dfrac{7}{3}x +5\)

Answer:

1,3

Step-by-step explanation:

Answer:2 hours 15 mins = 2 1/4 hours

2 1/4 hours = 25 miles

1 hour = 25 ÷ 2 1/4 = 25 ÷ 9/4 = 25 x 4/9 = 11.1 miles

Answer: 11.1 mph

Step-by-step explanation: