alaska ranks as the 48th states when comparing populations. In 1980, the population wa 410,851 and in 2017 the population was 739818. Which equation models the population of alska t years after 1980. If the population of Alaska continues to grow at the same rate, predict the population of Alaska in 2040

Answer:

13

an example:In words: 103 could be called "10 to the third power", "10 to the power 3" or simply "10 cubed"

Trust me its 13

10 + 3³/⁹ answer is  11.4422495703074083.

An algebraic expression is a combination of variables, constants, and mathematical operations. It represents a mathematical relationship between quantities and can be used to model real-world situations or solve problems.

Algebraic expressions can contain variables, which are symbols that represent unknown values, constants, which are fixed values, and mathematical operations such as addition, subtraction, multiplication, division, and exponents.

We can simplify the expression step by step as follows:

10 + 3³/⁹ = 10 + 3^(1/3) (since 3^(3/9) = (3^3)^(1/9) = 27^(1/9) = (3^3)^(1/3) = 3^(3/3) = 3^1 = 3)

= 10 + 1.4422495703074083 (using a calculator to evaluate 3^(1/3) to about 15 decimal places)

= 11.4422495703074083

Therefore, 10 + 3^(3/9) = 11.4422495703074083.

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The rational expression (2x-3)/((2x-3) (2x-3)) satisfies the given constraints.

To create a rational expression with the given constraints, we need to have a binomial in the numerator that cancels out with a binomial in the denominator to produce the desired expression, (1)/(2x-3).

One way to do this is to multiply the desired expression by a binomial that is the same as the one in the denominator. This will give us a rational expression with the desired constraints.

For example, we can multiply (1)/(2x-3) by (2x-3)/(2x-3) to get:

(1 * (2x-3))/((2x-3) * (2x-3))

Simplifying the numerator and denominator gives us:

(2x-3)/((2x-3)(2x-3))

This rational expression has a binomial in the numerator and simplifies to the desired expression, (1)/(2x-3).

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1. The volume of the prism and pyramid are thesame

2. The volume of the pyramid and cylinder are not thesame and cylinder will have the greater volume

3. The volume of the cone is be greater than the volume of cylinder.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

1. The volume of a prism = base area × height

volume of a pyramid = 1/3 base area × height

If the base area of pyramid is three times that of prism, then the volume of pyramid = 3×1/3 base area × height = base area × height

Since the height of the prism and pyramid are the same, the volume will be thesame.

2. Since the pyramid and the cylinder have thesame base area = πr²

The cylinder height = 3 times height of the pyramid

volume of pyramid = 1/3 base area × height

volume of cylinder = base area × height × 3

Therefore the volume are not thesame and cylinder will have the greatest volume

3. since the height of the cone and cylinder are thesame

volume of cone = 1/3πr²h

volume of cylinder = πr²h

radius of cone = 3× radius of cylinder

Therefore the volume of the cone = 1/3× 9 πr²h = 3πr²h

Therefore the volume of the cone is be greater than the volume of cylinder.

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Answer:

Step-by-step explanation:

Alright man, I got you.

So here is step-by-step

To solve the equation x^2 + 14x - 51 = 0 by completing the square, follow these steps:

Step 1: Move the constant term to the right-hand side

x^2 + 14x = 51

Step 2: Take half of the coefficient of x, square it, and add it to both sides of the equation

To find half of the coefficient of x, divide it by 2:

(14 / 2) = 7

Then square 7:

7^2 = 49

Add 49 to both sides of the equation:

x^2 + 14x + 49 = 51 + 49

Simplifying the right-hand side:

x^2 + 14x + 49 = 100

Step 3: Factor the left-hand side as a perfect square

The left-hand side is now a perfect square trinomial, which can be factored as:

(x + 7)^2 = 100

Step 4: Take the square root of both sides of the equation

Taking the square root of both sides of the equation gives:

x + 7 = ±10

Step 5: Solve for x

Subtracting 7 from both sides of the equation gives:

x = -7 ± 10

Therefore, the solutions to the equation x^2 + 14x - 51 = 0 are:

x = -7 + 10 = 3

or

x = -7 - 10 = -17

Answer:

[tex]\dfrac{x}{x + 1}\\\\\text{which is the first answer choice }[/tex]

Step-by-step explanation:

We are given
[tex]f(x) = x^2 - x\\g(x) = x^2 - 1\\\\\text{and we are asked to find $ \left(\dfrac{f}{g}\right)\left(x\right)$}[/tex]

[tex]\left(\dfrac{f}{g}\right)\left(x\right) = \dfrac{f(x)}{g(x)}\\\\\\= \dfrac{x^2-x}{x^2 - 1}[/tex]

[tex]x^2 - x = x(x - 1)\text{ by factoring out x}\\\\x&2 - 1 = (x + 1)(x - 1) \text{ using the relation $a^2 - b^2 = (a + 1)(a - 1)$}[/tex]

Therefore,

[tex]\dfrac{x^2-x}{x^2 - 1} = \dfrac{x(x-1)}{(x + 1)(x - 1)}[/tex]

x - 1 cancels out from numerator and denominator with the result
[tex]\dfrac{x}{x+1}[/tex]

So

[tex]\left(\dfrac{f}{g}\right)\left(x\right)$} = \dfrac{x}{x + 1}[/tex]

A) The probability of getting 3 or fewer students who play a sport in your sample is 0.014, or 1.4%.

B) The probability of getting 3 or fewer students who play a sport in your sample is much lower than the expected probability of 0.4 (40%). This suggests that your estimate of 40% of students in the whole school playing a sport may be too high.

C) There are 1140 different combinations of 3 students who play sports and 17 students who don't in your sample.

A) To find the probability of getting 3 or fewer students who play a sport in your sample, you can use the binomial probability formula:

P(X = x) = nCx * p^x * (1-p)^(n-x)

where n is the sample size, x is the number of successes, p is the probability of success, and nCx is the number of combinations of x successes in n trials.

For x = 0, 1, 2, and 3, the probabilities are:

P(X = 0) = 20C0 * 0.4^0 * 0.6^20 = 0.000006
P(X = 1) = 20C1 * 0.4^1 * 0.6^19 = 0.00016
P(X = 2) = 20C2 * 0.4^2 * 0.6^18 = 0.0019
P(X = 3) = 20C3 * 0.4^3 * 0.6^17 = 0.012

Adding these probabilities gives:

P(X <= 3) = 0.000006 + 0.00016 + 0.0019 + 0.012 = 0.014



C) The number of different combinations of 3 successes and 17 failures is given by:

20C3 = 20! / (3! * 17!) = 1140


D) The formula for the number of combinations of x successes in n trials is:

nCx = n! / (x! * (n-x)!)

For 20C2 and 20C17, the formulas are:

20C2 = 20! / (2! * 18!)
20C17 = 20! / (17! * 3!)

Since 2! * 18! = 17! * 3!, these two formulas are equivalent and give the same result. This is why 20C2 = 20C17.

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The probability that more than 91,000 cars will pass through the M50 toll is 0.2227, or 22.27% to 4 decimal places.

The Poisson distribution is a discrete probability distribution that describes the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. The probability mass function of the Poisson distribution is given by:

P(X = x) = (lambda^x * e^-lambda) / x!

Where lambda is the mean rate of occurrence and x is the number of occurrences. In this case, lambda = 90,000 and we want to find the probability that X > 91,000. We can use the cumulative distribution function (CDF) of the Poisson distribution to find this probability:

P(X > 91,000) = 1 - P(X <= 91,000)

Using the CDF of the Poisson distribution, we can calculate P(X <= 91,000) as follows:

P(X <= 91,000) = e^-lambda * sum_{i=0}^{91,000} (lambda^i / i!)

Using a calculator, we can find that P(X <= 91,000) = 0.7773. Therefore, the probability that more than 91,000 cars will pass through the M50 toll is:

P(X > 91,000) = 1 - 0.7773 = 0.2227

So the probability that more than 91,000 cars will pass through the M50 toll is 0.2227, or 22.27% to 4 decimal places.

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The axis of symmetry for the function f(x) = -(x-7)² - 30 is x = 0.

A relation is a function if it has only One y-value for each x-value.

To find the axis of symmetry for the function f(x) = -(x-7)²- 30

We can use the formula:

x = -b/2a

where a and b are the coefficients of the quadratic term and the linear term in the function, respectively.

In this case, the quadratic term is -(x-7)² and the linear term is -30, so a = -1 and b = 0.

Substituting these values into the formula, we get:

x = -0/(2(-1)) = 0

Therefore, the axis of symmetry for the function f(x) = -(x-7)² - 30 is x = 0.

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The probability is 4/8 = 1/2. The probability that the student answered True at least two times is 1/2.

The number of residents in a city is a discrete variable because it is a countable number of people. The level of measurement is a ratio level because there is a true zero point (no residents in a city) and the difference between values is meaningful. Therefore, the correct answer is discrete, ratio level.

The sample space for the three True (T) or False (F) questions is: {TTT, TTF, TFT, FTT, FTF, FFT, TFF, FFF}

The outcomes corresponding to the event "The student answered True at least two times" are: {TTT, TTF, TFT, FTT}

To evaluate the probability of the event "The student answered True at least two times", we need to divide the number of favorable outcomes by the total number of possible outcomes. The number of favorable outcomes is 4 (TTT, TTF, TFT, FTT) and the total number of possible outcomes is 8 (TTT, TTF, TFT, FTT, FTF, FFT, TFF, FFF). Therefore, the probability is 4/8 = 1/2. The probability that the student answered True at least two times is 1/2.

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Answer:

20.50 + 10m

Step-by-step explanation:

Basic expression:
8.50 + 12 + 6.25m + 3.75m

First, let's add the base payments which are 8.50 and 12.
8.50 + 12 = 20.50.
Now we have 20.50 + 6.25m + 3.75m

Next we have to add the monthly payments.
Assuming she's paying these all at the same time, 6.25m + 3.75m = 10m

Our finalized expression is:
20.50 + 10m = Club costs

If p-hat is equal to 0.65, then the complement (q-hat) is equal to 0.35.

We must deduct p-hat from 1 to obtain the complement q-hat when p-hat is known. The complement is the probability that the event won't occur, which is the same as the likelihood of every other scenario that isn't the one we're interested in.

Take p-hat out of 1 to get:

q-hat = 1 - p-hat

The value of p-hat is 0.65, therefore replace it as follows:

q-hat = 1 - 0.65

Condense the phrase:

q-hat = 0.35

As a result, the complement q-hat is 0.35 if the p-hat is 0.65.

It's critical to keep in mind that the probabilities p-hat and q-hat are complimentary and always sum up to 1. The equation q-hat = 1 - p-hat can be used to quickly compute the other if the first is known.

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The height of the container if it's a cylinder with a radius of 3 cm is 5 cm.

The cost of coffee is $2.83.

The height of the container if it's a cylinder with a radius of 5 cm is 1.8 cm.

The cost of hot chocolate powder is $9.90.

Mathematically, the volume of a cylinder can be calculated by using this formula:

Volume of a cylinder, V = πr²h

Where:

Picking a volume of 45π cm³, the height of this container is given by:

h = V/πr²

Height, h = 45π/π3²

Height, h = 5 cm.

For the cost of coffee, we have:

Cost of coffee = 45π cm³ × $0.02

Cost of coffee = $2.83.

When the radius is 5 cm, the height of this container is given by:

h = V/πr²

Height, h = 45π/π5²

Height, h = 1.8 cm.

For the cost of hot chocolate powder, we have:

Cost of hot chocolate powder = 45π cm³ × $0.07

Cost of hot chocolate powder = $9.90.

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a) The domain of (f o g)(x) is [-5/3, ∞).

b) The domain of (g o f)(x) is [0, ∞).

c) The domain of (f o f)(x) is [0, ∞).

d) (f o g)(x) = f(g(x)) = f(3x+5) = √(3x+5).

e) The domain of this composite function is all real numbers.

The domain of this composite function is all x values that make the expression inside the square root greater than or equal to 0. So, we need to solve the inequality:

3x+5 ≥ 0

3x ≥ -5

x ≥ -5/3

Therefore, the domain of (f o g)(x) is [-5/3, ∞).

(b) (g o f)(x) = g(f(x)) = g(√x) = 3√x + 5

The domain of this composite function is all x values that make the expression inside the square root greater than or equal to 0. So, we need to solve the inequality:

√x ≥ 0

x ≥ 0

Therefore, the domain of (g o f)(x) is [0, ∞).

(c) (f o f)(x) = f(f(x)) = f(√x) = √(√x)

The domain of this composite function is all x values that make the expression inside the square root greater than or equal to 0. So, we need to solve the inequality:

√x ≥ 0

x ≥ 0

Therefore, the domain of (f o f)(x) is [0, ∞).

(d) (g o g)(x) = g(g(x)) = g(3x+5) = 3(3x+5) + 5 = 9x + 20

The domain of this composite function is all real numbers, since there are no restrictions on the values of x. Therefore, the domain of (g o g)(x) is (-∞, ∞).

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By answering the above question, we may infer that The answer is yes, equation and Kaylee now has 26 nickels. Option B, or 50, is the correct response, therefore.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

Hence, she has twice as many nickels and quarters as normal.

The combined worth of Kaylee's coins is $30. This may be expressed as an equation:

[tex]0.05(2x) + 0.10x + 0.25(4x) = 30\\0.10x + 0.10x + 1.00x = 30\\2.20x = 30\sx = 13.64[/tex]

Kaylee has 2x = 28 nickels and 4x = 56 quarters if x = 14. These coins are worth 0.05(28), 0.10(14), and 0.25(56), for a total of $7.70.

This does not equal $30, hence the suggested solution is invalid.

Kaylee has 2x = 26 nickels and 4x = 52 quarters if x = 13. These coins are worth [tex]0.05(26) + 0.10(13) + 0.25(52) = $30.[/tex]

The answer is yes, and Kaylee now has 26 nickels.

Option B, or 50, is the correct response, therefore.

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If the price of each hot dog is set at 0.8, the revenue to be obtained is $120.

Income is the amount of money or value that a person, family, company or country receives during a given period of time, whether in the form of salary, rents, profits, interest, dividends or other sources.

According to the formula R = -50P +1 60, we can find the expected revenue by plugging in the given price and solving for R.

R = -50P+160

R = -50(0.8) + 160

R = -40 + 160

R = 120

Therefore, the expected revenue generated by setting the price to be 0.8 is $120.

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The required matches for the given figures are 1.HI || EG, 2. AC⊥DB and ∠KFJ.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,
In the figure, we can see.

Line HI is parallel to line Eg so the correct choice is HI || EG.

Line AC is perpendicular to line AC, so the correct choice is AC⊥DB.
Angle made by points KFJ is ∠KFJ. so the correct choice is ∠KFJ.

Thus, the required matches for the given figures are 1.HI || EG, 2. AC⊥DB and ∠KFJ.

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The solutions of the polynomial equation are x = 0, x = 4.09, and x = -1.59.

The solutions of the polynomial equation 4x^(4)-13x^(3)-21x^(2)+78x-18=0 can be found by factoring the equation and setting each factor equal to zero.

First, we can factor out a common factor of 4x^2 from the equation:
4x^2(x^2-3.25x-5.25)+78x-18=0

Next, we can use the quadratic formula to solve for x in the equation x^2-3.25x-5.25=0:
x = (-(-3.25) ± √((-3.25)^2-4(1)(-5.25)))/(2(1))
x = (3.25 ± √(29.3125))/2

This gives us two solutions for x:
x = (3.25 + √(29.3125))/2 ≈ 4.09
x = (3.25 - √(29.3125))/2 ≈ -1.59

Finally, we can set each factor equal to zero and solve for x:
4x^2 = 0 -> x = 0
x^2-3.25x-5.25 = 0 -> x = 4.09 or x = -1.59

So the solutions of the polynomial equation are x = 0, x = 4.09, and x = -1.59.

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Since, 13 is not less than 13. Therefore, x = 5 is not a solution to the inequality 13 < 2x+3.

To determine whether a value of x is a solution to the inequality 13 < 2x+3, we need to substitute the value of x into the inequality and see if it is true or false.

Let's try x = 5. Then: 13 < 2x+3

13 < 2(5)+3

13 < 10+3

13 < 13

This is not true, since 13 is not less than 13. Therefore, x = 5 is not a solution to the inequality 13 < 2x+3.

Note that if we had found 13 < 13 instead, then we would have concluded that x = 5 is not a solution to the inequality. But since the inequality is strict (i.e., "less than"), we need to have a strict inequality when we substitute the value of x to determine whether it is a solution.

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The areas of the three polygons are 102.87m², 726cm², and 288 ft², respectively.

To find the area of a regular polygon, we can use the formula A = (1/2)ap, where A is the area, a is the apothem, and p is the perimeter.

1. For a regular pentagon with radius 9m, we can first find the apothem using the formula a = r*cos(180/n), where r is the radius and n is the number of sides.

In this case, n = 5, so

a = 9*cos(180/5) ≈ 7.07m.

Next, we can find the perimeter using the formula

p = 2nr*sin(180/n),

where n = 5 and r = 9, so

p = 2(5)(9)sin(180/5) ≈ 29.08m.

Finally, we can plug these values into the formula for the area to get

A = (1/2)(7.07)(29.08) ≈ 102.87m².

2. For a regular hexagon with apothem 11cm, we can find the perimeter using the formula

p = 2na,

where n is the number of sides and a is the apothem.

In this case, n = 6 and a = 11, so

p = 2(6)(11) = 132cm.

Then, we can plug these values into the formula for the area to get

A = (1/2)(11)(132) = 726cm².

3. For an octagonal floor of a gazebo with apothem 6 ft, we can find the perimeter using the formula

p = 2na,

where n is the number of sides and a is the apothem.

In this case, n = 8 and a = 6, so p = 2(8)(6) = 96 ft.

Then, we can plug these values into the formula for the area to get

A = (1/2)(6)(96) = 288 ft².

Therefore, the areas of the three polygons are 102.87m², 726cm², and 288 ft².

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Answer:

376, and 122

Step-by-step explanation:

To solve for the surface area, we add up the areas for each side together.

([8×6] × 2) + ([8×10] × 2) + ([10×6] × 2) = 376

376 is the surface area for the 1st shape.

(10 × 5) + (4×3) + ([3×10] ×2)= 122

122 is the surface area for the 2nd shape

Answer:

9)376ft^2 10)132ft^2

Step-by-step explanation:

the first one is pretty easy use the formula 2(l*w+l*b+w*b) where l is length b is breadth and w is the width, l=10 b=8 w=6

2(10*6+10*8+6*8)

=376ft^2

the second one is also not that hard, first find out the area of the triangles in which the base is 3 and height is 4 so 4*3/2

=6

since there are two triangles, the surface area of the triangles combined is 12

now lets move the base where the width is 3 and the length is 10 as it also corresponds, now l*w is the formula to find the surface area of a rectangle so 10*3 is 30 now lets find the surface area of the square on the front which is just 10*5 which equals to 50 and lastly the rectangle at the back, for which we know that the width is 4 and length is 10 so 10*4 is 40 now simply just add all ofn these areas, 12+50+40+30

=132ft^2

Answer:

6x-4y=18

-x-6y=7

-x-6y=7

-x=7+6y

x=-7-6y

6x-4y=18

6(x-7-6y)-4y=18

-42-40y=18

-40y=18+42

-40y=60

y=-60/40

y=-3/2

x=-7-6y

x=-7-6(-3/2)

x=-7+9

x=2

(x,y) = (2,-3/2)

The measure of angle x is 19.5

Octagon interior angles sum is equal to 1080 degrees. Also, the sum of all eight exterior angles is equal to 360 degrees.

We have Polygon of 8 side called Octagon.

Also, a Regular Octagon have all of its angles equal

So, Using Angle Sum Property

sum of all internal angle of Octagon  = 1080

8 x 6(x+3)= 1080

6(x+3) = 1080/8

6x+ 18 = 135

6x = 135- 18

6x = 117

x= 19.5

Thus, the value of x is 19.5

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a)0.1359, or 13.59%

b)85,100,115

c)0.0062, or 0.62%.

d)0.9705, or 97.05%

a. The probability of a randomly selected person's IQ being over 120 is 0.1359, or 13.59%.

b. Q1 for IQ is 85, Q2 is 100, and Q3 is 115.

c. The probability of an outlier for IQ for a single person is 0.0062, or 0.62%.

d. The probability of the average IQ of 10 randomly selected people being over 105 is 0.9705, or 97.05%.

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The cost of the desktop computer was $2100, and the cost of the laptop computer was $2350.

A finance charge is a fee or interest payment that a borrower is required to pay to a lender for the use of credit or a loan. It represents the cost of borrowing money and is typically calculated as a percentage of the outstanding balance.

Finance charges can take many forms, including interest rates, annual fees, late payment fees, balance transfer fees, and cash advance fees. The specific amount of the finance charge depends on a variety of factors, such as the loan amount, the interest rate, the repayment period, and the borrower's credit history.

Let the cost of the desktop computer be x. Then, the cost of the laptop computer would be x + 250.

The finance charge for the desktop would be 8.5% of x, which is 0.085x.

The finance charge for the laptop would be 5% of (x + 250), which is 0.05(x + 250) = 0.05x + 12.5.

The total finance charges for one year were $296, so we can write the equation:

0.085x + 0.05x + 12.5 = 296

Combining like terms and solving for x, we get:

0.135x = 283.5

x = 2100

Therefore, the cost of the desktop computer was $2100, and the cost of the laptop computer was $2350.

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The value of the machine after 4 years can be calculated using the formula:
V = P * (1 - r) ^ n
Where:
V = value after n years
P = initial purchase price
r = annual depreciation rate
n = number of years

In this case, P = 3,000.00, r = 0.10 (10%), and n = 4.
Plugging these values into the formula, we get:
V = 3,000.00 * (1 - 0.10) ^ 4
V = 3,000.00 * 0.90 ^ 4
V = 3,000.00 * 0.6561
V = 1,968.30

Therefore, the value of the machine after 4 years is $1,968.30.

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The time needed for the number of people infected with the flu to reach 3072 is given as follows:

4 days.

The exponential function that models the situation has the definition given as follows:

y = ab^x.

In which the parameters are given as follows:

Assume a total of 12 people have the flu as of today, hence the parameter a is given as follows:

a = 12.

Each day the total number people who have the flu quadruples, hence the parameter b is given as follows:

b = 4.

Hence the function giving the number of people with the flu after x days is given as follows:

y = 12(4)^x.

The number of days needed for the number to reach 3072 is obtained as follows:

12(4)^x = 3072

4^x = 3072/12

4^x = 256.

2^(2x) = 2^(8)

Hence the value of x is obtained as follows:

2x = 8

x = 4.

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The given expression -5x⁶-7x³+7x²+4 is a polynomial.

A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable. The terms in a polynomial are called monomials, and they can be either constants or variables with a coefficient.

In the given expression, there are four terms: -5x⁶, -7x³, 7x², and 4. Each of these terms is a monomial. Since there are four terms in the expression, it is classified as a polynomial with four terms, also known as a quadrinomial.

Therefore, the given expression -5x⁶-7x³+7x²+4 is a quadrinomial, which is a type of polynomial.

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The state space is {0, 1, 2, 3},

The transition matrix is : P = [[(1-p)³, 3p(1-p², 3p²(1-p), p^3], [(1-p)², 2p(1-p)²+2p(1-p)², 2p²(1-p)+2p²(1-p), 2p³], [(1-p), p(1-p)²+2p(1-p), p²(1-p)+2p², p³], [0, p(1-p), 2p², 3p³]],  the probability of one idle machine 3 nights later is 0.33554432.

The state space of (Xn : n ≥ 0) is the set of all possible states that the system can be in at the end of a given day. The state space is {0, 1, 2, 3}, where 0 corresponds to all machines being broken, 1 corresponds to one machine working and two broken, 2 corresponds to two machines working and one broken, and 3 corresponds to all machines working.

The transition matrix is given by:
P = [[(1-p)³, 3p(1-p², 3p²(1-p), p^3], [(1-p)², 2p(1-p)²+2p(1-p)², 2p²(1-p)+2p²(1-p), 2p³], [(1-p), p(1-p)²+2p(1-p), p²(1-p)+2p², p³], [0, p(1-p), 2p², 3p³]]

Given that 2 machines are idle tonight (i.e., Xn = 1), the probability of one idle machine 3 nights later (i.e., Xn+3 = 2) is given by the (1, 2) entry of P^3, where P^3 is the matrix obtained by multiplying P by itself 3 times.

Using the given value of p = 0.8, we can calculate P^3 and find the (1, 2) entry to obtain the desired probability. The (1, 2) entry of P^3 is 0.33554432, so the probability of one idle machine 3 nights later is 0.33554432.

Therefore, the answer to part c is 0.335544.

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Therefore , the solution of the given problem of unitary method comes out to be t there are 1000 squirrels in the conservation area.

To finish a job using the unitary method, divide the lengths of just this minute subset by two. In a nutshell, the unit method eliminates a desired item from both the characterized by a set and colour subsets. 40 pens, for instance, variable will cost Rupees ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

The Lincoln-Petersen index can be used to calculate an approximate squirrel population estimate for the protected area:

There were n1 squirrels in the first group.

Second sample's fox count is equal to n2.

Second sample's total number of labelled squirrels is m2.

The following provides the Lincoln-Petersen index:

=> n1 * n2 / m2

Assume that the first sample consisted of 100 squirrels that were captured and tagged by the researcher. 20 of the 200 squirrels the researcher caught for the second group had tags on them. the following algorithm is used.

=> n1 * n2 / m2 = 100 * 200 / 20 = 1000

Therefore, it is believed that there are 1000 squirrels in the conservation area. It is crucial to keep in mind that this is only an approximation and might not be correct.

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