question attached below pls help

The United States population (in millions) between 1970 and 2010 can be modeled [tex]p(x) = 203.12e^{0.011x }[/tex], the population of Midwest changing in 1990 and in 2010 with 0.201 millions per decade and 0.213 million per decade respectively.

A population is a defined collected persons or anything that can be recognized by at least one characteristics for the purposes of data collection and data analysis in statistics and other fields of mathematics. Now, we have population (in millions) of the United States between 1970 and 2010 and it is modeled by the function [tex]p(x) = 203.12e^{0.011x }[/tex] million people where, x is number of decades after 1970.

The percentage of people in the United States who live in the Midwest between 1970 and 2010 it is modeled by [tex]m(x) = 0.002x² − 0.213x + 27.84 \\ [/tex] percent where, x is the number of decades since 1970. So, the population of Midwest will be equal to [tex]N(x)= p(x)× \frac{m(x)}{100}[/tex]

[tex] p(x) = 203.12e^{0.011x} (\frac{ 0.002x² − 0.213x + 27.84}{100} ) \\ [/tex]

[tex]= 203.12e^{0.011x }(0.00002x² − 0.00213x + 0.2784) \\ [/tex]

The rate of change of population of the Midwest x decades after 1970 will be equal to the derivative of the function N(x). So, [tex]N'(x) \frac{ d(203.12e^{0.011x} (0.00002x²− 0.00213x + 0.2784))}{dx} \\ [/tex]

[tex]= 0.0000447 e^{0.011x} x² + 0.0033657 e^{0.011x} x +0.1893981 e^{0.011x } \\ [/tex]

In 1990, the number of decades is equal to 2. So, x=2, so [tex]N'(2) = 0.0000447 e^{0.011 \times 2} \: 2² + 0.0033657 e^{0.011×2} ×2 +0.1893981 e^{0.011×2 } \\ [/tex] = 0.201

Now, in 2010, the number of decades is 4.So, x=4, [tex]N'(4) = 0.0000447 e^{0.011 \times 4} \: 4² + 0.0033657 e^{0.011×4} ×4 +0.1893981 e^{0.011×4 } \\ [/tex]

= 0.213

Hence, the population is changing at 0.213 million per decade in 2010.

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Answer:Step 1:

Enter the expression you want to simplify into the editor.

The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form. The calculator works for both numbers and expressions containing variables.

Step-by-step explanation: I really hope this helps

The unknown angle of the parallelogram is as follows:

m∠T = 63 degrees

A parallelogram is a quadrilateral with opposite sides parallel to each other and opposite congruent to each other.

Therefore, the opposite angles of a parallelogram are equal. Consecutive angles are supplementary angles to each other.

Hence,

10w + 53 + 17w + 100 = 180

27w + 153 = 180

27w = 180 - 153

27w = 27

divide both sides by 27

w = 27 / 27

w = 1

Therefore,

m∠T = 10(1) + 53 = 63 degrees

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Answer: 225 degree

5/8of full rotation is 225degrees

Answer:

0.625

Step-by-step explanation:

hope the his helping

The area of the segment is 9π - 18.

Option C is the correct answer.

We have,

Area of sector = 360/360 x πr²

Radius = 6

The area of sector AOB.

= 90/360 x π x 6²

= 1/4 x π x 36

= 9π

= 9π

Now,

The area of the triangle.

= 1/2 x base x height

= 1/2 x 6 x 6

= 18

Now,

Area of segment AXB.

= Area of the sector - Area of triangle

= 9π - 18

Thus,

The area of the segment is 9π - 18.

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The given relationship in the task content is not a function as more than one output value is paired with the same input value.

Recall that a relationship is said to be a function only if one output value is attached to each input value of the relationship.

On this note, by observation; the pair of coordinates (6, 3) and (6, 9) implies that two output values are assigned to the same input value. Consequently, the given relationship is not a function.

The complete and correct sentence is therefore; Since one input value is paired with two output values; the relationship is not a function.

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The increasing functions in this problem are given as follows:

B and D.

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The vertex of an angle would have the same coordinates after a rotation if it is rotated at angle of 360 degrees.

In Mathematics and Geometry, a rotation refers to a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Generally speaking, when a point (x, y) is rotated about the center or origin (0, 0) in a counterclockwise (anticlockwise) direction by an angle θ, the coordinates of the new point (x′, y′) formed include the following:

x′ = xcos(θ) − ysin(θ)

y’ = xsin(θ) + ycos(θ).

(x′, y′) → (x, y) ⇒ (360 degrees rotation).

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The height of the kite above the ground is approximately 433.76 feet. Rounded to the nearest foot, the answer is 434 feet.

We can use trigonometry to solve this problem. Let h be the height of the kite above the ground. Then, the opposite side of the triangle formed by the kite string and the ground is h, and the adjacent side is 300 feet. The angle between the ground and the kite string is 52 degrees.

We can use the tangent function to find the value of h:

[tex]tan(52) = h/300[/tex]

Multiplying both sides by 300, we get:

h = 300 t[tex]an(52)[/tex]

Using a calculator, we find:

h ≈ 433.76 feet

Therefore, the height of the kite above the ground is approximately 433.76 feet. Rounded to the nearest foot, the answer is 434 feet.

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Answer:

The answer is 56.52 .

Step-by-step explanation:

18 multiple 3.14

The distances obtained using the distance formula indicates that the distances between the points are;

(A) QS = 17 units

(B) PS = 15 units

(C) SR = 6 units

(D) PQ = 17 units

(E) QR = 10 units

The distance formula is a formula that can be used to find the distance, d, between two points (x₁, y₁), and (x₂, y₂), on the coordinate plane, and can be presented as follows;

d = √((x₂ - x₁)² + (y₂ - y₁)²)

The corresponding values of the coordinate points indicates;

QS = 10 - 2 = 8 units

PS = 16 - 1 = 15 units

SR = 22 - 16 = 6 units

The Pythagorean Theorem and the distance formula indicates that we get;

PQ = √((16 - 1)² + (10 - 2)²) = 17 units

QR = √((22 - 16)² + (10 - 2)²) = 10 units

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Answer:

x < -3.5 or x < -7/2

Step-by-step explanation:

We can solve the inequality by solving for and isolating x:

[tex]4(-x-3)-4 > -2\\-4x-12-4 > -2\\-4x-16 > -2\\-4x > 14\\\\x < -7/2\\or\\x < -3.5[/tex]

We can check that our solution is correct by plugging in a number less than -3.5 for x like -4:

[tex]4(-(-4)-3)-4 > -2\\4(4-3)-4 > -2\\4(1)-4 > -2\\4-4 > -2\\0 > -2[/tex]

The inequality is true for any value of x less than -3.5 so the answer is correct

The absolute minimum and absolute maximum values of the function f(x) = 3x^4 - 4x^3 - 36x^2 on the interval [-3, 5] are -283 and 81, respectively. To get the absolute minimum and absolute maximum values of the function f(x) = 3x^4 - 4x^3 - 36x^2 on the interval [-3, 5].

Step 1: Find the critical points by taking the derivative of the function and setting it equal to zero.
f'(x) = 12x^3 - 12x^2 - 72x
Step 2: Factor the derivative.
f'(x) = 12x(x^2 - x - 6)
Step 3: Solve for x to find the critical points.
x = 0, x = -1, x = 6
Step 4: Evaluate the function at the critical points and endpoints of the interval.
f(-3) = 81
f(0) = 0
f(-1) = 43
f(5) = -283
Step 5: Identify the absolute minimum and absolute maximum values.
The absolute minimum value of f(x) is -283 at x = 5.
The absolute maximum value of f(x) is 81 at x = -3.
So, the absolute minimum and absolute maximum values of the function f(x) = 3x^4 - 4x^3 - 36x^2 on the interval [-3, 5] are -283 and 81, respectively.

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The value of the missing ratio = 25. That is 5/25.

Ratio is an expression that shows the quantity of a variable that is found in another variable. It can be represented as a:b or can be written as a numerator all over a denominator. That is a/b.

To determine the missing part of the ratio, the following is carried out.

if 1 = 5, 2 = 10 then 5 = 25 = 1/5

Therefore the value of the missing part of the ratio is 5 and the complete ratio is written as 5/25.

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If Mexico, one of our largest trading partners, goes into a recession, it is likely to decrease its demand for our exports. This would shift the aggregate demand (AD) curve leftward, leading to a decrease in equilibrium GDP and price level in the short run.

In the AD/AS model, a decrease in aggregate demand would cause a leftward shift of the AD curve. As a result, the intersection point of the AD and the short-run aggregate supply (SRAS) curves would move to the left, causing a decrease in equilibrium GDP and price level.

In the long run, however, the economy is likely to adjust to the new equilibrium. The decrease in aggregate demand would cause a decrease in prices, which would shift the SRAS curve rightward. Eventually, the new intersection point of the AD and the SRAS curves would be reached, resulting in a new equilibrium GDP and price level.

Overall, a recession in Mexico would likely have a negative impact on the US economy, leading to a decrease in GDP and price level in the short run. However, the economy would eventually adjust to the new equilibrium in the long run.

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The likelihood of randomly selecting a terrier from the shelter is (g) unlikely

From the question, we have the following parameters that can be used in our computation:

P(terriers) = 15%

When a probability is at 15% or less than 50%, it means that

The probability is unlikely or less likely

Hence, the true statement is (b) unlikely

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The answers for finite functions are a.256 b.24 one-to-one functions

(a) To count the number of functions from A to B, we need to find the number of possible outputs for each input. Since there are 4 elements in A and 4 elements in B, there are 4 choices for each element in A.

Thus, there are 4^4 = 256 functions from A to B that can be defined.

(b) To count the number of one-to-one functions from A to B, we need to ensure that each element in A is mapped to a unique element in B. The first element in A can be mapped to any of the 4 elements in B. However, once we have chosen an element in B to map the first element in A to, we only have 3 choices left for the second element in A (since we cannot map it to the same element as the first).

Similarly, once we have chosen an element in B to map the first two elements in A to, we only have 2 choices left for the third element in A. Finally, once we have chosen an element in B to map the first three elements in A to, there is only 1 choice left for the fourth element in A.

Thus, there are 4*3*2*1 = 24 one-to-one functions from A to B that can be defined.

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We have proven that:

cost = Jo - 2J2 +2J4 – = .......

[infinity]

= Jo(x) + Σ (-1)^n j2n (x).

n=1

To prove this identity, we first start with the formula for the exponential function:

e^ix = cos(x) + i*sin(x)

where i is the imaginary unit.

Now, we can rewrite the right-hand side of the desired identity using this formula:

Jo(x) + Σ (-1)^n j2n (x)

= Jo(x) + Σ (-1)^n [i^nJn(x) - i^nYn(x)] (using the Bessel function identity j_n(x) = cos(x)J_n(x) - sin(x)Y_n(x))

= Jo(x) + Σ (-i)^nJn(x) + Σ i^nYn(x)

= Jo(x) + Σ (-i)^nJn(x) + Σ (-i)^{n+1}Jn(x) (using the Bessel function identity Y_n(x) = (J_n(x)cos(npi) - J_{-n}(x))/sin(npi))

= Jo(x) + 2Σ (-i)^nJn(x)

= Jo(x) + 2Σ (-1)^n*J2n(x) (since Jn(x) is real for all n)

Therefore, we have proven that:

cost = Jo - 2J2 +2J4 – = .......

[infinity]

= Jo(x) + Σ (-1)^n j2n (x).

n=1

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0.86​ inches. The departure from the average would then be 0.86​ inches since 2.43-1.57=0.86​​ inches.

a) 0.5​ inches. The difference between the average rainfall and the actual rainfall for last June is 0.67-0.17=0.50​ inches.

b) 1.14​ inches. Because the departure from the average was negative, the actual rainfall was 0.36​ inches less than the average rainfall. Thus, 1.5-0.36=1.14​ inches was the actual rainfall last July.

c) 2.43​ inches. The average rainfall for these three months is 0.67+1.5+1.57=3.74​ inches. Last June it rained 0.17​ inches and last July it rained 1.14 inches. So, it would need to have rained 3.74-0.17-1.14=2.43​ inches last August so that the total amount of rain equaled the average rainfall for these three months.  

0.86​ inches. The departure from the average would then be 0.86​ inches since 2.43-1.57=0.86​​ inches.

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Full Question ;

The departure from the average is the difference between the actual amount of rain and the average amount of rain for a given month.

The historical average for rainfall in Albuquerque, NM for June, July, and August is shown in the table.

June 0.67 inches

July 1.5 inches

August 1.57 inches

Last June only 0.17 inches of rain fell all month. What is the difference between the average rainfall and the actual rainfall for last June? Answer with decimals.

The departure from the average rainfall last July was -0.36 inches. How much rain fell last July? Answer with decimals.

How much rain would have to fall in August so that the total amount of rain equals the average rainfall for these three months? Answer with decimals.

What would the departure from the average be in August in that situation? Answer with decimals.

The final amount after 20 years, compounded quarterly is $6,353.98.

The final amount after 5 years, compounded continuously, is  $1,145.10.

we can use the formula for compound interest:

[tex]A = P(1 + r/n)^(^n^\times^t^)[/tex]

where A is the final amount,

P is the principal (starting amount),

r is the annual interest rate, t is the time in years, and n is the number of times compounded per year.

Plugging in the given values, we get:

[tex]A = 3750(1 + 0.035/4)^(^4^\times^2^0^)[/tex]

A = $6,353.98

Therefore, the final amount after 20 years, compounded quarterly, is approximately $6,353.98.

P= $1,000; r=2.8%, t= 5yrs compounded continuously ​

For the second problem, we can use the formula for continuous compounding:

[tex]A = Pe^(^r^t^)[/tex]

[tex]A = 1000e^(^0^.^0^2^8^\times^5^)[/tex]

A = $1,145.10

Therefore, the final amount after 5 years, compounded continuously, is  $1,145.10.

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The missing length of the triangle is given as follows:

x = 35 units.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the missing length is obtained as follows:

x² + 12² = 37²

x = sqrt(37² - 12²)

x = 35 units.

The image is blurry, hence the mistake in Jeff's part cannot be explained.

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The direction of the resultant vector is 251.57°

From the graph, we see that we have two vectors w = (10, 4) and v = (-14 , -16). Re-writing both vectors in component form, we have that

W = 10i + 4j and

v = -14i - 16j

So, the resultant vector is the sum of both vectors.

So, we have that

R = w + v

= 10i + 4j + (-14i - 16j)

= 10i - 14i + 4j - 16j

= -4i - 12j

So, the direction of the resultant vector is given by Ф = tan⁻¹(y/x) where y = -12 and x = -4

So, substituting the vaklues of the variables into the equation, we have that

Ф = tan⁻¹(y/x)

Ф = tan⁻¹(-12/-4)

Ф = tan⁻¹(3)

= 71.57°

Since the vector is in the 3rd quadrant, its directions is Ф = 180° + 71.57° = 251.57°

So, the direction is 251.57°

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Matter has mass and occupies space (volume).

The mass of an object is a measure of the amount of matter it contains, while the volume is a measure of the amount of space it occupies. These properties are fundamental to our understanding of the physical world and play a central role in many scientific disciplines, including physics, chemistry, and materials science.

Proton is a subatomic particle with a positive charge.

A proton is a subatomic particle that is found in the nucleus of an atom and has a positive electric charge. Its symbol is "p" or "p+" and its charge is equal in magnitude to that of an electron but with a positive sign. The number of protons in an atom's nucleus determines its atomic number and its identity as a specific element.

Atomic number represents the number of protons.

The atomic number of an element represents the number of protons in the nucleus of an atom of that element. It is also the number of electrons that surround the nucleus in a neutral atom. The atomic number is a unique identifier for each element, and elements are arranged in the periodic table based on their atomic number.

Atom is the simplest form of matter or basic unit.

An atom is the basic unit of matter and is considered the simplest form of matter. It consists of a central nucleus made up of positively charged protons and electrically neutral neutrons, surrounded by negatively charged electrons that orbit the nucleus. The number of protons in the nucleus determines the atom's identity as a particular element, while the number of electrons determines its chemical behavior.

Mixtures are separated by physical means.

Mixtures are combinations of two or more substances that are physically combined but not chemically bonded. Since the substances in a mixture retain their individual properties and can be separated by physical means, mixtures are different from compounds, which are chemically bonded substances that cannot be separated by physical means.

Compounds consist of two or more elements.

Compounds are substances made up of two or more different elements that are chemically bonded together in a fixed ratio. In other words, the elements in a compound are combined in a specific way through chemical reactions to form a new substance with its own unique properties.

Metals will conduct electricity.

Metals are generally good conductors of electricity. This is due to the unique properties of the metallic bond, which is the bond that holds the metal atoms together in a solid.

Electron has a negative charge.

Electrons are negatively charged subatomic particles that are found in orbit around the nucleus of an atom. They have a relative charge of -1 and a mass that is approximately 1/1836th that of a proton. The number of electrons in an atom determines its chemical behavior and reactivity, as well as its electrical conductivity and other physical properties.

Neutron is an uncharged atomic particle.

A neutron is a subatomic particle that is found in the nucleus of an atom, alongside protons. Unlike protons, however, neutrons are electrically neutral, meaning they have no electrical charge. Neutrons have a mass that is slightly larger than that of protons but they do not contribute to the atomic number or the electrical charge of an atom. The stability of the nucleus of an atom is largely determined by the balance between the number of protons and neutrons present.

Nonmetals will not conduct electricity.

The reason for this is that nonmetals typically have high electronegativity, which means they have a strong attraction for electrons and tend to hold onto them tightly. This makes it difficult for electrical current to flow through nonmetallic materials, as the electrons are not free to move around and carry the current.

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6 The probabilities of both questions are a.1/20, and b.9/20.

(a) To find the probability that both David and Mary hit the target, we can use the formula for independent events: P(A and B) = P(A) x P(B).

So, P(David hits the target) = 1/5, and P(Mary hits the target) = 1/4.

Therefore, P(both hit the target) = (1/5) x (1/4) = 1/20.

(b) To find the probability that the target will be hit at least once, we can use the formula P(A or B) = P(A) + P(B) - P(A and B).

So, P(David hits the target) = 1/5, and P(Mary hits the target) = 1/4.

Therefore, P(at least one hits the target) = P(David hits the target) + P(Mary hits the target) - P(both hit the target) = (1/5) + (1/4) - (1/20) = 9/20.

7. The probabilities of both questions are a.0.0625, and b.0.0588.

(a) If the first card is replaced, the probability of drawing a Heart on the first card is 13/52 (since there are 13 Hearts in a deck of 52 cards). After the first card is drawn and replaced, there are still 52 cards in the deck, with 13 of them being Hearts.

So, the probability of drawing a Heart on the second card is also 13/52.

Therefore, the probability of drawing two Hearts with replacement is (13/52) x (13/52) = 169/2704, which simplifies to 0.0625 (correct to 4 decimal places).

(b) If the first card is not replaced, the probability of drawing a Heart on the first card is 13/52 (since there are 13 Hearts in a deck of 52 cards). After the first card is drawn and not replaced, there are now only 51 cards left in the deck, with 12 of them being Hearts.

So, the probability of drawing a Heart on the second card is 12/51.

Therefore, the probability of drawing two Hearts without replacement is (13/52) x (12/51) = 156/2652, which simplifies to 0.0588 (correct to 4 decimal places).

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The coordinates of H' using the scale factor k is H' = (kx, ky)

From the question, we have the following parameters that can be used in our computation:

The graph of the pre-image and a scale factor

Representing the coordinates of H with

H = (x, y)

And the scale factor with

Scale factor = k

The coordinates of H' is calculated using

H' = H * Scale factor

Substitute the known values in the above equation, so, we have the following representation

H' =(x, y( * k

Evaluate

H' = (kx, ky)

Hence, the image of H' is (kx, ky)

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If a particular bowling ball has a mass of 12 kilograms, and has a volume of 4 liters, the volume of a ball with a mass of 9 kilograms is 3 liters.

If the mass of a bowling ball varies directly with its volume, then we can use the formula:

mass = k * volume

where k is the constant of proportionality.

To find the value of k, we can use the given information:

12 = k * 4

k = 3

Now, we can use the value of k to find the volume of a ball with a mass of 9 kilograms:

9 = 3 * volume

volume = 3

This result makes sense, as we would expect the volume to be smaller if the mass is smaller, assuming the density of the ball remains constant.

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Step-by-step explanation:

See image:

Answer:

Step-by-step explanation:

4x is in a multiplication form

4x=36

meaning a number when multiplied with 4 gives the answer 36

hence in order to find the answer

36 divided by 4 which is equivalent to 9

answer is 9

Answer:  [tex]x = 9[/tex]

Step-by-step explanation:

We must isolate [tex]x[/tex] on one side of the equation in order to solve the equation [tex]4x = 36[/tex] for [tex]x[/tex].

Step 1: Divide both sides of equation by 4:

[tex]\frac{4x}{4} = \frac{36}{4}[/tex]

Step 2: Simplify

[tex]x = 9[/tex]

Therefore, the solution to the equation is [tex]x = 9[/tex].

----------------------------------------------------------------------------------------------------------

Rearranging an algebraic equation so that [tex]x[/tex] is on one side and all other terms are on the other side of the equal sign is known as isolating [tex]x[/tex].

The 90% confidence interval for the mean of all tree-ring dates from this archaeological site is (1233, 1303) A.D. (rounded to nearest whole number).

To find the sample mean year x and sample standard deviation s, we can use the calculator's mean and standard deviation functions:

x = 1268 (rounded to nearest whole number)

s = 43 (rounded to nearest whole number)

To find the critical value for a 90% confidence interval, we can use a t-distribution with n-1 degrees of freedom (where n is the sample size). Since the sample size is not given, we'll assume it's 9 (the number of years listed in the data set). Using a t-table or calculator, the critical value for a 90% confidence interval with 8 degrees of freedom is approximately 1.860 (rounded to three decimal places).

The maximal margin of error for a 90% confidence interval can be found using the formula:

E = tc * s / sqrt(n)

where tc is the critical value, s is the sample standard deviation, and n is the sample size. Plugging in the values we have, we get:

E = 1.860 * 43 / sqrt(9) = 35.13 (rounded to nearest whole number)

To find the 90% confidence interval for the mean of all tree-ring dates from this archaeological site, we can use the formula:

(lower limit, upper limit) = (x - E, x + E)

Plugging in the values we have, we get:

(lower limit, upper limit) = (1268 - 35, 1268 + 35) = (1233, 1303)

So the 90% confidence interval for the mean of all tree-ring dates from this archaeological site is (1233, 1303) A.D. (rounded to nearest whole number).

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The probability P(56< X ≤ 6) is 0.0398. ​To draw a normal curve with the area corresponding to the probability shaded we would shade the area to the right of 56 and to the left of 6 on the curve.

To compute the probability P(56< X ≤ 6), we first need to standardize the values using the formula:
z = (x - μ) / σ
where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

For 56:
z = (56 - 45) / 10 = 1.1

For 6:
z = (6 - 45) / 10 = -3.9

Now, we can look up the probabilities for these values of z in a standard normal distribution table or use a calculator to find the area under the curve between these two values:
P(56< X ≤ 6) = P(1.1 < Z ≤ -3.9)

Using a standard normal distribution table or a calculator, we find that:
P(56< X ≤ 6) = 0.0398 (rounded to four decimal places)

To draw the normal curve with the shaded area corresponding to this probability, we can use a graphing calculator or a standard normal distribution table. The area between 56 and 6 corresponds to the area to the right of 56 minus the area to the right of 6. So, we would shade the area to the right of 56 and to the left of 6 on the curve, which would look like this:
[insert normal curve with shaded area between 56 and 6]

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