Expand: y(0.5 +8)
Expand: 4(3+4x-2)

The function that approximates Australia's per capita GDP in t years after 1950 is \(G(t) =$1800(1.067)^t.\)

A function sets the value of one set's elements to the value of another set's specified element.

GDP represents the monetary worth of final products and services (those purchased by the final user) generated in a country over a certain time period.

According to the given information:

Given that Australia's GDP in 1950 was $1800, and that it is expanding by 6.7% per year, the GDP of Australia will increase by 6.7% each year after 1950.

As a result of the compounding effect, a function that gives the estimated per capita GDP of Australia in t years following 1950 can be expressed as follows:

\(GDP = 1800 + (1+6.7)^{t}\)

\(GDP = $1800 + (1+0.067)^t\)

\(GDP = $1800 + (1.067)^t\)

Hence, The function that approximates Australia's per capita GDP in t years after 1950 is \(G(t) =$1800(1.067)^t.\)

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Based on the exponential decay equation, the number of employees for the company that has been decreasing yearly by 5%, will in 10 years be approximately 515.

The exponential decay equation or function gives the value in t years that has a constant ratio of decrease.

Exponential decay equation is one of the two exponential functions.  The other is the exponential growth equation.

The annual decrease in the number of employees = 5%

The current number of employees in the company = 860

The expected time = 10 years.

The exponential decay equation is as follows, y = 860 x 0.95^10.

y = 860 x 0.95^10 = 515

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To find coterminal angles, you have to either add or subtract 2π. In this case, you would use 8π/4 so there is a common denominator.

Positives:

-3π/4+8π/4 = 5π/4

5π/4+8π/4 = 13π/4

Negative:

-3π/4-8π/4 = -11π/4

-11π/4-8π/4 = -19π/4

In geometry, an angle measure is the length of the angle formed by two rays or arms intersecting at a common vertex.

Using a protractor, angles are measured in degrees (°). Joseph Huddart created the protractor in 1801. It was a more sophisticated protractor.

The angle created at the center of a circle is measured in radians, the unit of angular measurement. It is described as an angle that subtends from a circle's center and intercepts at an arc with a radius equal to the circle's radius. 57.3° is equal to one radian.

Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle, and full rotation are the names of basic angles.

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Answer:

107

Step-by-step explanation:

Given

See attachment for boat and hiker

Required

The distance between the boat and the hiker

To do this, we make of sine rule.

\(\frac{a}{\sin A} = \frac{b}{\sin B} =\frac{c}{\sin C}\)

In this case:

\(x = ??\)

\(X = 68\)

\(a = 66\)

\(A = 35\)

So, we have:

\(\frac{x}{\sin 68} = \frac{66}{\sin 35}\)

Make x the subject

\(x = \frac{66}{\sin 35} * \sin 68\)

Using a calculator, we have:

\(x = \frac{66}{0.5736} * 0.9272\)

\(x = 115.063* 0.9272\)

\(x = 106.68\)

\(x \approx 107\)

An iterative version of a preorder traversal for a binary tree uses a stack.

Preorder traversal of a binary tree is a depth-first traversal algorithm that follows the order: root, left subtree, right subtree. In a recursive implementation, the function would first visit the root, then call itself recursively for the left subtree, and then call itself recursively for the right subtree.

In an iterative implementation, we use a stack to keep track of the nodes we need to visit. We push the root node onto the stack, and then while the stack is not empty, we pop a node from the stack and visit it. If the popped node has a right child, we push the right child onto the stack. If the popped node has a left child, we push the left child onto the stack. By doing so, we ensure that the nodes are visited in the correct order: root, left subtree, right subtree.

Using a stack instead of recursion can be more memory-efficient, since we are not storing all the recursive function calls on the call stack.

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Answer:

3/2

Step-by-step explanation:

The statement "The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is 1/(a-b)" is False.

In a uniform distribution, the probability density function (PDF) is constant within the interval [a, b]. The height of the PDF represents the density of the probability distribution at any given point within the interval. Since the PDF is constant, the height remains the same throughout the interval.

To determine the height of the PDF, we need to consider the interval length. In a uniform distribution defined on the interval [a, b], the height of the PDF is 1/(b - a) for the PDF to integrate to 1 over the entire interval. This means that the total area under the PDF curve is equal to 1, representing the total probability within the interval [a, b].

Therefore, the correct statement is that the height of the probability density function f(x) of the uniform distribution defined on the interval [a, b] is not 1/(a - b), but rather it is a constant value necessary for the PDF to integrate to 1 over the interval, i.e., 1/(b - a).

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The expected number of claims made by people under 25 years of age is 5.74.

For this problem, we can use the binomial distribution which states that the probability of success (p) is equal to the proportion of people under 25 making claims (82%) and the probability of failure (q) is equal to the proportion of people over 25 making claims (1 - 82% = 18%).

The expected number of claims made by people under 25 is equal to the total sample size (7) times the proportion of people under 25 making claims (0.82) so the expected number of claims made by people under 25 is 7×0.82 = 5.74.

Hence, the expected number of claims made by people under 25 years of age is 5.74.

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Answer:

y=5x−2

I hope this helps!

Answer: 2.75+ 3/4 = 3.5

Step-by-step explanation:

Answer:

1+1+3/4 is the correct answer, so in the first box put 1, and in the 2nd box put 1, and you'll be correct

Answer:

400000000 dollar

Step-by-step explanation:

because why not

The answer is ,  the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.

The Taylor series of a function f(x) centered at c is given by the formula:

\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)

Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)

\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)

Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:

\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)

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The Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:

f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...

First, let's find the derivatives of f(x) = e^(4x):

f'(x) = d/dx(e^(4x)) = 4e^(4x)

f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)

f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)

Now, let's evaluate these derivatives at x = c = 0:

f(0) = e^(4*0) = e^0 = 1

f'(0) = 4e^(4*0) = 4e^0 = 4

f''(0) = 16e^(4*0) = 16e^0 = 16

f'''(0) = 64e^(4*0) = 64e^0 = 64

Now we can write the Taylor series expansion:

f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...

Substituting the values we found:

f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...

Simplifying the terms:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:

f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...

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Answer:

  C.  x ≥ 5

Step-by-step explanation:

You must meet both conditions:

  (x -5) ≥ 0 and (x +2) ≥ 0

For the first condition, ...

  x ≥ 5 . . . . add 5 to both sides

For the second condition ...

  x ≥ -2 . . . . subtract 2 from both sides.

Since both conditions must be met, we must have ...

  x ≥ 5

At time t, the position is x(t) = 0.5t3 - 3t2 + 3t + 2.

To find the position:

The derivative of x with respect to t is zero when the velocity is zero. That is to say,

Use the quadratic formula to solve.

When t =0.5858 s, the position is:

When t=3.4142 s, the position is:

Reject the negative answer.

So, when t = 0.586 s, the velocity is zero and the distance is 2.83 m.

The second derivative of x with respect to t is zero when the acceleration is zero.

That is to say,

The distance traveled is:

So, when the acceleration is zero, t = 2 s, and the distance traveled is zero.

Therefore, at time t, the position is x(t) = 0.5t3 - 3t2 + 3t + 2.

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The correct question is given below:

A girl operates a radio-controlled model car in a vacant parking lot. the girl’s position is at the origin of the XY coordinate axes, and the surface of the parking lot lies in the XY plane. she drives the car in a straight line so that the x coordinate is defined by the relation x(t) = 0.5t3 - 3t2 + 3t + 2 where x and t are expressed in meters and seconds, respectively. determine when the velocity is 0 m/s, and the position and the total distance traveled when the acceleration is zero.

The slope indicates how steep the line is, while the y-intercept indicates where the line intersects the y-axis. We have to solve the equation in the interval [0,π)The general solution for any cosine equation $cosθ=cosα$the general solution is $θ=2nπ+α$. All we need to find out the values of α and substitute the values of n.

We know that cos value is positive in first and fourth quadrant.$\frac{\pi}{3}$ is the angle which is between $0$ and $\pi$ and whose cos is Thus the solutions will be:  and

Thus, the solutions in the interval $[0,\pi)$ are $x=\frac{\pi}{9}, \frac{5\pi}{9}$.

Hence, the solutions are $\frac{\pi}{9},\frac{5\pi}{9}.$

The slope-intercept form of a linear equation in mathematics is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point at which the line meets the y-axis. The slope-intercept form is a handy approach to represent a line's equation because it allows you to quickly see the line and determine its slope and y-intercept. The slope indicates how steep the line is, while the y-intercept indicates where the line intersects the y-axis.

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The determinant of matrix A, det(A), is equal to 8i.

To find the determinant of matrix A, we are given its characteristic polynomial p(A) = 13 - 412 + 8 det(A) = i. According to Theorem 7.1.4, if we set A = 0 in the polynomial p(A), we can obtain the determinant of -A.

Setting A = 0 in the polynomial p(A), we get p(0) = 13 - 412 + 8 det(0) = i. Simplifying this equation, we have 13 - 412 + 8 det(0) = i. Since det(0) is the determinant of a zero matrix, which is always zero, we can rewrite the equation as 13 - 412 = i. Solving for i, we find that i = -399.

Now, using the result from Theorem 7.1.4, we have det(-A) = C(-1)^n det(A). Plugging in the given value det(11 - A) = 1 + C21n-1 + ... + C, we can set A = 0 to find det(-A). By substituting A = 0 into the equation, we get det(11 - 0) = 1 + C21n-1 + ... + C, which simplifies to det(11) = 1 + C21n-1 + ... + C. Since det(11) is the determinant of matrix 11, which is just 11, we have 11 = 1 + C21n-1 + ... + C. Simplifying further, we get 10 = C21n-1 + ... + C.

Finally, we can substitute det(A) = 8i (from the given characteristic polynomial) into the equation det(-A) = C(-1)^n det(A). Since we found i = -399, we have det(-A) = C(-1)^n * 8 * -399 = -3192C(-1)^n.

In conclusion, the determinant of matrix A, det(A), is equal to 8i, which simplifies to -3192C(-1)^n.

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Answer:

Using the Pythagorean theorem we can first put the points into x and y

x1 = 7

y1 = 9

x2 = 1

y2 = 1

The distance between the two points can be found as follows:

d = √((x2 - x1)² + (y2 - y1)²)

= √((1 - 7)² + (1 - 9)²)

= √((-6)² + (-8)²)

= √(36 + 64)

= √100

= 10

Therefore, the distance between the points (7, 9) and (1, 1) is 10 units.

Answer: 108 degrees.

Step-by-step explanation:

I think this is how you solve it:

A circle has a total of 360 degrees.

Having 5 equally placed sensors with a certain detection angle means that the sensors form a regular pentagon.

Finding the measure of the interior angles of a regular pentagon can be found using the formula

(180(n-2))/n, with n being the number of vertices of the polygon.

180(5-2)/5 ; 180(3)/5 ; 540/5 = 108

I think this means the detection angle is 108 degrees. Hope this helps!

If you get it wrong I'm terribly sorry T-T

Answer:

A integer is number that can be written without a fractional or decimal component

Step-by-step explanation:

Answer:

An integer is a whole number. It doesn't matter whether it's positive or negative as long as its a whole number

(sorry if this doesn't make sense but I hope it helped)

Answer:

A. 400 ounces is 25lbs so yeah

Step-by-step explanation:

Answer:

2.25 feet, 45 inches, and 6 yards

Step-by-step explanation:

first, convert all to the same unit of measurement

I will use inches

45 inches = 45 inches

6 yards, 1 yard = 3 feet so 6 yards are equal to 18 feet and 1 foot is equal to 12 inches so 12*18 is 216 inches so 6 yards = 216 inches

Next 1 foot equals 12 inches so 2.25 * 12 = 27 so 2.25 feet = 27 inches.

Now let's look at the complete conversion

45 inches

6 yards = 216 inches

2.25 feet = 27 inches

looking at the inches we can see that 27 is the least then 45 then 216 therefore

2.25 feet < 45 inches <  6 yards so the order is

2.25 feet, 45 inches, and 6 yards

Answer:

C.  69°

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180

two of the angles are given to find the third one we subtract their sum from 180

180 - (36+75) = 69 degrees

Answer:

the answer is x=+/- 3 sqrt 2

Answer:

3.5

Step-by-step explanation:

find the ratio between any two corresponding sides. for example : 1.4/2 = 0.7

this should be the same number for all sides

thus 5 * 0.7 = 3.5

Answer:

23456892245u

Step-by-step explanation:

Allah sh all will am am well ram chirac flow

Answer:4.62x10^13

Step-by-step explanation:

The width of a confidence interval decreases as the sample size increases and increases as the confidence level increases.

So, we know that smaller samples result in narrower intervals.

Therefore, a confidence interval narrows as the sample size grows and widens as the level of confidence rises.

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Answer:

\(f^{-1}(x)=\frac{3x}{2} +6\)

Step-by-step explanation:

hope this helps

The coordinate of the midpoint of the segment with the given endpoints is ( 1/2, -6 ).

The midpoint formular used in finding the midpoint of a segment is expressed as;

( [x₁+x₂]/2 , [y₁+y₂]/2 )

Given the data in the question;

Point V(-2,5)

Point Z(3,-17)

Plug these values into the equation above.

( [x₁+x₂]/2 , [y₁+y₂]/2 )

( [(-2) + 3]/2 , [5 + (-17)]/2 )

( 1/2 , -12/2 )

( 1/2, -6 )

The coordinate of the midpoint of the segment with the given endpoints is ( 1/2, -6 ).

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Answer:

2

Step-by-step explanation:

hope this helps :3

if it did pls mark brainliest

Answer:

2

Step-by-step explanation:

Numbers go in the order 1,2,3,4,5,6,7,8,9,10

If we go up one we will have two

Hope this helps

Answer:

b

Step-by-step explanation: