The length of a rectangle l is 4 units longer than its width. What is the area of the rectangle?

The equivalent function in the form [tex]R(t) = ab^t[/tex] is: [tex]R(t) = 4001 * 0.9^t.[/tex]

What is an equivalent function?

The domain and range of an equivalent function are the same. In mathematics, the phrases equivalent and equal do not have the same meaning.

The equation R(t) = 4000(0.9)^t + 1 can be rewritten in the form [tex]R(t) = ab^t[/tex]by separating the constant factor and the exponential factor. We can do this by defining a = 4000 and b = 0.9:

 [tex]R(t) = 4000 * (0.9)^t + 1\\\\= 4000 * b^t + 1\\\\= (4000 + 1) * b^t\\\\= 4001 * b^t\\\\= ab^t[/tex]

where, a = 4001 and b = 0.9.

So, the equivalent function in the form [tex]R(t) = ab^t[/tex] is:

[tex]R(t) = 4001 * 0.9^t.[/tex]

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Answer 26550

Step-by-step explanation:

Where the above condition exists, the probability that the lawn mower will not start on the first try exactly once out of the next two times you mow the lawn is 5/18, or approximately 0.278.

We can calculate the probability that the lawn mower will not start on the first try exactly once out of the two rounds using a binomial probability distribution.

Let's define a success as the lawn mower starting on the first try, and a failure as the lawn mower not starting on the first try.

The probability of a success is p = 5/6, since the lawn mower does not start on the first try 1/6 of the time.

The probability of a failure is q = 1/6.

The probability of getting exactly one failure out of two trials can be calculated using the binomial probability formula:

P(X = 1) = (2 choose 1) * (5/6)^1 * (1/6)^1

where (2 choose 1) is the number of ways to choose one failure out of two trials.

Simplifying this formula, we get:

P(X = 1) = 2 * 5/6 * 1/6

P(X = 1) = 5/18

Therefore, the probability that the lawn mower will not start on the first try exactly once out of the next two times you mow the lawn is 5/18, or approximately 0.278.

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The area of the rose garden is 129 sq. ft.

Consider the following diagram.

The dimensions of the rectangular garden:

length = 15 ft and width = 9 ft

Using the formula for the area of rectangle,

The area of the rectanguler garden would be,

A₁ = 15 × 9

A₁ = 135 ft²

In the center of the garden, she puts a smaller rectangular patch of grass. And the dimensions of the grass is 2 feet by 3 feet.

The area of rectangular patch is:

A₂ = 2 × 3

A₂ = 6 ft²

So, the area of the rose garden would be,

A = A₁ - A₂

A = 135 - 6

A = 129 ft²

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Find the complete question below.

The amount that Cameron is paid per hour, given the number of hours he worked, is $ 17 per hour

To find the payment that Cameron got per hour, you first need to find the number of hours that he worked.

This number of hours is:

= 4 pm  - 8 am

= 1500 hours - 0800 hours

= 7 hours

The payment per hour is therefore:

= Amount Cameron paid / Number of hours worked

= 120 / 7

= $ 17 per hour

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Answer: $1486.01

Step-by-step explanation: 200*(1.2^(12-1))

Answer:: 80% of 22 is 16.

Answer:

80% of 22 is 16. Hope I helped you!!

The puddle is 29.8 feet away from his residence.

The angle of depression is the angle formed by the horizontal line and the horizontal line's observation of the item.

From the given diagram, we need to calculate the distance of the puddle from his house. This is the adjacent side of the triangle.

Using trigonometry identity;

tan 40 = opposite/adjacent

tan 40 = 25/d

d = 25/tan40

d = 29.8 feet

Hence the distance of the puddle from his house is 29.8 feet

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Answer:

The solution to the system of two linear equations is p = -6.

Step-by-step explanation:

First, we can isolate the variable p on one side of the equation. Subtract 8 from both sides to get 1/6p = -1/3p + 6.

Next, we can subtract -1/3p from both sides to get 4/6p = 6.

Finally, we can divide both sides by 4/6 to get p = -6.

The equation 5 + 4 - 2 = 9 - 2 represents a situation in which the scientist is measuring the mass of an object using a pan balance.

The equation shows that 5 units of mass are added to one pan, 4 units of mass are added to the other pan, and then 2 units of mass are removed from each pan. The equation shows that the total mass in both pans remains unchanged, which indicates that the pans are still in balance. The fact that the equation is balanced, with the same amount of mass on each side, suggests that the pans are in balance because the mass has been distributed evenly between them. The balance operates on the principle of equal weights, where equal weights on opposite sides will cancel each other out, resulting in a balanced state.

Therefore, by removing 2 units of mass from each pan, the scientist is maintaining the balance between the two pans. As long as the pans remain balanced, the scientist can accurately determine the mass of the object being measured. The equation 5 + 4 - 2 = 9 - 2 represents the scientist's assurance that the pans are still in balance and that the measurement of mass can be considered accurate.

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Answer:

  domain: x ≥ 2

Step-by-step explanation:

Given a function with domain x ≥ -5 and range y ≥ 2, you want the domain of its inverse.

The domain of an inverse function is the same as the range of the function.

The domain is x ≥ 2.

__

Additional comment

If a function tells you ...

  y = f(x)

The inverse function is ...

  x = f(y)   ⇒   y = f⁻¹(x)

The domain and range of the inverse function are swapped from those of the original function.

The amount Micah withdrew can be represented as a rational number as 4.5 or 9/2.

A rational number is a number that can be expressed as the ratio of two integers. In this situation, we can represent the amount Micah withdrew as a rational number by expressing it as a fraction.

To do this, we can treat the dollar amount as a whole number (i.e. 4 dollars), and the cents amount as another whole number (i.e. 50 cents), and then express the total amount as a fraction with the sum of these two whole numbers as the numerator and 100 as the denominator (since there are 100 cents in a dollar).

So, the rational number representation of Micah's withdrawal would be:

(4 * 100 + 50) / 100 = 450 / 100 = 9 / 2

In other words, Micah withdrew 9/2 dollars from his bank account.

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Answer:

2

Step-by-step explanation:

The distance between point R(3, 1) and S(3, -6) is 7 units

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

The distance between two points A(x₁, y₁) and B(x₂, y₂) on the coordinate plane is:

[tex]AB=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

Point R is located at ( 3, 1) and point S is located at ( 3, -6). Hence:

[tex]RS=\sqrt{(-6-1)^2+(3-3)^2}=7\ units[/tex]

The distance between point R and S is 7 units

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Answer:

Step-by-step explanation:

just count down which gives you 7

A conclusion that the class can make is: there is no relationship between the number of books and the number of pens. The Option D is correct.

A relation is simply a link between two sets of data. When two values, x and y, are linked in an equation or inequality, they are related and thus represent a relation.

From the graph given, we can not draw any association or relationship between the number of books and the number of pens, rather, their quantity in the classroom is deducable.

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Answer:

Hope this help :)

Step-by-step explanation:

Answer:

64.4 meters

Step-by-step explanation:

divide 7000 cm (7 metre) by 5 cm

you get 1400

multiply that by the smaller wingspan

Answer:

65.71

Step-by-step explanation:

According to the model's scale, which is 5 cm to 7 m, there are 7 m on the actual plane for every 5 cm on the model. By dividing the wingspan of the model by the scale factor and multiplying the result by the equivalent size in metres, we may determine the real plane's wingspan.

 With a model's wingspan of 46 cm, this means: (46 cm) * (7 m/5 cm) = 65.71 m (46 cm) / (5 cm/7 m) 

The actual airplane's wingspan is therefore roughly 65.71 metres.

Hope it helps! : )

Step 1: Calculate the area of the room. To calculate the area of the room, multiply 12 feet by 15 feet, which gives us a total of 180 square feet.

Step 2: Calculate the area of one tile. To calculate the area of one tile, multiply 113 feet by 113 feet, which gives us a total of 1.369 square feet.

Step 3: Calculate the number of tiles needed. To calculate the number of tiles needed, divide the area of the room (180 square feet) by the area of one tile (1.369 square feet). This gives us a total of 131 tiles.

Therefore, 131 tiles are needed to cover the entire floor.

Start by multiplying the tile's length by its breadth in inches to determine the tile's square footage. Lastly, multiply the area of one tile by the determined size of the space. The outcome is the precise quantity of tiles needed for the space.

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The balance at the end of three months is $652.

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

[tex]I = \dfrac{P \times R \times T}{100}[/tex]

Given;

P=$630

R=0.14/12

= 0.01166

n=3

Interest rate = 14%

Using the formula;

A=P(1+r)^n

we can now insert the values

A=630(1+0.01166)^3

A=652.29

Therefore, the by interest of 14% the amount will be $652.29.

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Answer:

Step-by-step explanation:

The volume of a cylinder with height "h" and radius "r" is given by the formula: V = πr^2h.

The volume of a cone with height "h" and radius "r" is given by the formula: V = (1/3)πr^2h.

To find the volume of a cone with the same height and radius as a cylinder with a volume of 234 cubic inches, we need to find the height and radius of the cylinder. We can use the volume formula for the cylinder to do this:

V = πr^2h

234 = πr^2h

Dividing both sides by πr^2:

h = 234 / (πr^2)

Now that we know the height, we can use it to find the radius using the volume formula for the cylinder:

234 = πr^2h

Taking the square root of both sides:

r = √(234 / πh)

Finally, we can use the height and radius to find the volume of the cone:

V = (1/3)πr^2h

This answer will give us the volume of a cone with the same height and radius as a cylinder with volume 234 cubic inches.

The two resulting equations are set equal to one another and solved for the values of the variables. Therefore, the solution to the system of equations is x = 3 and y = -45.

The equal values method is a way of solving systems of equations. It involves isolating each variable on its own side of the equation and then setting the two equations equal to one another. This results in an equation with only one variable, which can then be solved. For example, the system of equations given is -8x - 21 = 6x + 7. To solve this system with the equal values method, one must first isolate the variables. The first equation can be rearranged to -8x = 21 + 6x, and then solved for x to find x = 3. Then, the same value of x can be substituted into either of the original equations to solve for y. For example, substituting x = 3 into the first equation gives -8(3) - 21 = -24 - 21 = -45, so y = -45. Therefore, the solution to the system of equations is x = 3 and y = -45.

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The height of the tree is solved to be x = 50 * tan(57°)

The description is modelled to a right triangle. The height, x, of the tree can be found using trigonometry.

Using the tangent function:

tan 57 = height of the tree, x / distance from the tree

tan 57 = x / 50

x = 50 * tan(57°)

The sin and cos will require the hypotenuse which is the slant distance and this is not given

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Consequently, x = 12 is the value of x that equals the equations 2/3x Plus 2 and 4/3x - 6.

Depending about where it is in the number, each character has a different meaning, which is referred to as value. We figure it out by increasing the digit's place value by its face value. Location value plus face value equals value.

We can assign the equations 2/3x + 2 and 4/3x - 6 equal to one another and solve for x to determine the value of x at which they are equal:

2/3x + 2 = 4/3x - 6

First, by multiplying both sides by the least common multiple of the denominators, which is 3, we can reduce the expressions:

2x + 6 = 4x - 18

Next, we can simplify by subtracting 2x from both sides:

6 = 2x - 18

Adding 18 to both sides gives:

24 = 2x

Dividing both sides by 2 gives:

x = 12

Therefore, the value of x that makes the expressions 2/3x + 2 and 4/3x - 6 equal is x = 12.

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The numbers that are possible for Janet's number are 335, 36, and 37.

We start by finding the value of n using the equation n > 56 - 22. Solving this equation, we get n > 34.

So, Janet's number must be greater than 34, and it must be a two-digit positive whole number. Based on this, we can conclude that the following numbers are possible for Janet's number:

1. 35

2. 36

3. 37

These numbers are possible because they meet the criteria of being two-digit positive whole numbers and greater than 34.

Hence, the required three numbers are 35, 36, and 37.

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Answer:

The two angles are [tex]75^{o}[/tex] ([tex]\frac{5\pi}{12}[/tex]radians) and [tex]15^{o}[/tex] ([tex]\frac{\pi}{12}[/tex]radians)

Step-by-step explanation:

Right angle = [tex]90^{o}[/tex] = [tex]\frac{\pi }{2}[/tex] radians
Let x = Lesser angle

     y = Greater angle

Angles in degrees:

Sum of angles in a right-angled triangle = [tex]180^{o}[/tex]

[tex]x^{o} + y^{o} + 90^{o} = 180^{o}[/tex]

[tex]= x + y = 180 - 90[/tex]

[tex]= x + y = 90[/tex]

[tex]= x = 90 - y[/tex] ——(equation i)

[tex]y^{o} -x^{o} =\frac{2}{3} (90^{o})[/tex]

[tex]= y - x = 60[/tex] ——(equation ii)

These two equations are linear simultaneous equations, which can be solved by substitution, elimination or graphical method:

Substitution method:

Substitute (equation i) into (equation ii) to solve for y:

Expand the brackets by applying the Distributive Law and bring all the like terms together:

[tex]= y - (90-y)= 60[/tex]

[tex]= y - 90 + y = 60[/tex]

[tex]= y + y = 60 + 90[/tex]

[tex]= 2y = 150[/tex]

[tex]= y = \frac{150}{2}[/tex]

[tex]= y = 75^{o}[/tex]

Substitute this calculated value in any of the equations to determine the value of x:

[tex]x = 90 - 75[/tex]

[tex]= x = 15^{o}[/tex]

Angles in Radians:

To convert an angle measured in degrees to radians, multiply by [tex]\frac{\pi }{180^{o} }[/tex]

[tex]= y = 75^{o} .\frac{\pi}{180^{o}}[/tex]

Divide both the numerator and denominator by the Highest Common Factor ‘15’:

[tex]= y = \frac{5\pi }{12}[/tex] radians

[tex]x = 15^{o}.\frac{\pi }{180^{o}}[/tex]

[tex]= x = \frac{\pi}{12}[/tex] radians

If Hank bought a 4 room home for a rental, and he put 20% down on the $300,00. 00 rental unit, the annual depreciation amount would be $8,727.27 .

To determine the depreciation amount, we first need to determine the depreciable basis of the rental property. The depreciable basis is the portion of the property's value that can be depreciated over time.

In this case, Hank put 20% down on a $300,000 rental unit, which means he paid $60,000 as a down payment. Therefore, the depreciable basis of the rental property is the remaining $240,000 ($300,000 - $60,000).

The IRS allows rental property owners to depreciate the depreciable basis of their property over 27.5 years using the straight-line method. To calculate the annual depreciation amount, we divide the depreciable basis by the number of years of useful life.

So, in this case, the annual depreciation amount would be $8,727.27 ($240,000 / 27.5). This means that Hank would be able to deduct $8,727.27 from his rental income each year for 27.5 years to account for the wear and tear of the property.

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Answer:

103.42

Step-by-step explanation:

use the big circle area - 2 little white circles' area

big r = 12.5/2 = 6.25 so big circe area = π r² =π * 6.25²

small r = 3.5/2 = 1.75 so small circe area = π r² =π * 1.75²

2 of them = 2π * 1.75²

so π 6.25² - 2π * 1.75² = 39.06π-6.13π=103.42

well, looking at the picture above, we can see that the diameters are 12.5 and 3.5 for those circles, that means the radii for them will be half that for each, namely 6.25 and 1.75 respectively.

let's get the whole area for containing circle, and then subtract the area of  the small ones, what's leftover is the shaded area.

[tex]\stackrel{large~one}{\textit{area of a circle}}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=6.25 \end{cases}\implies A=\pi 6.25^2 \\\\\\ \stackrel{small~one}{\textit{area of a circle}}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=1.75 \end{cases}\implies A=\pi 1.75^2 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Areas}}{\stackrel{large}{\pi 6.25^2}~~ - ~~\stackrel{\textit{two small ones}}{2(\pi 1.75^2)}} ~~ \approx ~~ \text{\LARGE 103.48}[/tex]

The representation and comparison of a function f(x) and f(x - 4) are illustrated below with the attached graph.

Suppose we have a function f(x).

f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).

f(x ± c) = Horizontal left/right shift by c units (x - + c, y).

(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).

f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).

f(-x) = Reflection over y-axis, (-x, y).

-f(x) = Reflection over x-axis, (x, -y).

Let, The function f(x) = x², It is a quadratic function and the graph of this function is a parabola that opens upwards.

And, Let g(x) = f(x - 4) = (x - 4)²,

Now, The graph of this function is also a parabola that opens upwards but it is shifted 4 units to the right along the x-axis to the parent function

f(x) = x².

The table for f(x) and g(x) would be,

At x = 1,

f(x) = 1 and g(x) = 9.

At, x = 3,

f(x) = 9 and g(x) = 1.

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Answer: 5 hrs

Step-by-step explanation:

650 miles (total distance) / 130 miles (speed per hour)

= number of hours it takes to get to Paris from Barcelona

650/130

= x

x = 5 hrs

Answer: The correct answer is 5 hours.

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