Which function represents the inverse of the function f(x)=x^2+5

The equation that models the relationship between the models to show Ethan's employee benefits is y = 14 + 3(x - 1).

The number of paid vacation days Ethan earned was 35 paid vacation days .

Ethan will reach the maximum number of paid vacation days in 7 years.

Let x represent the number of years he has worked for this employer and y represent the number of paid vacation days he has earned.

The equation that models the relationship between x (years worked) and y (paid vacation days earned) is:

y = 14 + 3(x - 1)

Using the equation from part a, we can find out how many paid vacation days Ethan has earned after eight years:

y = 14 + 3(8 - 1)

y = 14 + 3(7)

y = 14 + 21

y = 35

To determine when Ethan will reach the maximum number of paid vacation days, we can set y equal to 30 and solve for x:

30 = 14 + 3(x - 1)

16 = 3(x - 1)

16/3 = x - 1

x = 16/3 + 1

x = 16/3 + 3/3

x = 19/3

x = 7

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The final charge of the spheres when they are touching after calculated using Coulomb's law , is 1.24 * 10^-6 C

According to the given information, two charged spheres with charges |q1| > |q2| attract each other with a force of magnitude 90.4 mn when separated by a distance of 4.64 m. When the spheres are brought together until they are touching, they attain the same final charge q.

We can use Coulomb's law to find the final charge q. Coulomb's law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, Coulomb's law is expressed as:

F = k * (q1 * q2) / r^2

Where F is the force between the charged particles, k is Coulomb's constant (8.99 * 10^9 N*m^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between them.

We can rearrange the equation to solve for q:

q = sqrt(F * r^2 / k)

Plugging in the given values:

q = sqrt(90.4 * 10^-6 N * (4.64 m)^2 / (8.99 * 10^9 N*m^2/C^2))

q = 1.24 * 10^-6 C

Therefore, the final charge of the spheres when they are touching is 1.24 * 10^-6 C

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Provide the given right triangle

I'm sorry, but I cannot see the following exercises that you are pertaining to. Please provide the given right triangle and the specific angle you want to find so I can assist you accordingly.

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Answer:

(-2,6)

Step-by-step explanation:

y=f(x) has vertex (-4,6)

g(x)=-f(x-2) shifts the graph 2 units to the right, not to the left, and the graph is reflected over the x-axis

therefore the vertex is (-2,6) and the reflection over the x-axis has no affect on the vertex

Assuming that David sold the stock at $10 per stock today, then, we will agree that he bought the Oracle stock yesterday at a price of approximately $9.89 per share.

A share, also known as a stock or equity, is a unit of ownership in a corporation. Stock investments provide investors with returns in the form of dividends and capital gains. The higher the expected returns, the more shares an investor owns.

Let the price at which David bought each share of Oracle stock yesterday be x. Then, his total cost for buying 200 shares would be: 200x

Similarly, his total revenue for selling 200 shares at $10 per share today would be:

= 200*($10)

= $2000

His profit was $22, so we can set up the equation which is $2000 - 200x = $22.

Simplifying and solving for x, we get:

$1978 = 200x

x = $1971/200

x = $9.89.

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For a point P plotted on a given number line, the number represented by the point P is 5.80⁻³.

A number line is a linear visual representation of numbers and integers. This line is used to compare equally spaced numbers on an infinity line that extends horizontally or vertically on either side. A number line shows point values ​​and equal divisions on the line. Between point 5.10⁻³ and point 6.10⁻³ there are 10 evenly spaced points.

Counting from the left, it looks like this:

5.10⁻³, 5.20⁻³, 5.30⁻³, 5.40⁻³, 5.50⁻³, 5.60⁻³, 5.70⁻³, 5.80⁻³, 5, 90⁻³, 6.00⁻³, 6.10⁻³.

Point P drops to 5.80⁻³, so the value of point P is 5.80⁻³.  

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The complete question is as follows:

Part A: The equation to represent the problem is 259.99 + 3.75r = 436.24. The variable 'r' represents the number of times Derek used one of the racquetball courts.

Part B

Derek used a racquetball court 46.93 times

Part A: The equation to represent the problem is: 259.99 + 3.75r = 436.24. The “r” represents the number of times Derek used one of the racquetball courts. 259.99 is the yearly membership fee and the 3.75 is the cost of each time Derek used a racquetball court. 436.24 is the total amount Derek paid for the entire year at the health club.

Part B: To solve the equation, we need to isolate “r” on one side of the equation. To do this, we need to subtract 259.99 from both sides of the equation. We then get 3.75r = 176.25. We divide both sides by 3.75 to get r = 46.93. This means that Derek used a racquetball court 46.93 times.

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Answer:

5/6

Step-by-step explanation:

Answer:

Step-by-step explanation:44,4444444

Answer:

0.0225

Step-by-step explanation:

18÷800=0.0225

Answer:41

Step-by-step explanation:

add 25 and 16 together

ln(y) = -0.544x + 1.099

The logarithmic equation that relates x and y is given by ln(y) = -0.544x + 1.099. To get this equation, the given table of values is considered.Let's first find the value of "a" in the general logarithmic equation, which is y = a ln(x). We use the given table of values to get this value. When x = 1, y = 1, and so a ln(1) = 1, which implies that a = 1. Hence, the equation becomes y = ln(x).Now, we need to convert this to an equation in terms of y and x. That is, we need to find ln(y) in terms of x. To do this, we substitute y for x in the equation y = ln(x). That is, we get ln(y) = ln(x).Now, we substitute the given values of x and y in this equation to get the required logarithmic equation. That is, we have:ln(y) = -0.544x + 1.099 (rounded to three decimal places). Therefore, the logarithmic equation that relates x and y is ln(y) = -0.544x + 1.099.

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Answer:

the answer is 5 simplify

Answer:

20/14

10/7

0r 5/56

Step-by-step explanation:

i hope you find it helpful

Answer: It is rational

Step-by-step explanation:

a) The surface area of a cube with edge length x is

b) The edge length of the cube is solved to be 14 cm.

a) The surface area of a cube with edge length x is given by the formula:

SA = 6x^2

b) We are given that the surface area of the cube is 1176 cm^2. Setting this equal to the formula for surface area of a cube, we get:

6x^2 = 1176

Dividing both sides by 6, we get:

x^2 = 196

Taking the square root of both sides, we get:

x = ± 14

Since the edge length must be a positive number, we discard the negative solution and conclude that the edge length of the cube is 14 cm (to 1 decimal place).

Therefore, the edge length of the cube is 14 cm.

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68% of the data will fall within one standard deviation, 95% of the data will fall within two standard deviations and 99.7% of the data will fall within three standard deviations of the mean.

The empirical rule, which is also referred to as the three-sigma rule or the 68-95-99.7 rule, gives a rapid estimate of the distribution of data in a normal distribution, provided the mean and standard deviation. The empirical rule describes that in a normal distribution:68% of the data will fall within one standard deviation of the mean.95% of the data will fall within two standard deviations of the mean.99.7% of the data will fall within three standard deviations of the mean.This empirical rule is useful in determining whether the data is roughly normally distributed. When a number of data points fall outside the three standard deviation range, it indicates non-normal distributions. Consequently, the empirical rule is a valuable tool for approximating normal distributions, but it is important to remember that it is just an approximation, and not all normal distributions will follow this rule exactly.

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Amanda can spend 9/48 of her budget on entertainment, which can be simplified to 3/16.

In mathematics, an expression is a combination of numbers, symbols, and/or operators that represents a mathematical quantity or relationship. Expressions can be composed of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, as well as functions and other mathematical constructs.

The fractions of Amanda's budget allocated to each category are:

Venue: 5/24

Invitations: 1/16

Food: 1/4

Decorations: 3/16

The sum of these fractions is:

5/24 + 1/16 + 1/4 + 3/16 = 15/48 + 3/48 + 12/48 + 9/48 = 39/48

This means that Amanda has allocated 39/48 of her budget to these four categories. To find out what fraction of her budget she can spend on entertainment, we need to subtract this fraction from 1 (since the remaining fraction is what she can spend on entertainment):

1 - 39/48 = 9/48

Therefore, Amanda can spend 9/48 of her budget on entertainment, which can be simplified to 3/16.

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Answer:

7.19

Step-by-step explanation:

Take the total cost and subtract the eyebrow pencil to find the cost of the concealer.

14.13

- 6.94

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

7.19

Answer:

Below

Step-by-step explanation:

With questions like this it is helpful to draw the scenario as in the image below.     Using Pyhtagorean theorem , you can calculate 'x'..... then the highway distance in range is two times this = 12.6 km  

Therefore , the solution of the given problem of unitary comes out to be C is the correct response. $94.50.

The task can be finished by combining the data expression obtained to use this nanosection methodology with in all supplemental data from two people who employed a particular variable tactic. In plain English, this indicates that, if the desired result occurs, either the stated individual will be known or, in fact, the colour by both enormous processes would be skipped. A refundable fee of Rupees ($1.01) may be necessary for forty pens.

Here,

By dividing both sides by D, we can determine B if P = DB:

=> B = P/D

Sandra's premium P will be equal to the $567 base premium because her risk factor D is 1.0.

So,

=> B = P/D = $567/1.0 = $567

Her monthly payment will be as follows because this is her six-month premium:

=> Monthly premium = six-month premium / six,

which equals $567 / six, or $94.50.

Thus, C is the correct response. $94.50

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The probability of being able to hit the blot on the next roll is 11/36, and the probability of entering from the bar without hitting the blot is 2/36 or 1/18.

The probability of being able to hit the blot on the next roll is 11/36. The probability of entering from the bar without hitting the blot is 2/36 or 1/18. The given situation can be represented by the following diagram:In the given scenario, the player has one piece on the bar, and the opponent controls the inner 2, 4, and 6 points while also having a blot on the 5 point. This means that the player needs to roll a 5 in order to hit the opponent's blot. The probability of rolling a 5 is 4/36 or 1/9.The player can also enter from the bar without hitting the blot. To do this, the player must roll a 1 or a 2. The probability of rolling a 1 or a 2 is 2/36 or 1/18.Therefore, the probability of being able to hit the blot on the next roll is 11/36, and the probability of entering from the bar without hitting the blot is 2/36 or 1/18.

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The mean of Y is -5/4 and the variance of Y is 144.

In statistics, the mean is a measure οf central tendency that represents the average οf a set οf data. It is alsο knοwn as the arithmetic mean. The mean is calculated by adding up all the values in the dataset and dividing the sum by the tοtal number οf values. It is οften used tο describe the typical οr average value in a set οf data.

Variance is a statistical measure that describes hοw much the values in a set οf data vary frοm the average value οr mean. It measures the spread οr dispersiοn οf the data pοints arοund the mean.

In the given questiοn,

Tο find the mean and variance οf the randοm variable Y, we need tο use the fοrmulas fοr the expected value and variance οf a functiοn οf a randοm variable:

The expected value (mean) of Y is given by:

E(Y) = E(3X - 2) = 3E(X) - 2

The variance of Y is given by:

Var(Y) = Var(3X - 2) = 9Var(X)

To find E(X), we need to integrate the density function f(x) over all possible values of X:

E(X) = ∫0∞ x f(x) dx

= ∫0∞ x (1/4)[tex]\rm e^{(-x/4)[/tex]dx

This integral can be solved using integration by parts, with u = x and dv/dx = (1/4)[tex]\rm e^{(-x/4)[/tex] dx.

Integrating by parts, we get:

E(X) = [-x/4 [tex]\rm e^{(-x/4)[/tex]]_0∞ + ∫0∞ (1/4)[tex]\rm e^{(-x/4)[/tex] dx

= [0 + (1/4)]/1 + [0]

= 1/4.

Therefore, the expected value of Y is:

E(Y) = 3E(X) - 2 = 3(1/4) - 2 = -5/4.

To find Var(X), we can use the formula for the variance of an exponential distribution, which is:

Var(X) = (1/λ²) = (4²) = 16.

Therefore, the variance of Y is:

Var(Y) = 9Var(X) = 9(16)

= 144.

Therefore, the mean of Y is -5/4 and the variance of Y is 144.

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The mean of Y is 10 minutes, and the variance of Y is 144 minutes squared.

What is integration?

Integration is a mathematical operation that is the reverse of differentiation. Integration involves finding an antiderivative or indefinite integral of a function.

To find the mean and variance of Y, we will first need to find the mean and variance of X.

Mean of X:

The mean of X is given by:

E(X) = integral from 0 to infinity of xf(x) dx

E(X) = integral from 0 to infinity of x * 1/4 e^(-x/4) dx

Using integration by parts with u = x and dv = e^(-x/4) dx, we can evaluate this integral to get:

E(X) = 4

Variance of X:

The variance of X is given by:

Var(X) = E(X^2) - [E(X)]^2

We will first need to find E(X^2). Using integration by parts again, we can evaluate this integral as:

E(X^2) = integral from 0 to infinity of x^2 * 1/4 e^(-x/4) dx

E(X^2) = 32

Therefore, the variance of X is:

Var(X) = E(X^2) - [E(X)]^2

Var(X) = 32 - 16

Var(X) = 16

Now, we can use the formula for the mean and variance of a linear transformation of a random variable to find the mean and variance of Y.

Mean of Y:

The mean of Y is given by:

E(Y) = E(3X - 2)

E(Y) = 3E(X) - 2

E(Y) = 10

Variance of Y:

The variance of Y is given by:

Var(Y) = Var(3X - 2)

Var(Y) = 9Var(X)

Var(Y) = 144

Therefore, the mean of Y is 10 minutes, and the variance of Y is 144 minutes squared.

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The value of x in the equation 2x³ + 3x² + 12x + 1 = 0​ when solved is x = -0.085

Given the following equation

2x³ + 3x² + 12x + 1 = 0​

The equation cannot be factorized

So, we solved graphically

See attachment for the graph of the equation 2x³ + 3x² + 12x + 1 = 0​

On the graph, we observe that the curve of the equation crosses the x-axis at

x = -0.085

This means that the solution for x in the equation is x = -0.085

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Answer:

[tex]\large\boxed{\textsf{x=3}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to find the value of x.}[/tex]

[tex]\textsf{Notice that we have Intersecting Chords inside of the circle.}[/tex]

[tex]\large\underline{\textsf{What are Chords?}}[/tex]

[tex]\textsf{Chords are line segments that have endpoints on the circumference of a circle.}[/tex]

[tex]\textsf{Note that some Chords can be Diameters, but not for this problem. There's no Center.}[/tex]

[tex]\textsf{These Chords don't create Perpendicular Lines, which means the angles aren't equal.}[/tex]

[tex]\textsf{We can identify the unknown angles with a postulate.}[/tex]

[tex]\large\underline{\textsf{What is a Postulate?}}[/tex]

[tex]\textsf{A Postulate is a statement that can never be false. No matter what, it's always}[/tex]

[tex]\textsf{true.}[/tex]

[tex]\textsf{We can use the Linear Pair Postulate to find the needed angle.}[/tex]

[tex]\large\underline{\textsf{What is the Linear Pair Postulate?}}[/tex]

[tex]\textsf{Linear Pair Postulate is a Postulate that proves 2 angles add up to 180}^{\circ}.[/tex]

[tex]\textsf{A Linear Pair is 2 Adjacent Angles that form a Straight Angle.}[/tex]

[tex]\large\underline{\textsf{For our Problem;}}[/tex]

[tex]\tt \angle HLJ \ and \ \angle ILJ \ are \ Linear \ Pairs.[/tex]

[tex]\large\underline{\textsf{Find} \ \angle \textsf{HLJ;}}[/tex]

[tex]\tt \angle HLJ + \angle ILJ = 180^{\circ}.[/tex]

[tex]\tt \angle HLJ + 85.5^{\circ} = 180^{\circ}.[/tex]

[tex]\underline{\textsf{Subtract 85.5 from both sides of the equation;}}[/tex]

[tex]\tt \angle HLJ = 94.5^{\circ}[/tex]

[tex]\textsf{Now that we have} \tt \ \angle HLJ, \textsf{we can find x.}[/tex]

[tex]\textsf{We are given 2 arc measures and we have 2 Intersecting Chords.}[/tex]

[tex]\textsf{We should use} \tt \ \angle HLJ \ \textsf{to find x.}[/tex]

[tex]\large\underline{\textsf{How?}}[/tex]

[tex]\textsf{The Angle is equal to half the sum of the 2 arcs.}[/tex]

[tex]\underline{\textsf{For our Problem;}}[/tex]

[tex]\tt \angle HJL = \frac{1}{2} (42x-6 + 15x+24)[/tex]

[tex]\tt 94.5^{\circ} = \frac{1}{2} (42x-6 + 15x+24)[/tex]

[tex]\large\underline{\textsf{Solve;}}[/tex]

[tex]\textsf{Multiply each side by 2 first.}[/tex]

[tex]\tt 189^{\circ} = 42x-6 + 15x+24[/tex]

[tex]\underline{\textsf{Combine Like Terms;}}[/tex]

[tex]\tt 189^{\circ} = 57x+18[/tex]

[tex]\underline{\textsf{Subtract 18 from both sides;}}[/tex]

[tex]\tt 171^{\circ} = 57x[/tex]

[tex]\underline{\textsf{Divide each side by 57;}}[/tex]

[tex]\large\boxed{\textsf{x=3}}[/tex]

There are 1200 ways for the boy's mother to get 3 arcades and 2 sports games from his collection.

We can use the combination formula which is:

nCr = n! / (r! * (n-r)!)

where n is the total number of items, r is the number of items to choose, and ! denotes the factorial function.

In this case, we want to choose 3 arcade games and 2 sports games from a collection of 10 arcade games and 5 sports games. So, we have:

Number of ways to choose 3 arcade games from 10 arcade games = 10C3 = 120

Number of ways to choose 2 sports games from 5 sports games = 5C2 = 10

Therefore, the total number of ways to choose 3 arcade games and 2 sports games is:

120 * 10 = 1200

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Mrs. Rose receives the greater pay rise of £660 per year compared to Mrs. Patel's pay rise of £645.

To compare the pay rise for Mrs Patel and Mrs Rose, we need to calculate the actual amount of the pay rise for each of them.

For Mrs Patel, her pay rise is 2.5% of her current salary of £25,800:

Pay rise for Mrs Patel = 2.5% of £25,800 = £645

For Mrs. Rose, her pay rise is £55 per month, which is:

Pay rise for Mrs. Rose = £55 x 12 = £660 per year

Comparing the two pay rises, we see that Mrs. Rose receives a greater pay rise of £660 per year, compared to Mrs. Patel's pay rise of £645. Therefore, Mrs. Rose receives the greater pay rise.

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The coordinates of M, B, and D of a square with vertices A(-2,0) and C(6,4) where AC and BD diagonals intersect at M are M(2,2), B(6,-8), and D(-2,8), respectively.

To locate the coordinates of M, we will first find the midpoint of AC, which is also the middle of the square. The midpoint of AC is ((-2+6)/2, (0+4)/2), which simplifies to (2,2).

Hence, M is in the middle of the square. To locate the length of a side of the square, we are able to use the distance formula.

The distance between a and C is √((6-(-2))² + (4-0)²), which simplifies to √(64+16), that is 8. Accordingly, each side of the square has a length of 8. Given that M is in the middle of the square, we can use this truth to discover the coordinates of B and D.

Because B and D are on opposite sides of M, their x-coordinates and y-coordinates should differ via 8. Seeing that a is at (-2,0), B needs to be 8 units to the proper and 8 units down, so B is at (6, -8). Further, on the grounds that c is at (6,4), D should be 8 gadgets to the left and 8 units up, so d is at (-2, 8).

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Using Algebraic equations, the dimensions of the frame are 6in: 9 in.

The word "area" refers to a free space. A shape's length and width are used to compute its area. Unidimensional length is expressed in terms of feet (ft), yards (yd), inches (in), etc. But a shape's area is a two-dimensional measurement. Hence, it is expressed in square units such as square inches (in2), square feet (ft 2), square yards (yd2), etc.

Given, the area of the rectangular picture frame is 54 in².

length of the frame is 3 feet longer than the width,

Let us assume width = x

length of the frame will be = x + 3,

Area of rectangle = length × breadth

⇒ 54 = (x) (x + 3)

⇒ 54 = x² + 3x

Now, factorizing the given equation,

x² + 3x - 54

x² + 9x - 6x - 54

x(x + 9) -6 (x + 9)

(x + 9) (x - 6)

The value of x will be x = -9 and x = 6

As the negative length of the rectangle is not possible, we will consider, x = 6 and width = 9,

∴ The length of the rectangle = 6 inch,

Width of the rectangle will be = 6 + 3 = 9 inch.

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This program creates [tex]N=100000[/tex] trials in which [tex]n=100[/tex] coins are tossed, and it counts the trials in which precisely [tex]k=35[/tex] heads are thrown. This code's output will be the calculated probability of receiving [tex]35[/tex] heads.

It is based on the possibility that something will materialize. The fundamental underpinning of maximum possible is just the explanation of likelihood. For instance, while flipping a coin, there is a 12-percent probability that it will land on its head.

Determine the number of alternative ways to roll a 4 as well as multiply it by the overall number of outcomes to determine the likelihood of the event occurring.

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The cοrrect answer is Nο. The prices οf fοur-year-οld vehicles with a V6 and V8 engine vary greatly, depending οn the make and mοdel, mileage, and any additiοnal features.

An engine is a machine that cοnverts energy intο mechanical mοtiοn. It is a device that creates thrust οr pοwer thrοugh the cοnversiοn οf energy frοm fuel, such as gasοline, diesel, οr natural gas. Engines are used in a variety οf applicatiοns, such as in cars, bοats, planes, and electric generatοrs. They are alsο used in industrial machinery and manufacturing plants. Engines prοvide the pοwer that drives numerοus types οf transpοrtatiοn and prοductiοn.

Mοnica Rizzο's V6 fοur-dοοr sedan with a DVD player, leather seats, frοnt bucket seats, and pοwer sunrοοf but nο air cοnditiοning wοuld have an average retail value οf arοund $35,000. Kurt Sοrensen's V8 fοur-dοοr sedan with the same features, hοwever, wοuld have an average retail value οf arοund $58,400. The difference in value is largely due tο the V8 engine, which has mοre pοwer and thus requires mοre fuel. The additiοnal features alsο affect the value, but the engine is the biggest factοr.

Therefοre, Kurt Sοrensen will have tο pay significantly mοre fοr his V8 sedan than Mοnica Rizzο will have tο pay fοr her V6 sedan.

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