Find ​f(−3​), ​f(0​) and ​f(1​) for the following function.
​f(x)=2x

Note that the limit of the expression as x approaches infinity is 1/2.

start by multiplying both the numerator and denominator by the conjugate  expression

√ (x ² - 9x + 1) + x,

this will eliminates the root in the numerator

lim x->∞ [(√(x ² - 9x + 1) - x)  * (√(x² - 9x + 1) + x)] / (√(x² - 9x + 1) + x)

Expanding the numerator

lim x- >∞ [(x² - 9x + 1) - x^2] / (√(x² - 9x + 1) + x)

Simplifying further:

lim x->∞ [(1 - 9/x + 1/ x²)] / (√(1 - 9/x + 1 /x²) + 1)

we can see that the 1/x ² term approaches zero, and the expression simplifies to

lim x->∞ [(1 - 0)]  / (√(1 - 0) + 1)

= 1/2

So it is correct to state that the limit of the expression as x approaches infinity is 1/2.

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Real-estate agent tested the effect of staging on home sale prices. Out of 10 comparable homes, 5 were staged. Staged homes sold for $15k more on average, with no skewness or outliers.

Based on the information given, the real-estate agent conducted an experiment to test the effect of selling a staged home vs. selling an empty home.

The hypothesis is that empty homes sell for lower prices than staged homes. The agent randomly assigned 5 empty homes to be staged and obtained a list of 10 comparable homes.

The mean selling price of the 5 empty homes was $150,000 with a standard deviation of $22,000. The mean selling price of the 5 staged homes was $175,000 with a standard deviation of 35,000. There was no strong skewness or outliers in the dot plots of the two samples.

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Starting at vertex A and using the nearest neighbor algorithm, the path is: A-C-B-D-A, with a total distance of 95. This means visiting vertices in the order A, C, B, D, and back to A, and the total distance traveled is 95 units.

The nearest neighbor algorithm is used to find the shortest path between a set of points. Here are the steps to apply the algorithm in this case

Start at vertex A. Look for the closest neighboring vertex to A. In this case, the closest vertex is B, which is 7 units away from A. Move to vertex B and mark it as visited. Look for the closest neighboring vertex to B that has not been visited. In this case, the closest vertex is C, which is 11 units away from B.

Move to vertex C and mark it as visited. Look for the closest neighboring vertex to C that has not been visited. In this case, the closest vertex is D, which is 18 units away from C. Move to vertex D and mark it as visited.

Look for the closest neighboring vertex to D that has not been visited. In this case, the closest vertex is B, which is 15 units away from D. Move to vertex B and mark it as visited.

Look for the closest neighboring vertex to B that has not been visited. In this case, the closest vertex is E, which is 20 units away from B. Move to vertex E and mark it as visited.

Look for the closest neighboring vertex to E that has not been visited. In this case, the closest vertex is A, which is 24 units away from E. Move to vertex A and mark it as visited. All vertices have been visited, so the algorithm is complete.

The list of vertices visited, starting and ending at A, is A, B, C, D, B, E, A and the distance is 95.

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Answer:

Step-by-step explanation:

To estimate the monthly cost of electric, gas, and water utilities as 0.1% of the price of your house, you can multiply the price of your house by 0.001. For example, if the price of your house is $300,000, then the estimated monthly cost of these utilities would be $300,000 * 0.001 = $300.

It’s important to note that this is just an estimate and the actual cost of these utilities can vary depending on factors such as the size of your house, the number of people living in it, and your usage habits.

A principal of $1,380.89 will earn $55.99 interest at 9.75% from February 4, 2021, to July 6, 2021.

To calculate the interest earned by a principal at a given interest rate over a certain period of time, we use the following formula:

Interest = Principal x Rate x Time

In this case, we need to find the principal, so we can rearrange the formula as follows:

Principal = Interest / (Rate x Time)

First, we need to calculate the time period in years between February 4, 2021, and July 6, 2021.

February 4, 2021 to July 6, 2021 is 152 days or approximately 0.416 years (calculated as (July 6, 2021 - February 4, 2021) / 365).

Principal = 55.99 / (0.0975 x 0.416) = $1,380.89 (rounded to the nearest cent)

Therefore, a principal of $1,380.89 will earn $55.99 interest at 9.75% from February 4, 2021, to July 6, 2021.

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(a) The domain of f of g is {1, 8}.

(b) The range of f of g is {0, 1}.

The domain of f of g consists of all the inputs in the domain of g that are also in the domain of f.

(a) Domain of f of g:

The inputs in the domain of g that are also in the domain of f are 1, and 8. Therefore, the domain of f of g is {1, 8}.

To find the range of f of g, we need to apply the function composition f(g(x)) to each input in the domain of f of g, and collect all the outputs.

(b) Range of f of g:

The range of f of g consists of all the outputs obtained by applying f(g(x)) to each input in the domain of f of g.

We have:

f(g(1)) = f(8) = 0

f(g(4)) = f(2) = 1

f(g(8)) = f(0) = 1

Therefore, the range of f of g is {0, 1}.

Thus, in set notation, the domain of f of g is {1, 8}, and the range of f of g is {0, 1}.

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The measure of angle U = 41.83 degree.

In the given right angle triangle

VW = 6

UV = 9

Since sinΘ  = (opposite side)/(hypotenuse)

Therefore,

sin U = VW/UV

        = 6/9

        = 0.667

Take inverse of sin both sides

     ∠U =  arcsin(0.667)

            = 41.83

Hence  ∠U = 41.83 degree

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After Cami cut 17¹/₂ inches of a rope that was 50 inches long, the length of the remaining rope in inches, written in decimal form, is 32.5 inches.

To determine the remaining length of the rope, we apply subtraction operation.

However, since the cut rope was expressed in fractions, we can convert it to decimals before the subtraction.

The total length of the rope = 50 inches

The cut portion of the rope = 17¹/₂ inches

The remaining portion = 32¹/₂ inches or 32.5 inches (50 - 17¹/₂)

Thus, the remaining portion of the rope after Cami cut 17¹/₂ inches is 32.5 inches.

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The height and radius that minimize the amount of material needed to manufacture the can are both approximately 6.39 cm.

The total surface area of the can is therefore:

A = 2πr² + 2πrh

We know that the volume of the can is 810 cm³, which is given by:

V = πr²h

We can solve this equation for h to get:

h = V/(πr²)

Substituting this expression for height h into the equation for the surface area, we get:

A = 2πr² + 2πr(V/(πr²))

Simplifying, we get:

A = 2πr² + 2V/r

Now we have an equation for the surface area of the can in terms of the radius, r.

To minimize the surface area, we need to take the derivative of this equation with respect to r, set it equal to zero, and solve for r.

dA/dr = 4πr - 2V/r² = 0

Solving for radius r, we get:

[tex]r = (810/\pi)^1^/^3[/tex]

r=∛810/3.14

r=6.35 cm

Now find h:

h = 810/πr²

h=810/3.14×6.35²

h=810/126.6

h=6.39 cm

Hence, the height and radius that minimize the amount of material needed to manufacture the can are both approximately 6.39 cm.

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The graph that shows the solution set for the given inequality is the one in option B.

Here we want to identify the graph of the inequality:

|x| ≤ 3

So, the absolute value of x is smaller or equal to 3, that means that the graph of the solution set is a segment whose endpoints are closed circles at x = -3 and x = 3.

(We use closed circles because these values are also solutions for the inequality).

With that in mind, we can see that the correct option in this case will be graph B.

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Note that  the following probability as a simplified fraction and as a decimal is:  0.88617886178 and 109/123

Note that the key phrase here is “given that this person is a man.”

This means that all we are interested in is the row labeled Male.

           Married      Never      Div       Widowed    Total

Male    69                  40       11                   3           123    

We are asked to find the probability that the person was either Married or Never. So the fraction you want is (69 + 40) / 123.

⇒ (69 + 40) / 123.

⇒ 109/123

or 0.886179

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Express the following probability as a simplified fraction and a decimal.

if one person is selected from the population described in the table, find the probability that the person has never been married or is married, given that this person is a man.

  Married  Never Married  Divorced   Widowed   Total

Male    69    40     11     3     123

Female  67    33     20     5     125

Total    136    73     31     8     248

Question 1.Express the probability as a simplified fraction

Answer: The function given is f(x) = (x^2 + 8x + 7)/(x + 1).

The domain of a function is the set of all possible input values for which the function is defined. In this case, the function f(x) is defined for all real numbers except for x = -1, because division by zero is undefined in mathematics. Therefore, the domain of f(x) is all real numbers except x = -1, or in interval notation: (-∞, -1) ∪ (-1, ∞).

The range of a function is the set of all possible output values that the function can produce. For this rational function, the range depends on the behavior of the function as x approaches positive and negative infinity. As x approaches positive or negative infinity, the function f(x) approaches 0, because the highest power of x in the numerator (x^2) and the highest power of x in the denominator (x) have the same degree, and their coefficients (1 in the numerator and 1 in the denominator) are equal. Therefore, the range of f(x) is all real numbers except 0, or in interval notation: (-∞, 0) ∪ (0, ∞). Note that f(x) never actually equals 0, because the function is defined for all real numbers except x = -1. However, it can arbitrarily approach 0 as x approaches positive or negative infinity. So, 0 is excluded from the range. Therefore, the correct answer is: Range = (-∞, 0) ∪ (0, ∞). Note that the range is expressed in interval notation, which uses parentheses to indicate open intervals (excluding the endpoints) and the union symbol (∪) to indicate the combination of two or more sets. In this case, the range consists of all real numbers except 0, expressed as two separate open intervals. The domain is also expressed in interval notation, with the union symbol (∪) used to indicate the combination of two disjoint sets. In this case, the domain consists of all real numbers except -1, expressed as the union of two separate intervals. So, the final answer is: Domain = (-∞, -1) ∪ (-1, ∞) and Range = (-∞, 0) ∪ (0, ∞). I hope this helps! Let me know if you have any further questions. I am here to help! Keep in mind that if you need to use the function f(x) in a real-world context, you should also consider any additional restrictions or conditions that may apply. It's always important to carefully analyze the properties of a function in the context of the problem you are trying to solve.

Step-by-step explanation:

a. To create an exponential model for new cases in terms of days, we can use the formula: y = a * b ^ x, where y is the number of new cases, x is the number of days since the first observation, and a and b are constants that we need to determine. Using the two data points given, we can set up a system of equations:

235 = a * b ^ 0

395 = a * b ^ 10

Solving for a and b, we get:

a = 235

b = (395/235)^(1/10) = 1.067

Therefore, the exponential model for new cases in Milwaukee is:

y = 235 * 1.067 ^ x

b. To find the number of new cases on Oct. 31, 2020, we need to plug in x = 19 (since Oct. 31 is 19 days after Oct. 12) into the model:

y = 235 * 1.067 ^ 19 = 1018.5

Therefore, based on the exponential model, we would expect around 1019 new cases on Oct. 31, 2020.

c. The actual number of new cases on Oct. 31, 2020, was 1043. This is higher than the predicted value of 1019, but not by a huge margin. Overall, the model seems to fit the data reasonably well, especially considering that there are many factors that can affect the number of new cases in a given area, and that the model is based on only two data points. However, it is worth noting that the exponential model assumes that the growth rate of new cases remains constant over time, which may not be a realistic assumption in the long run.

The weights of the debt, preferred stock, and common equity financing are 28.6%, 30.4%, and 41.0%, respectively.

To calculate the weighted cost of capital (WACC), the proportion of each component of capital structure is needed. The weight of each component of the capital structure is determined by dividing the market value of the component by the total market value of all the components of the capital structure.

In this case, the total market value of the company's capital structure is the sum of the market value of debt, preferred stock, and common equity.

The weights for each component are calculated as follows:

Weight of debt = Market value of debt / Total market value of capital structure

= $3.3 million / ($3.3 million + $3.5 million + $4.3 million)

= 0.286 or 28.6%

Weight of preferred stock = Market value of preferred stock / Total market value of capital structure

= $3.5 million / ($3.3 million + $3.5 million + $4.3 million)

= 0.304 or 30.4%

Weight of common equity = Market value of common equity / Total market value of capital structure

= $4.3 million / ($3.3 million + $3.5 million + $4.3 million)

= 0.410 or 41.0%

These weights can be used to calculate the weighted cost of capital for Romero Company.

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Answer: D

Step-by-step explanation: it equals 181

To find out how many total miles Mario swam in the first week of training, we need to add up the distances he swam each time:

3/5 + 3/5 + 3/5 + 9/10 + 9/10 + 23/25 + 23/25

To add these fractions, we need to find a common denominator. The smallest common multiple of 5, 10, and 25 is 50.

3/5 = 30/50

9/10 = 45/50

23/25 = 46/50

Now we can add the fractions:

30/50 + 30/50 + 30/50 + 45/50 + 45/50 + 46/50 + 46/50

= (30 + 30 + 30 + 45 + 45 + 46 + 46)/50

= 272/50

= 5.44

Therefore, Mario swam a total of 5.44 miles in the first week of training.

The calculations of the down payments, monthly income or payments are as follows:

Part 1:

Annual income = $226,000

Federal Tax = $62,582

State Tax = $16,385

Local Tax = $5,537

Healthcare = $4,520

Yearly income = $136,976

Monthly income = $11,414.67.

Part 2:

Down payment = $150,000

The amount to borrow (Mortgage loan) = $600,000

Estimated interest = $810,000

Total installment payments = $1,410,000

Monthly payment = $3,916.67.

Part 3:

Down payment = $2,902.50

Mortgage loan = $16,447.50

Estimated interest = $3,700.69

Interest + Mortgage loan = $20,148.19

Monthly payment = $335.80.

Part 1:

Annual income = $226,000

Federal Tax:

25% of $89,350 = $22,337.50

28% of $97,000 = $27,160.00

33% of $39,650 = $13,084.50

Total federal tax = $62,582

State Tax = 7.25% of $226,000 = $16,385

Local Tax = 2.45% of $226,000 = $5,537

Healthcare = 2% of $226,000 = $4,520

f) Total of Federal, State, Local, and Healthcare = $89,024

Yearly income = $136,976 ($226,000 - $89,024)

Monthly income = $11,414.67 ($136,976 ÷ 12)

Part 2:

a) House price = $750,000

b) Down payment = 20%

= $150,000 ($750,000 x 20%)

c) Mortgage loan = $600,000 ($750,000 - $150,000)

d) Interest rate = 4.5%

Number of mortgage years = 30 years

Mortgage period in months = 360 months (30 x 12)

Estimated interest = $810,000 ($600,000 x 4.5% x 30)

Interest + Mortgage loan = $1,410,000 ($600,000 + $810,000)

Monthly payment = $3,916.67 ($1,410,000 ÷ 360)

Part 3:

Price of car = $19,350

Down payment = 15%

= $2,902.50 ($19,350 x 15%)

Mortgage loan = $16,447.50 ($19,350 - $2,902.50)

Number of years = 5 years

Mortgage period in months = 60 months (5 x 12)

Estimated interest = $3,700.69 ($16,447.50 x 4.5% x 5)

Interest + Mortgage loan = $20,148.19 ($16,447.50 + $3,700.69)

Monthly payment = $335.80 ($20,148.19 ÷ 60)

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Answer:

2y - 3> 9 it is not y + 6< 10

The distance between the two lines is about 6/√17 units, which is approximately 1.46 units

To find the distance between two parallel lines, we need to find the length of the perpendicular segment that connects them.

Both lines have the same slope (4), so they are parallel and never intersect.

The shortest distance between them will be the perpendicular distance between any point on one line and the other line.

Let's choose a point on the first line, say (0, -1), and find the perpendicular distance from this point to the second line.

We can use the formula for the distance between a point (x₁, y₁) and a line in slope-intercept form y = mx + b:

Distance = |m(x₁) - y₁+ b| /√m² + 1

Plugging in the values for the second line, we get:

Distance = |4(0) - (-1) + 5| / √4² + 1

Distance = 6 / sqrt(17)

Therefore, the distance between the two lines is about 6/√17 units, which is approximately 1.46 units

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Answer:

The answer to the question provided is option 2.

According to the graph, the function that best describes the graph is

[tex]f(x)=|x| = \left\{ \begin{array}{cl}x - 2 \text{ for x \lt -3 } \\8 \text{ for -3 \lt x \lt 5}\\-x + 10 \text{ for x \gt 6}\end{array} \right.[/tex]
(option d).

As we all know that the term function is defined as a rule or relationship that maps each element in one set, called the domain, to exactly one element in another set, called the range.

While we looking into the graph we have identified that there is a straight line that cross the point (0, 8) within the range of -3 to 5.

And then the next line is moves downwards from the range of x whose value is greater than 6.

Final upward slope is moves the range of -3 or less While we looking into these range value we have identified that the the function that refers the graph is (option d).

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Answer:  To determine if the relationship between x and y is linear, we need to graph the data and look for a straight-line pattern.

If the graph shows a straight-line pattern, then the relationship is linear. If the graph shows a curve or a non-linear pattern, then the relationship is not linear. So it is linear

Step-by-step explanation: can i get brainliest :D

Answer:

$162.01

Step-by-step explanation:

amount of money she earns: 12($18.50) = $222

spends $59.99

amount of money after her purchase: $222-$59.99=$162.01

Answer:

[tex]\Large \boxed{(5x - 1)(x + 3)}[/tex]

Step-by-step explanation:

To factor the expression [tex] {5x}^{2} + 14x - 3 [/tex], we need to find two numbers that multiply to give the coefficient of [tex] {x}^{2} [/tex] (which is 5)

And add up to give the coefficient of x (which is 14).

These two numbers are 5 and 3. We can then rewrite the expression as follows:

[tex]\boxed{{5x}^{2} + 14x - 3 = (5x - 1)(x + 3)}[/tex].

Therefore, the factored form of the expression is [tex](5x - 1)(x + 3)[/tex]

Answer:

Step-by-step explanation:

6x² - 10x + 21x - 35 = 6x² + 11x - 35

6x² - 6x² + 11x - 11x - 35 + 35 = 0

0 = 0

The equation is an identity. Its solution set is {all real numbers}.

The vertical shift and vertical shrink of the exponential function are 2 and 1/2 respectively and the graph of the function is attached below

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The vertical shift and vertical shrink of the function f(x) = 1/2(4 - eˣ) are 2 and 1/2

The vertical shift = 2

vertical shrink = 1/2

Kindly find the attached graph below

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Carolyn will need 15 square units of carpet to cover her front room. Carolyn will need 16 units of skirting board to go around the sides of her front room.

To find the area of Carolyn's front room, we need to multiply the length by the width. In this case, the dimensions are given as 5 x 3, so the area is:

Area = length x width = 5 x 3 = 15 square units

To find the perimeter of the room, we need to add up the lengths of all four sides. Since the room is rectangular, opposite sides are of equal length. So, we can find the perimeter by adding twice the length and twice the width, which gives:

Perimeter = 2(length + width) = 2(5 + 3) = 16 units

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Answer: the answer is f

Step-by-step explanation:

Answer:

answer is f

Step-by-step explanation: