If f(x) = (3+x)/(x-3)
what is f(a + 2)?

The local minimum value of the function f(x) = \(x^{5}\) + 5\(x^{4}\)+ 10\(x^{2}\) - 1 occurs at x = -1, with a value of -6. The local maximum value of the function occurs at x = 0, with a value of -1. As x approaches negative or positive infinity, the function increases without bound, and as x approaches negative or positive infinity, the function decreases without bound.

To find the local minimum and maximum values of the function, we can take the derivative of the function and set it equal to zero to find the critical points. Taking the derivative of f(x) with respect to x gives us f'(x) = 5\(x^{4}\)+ 20\(x^{3}\) + 20x. Setting f'(x) equal to zero and solving for x, we find that x = -1 and x = 0 are the critical points.

To determine whether these critical points are local minimum or maximum points, we can use the second derivative test. Taking the second derivative of f(x) gives us f''(x) = 20\(x^{3}\) + 60\(x^{2}\)+ 20. Evaluating f''(x) at x = -1 and x = 0, we find that f''(-1) = 100 and f''(0) = 20. Since f''(-1) > 0 and f''(0) > 0, we can conclude that x = -1 is a local minimum and x = 0 is a local maximum.

Therefore, the local minimum value of the function f(x) = \(x^{5}\) + 5\(x^{4}\) + 10\(x^{2}\) - 1 is -6 at x = -1, and the local maximum value is -1 at x = 0. The function increases without bound as x approaches negative or positive infinity, and it decreases without bound as x approaches negative or positive infinity.

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The exponential function that best models this data is given as follows:

C. y = 80(0.75)^x + 20.

An exponential function, considering it's asymptote, is defined as follows:

y = a(b)^x + c.

In which the parameters are given as follows:

From the graph, the horizontal asymptote is at y = 20, hence the parameter c is defined as follows:

c = 20.

When x = 0, y = 100, hence the parameter a is obtained as follows:

100 = a(b)^0 + 20

a + 20 = 100

a = 80.

When x = 5, y = 40, hence the parameter b is obtained as follows:

40 = 80b^5 + 20

80b^5 = 20

b^5 = 1/4

b = (1/4)^(1/5)

b = 0.75. (approximately).

Hence the function is defined as follows:

y = 80(0.75)^x + 20.

Meaning that the correct option is given by option C.

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Answer:

-5a+a

= -4a

Step-by-step explanation:

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Approximately 95% of housing prices are between a low price of $164,000 and a high price of $192,000.

To determine the range of housing prices between which approximately 95% of prices fall, we can use the empirical rule, also known as the 68-95-99.7 rule. According to this rule, for a normal distribution:

- Approximately 68% of the data falls within one standard deviation of the mean.

- Approximately 95% of the data falls within two standard deviations of the mean.

- Approximately 99.7% of the data falls within three standard deviations of the mean.

In this case, the mean housing price is $178,000, and the standard deviation is $7,000. To find the low and high prices within which approximately 95% of the housing prices fall, we can apply the empirical rule.

First, we calculate one standard deviation:

Standard deviation = $7,000

Next, we calculate two standard deviations:

Two standard deviations = 2 * $7,000 = $14,000

To find the low price, we subtract two standard deviations from the mean:

Low price = $178,000 - $14,000 = $164,000

To find the high price, we add two standard deviations to the mean:

High price = $178,000 + $14,000 = $192,000

Therefore, approximately 95% of housing prices are between a low price of $164,000 and a high price of $192,000.

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The distribution of the given function is a uniform distribution.

A strictly increasing function is the one which increases continuously in a given interval. If f-1(u) is a strictly increasing function of u, then the distribution of f-1(u) is the same as that of u. This is because a strictly increasing function preserves the rank ordering of its input, so if u-1 and u-2 are two random variables with a uniform distribution on the interval (0,1), then the rank order of f-1(u-1) and f-1(u-2) will be the same as the rank order of u-1 and u-2. Since the uniform distribution is defined by the rank order of its values, this means that the distribution of f-1(u) is also uniform on the interval (0,1).

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The probability to answer 5 questions correctly from 14 true or false questions is 0.1222

The given situation represents a binomial experiment, where there are only two possible outcomes for each trial: success (answering correctly) and failure (answering incorrectly). To find the probability of a particular number of successes, we use the binomial probability formula:

P(x)= nCx × p^x × q^(n-x)

Where, n is the total number of trials, p is the probability of success on each trial, q is the probability of failure on each trial (1-p), and x is the number of successes desired.

n = 14 (total number of questions)

p = 1/2 (probability of answering correctly when guessing randomly), and q = 1/2 (probability of answering incorrectly when guessing randomly).

To find P(5), we substitute these values in the formula

P(5) = 14C5 * (1/2)^5 * (1/2)^9= 2002 * (1/32) * (1/512)= 2002 / 16384≈ 0.1222

Therefore, the answer is option D, 0.1222.

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Answer:

Step-by-step explanation:

Add the 21 then divide by 2

Answer:

x = 16, x = -7

Step-by-step explanation:

The question is;

35 * 4 = ( x - 7 ) ( x - 3 )

Combine like terms on one side;

140 = ( x - 7 ) ( x - 3 )

Distribute, remember to multiply every term with one another;

140 = \(x^{2}\) - 3x - 7x + 21

Combine like terms;

140 = \(x^{2}\) - 10x + 21

Inverse operations;

140 = \(x^{2}\) - 10x + 21

-21                  -21

119 = \(x^{2}\) - 10x

Factor;

119 = x ( x - 10 )

At this point it is fairly obvious that;

x = 16, x = -7

Note; One could have used a multitude of methods to solve this problem, one could have factored, completed the square, or used the quadratic formula, this method was simply chosen because it is easy to explain

Option (b) is correct that the y-intercept in a regression equation is not represented by Y hat. Here, we will discuss the concept of the y-intercept, regression equation, and Y hat.

Regression analysis is a statistical tool used to analyze the relationship between two or more variables. It helps us to predict the value of one variable based on another variable's value. A regression line is a straight line that represents the relationship between two variables.

Thus, Y hat is the predicted value of Y. It's calculated using the following formulary.

hat = a + bx

Here, Y hat represents the predicted value of Y for a given value of x. In conclusion, the y-intercept is not represented by Y hat. The y-intercept is represented by the constant term in the regression equation, while Y hat is the predicted value of Y.

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Answer:

Plugged this into my calculator and got this

cos 75 = 0.2588190451

under the restrictions that c is negative to ensure strict concavity, the utility function u(w) = -(b - w)c displays increasing absolute risk aversion.

To ensure that u(w) is strictly increasing, we need the derivative of u(w) with respect to w to be positive for all values of w. Taking the derivative, we have du(w)/dw = -c. For u(w) to be strictly increasing, -c must be positive, which implies c must be negative.

To ensure that u(w) is strictly concave, we need the second derivative of u(w) with respect to w to be negative for all values of w. Taking the second derivative, we have d²u(w)/dw² = 0. Since the second derivative is constant and negative, u(w) is strictly concave.

Now, let's examine the concept of increasing absolute risk aversion. If a utility function u(w) exhibits increasing absolute risk aversion, it means that as wealth (w) increases, the individual becomes more risk-averse.

In the given utility function u(w) = -(b - w)c, when c is negative (as required for strict concavity), the absolute risk aversion increases as wealth (w) increases. This is because the negative sign implies that the utility function is concave, indicating that the individual becomes more risk-averse as wealth increases.

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Answer:

Step-by-step explanation:

Well, all we have to do is square 12.

= \(12^{2}\)

= 12 x 12

= 144

The total square footage of the room is 144 feet.

I am not sure if this answer is correct, so please tell me if I am wrong. I hope this answer helped you! :)

Answer:

Step-by-step explanation:

Point M being midpoint of AB means:

\(x_M-x_A=x_B - x_M\qquad\quad\ \wedge\qquad y_M-y_A=y_B - y_M\\\\ 3-(-1)=x_B-3\qquad\wedge\qquad 0-4=y_B -0\\\\ {}\qquad x_B=7\qquad\qquad\wedge\qquad\qquad \ y_B=-4\)

Answer:

Quadrant 1

Step-by-step explanation:

The number of gallons of water sprayed after x minutes would never be negative, nor would time be negative, so the first quadrant would be all that you need

F

1) For variables like these, we most often use the mean that will compute all data points (in this case, the number of jobs a person had throughout his life ) for a central tendency measure.

2) Examining the options, then we can state that the answer is: F

and that is the answer.

To find the probability that at least 2 of the comments are positive, we can use the concept of complementary probability. We'll find the probability that fewer than 2 comments are positive and then subtract it from 1 to get the desired probability.

Let's consider the following scenarios:

1. No comments are positive (all 10 comments are negative).

2. Exactly 1 comment is positive.

Let's calculate the probability of each scenario:

1. Probability of no comments being positive:

P(No positive comments) = (0.9)^10 = 0.3487 (rounded to four decimal places)

2. Probability of exactly 1 comment being positive:

P(Exactly 1 positive comment) = 10 * (0.1)^1 * (0.9)^9 ≈ 0.3874 (rounded to four decimal places)

To find the probability that at least 2 comments are positive, we subtract the sum of the above probabilities from 1:

P(At least 2 positive comments) = 1 - P(No positive comments) - P(Exactly 1 positive comment)

                             = 1 - 0.3487 - 0.3874

                             ≈ 0.2639 (rounded to four decimal places)

Therefore, the probability that at least 2 of the comments are positive is approximately 0.2639 or 26.39%

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Awnser: 4. 4/8 simplified=1/2 6/8 simplified=3/4.

Answer:

c

Step-by-step explanation:

i got irt right on the test

From the given set of statements, the conjecture which represent the inductive reasoning are given by :

a. Given : Everyone dressed casually on Friday

Conjecture : All Fridays are casual days.

c. Given : WXYZ is a rectangle.

Conjecture : WX = YZ and WZ = XY

d. All donuts are unhealthy.

Conjecture : This chocolate donut is unhealthy.

As given in the question,

Inductive reasoning is the conclusion which is based on the process of observed pattern.

Given set of statements represents the inductive reasoning or not:

a. Given : Everyone dressed casually on Friday

Conjecture : All Fridays are casual days.

From observing pattern based on Friday dressing we conclude all Fridays are casual days.

Represent inductive reasoning.

b. Given : 3a² = 48

Conjecture : a = 6

Here we cannot observe the process , we have to show the calculation.

Not representing inductive reasoning.

c. Given : WXYZ is a rectangle.

Conjecture : WX = YZ and WZ = XY

From observing pattern based on property of rectangle it is concluded that WX = YZ and WZ = XY.

Represent inductive reasoning.

d. All donuts are unhealthy.

Conjecture : This chocolate donut is unhealthy.

From observing pattern based on all donuts property it is concluded that   chocolate donuts is also unhealthy.

Represent inductive reasoning.

Therefore, from the given set of statements, the conjecture which represent the inductive reasoning are given by :

a. Given : Everyone dressed casually on Friday

Conjecture : All Fridays are casual days.

c. Given : WXYZ is a rectangle.

Conjecture : WX = YZ and WZ = XY

d. All donuts are unhealthy.

Conjecture : This chocolate donut is unhealthy.

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A woman purchased a total of 50 yams, some costing 40 naira each and others costing 50 naira each.  The total amount spent on the yams was 2200 naira. The task is to determine the number of yams purchased at each price.

Let's assume the number of yams purchased at 40 naira each is 'x' and the number of yams purchased at 50 naira each is 'y.'  The total number of yams purchased is given as 50, so we have the equation x + y = 50. Additionally, the total amount spent on the yams is 2200 naira, which can be expressed as 40x + 50y = 2200. By solving this system of equations simultaneously, we can find the values of 'x' and 'y,' representing the number of yams purchased at each price.  The solution will provide the specific quantities of yams bought at 40 naira and 50 naira, respectively, satisfying both the total number of yams and the total amount spent.

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Answer

7560

Step-by-step explanation:

42* 60= 2520

2520* 3= 7560

The height of flying after 3 minutes will be 7560 meters.

The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall, and the difference between the abscissa is called run.

If an airplane rises at a rate of 42 meters per second.

Slope = 42 meters per second

Then the height of flying after 3 minutes will be

⇒ 42 meters per second x 3 minutes

⇒ 42 meters per second x 3 x 60 seconds

⇒ 7560 meters

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Answer:

8

Step-by-step explanation:

.13 times 8 = 1.04

The bar height for the price range of less than $5,000 will increase by 200.

In the given histogram, the x-axis represents the car prices ranging from $0 to $40,000, while the y-axis represents the number of cars sold over 10 years, ranging from 0 to 700.

Based on the provided information, we can observe that between the price ranges of $20,000 and $30,000, the bar height exceeds the maximum y-axis value of 700. Similarly, between the price ranges of $5,000 and $10,000, and $40,000 and $45,000, the bar height is indicated as 200.

If the car salesman decides to include cars with prices less than $5,000 and projects selling 200 of them over the next 10 years, the distribution will be affected as follows:

The bar representing the price range of less than $5,000 will increase in height by 200, indicating the projected sale of those additional cars. This means that the histogram will show a higher number of cars sold in the lower price range, reflecting the demand from students and the inclusion of more affordable cars in the sales strategy. This modification will result in a redistribution of the bars, with an additional bar added to represent the projected sales of cars below $5,000.

Overall, the distribution in the histogram will be affected by an increase in the bar height for the price range of less than $5,000 by 200 units, indicating the projected sale of those additional affordable cars over the next 10 years.

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Answer:

\( {x}^{2} + x - 2\)

Step-by-step explanation:

\(p(x)=x^2+2x-5 \: and \: q(x)=x-3 \\ \\ p(x) - q(x) \\ \\ = x^2+2x-5 - (x - 3) \\ \\ = x^2+2x-5 - x + 3 \\ \\ = {x}^{2} + 2x - x + 3 - 5 \\ \\ p(x) - q(x) = {x}^{2} + x - 2\)

Answer:c

Step-by-step explanation:

It is already in the simplest form.

Answer: 7e-5 millimeters, and the nanometer scale is more appropriate

Step-by-step explanation: PLEASE MARK ME BRAINLIEST!!!!!!

-divide the length value by 1e+6

-The millimeter scale and the centimeter scale are two huge, while the nanometer scale is too small. The nanometer scale is often used to measure atoms and viruses.

Answer:

a) The length of the virus in millimetres is 0.000 07 mm.

b) Viruses are microscopic and so nanometres are the more appropriate unit for writing the length of the virus since the nanometre is a smaller unit of measurement than the millimetre.

Step-by-step explanation:

SI is the abbreviation for The International System of Units.

The SI base unit for length is metres (m).

Milli and nano are SI prefixes used to form decimal multiples or submultiples of SI units.

Therefore, to convert nanometres to millimetres, multiply the nanometres by 10⁻⁶:

So 70 nanometres is:

Viruses are microscopic and so nanometres are the more appropriate unit for writing the length of the virus since the nanometre is a smaller unit of measurement than the millimetre.

The dimensions are 3 inches, 10 inches, and 13 inches.

It should be noted that the diagonal is the longest side. This will be solved by using Pythagoras theorem.

Therefore,

(2x + 6)²

4x²+ 24x + 36

Reduce to lowest term

x² + 6x + 9

x² + 3x + 3x + 9

x(x + 3) - 3(x + 3)

(x - 3) = 0

x = 0 + 3 = 3

Therefore x = 3

Therefore the dimensions will be:

x = 3

2x + 4 = 2(3) + 4 = 10

2x + 6 = 2(3) + 6 = 12

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Answer:

35%

Step-by-step explanation:

The price it cost the site to buy the grills was $580 but they were selling them for $783. So for each grill, they get a profit of $203. (783-580=203).

35% of $580 is 203 which adds up to $783

So therefore the markup rate is 35% I hope this helps!

If an area of the circle is 200.96 cm^2 , then the circumference of the same circle is approximately around 28.28 cm^2.

The formula for the area of a circle is given by:

A = πr^2,

where A is the area and r is the radius of the circle.

To find the circumference of a circle, we can use the formula:

C = 2πr,

where C is the circumference and r is the radius.

To solve for the circumference, we first need to find the radius of the circle. We can use the formula for the area to find the radius:

A = πr^2

200 = πr^2

r^2 = 200 / π

r = √(200 / π)

Next, we can substitute the value of r into the formula for the circumference to find the circumference:

C = 2πr

C = 2π * √200 / π)

C = 2 * √(200)

Approximating √(200) to 14.14, we get:

C ≈ 2 * 14.14 = 28.28

So the approximate circumference of a circle with an area of 200 square cm is 28.28 square cm.

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Answer:

#1 is A #2 is A

Step-by-step explanation: