It’s asking to Examine the relation h(x) defined at right. Then to estimate the values

a. h(1)
b. h(3)
c. x when h(x)=0
d. h(-1)
e. h(-4)

Answer:

800 m^2

Step-by-step explanation:

= 1250 - 450

= 800 m^2 est la superficie de la terre de M. Vergne

j'espère que ma réponse t'aidera.

Answer:

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Average speed equation:

Substitute 350 for d and 5.15 for t:

The average speed must be approximately 68 km per hour.

Step-by-step explanation:

Let's verify

\(\\ \tt{:}\leadsto - \frac{1 }{3} x + 6 = - 6 + \frac{2}{3} x \\ \\ \tt{:}\leadsto 6 + 6 = \frac{2}{3} x + \frac{1}{3} x \\ \\ \tt{:}\leadsto 36 = \frac{3}{3} x \\ \\ \tt{:}\leadsto 36 = x\)

1. y = 1/2x: This function represents a straight line with a slope of 1/2.

2. y = 1/2^(x^2) + 4: This function represents an exponential decay.

3. y = 4^(x^2) + 1/2: This function represents exponential growth.

4.  y = 4(1/2)^x: This function represents an exponential decay with a different base.

The table of values you provided includes four different equations, each with a different expression for y. To analyze this table, we need to look at the different values of x and y that result from each equation.

1. y = 1/2x:
This function represents a straight line with a slope of 1/2. As the value of x increases, the value of y increases by half as much. In this case, as x increases, y increases at a slower rate. For example, when x = 2, y = 1, but when x = 4, y = 2. This suggests that the equation represents a linear relationship between x and y, where the value of y increases by a constant factor (in this case, 1/2) for each unit increase in x.

2. y = 1/2^(x^2) + 4:
This function represents an exponential decay. As the value of x increases, the value of y approaches 4, but never actually reaches it due to the exponential decay term (1/2(x2)). Here, as x increases, y decreases rapidly. For example, when x = 2, y = 1/20.25, but when x = 4, y = 1/273. This suggests that the equation represents an exponential relationship between x and y, where the value of y decreases exponentially as x increases.

3. y = 4^(x^2) + 1/2:
This function represents exponential growth. As the value of x increases, the value of y grows rapidly due to the exponential growth term (4(x2)). The function is shifted upward by 1/2. It exhibits a similar exponential relationship, but in this case, y increases rapidly as x increases. For example, when x = 2, y = 64.5, but when x = 4, y = 421.5. This suggests that the equation represents an exponential relationship between x and y, where the value of y increases exponentially as x increases.

4. y = 4(1/2)^x:
This function represents an exponential decay with a different base. As the value of x increases, the value of y decreases due to the exponential decay term (1/2)x. The function is multiplied by a factor of 4. It represents another exponential relationship where y increases rapidly as x increases. For example, when x = 2, y = 8, but when x = 4, y = 32. This suggests that the equation represents an exponential relationship between x and y, where the value of y increases exponentially as x increases.

By analyzing each function, we can understand how the value of y changes based on the value of x. This helps us identify the overall behavior and trends of each function.

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20,000 = 1750 e^(0.6t)

Divide both sides by 1750:

11.43 = e^(0.6t)

Take the natural log of both sides:

ln(11.43) = 0.6t

Divide both sides by 0.6:

t ≈ 6 years

So it will take approximately 6 years (rounded to the nearest year) for the town's population to reach 20,000.
To find the number of years it takes for the population to reach 20,000, we need to solve the equation for t, using the given equation:

20,000 = 1750 * e^(0.6 * t)

Step 1: Divide both sides of the equation by 1750:
20,000 / 1750 ≈ 11.43 = e^(0.6 * t)

Step 2: Take the natural logarithm (ln) of both sides:
ln(11.43) ≈ 2.435 ≈ 0.6 * t

Step 3: Divide both sides by 0.6 to isolate t:
2.435 / 0.6 ≈ t

Step 4: Calculate t:
t ≈ 4.06

Approximately, it will take 4 years (rounded to the nearest year) for the town's population to reach 20,000.

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The utility functions in options a, b, c, and f are not risk-averse on the interval [a,b], while the utility functions in options d and e are risk-averse on the interval [a,b].

In economics and finance, risk aversion refers to a preference for less risky options over riskier ones. Utility functions are mathematical representations of an individual's preferences, and they help determine whether someone is risk-averse, risk-neutral, or risk-seeking. A risk-averse individual would have a concave utility function, indicating a decreasing marginal utility of wealth.

For options a, b, c, and f, the utility functions are and f(x) = -ln(x), g(x) = \(-e^(^-^x^)\), h(x) = \(-4x^2\) - 10x, respectively. These utility functions do not exhibit concavity, which means they are not risk-averse. Instead, they either show risk-seeking behavior (options a and b) or risk-neutrality (options c and f).

On the other hand, options d and e have utility functions f(x) = ln(x), g(x) = 1/(e^(2x)), h(x) = \(-x^2\) + 10,000x and f(x) = ln(-2x), g(x) = -1/(\(e^(^2^x^)\)), h(x) = \(x^2\) - 100,000x, respectively. These utility functions display concavity, indicating a decreasing marginal utility of wealth. Thus, options d and e can be considered risk-averse on the interval [a,b].

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Answer:

Step-by-step explanation:

The rate of change is the slope of the line formed by connecting the two data points:

1.  (2010,1510). and   [enrollment for a school in 2010 was 1510 students]

2.  (2020, 860)         [In 2020, the enrollment was 860 students]

Slope is the Rise/Run of the line.  Lets go from the first point to the second.

The Rise:  (1510 - 860) = 650

The Run:   (2020-2010) = 10

The slope, or rate of change, is = 65

The interpretation is that "The enrollment at the school increase by an average of 65 students every year since 2010 until 2020."

The largest rectangle that fits into the triangle with sides x=0, y=0, and x=4, y=6 has an area of 24 square units.

The coordinates of the vertices of the triangle are given by;

x=0 ⇒ (0, 0)

y=0 ⇒ (0, 0)

x=4 ⇒ (4, 0)

y=6 ⇒ (0, 6)

The base of the rectangle will be parallel to the x-axis and the height of the rectangle will be parallel to the y-axis. The vertices will lie along the sides of the triangle with lengths 4 and 6.

The area of the largest rectangle is base × height

where;

base (b) = 4

height (h) = 6

By substituting the values of (b) and (h) in the equation, we get;

Area of the rectangle = 4 × 6

⇒ 24 square units.

Therefore, the largest rectangle that fits into the given triangle has an area of 24 sq. units.

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Answer: B

y=3/5 x +4

Step-by-step explanation:

Insert each equasion into the graph with the points from the table and whichever line , lines up with the points is your answer

Answer:

Step-by-step explanation:

p(x) = 8x^2 is an increasing exponential curbed graph which starts from quadrant 2 , passes through the point (0, 8)  on the y axis and rises steeply to the right.

g(x) = x^2 is a parabola ( shaped like a U) which has a minimum value at (0, 0).

and opens upwards either side of the y-axis. This type of curve is called a parabola.

Answer:

I'm thinking that -3 is the y-intercept since it's the only number without an exponent and it's not being raised to anything. Maybe?

Answer:

b 2，3，8

Step-by-step explanation:

Y=234678

Z=278910

X=12358

234678910 n 12358

=238

Answer:

1090

Step-by-step explanation:

I can't write the final answer in exponential form.

Answer:

Step-by-step explanation:

How I got 1090 was because..

You just do 109 times 10

So you will get your answer.

Hope this helps! <3

The sum of the squares of the differences between each data value and the mean is equal to Sum=828

we have that

the mean is 33

so

Fill the table

15 (15-33)=-18 (15-33)^2=324

27 (27-33)=-6 (27-33)^2=36

28 (28-33)=-5 (28-33)^2=25

34 (34-33)=1 (34-33)^2=1

42 (42-33)=9 (42-33)^2=81

52 (52-33)=19 (52-33)^2=361

therefore

The sum of the squares of the differences between each data value and the mean is equal to

Sum=324+36+25+1+81+361

Sum=828

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So, when x = 4, y = 2, and dx/dt = 3, dy/dt = -8/3. we need to use the chain rule and implicit differentiation,

(a) If x = 4 and y = 2, we can substitute these values into the equation 4x^2 + 9y^2 = 100 to get:4(4)^2 + 9(2)^2 = 100 .

Simplifying, we get: 16 + 36 = 100, This is not true, so there is no solution for when x = 4 and y = 2. (b) To find dy/dt when x = -4 and y = 2 and dx/dt = 3, we first need to differentiate both sides of the equation 4x^2 + 9y^2 = 100 implicitly with respect to t: d/dt (4x^2 + 9y^2) = d/dt (100) .

Using the chain rule, we get: 8x (dx/dt) + 18y (dy/dt) = 0, We can substitute the given values to get: 8(-4) (3) + 18(2) (dy/dt) = 0, Simplifying, we get:
-96 + 36(dy/dt) = 0

Adding 96 to both sides and dividing by 36, we get:
dy/dt = 96/36
Simplifying, we get:
dy/dt = 8/3


Given the equation 4x^2 + 9y^2 = 100, where x and y are functions of t, let's find dy/dt when x = 4, y = 2, and dx/dt = 3.
First, differentiate both sides of the equation with respect to t:
8x(dx/dt) + 18y(dy/dt) = 0

Now, plug in the given values (x = 4, y = 2, and dx/dt = 3):
8(4)(3) + 18(2)(dy/dt) = 0,

Solve for dy/dt: 96 + 36(dy/dt) = 0

Divide by 36:
(dy/dt) = -96/36, Simplify: (dy/dt) = -8/3, So, when x = 4, y = 2, and dx/dt = 3, dy/dt = -8/3.

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The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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Answer: To apply l'Hospital's Rule, we need to take the derivative of the numerator and denominator separately with respect to θ.

Taking the derivative of the numerator:

d/dθ [1 - sin(θ)] = -cos(θ)

Taking the derivative of the denominator:

d/dθ [1 + cos(6θ)] = -6 sin(6θ)

Now we can apply l'Hospital's Rule by taking the limit of the ratio of the derivatives:

lim θ→π/2 (-cos(θ)) / (-6 sin(6θ))

When θ approaches π/2, cos(θ) approaches 0 and sin(6θ) approaches 1. Therefore, the limit simplifies to:

= 0 / (-6)

= 0

Hence, the limit of (1 - sin(θ)) / (1 + cos(6θ)) as θ approaches π/2 is 0.

Answer:

0.7 km per minute , -0.17 km per minute

Step-by-step explanation:

The computation of the average speed is shown below

As we know that

Average speed = Total distance ÷ total time

= (4 + 2 + 1) ÷ (32 + 22 + 16)

= 0.7 km per minute

Now the velocity is

= Change in displacement ÷ change in time

= (4 - 2 - 1) ÷ (32 -22 -16)

= 1 ÷ -6

= - 0.17km per minute

Answer:

4 4/7 is the answer

Answer:

4 4/7

Step-by-step explanation:

(2 2/3)(1 5/7) = 4 4/7

Richard's net pay for the week, considering Social Security, Medicare, and FIT deductions, can be calculated by subtracting the total deductions from his gross earnings.

First, let's determine the amount deducted for Social Security. The Social Security rate is 6.2%, and the maximum earnings subject to this deduction are $118,500. Since Richard is $1,000 below the maximum level, the amount subject to Social Security deduction is $1,000. Therefore, the Social Security deduction is 6.2% of $1,000.

Next, we calculate the Medicare deduction. The Medicare rate is 1.45%, and it is applied to the entire earnings of $1,700.

To calculate the FIT deduction, we need additional information about Richard's taxable income, tax brackets, and exemptions. Without this information, we cannot provide an accurate calculation for the FIT deduction.

Finally, we subtract the total deductions (Social Security, Medicare, and FIT) from Richard's gross earnings of $1,700 to obtain his net pay for the week.

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When t is equal to 14(π/3) in the function r(t) = sin(t), the corresponding output value is √3/2.

In mathematics, functions play a crucial role in describing relationships between variables. One type of function is the trigonometric function, which deals with the properties and relationships of angles.

In this problem, we are given a trigonometric function r(t) = sin(t) and asked to find the value of r(14)(π/3).

The function r(t) = sin(t) represents a sine function, where t is the input variable (in this case, representing time) and r(t) is the corresponding output. The sine function, denoted by sin(t), calculates the ratio of the length of the side opposite a given angle in a right triangle to the hypotenuse. However, in this context, we are dealing with the unit circle, where the x and y coordinates of a point on the circle correspond to the sine and cosine values of the angle, respectively.

To find r(14)(π/3), we need to substitute 14(π/3) into the function

r(t) = sin(t).

Step 1: Multiply 14 by π/3:

14(π/3) = (14π)/3

Step 2: Substitute the result into the function:

r(14)(π/3) = sin((14π)/3)

At this point, we have the expression sin((14π)/3), which represents the value of the sine function at an angle of (14π)/3.

To evaluate sin((14π)/3), we can use the properties of the sine function and the unit circle. In the unit circle, the x-coordinate of a point on the circle corresponds to the sine value of the angle.

Step 3: Simplify the angle:

(14π)/3 = (12π)/3 + (2π)/3 = 4π + (2π)/3

Step 4: Find an equivalent angle within the unit circle:

To find an equivalent angle within the unit circle, we need to subtract or add full revolutions (2π) until the angle falls within the range [0, 2π].

In this case, 4π is equivalent to 2 full revolutions (2π) since it takes us back to the same point on the unit circle.

Thus, we can simplify the angle to (2π)/3.

Step 5: Evaluate the sine function at (2π)/3:

To find the sine value at (2π)/3, we can refer to the unit circle. At (2π)/3, the x-coordinate of the corresponding point on the unit circle is √3/2.

Therefore, r(14)(π/3) = sin((14π)/3) = sin((2π)/3) = √3/2.

After evaluating the given expression, we find that r(14)(π/3) = √3/2. This means that when t is equal to 14(π/3) in the function r(t) = sin(t), the corresponding output value is √3/2.

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Answer:

2 x 2 x 2 x 2 x 3.

Step-by-step explanation:

The number 48 expressed as a product of its prime factors is 2 x 2 x 2 x 2 x 3.

Answer:

2 x 2 x 2 x 2 x 3.

Step-by-step explanation:

^^^

The process that generates more values that are more than 2 standard deviations from the mean is called a "fat-tailed" distribution.

In a fat-tailed distribution, the probability of extreme values occurring is higher compared to a normal distribution.

To understand this concept, let's consider two processes: Process A and Process B.

Process A generates a dataset with a normal distribution, while Process B generates a dataset with a fat-tailed distribution.

In a normal distribution, the majority of the data falls close to the mean, with fewer values farther away.

The probability of values more than 2 standard deviations from the mean is relatively low.

On the other hand, in a fat-tailed distribution, there is a higher likelihood of extreme values occurring.

This means that the probability of values more than 2 standard deviations from the mean is higher.

For example, let's say we have two datasets: Dataset A generated by Process A and Dataset B generated by Process B.

We calculate the mean and standard deviation for both datasets.

In Dataset A, if the mean is 50 and the standard deviation is 5, then values more than 2 standard deviations away from the mean would be greater than 60 or less than 40.

In Dataset B, if the mean is 50 and the standard deviation is also 5, then values more than 2 standard deviations away from the mean would have a wider range.

These values could be significantly higher than 60 or lower than 40, depending on the specific distribution of Dataset B.

Therefore, if Process B generates a fat-tailed distribution, it is more likely to produce values that are more than 2 standard deviations from the mean compared to Process A and its normal distribution.

In summary, the process that generates more values that are more than 2 standard deviations from the mean is a fat-tailed distribution, which has a higher likelihood of extreme values occurring.

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Answer: -1/18 im pretty sure

Step-by-step explanation: Find the exact value using trigonometric identities.

Answer:

The slope is -2 and the y-intercept is 4.

The given graph consists of two parabolas. One is an upward opening parabola that decreases from (-3, 4) to a minimum at (-1, 0) and then increases to (1, 4). The equation of such a parabola is f(x) = -x^2 + 2x + 1. The other is a downward opening parabola that increases from (-2, -3) to a maximum at (0, 1) and then decreases through (2, -3). The equation of such a parabola is g(x) = x^2 + 1.

Therefore, the set of systems of equations that represents the solution to the graph is:

f(x) = -x^2 + 2x + 1

g(x) = x^2 + 1