(x ^ 3 - 13x ^ 2 + 40x + 18)/(x - 3) pls solve this

The inflection point of f(t) is approximately t = 3.73.

(a) To determine if the function f(t) = -0.425t^3 + 4.758t^2 + 6.741t + 43.7 is increasing or decreasing, we need to find its derivative and examine its sign.

Taking the derivative of f(t), we have:

f'(t) = -1.275t^2 + 9.516t + 6.741

To determine the sign of f'(t), we need to find the critical points. Setting f'(t) = 0 and solving for t, we have:

-1.275t^2 + 9.516t + 6.741 = 0

Using the quadratic formula, we find two possible values for t:

t ≈ 0.94 and t ≈ 6.02

Next, we can test the intervals between these critical points to determine the sign of f'(t) and thus the increasing or decreasing behavior of f(t).

For t < 0.94, choose t = 0:

f'(0) = 6.741 > 0

For 0.94 < t < 6.02, choose t = 1:

f'(1) ≈ 14.982 > 0

For t > 6.02, choose t = 7:

f'(7) ≈ -5.325 < 0

From this analysis, we see that f(t) is increasing on the intervals (0, 0.94) and (6.02, ∞), and decreasing on the interval (0.94, 6.02).

(b) To find the inflection point of f(t), we need to find the points where the concavity changes. This occurs when the second derivative, f''(t), changes sign.

Taking the second derivative of f(t), we have:

f''(t) = -2.55t + 9.516

Setting f''(t) = 0 and solving for t, we find:

-2.55t + 9.516 = 0

t ≈ 3.73

Therefore, The inflection point of f(t) is approximately t = 3.73.

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Answer:

(-1,3)

Step-by-step explanation:

\( - x + 2 = 3x + 6\)

\( - x - 3x = 6 - 2\)

\( - 4x = 4\)

\(x = - 1\)

\(y = - ( - 1) + 2 = 3\)

Edward has 12 coins of the quarter and 8 coins of nickel with him

Total number of coins = 20

The total amount of money = $3.40

Let x represent the number of quarters and y represent the number of nickels

Formulating the equations we get:

x + y = 20-------(1)

0.25x + 0.05y = 3.40

Simplifying by removing the decimals and solving

25x + 5y = 340------(2)

Multiplying equation (1) by 5 and subtracting with equation (2) we get the following:

5x + 5y = 100

25x + 5y = 340

= 20x = 240

x = 12

So, y = 8

So, the number of quarters is 12 and the number of nickels is 8

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Answer:

1/4

Step-by-step explanation:

because you basically divided by two on

Answer:

1/4 is the answer mark me brainliest

Answer:

D & E

Step-by-step explanation:

The figures are parallelograms because their opposite sides are parallel

The figures are quadrilaterals because each had four sides

Answer:

D&E

Step-by-step explanation:

Edge 2021

Answer: 12.

Step-by-step explanation:

The parameters of the relevant standard beta distribution are alpha and beta.

These are two parameters that determine the shape of the beta distribution

.The standard beta distribution is a continuous probability distribution that is defined on the interval [0, 1]. It is often used to model the probability of success or failure in a binary experiment.

The two parameters of the standard beta distribution determine the shape of the distribution. Alpha is the shape parameter that determines the slope of the distribution, while beta is the shape parameter that determines the height of the distribution.

The standard beta distribution is often used in Bayesian statistics to model the prior probability of a parameter. It is also used in applications such as modeling the proportion of a population that has a particular characteristic or modeling the probability of default on a loan.

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Answer:

The common for the second question is 30

Answer:

39/30 Here 30 will be common in denominators

Step-by-step explanation:

6/15×2/2=12/30

3/10×3/3=9/30

3/5×6/6=18/30

= 12/30+9/30+18/30

39/30

The inequality which is used to represent normal "temperature-range" for  "human-body", is (d) |t − 98.6| ≤ 1.8.

The "average-temperature" of body is = 98.6° F, and it can vary by 1.8°F.

The inequality |t − 98.6| ≤ 1.8 indicates that the absolute difference between the body temperature and the average temperature is less than or equal to 1.8° F.

This means that the body temperature t can vary within a range of 1.8° F from the average temperature of 98.6° F.

Which means, the temperature cam range from :

⇒ 98.6-1.8 ≤ t ≤ 98.6+1.8,

⇒ 96.8 ≤ t ≤ 100.4;

Therefore, the correct inequality is (d) |t − 98.6| ≤ 1.8.

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The given question is incomplete, the complete question is

The average human body temperature is 98.6° F, but it can vary by as much as 1.8° F. Write an inequality to represent the normal temperature range of the human body, where t represents body temperature.

(a) |t − 1.8| ≥ 98.6

(b) |t − 1.8| ≤ 98.6

(c) |t − 98.6| ≥ 1.8

(d) |t − 98.6| ≤ 1.8

Answer: |t − 98.6| ≤ 1.8

Step-by-step explanation: If takes then takes then takes then takes then takes.

Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

Probability is the concept that describes the likelihood of an event occurring. In real life, we frequently have to make predictions about how things will turn out. We may be aware of the result of an occurrence or not. When this is the case, we refer to the likelihood that the event will occur or not.

Here,

X υ N (22,1)

Probability that  basketball  will weigh between 20.5 and 23.5

is:

=> P(20.5 < x < 23.5)= P[ 20.5-22/1 < z < 23.5-22/ 1   ]

=>   P(20.5 < x < 23.5) = P(-1.5 < z < 1.5)

=>  P(20.5 < x < 23.5) = 0.866

Therefore,  the probability that  basketball  will weigh between 20.5 and 23.5 is 0.866

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(a) shows that every pair of opposite sides in the hexagon a′b′c′d′e′f′ are parallel and equal in length. On the other hand, (b) demonstrates that the triangles a′c′e′ and b′d′f′ have equal areas.

(a) To show that every pair of opposite sides in hexagon a'b'c'd'e'f' are parallel and equal in length, we can use the fact that the centroids of triangles divide the medians into segments of equal length.

Let's consider a'b' and d'e'. The centroid of triangle fab, a', divides the median fb into two segments, a'f and a'b', such that a'f = 2/3 * fb. Similarly, the centroid of triangle def, e', divides the median de into two segments, e'd and e'f', such that e'd = 2/3 * de.

Since fb = de (opposite sides of hexagon abcdef), we have a'f = e'd. Now, we can consider the triangles a'f'd' and e'df'. By the properties of triangles, we know that if two sides of a triangle are equal, and the included angles are equal, then the triangles are congruent.

In this case, a'f' = e'd' (as shown above) and angle a'f'd' = angle e'df' (corresponding angles). Therefore, triangle a'f'd' is congruent to triangle e'df'.

By congruence, the corresponding sides a'd' and e'f' are equal in length.

By similar reasoning, we can show that b'c' and e'f', as well as c'd' and f'a', are parallel and equal in length.

(b) To show that triangles a'c'e' and b'd'f' have equal areas, we can use the fact that the area of a triangle is one-half the product of its base and height.

In triangle a'c'e', the base is c'e' and the height is the perpendicular distance from a' to c'e'. Similarly, in triangle b'd'f', the base is d'f' and the height is the perpendicular distance from b' to d'f'.

Since opposite sides in hexagon a'b'c'd'e'f' are parallel (as shown in part (a)), the perpendicular distance from a' to c'e' is equal to the perpendicular distance from b' to d'f'.

Therefore, the heights of triangles a'c'e' and b'd'f' are equal. Additionally, the bases c'e' and d'f' are equal (as shown in part (a)).

Using the area formula, area = 1/2 * base * height, we can see that the areas of triangles a'c'e' and b'd'f' are equal.

Hence, we have shown that triangles a'c'e' and b'd'f' have equal areas.

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Answer:

The weight in kilograms of a 150 pound person is 68.039 kg

Step-by-step explanation:

Weight = 150 pounds.

We need to convert this to kg,

Now, 1 pound = 0.453592 kg.

Then, 150 pounds will be,

150 pounds = 150(0.453592) kg

So, 150 pounds = 68.039 kg

The weight of a 150 pound person is approximately 68.04 kilograms.

To convert the weight of a person from pounds to kilograms, we can use the conversion factor of 1 pound = 0.4536 kilograms.

Given that the person weighs 150 pounds, we can multiply this value by the conversion factor to find the weight in kilograms:

Weight in kilograms = 150 pounds * 0.4536 kilograms/pound

Weight in kilograms = 68.04 kilograms

Therefore, the weight of a 150 pound person is approximately 68.04 kilograms.

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The constant average rate of change is the slope of the line which can be used to write the linear function.

What is a Data Table ?

A table of data is linear if there is a constant average rate of change between all pairs of points.

Testing for Linearity

Finding a Function from a Table that is Linear

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 ∠O  ≅  ∠U is third statement which is congruent .

What is congruent triangle?

ΔONP and ΔUTV are congruent .

By using ASA Theorem ,

                 NP ≅ TV

                ∠P  ≅  ∠V

                ∠O  ≅  ∠U

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Answer:

∠O  ≅  ∠U is third statement which is congruent .

Step-by-step explanation:

What is congruent triangle?

Two figures are said to be "congruent" if they can be placed perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other.

Congruent refers to having precisely the same form and size.

If all three sides of two triangles are the same, they are said to be congruent.

If we have a side, an angle between the sides, and then a second side that is congruent, we know they are congruent. In other words, side, angle, side.

ΔONP and ΔUTV are congruent .

By using ASA Theorem ,

                NP ≅ TV

               ∠P  ≅  ∠V

               ∠O  ≅  ∠U

BRAINLIST??

The net outward flux across the boundary of the tetrahedron is 5, using the concept of the gradient of a function.

The gradient  function in a vector field

The gradient function is related to a vector field and it is derived by using the vector operator ∇ to the scalar function f(x, y, z). The gradient is a fancy word for derivative or the rate of change of a function. It's a vector (a direction to move) that. Points in the direction of greatest increase of a function are zero at a local maximum or local minimum because there is no single direction of increase

Vector field:

F = ( -x, 3y, 2 z )

Δ . F = (i δ/δx + j δ/δy + k δ/δz) (-x, 3y, 2 z )

Δ . F = [δ/δx(-x)] + δ/δy (3y) + δ/δz (2z)]

Δ . F = - 1 + 3 + 2

Δ . F = 4

According to divergence theorem

Divergence Theorem

The divergence theorem states that the surface integral of the normal component of a vector point function F over a closed surface S is equal to the volume integral of the divergence. F  took over the volume V enclosed by the surface S. The divergence theorem says that when adding up all the little bits of outward flow in a volume using a triple integral of divergence, the total outward flow from that volume, as measured by the flux through its surface.

Flux =  ∫∫∫ Δ. (F) DV

x+ y +z = 1; so, 1st octant

x from 0 to 1

y from 0 to 1 -x

z from 0 to 1-x-y

∫₀¹∫₀¹⁻ˣ∫₀¹⁻ˣ⁻y (4) dz dy dx

= 4 ∫₀¹∫₀¹⁻ˣ (1 - x - y) by dx

= 5

Therefore, conclude that the net outward flux across the boundary of the tetrahedron is  5

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Answer:

$41.60

Step-by-step explanation:

5.30 *4= 21.20

6*3.80=20.40

20.40+21.20=41.60

Answer:

the period is the to top points of the highest points on top of the crests

The period of function is,

P = 5

Since, In order to find the period of a graph in general, first, find the period of the parent function, and divide that by the absolute value of the coefficient of the independent variable.

Here, Graph of function is shown.

Hence, The period of function is,

P = 10/2

P = 5

Because there is two wave are shown.

Therefore, The period of function is,

P = 5

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Answer:

y=3x+2

Step-by-step explanation:

I am in pre calculus I know how to do this.

Hi!

\(|15x+2|=8\\\\\\15x+2=8\\15x=8-2\\15x=6 \ \ |:15\\\boxed{x_1=0,4}\\\\\\15x+2=-8\\15x=-8-2\\15x=-10 \ \ |:15\\\boxed{x_2=-\frac{2}{3}}\)

Answer:

x = 2/5      x = -2/3

Step-by-step explanation:

|15x + 2 |= 8

There are two solutions, one positive and one negative

15x + 2 = 8  and 15x + 2 = -8

Subtract 2 from each side

15x + 2-2 = 8-2  and 15x + 2-2 = -8-2

15x = 6                             15x = -10

Divide by 15

15x/15 = 6/15                   15x /15 = -10/15

x = 2/5                               x = -2/3

Answer:

5/2

Step-by-step explanation:

Divide both sides by the same factor then simplify

Answer:

m=2.5

Step-by-step explanation:

10m=25

m=25/10

m=5/2

m=2.5

When E is the region bounded by the spheres then the answer to the triple integral is -π/2 (e⁻¹ - e⁻¹⁶)

To evaluate the triple integral using spherical coordinates, we need to express the volume element dV in terms of spherical coordinates and determine the limits of integration.

In spherical coordinates, the volume element dV is given by:

dV = ρ² sin(φ) dρ dφ dθ

where ρ represents the radial distance, φ represents the polar angle (measured from the positive z-axis), and θ represents the azimuthal angle (measured from the positive x-axis in the xy-plane).

The given region E is bounded by the spheres x² + y² + z² = 1 and x² + y² + z² = 16. These can be expressed in terms of ρ as:

1 ≤ ρ ≤ 4

To determine the limits of integration for φ and θ, we consider the spherical symmetry of the problem. Since the region is bounded by spheres, the limits for both φ and θ will be the full range of [0, π] and [0, 2π], respectively.

Now, let's evaluate the triple integral:

∭E e(-x² - y² - z²) / √(x² + y² + z²) dV

= ∫₀²π ∫₀ᴨ ∫₁⁴ e(-ρ²) / ρ ρ² sin(φ) dρ dφ dθ

= ∫₀²π ∫₀ᴨ ∫₁⁴ e(-ρ²) ρ sin(φ) dρ dφ dθ

Since the integrand does not depend on θ, we can simplify the triple integral:

= ∫₀²π ∫₀ᴨ [-e(-ρ²) cos(φ)]₁⁴ sin(φ) dφ dθ

= ∫₀²π [-e(-ρ²) cos(φ) sin(φ)]₁⁴ dθ

= ∫₀²π [-e(-ρ²) / 4] dθ

= -e(-ρ²) / 4 [θ]₀²π

= -e(-ρ²) / 4 (2π - 0)

= -π/2 (e(-ρ²))

Now, we need to evaluate this expression within the limits of ρ:

= -π/2 ∫₁⁴ e(-ρ²) dρ

To solve this integral, we can use the substitution u = -ρ², which gives du = -2ρ dρ. The limits of integration transform accordingly:

u = -1, u = -16

∫ eu du = eu [u]_{-1}{-16} = e⁻¹ - e⁻¹⁶

Please note that the above expression represents the numerical value of the triple integral.

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The first function is continuous everywhere in the complex plane. The second function is continuous everywhere except at z=0. The third function is continuous everywhere except at z=-2 and z=1.

The function z⁴ - 9z² + iz -2 is continuous everywhere in the complex plane.

The function z + 1/z² + 1 is continuous everywhere in the complex plane except at z = 0.

The function z² + 6x + 5/z² + 3z + 2 is continuous everywhere in the complex plane except at z = -2 and z = -1/3.

The function z⁴ + 1/Z² + 2z + 2 is continuous everywhere in the complex plane except at z = 0.

The function x + iy/x - 1 is continuous on the complex plane excluding the negative x-axis.

The function x + iy/|z| - 1 is continuous everywhere in the complex plane except at z = 0.

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Complete question is in the image attached below

The x-intercept of CD is 17.

Since CD is perpendicular to AB and passes through point C(5, 12), we can find the equation of CD using the slope-intercept form.

The slope of CD can be determined using the negative reciprocal of the slope of AB.

Slope of AB = (change in y) / (change in x) = (14 - (-3)) / (7 - (-10)) = 17 / 17 = 1

The negative reciprocal of 1 is -1. Therefore, the slope of CD is -1.

Using the slope-intercept form, we can write the equation of CD as:

y - y1 = m(x - x1),

where (x1, y1) is a point on CD. Let's use point C(5, 12):

y - 12 = -1(x - 5)

Simplifying the equation, we have:

y - 12 = -x + 5

y = -x + 17

To find the x-intercept, we set y = 0 and solve for x:

0 = -x + 17

x = 17

Therefore, the x-intercept of CD is 17.

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a) The equation expressing the total revenue in terms of the number of $1 price increases (x) is R(x) = (5000 - 100x)(30 + x).

b) There are restrictions on x. Since each $1 increase in ticket price leads to 100 fewer people attending, the number of people attending cannot be negative. Therefore, x must be limited to values where (5000 - 100x) is greater than or equal to zero. Solving this inequality gives x ≤ 50, meaning x cannot exceed 50. Additionally, it is not meaningful to have a negative number of price increases since we are considering the effect of increasing the ticket price.

c) To find the ticket price that maximizes revenue, we need to determine the value of x that maximizes the revenue function R(x). One way to do this is by finding the critical points of the revenue function. We can take the derivative of R(x) with respect to x and set it equal to zero to find the critical points. Differentiating R(x) = (5000 - 100x)(30 + x) with respect to x gives us R'(x) = -200x + 2000.

Setting R'(x) equal to zero and solving for x, we get -200x + 2000 = 0, which gives x = 10. So, the critical point is x = 10. To determine if this critical point is a maximum, we can check the second derivative of R(x). Taking the second derivative of R(x) gives us R''(x) = -200, which is a constant value. Since R''(x) is negative, the critical point x = 10 corresponds to a maximum revenue.

Therefore, the ticket price that maximizes revenue is obtained by taking the initial price of $30 and increasing it by $1 for 10 times, resulting in a ticket price of $40. At this price, the revenue will be maximized.

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A secant crosses the circle without passing through the center

The secant line is (c) line segment AB

From the question, we understand that line segment AB passes through the circle, without passing through the center (i.e. point A) of the circle

This indicates that line segment AB is a secant

Given that the center of the circle is point D

Hence, the secant line is (c) line segment AB

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Answer:

D. Line GH

Step-by-step explanation: I just did it on edge 2023. Hope this helps!

Answer:

Step-by-step explanation:

The "switch" statement is useful when you need to test a single variable against a series of exact integer, character, or string values.

The switch statement is a control structure found in many programming languages, including C++, Java, and JavaScript. It allows you to evaluate a variable or expression and compare it against multiple cases.

Each case represents a specific value that the variable or expression is tested against. When a match is found, the corresponding block of code associated with that case is executed.

The switch statement is particularly useful when you have a variable that can take on different values and you want to perform different actions based on those values. Instead of writing multiple if-else statements, the switch statement provides a more concise and efficient way to handle such scenarios.

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