Suppose that f'(x) > 0 for all x € R. Let g(x) = f(2x-x2) for all € R. Then on [3, 5],
(a) g(3) is the min and g(5) is the max value
(b) g(3) is the max and g(5) is the min value
(d) g(xo) is the min value of g for some 3 < xo <5
(c) g(uo) is the max value of g for some 3 < uo < 5
(e) none of these

Answer:

700,000, 100+80+2, 9,000

The integral of f(x,y,z)=8xz over the region in the first octant (x,y,z≥0) above the parabolic cylinder \(z=y^{2}\) and below the paraboloid \(z=8-2x^{2} -y^{2}\) is 128/9.

The first step is to find the bounds of integration. The region in the first octant (x,y,z≥0) is bounded by the planes x=0, y=0, and z=0.

The parabolic cylinder z=y2 is bounded by the planes x=0 and \(z=y^{2}\). The paraboloid \(z=8-2x^{2} -y^{2}\) is bounded by the planes x=0, y=0, and z=8.

The next step is to set up the integral. The integral is:

\(\int\limits {0^{1} } \int\limits {0^{\sqrt{x} } }\int\limits {y^{8}-2x^{2} -y^{2} 8xzdxdy\)

We can evaluate the integral by integrating with respect to z first. The integral with respect to z is:

\(8x^{2} (8-2x^{2}-y^{2} )-8xy^{2} -y^{8} -2x^{2} -y^{2}\)

Simplifying this expression, we get the equation:

\(8x^{2} (8-2x^{2}-y^{2} )-8xy^{2}\)

We can now integrate with respect to x. The integral with respect to x is:

\(4(8-2x^{2}-y^{2} )^{2} -4xy^{2}-0^1\)

Simplifying this expression, we get the equation:

\(4(8-2x^{2}-y^{2} )^{2} -4xy^{2}\)

We can now integrate with respect to y. The integral with respect to y is:

\(4\frac{(8-2-y)^{3} }{3} -4y^{3} -0^1\)

Simplifying this expression, we get the equation:

\(\frac{128}{9}\)

Therefore, the integral of f(x,y,z)=8xz over the region in the first octant (x,y,z≥0) above the parabolic cylinder \(z=y^{2}\) and below the paraboloid \(z=8-2x^{2} -y^{2}\) is \(\frac{128}{9}\).

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It is not possible to find the triangular formula of a pentagon because a pentagon is a polygon with five sides and does not have a triangular formula.

We have,

A triangular formula is used to calculate the area of a triangle, which is a polygon with three sides.

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

Area = 1/2 x base x height

where the base and height are two of the sides of the triangle.

If you want to calculate the area of a pentagon, you can use the formula for the area of a regular pentagon, which is given by:

Area = (5/4) x s² x tan(π/5)

where s is the length of one of the sides of the Pentagon.

Thus,

It is not possible to find the triangular formula of a pentagon because a pentagon is a polygon with five sides and does not have a triangular formula.

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Answer:

Pounds of candy      Cost ($)       Cost/pound

1                                  $3                $3/1                                                  

3                                 $9                $3/1                                      

7                                 $21               $3/1                                                          

10                               $30              $3/1                                                      

As a result, 12 is the exponential expression employing a rational exponent.

An exponent of a fraction or rational number is said to have a rational exponent. With x as the base, p as the power, and q as the root 21, it may be represented as x(p/q). It can be transformed into the corresponding radical form,

for example, x(p/q) = (x(1/q))p = qxp 21. Similar rules apply to rational exponents and integer exponents 1.

With a rational exponent, the expression 3√24 can be expressed exponentially as follows:

3√2⁴= 3(2²)

= 3(2²) = 12

As a result, 12 is the exponential expression employing a rational exponent.

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Answer:

15

Step-by-step explanation:

mean means add all the numbers and divide them by how many there are

plot 1: 63 divided by 9 equals 7

plot 2: 330 divided by 15 equals 22

so now we need to subtract 22 minus 7 equals 15

hope this helps

Answer:

15

Step-by-step explanation: you have to add all of the numbers and then divide the answer by the number of numers you added

Answer:

yooo anythingg

Step-by-step explanation:

Answer:your answer will be afdhbgaefijhbaefljbhadfljvmbadflkjv

Step-by-step explanation: because monke

Answer:

First then second answer below

Step-by-step explanation:

-x+y 4

-1/-1=1      x=1    y=1  

y/1=1/1+4/1

y=1x+4

-x+7y 21

-1/-1=1

7y/7=1/7+21/7

y=1/7x+3

Answer:

$22.50....................

The value of x will be 6° according to the remaining angles values in the diagram.

What is a Triangle?

With three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object. A polygon also includes a triangle.

How are the sum of triangles calculated in a triangle?

In a triangle, the total interior angles are supplementary. In other words, the sum of a triangle's inner angle measurements is 180°. Hence, we can write the triangle sum theorem's formula as A + B + C = 180° for the triangle ABC.

Now according to the question

                          => 40+110+8x-18=180 (Theorem)

                          => 150+8x-18=180

                          => 8x=180-150+18

                          => 8x=48

                          => x=6°

The  value of x will be : 6°

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The approximate area of the trapezoid is determined as  13.95 unit².

The approximate area of the trapezoid is calculated as follows;

Area = ¹/₂(b₁ + b₂)h

Where;

The y-coordinates of the points on the curve at x=3/2 and x=4 is calculated as follows;

y(3/2) = - (3/2)²/2 + 3/2 + 5

y(3/2) = -9/8 + 3/2 + 5

y(3/2) = 5.375

y(4) = -4²/2 + 4 + 5

y(4) = -8 + 9

y(4) = 1

h = 5.375 - 1 = 4.375

The approximate area of the trapezoid is calculated as;

Area = ¹/₂(5.375 + 1) x 4.375

Area = 13.95 unit²

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Answer:

Step-by-step explanation:

This equation is in standard form and we need to change it to slope-intercept form which is y = mx + b

So 5x - 15y = 6 needs a bit of work to have the y all by itself on the left side.

First, take away 5x from both sides if the equation.

5x - 15y = 6

-5x -5x

-15y = 6 - 5x Don't lose the minus in front of the 15, also probably go ahead and rearrange the right side so the x term comes first

-15y = -5x + 6 Almost there!

Divide everything by -15

y = -5x/-15 + 6/-15

Simplify the fractions.

-5/-15 is the same as 1/3

and 6/-15 is the same as -2/5, so the equation ends up looking like this:

y = 1/3 x - 2/5

Just make sure the x doesn't go beside the 3 on the bottom of the fraction. The 1/3 should be beside the x or the x has to be on top of the fraction kind of like this:

y = x/3 - 2/5

the hourly growth rate parameter is approximately 0.0381, indicating that the population of bacteria is increasing by approximately 0.0381 per hour according to the continuous exponential growth model.

In this case, the initial population size A₀ is 3000 bacteria, the final population size A is 3622 bacteria, and the time period t is 6 hours. We want to find the growth rate parameter k.

Using the formula A = A₀ × \(e^(kt)\), we can rearrange the equation to solve for k:

k = (1/t) × ln(A/A₀)

Substituting the given values:

k = (1/6) × ln(3622/3000) ≈ 0.0381 per hour

Therefore, the hourly growth rate parameter is approximately 0.0381, indicating that the population of bacteria is increasing by approximately 0.0381 per hour according to the continuous exponential growth model.

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Answer: x < -6

Step-by-step explanation:

16 > -3x-2

18 > -3x

x < -6

(flip the sign because you are diving by a negative number.)

The slope of a function is defined as the change in y-coordinate with respect to the change in x-coordinate of the line.

m = Δy/Δx

∆y --> net change in the y coordinate

∆x ---> net change in x coordinate

m ---> slope of fution

The y-intercept of both functions 'f' and 'g' are equal and slope of f(x) is less than the slope of g(x). So, the correct option is option (A).

We have given a function, g (x) = 2x + 1

comparing the g(x) with standard equation

y = mx + b

where m is slope of this line

b --> y-intercept

Thus we get m = 2 , b= 1 . So, the slope of g(x) is 2 and y-intersecpt is 1 .

Now, we have a table for function f(x) that is function f(x) passing through all points as given in table. The slope of function passing through (h,k) and (a,b) is expressed as (k-b)/(h-a)

Thus, slope of function 'f' passing through (0,1) and (2,4) = (1-4)/(0-2) = -3/-2

= 3/2

=> f (x) = (3/2)x + b

where , b --> y-intercept

plug the value x= 4 and corresponding to it

f(x) = 7 we get , 7 = 3/2× 4 + b

=> b = 7-6 = 1

Therefore, slope of function g(x) is greater than slope of function f(x) and y-intercept of f(x) is equal to y-intercept g(x) .

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Complete question:

The Table represents the linear function f(x), and the equation represents the linear function g(x). Compare the y-intercepts and the slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.

x / f(x)

0/1

2/4

4/7

g(x)= 2x+1

A. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).

B. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).

C. The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).

D. The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).

Answer:60

Step-by-step explanation:

The 90% confidence interval for the proportion of lactose intolerant people in the population is (0.5746, 0.6947).Therefore, the correct option is (0.57464, 0.69468).

The proportion of lactose intolerant in the sample is 271/427 = 0.634. To construct a confidence interval, we need to use the formula:

Sample proportion ± Margin of errorwhere the margin of error is given by zα/2 times the standard error of the sample proportion.

Standard error of sample proportion is given by:sqrt(p*q/n), where p is the sample proportion, q = 1 - p, and n is the sample size.In this problem:p = 0.634, q = 1 - p = 0.366, and n = 427.

At 90% confidence level, α = 1 - 0.90 = 0.10, and since the confidence interval is two-sided,

we use the z-value corresponding to 0.05 in the z-table. This value is 1.645.Now we can calculate the margin of error as follows:Margin of error = 1.645 * sqrt(0.634*0.366/427) = 0.0573.

Thus, the confidence interval is:Sample proportion ± Margin of error = 0.634 ± 0.0573 = (0.5767, 0.6913)Rounding to four decimal places, the answer is (0.5746, 0.6947).

The 90% confidence interval for the proportion of lactose intolerant people in the population is (0.5746, 0.6947).Therefore, the correct option is (0.57464, 0.69468).

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Answer:

if am correct your answer will be letter d

Step-by-step explanation:

Answer:

what the other guy said you can make him brainliest now

Step-by-step explanation:

Classroom objects can be categorized as vertical or horizontal. Examples of vertical objects include doors, bookshelves, and clocks, while horizontal objects include desks, tables, and chairs.

In a classroom, there are many objects that are vertical and horizontal. Here are ten examples of each:

Vertical objects in a classroom:

1. Door                     6. Clock

2. Cabinet               7. Electrical outlets

3. Bookshelf            8. Light switches

4. Whiteboard         9. Window blinds

5. Flagpole             10. Bulletin board

Horizontal objects in a classroom:

1. Desks                  6. Keyboard trays

2. Chairs                 7. Carpet tiles

3. Tables                 8. Ceiling tiles

4. Countertops       9. Whiteboard markers

5. Shelves              10. Paper trays

These are just a few examples of vertical and horizontal objects that can be found in a classroom.

It is important to recognize the different shapes and orientations of objects in our environment, as they can affect the way we perceive and interact with them.

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Answer:

3 terms.

Step-by-step explanation:

Each term is separated by a symbol. +, -, =, etc.

All you must do is count the number of sequences between symbols.

You have 3 terms.

Brainliest appreciated!

Number of terms in polynomial 8c⁴ + 4c³ + 3c² is 3.

The correct option is D.

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms.

For example, in the expression 4x + y, the two terms are 4x and y.

Given polynomial,

8c⁴ + 4c³ + 3c²

Terms in the above polynomials are = 8c⁴, 4c³ and 3c²

Number of terms = 3

Hence, 3 terms are in polynomial 8c⁴ + 4c³ + 3c².

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Answer:

6

Step-by-step explanation:

The correct statement is: provided that the sample size is reasonably large (for any population).

The Central Limit Theorem states that, under certain conditions, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution.

These conditions include a random sample from the population and a sufficiently large sample size (typically, n > 30 is considered large enough).

Therefore, the Central Limit Theorem is important because it allows us to make inferences about the population mean using the normal distribution, even if we do not know the population distribution.

This is useful in many applications of statistics, including hypothesis testing, confidence intervals, and estimating population parameters

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The provided questions cover various aspects of a 2-period production economy, including the household's problem, firm's problem, market clearing conditions, Social Planner's Problem, competitive equilibrium, and welfare theorems.

(a) The Household's problem is to maximize its utility over two periods subject to its budget constraint. The household's problem can be formulated as follows:

Max U(Co, C1) = log(Co) + ß log(C1)

subject to the budget constraint:

Co + (1+r)C1 ≤ (1+r)Ko + W0 + W1,

where Co and C1 are consumption in period 0 and 1 respectively, ß is the discount factor, r is the interest rate, Ko is the initial capital endowment, W0 and W1 are the wages in periods 0 and 1 respectively.

(b) The Firm's problem is to maximize its profit by choosing the optimal combination of capital and labor. The firm's problem can be formulated as follows:

Maximize F(K, L) - RK - WL,

where F(K, L) is the production function, K is capital, L is labor, R is the rental rate of capital, and W is the wage rate.

(c) The market clearing conditions are:

Capital market clearing: K1 = (1 - δ)K0 + S - C0, where δ is the depreciation rate, S is savings, and C0 is consumption in period 0.

Labor market clearing: L = L0 + L1, where L0 and L1 are labor supplies in periods 0 and 1 respectively.

(d) The Social Planner's Problem is to maximize social welfare, which is the sum of the household's utility and the firm's profit. The Social Planner's Problem can be formulated as follows:

Maximize U(C0, C1) + F(K, L) - RK - WL,

subject to the production function F(K, L) and the market clearing conditions.

(e) A Competitive Equilibrium is a situation where all markets clear and agents (household and firm) make optimal decisions based on prices and market conditions. It is characterized by the following conditions:

Household's problem is solved optimally.

Firm's problem is solved optimally.

Market clearing conditions hold.

(f) To solve the Social Planner's Problem, we need to set up the Lagrangian and solve for the optimal values of consumption, capital, and labor. The Lagrangian can be written as:

L = U(C0, C1) + F(K, L) - RK - WL + λ1[(1+r)K0 + W0 + W1 - Co - (1+r)C1] + λ2[K1 - (1 - δ)K0 + S - C0] + λ3[L - L0 - L1],

where λ1, λ2, and λ3 are the Lagrange multipliers.

(g) To solve the Competitive Equilibrium, we need to determine the prices of capital (R) and labor (W) that clear the markets. This can be done by equating the demand and supply of capital and labor, and solving the resulting equations.

(h) The First Welfare Theorem states that under certain conditions, a competitive equilibrium is Pareto efficient. It implies that a competitive equilibrium is a socially optimal allocation of resources. To verify the theorem, we need to demonstrate that the competitive equilibrium allocation is Pareto efficient.

(i) The Second Welfare Theorem states that any Pareto efficient allocation can be achieved as a competitive equilibrium with appropriate redistribution of initial endowments.

To verify the theorem, we need to show that given an initial Pareto efficient allocation, we can find prices and redistribution of endowments that lead to a competitive equilibrium that achieves the same allocation.

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Answer:

https://brainly.com/question/6423861

Step-by-step explanation:

Use link and give me 5 stars and brainliest

Answer:

tan²x + tan x - 12 = 0 (1)

suppose: tan x = t

(1)=> t² + t - 12 = 0

a = 1    b = 1     c = -12

⇒ Δ = b² - 4ac = 1 + 48 = 49 > 0 => has 2 solutions

=> t = \(\frac{1+\sqrt{49} }{2}=\frac{8}{2}=4\)

or t = \(\frac{1-\sqrt{49} }{2}=\frac{-6}{2}= -3\)

because t = tan x => tan x = 4 or tan x = -3

because x ∈ [0;2pi) => with tan x = 4 => x = arctan(4)  or x = arctan(4) + pi

                                     with tan x = -3 => x = arctan(-3) + pi

Step-by-step explanation: