Rewrite this expression using the distributive property.
(3x2 + 4x-7)(x-2)

The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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Explanation:

3/6 = 1/2 of the numbers on the cube are even (2,4,6)

If we wanted both cubes to show an even number, then this comes up (1/2)*(1/2) = 1/4 of the time.

There are 6*6 = 36 outcomes total, so there are (1/4)*36 = 9 outcomes when both dice show an even number.

---------

Those nine outcomes are listed below

You probably have noticed that A has 3 choices (2,4,6) and so does B. That gives 3*3 = 9 outcomes total. This is an alternative pathway compared to the previous section.

The random walk with absorbing barriers on the set {0, 1, 2, 3, 4} can be represented as a Markov chain with a transition probability matrix. This chain is irreducible since it is possible to reach any state from any other state. By evaluating the probabilities and the corresponding states, we can find the expected value E(X5 | X3 = 1, X0 = 2) for the given random walk with absorbing barriers.

(a) The graphical diagram representing the random walk with absorbing barriers on {0, 1, 2, 3, 4} can be visualized as a directed graph. Each state is represented by a node, and the arrows indicate the transition probabilities between states according to the given transition probability matrix P.

(b) The chain is irreducible because it is possible to reach any state from any other state. Starting from any state, there is always a positive probability of transitioning to any other state, including the absorbing states (0 and 4). This means that the chain does not have any disjoint subsets of states that are unreachable from one another.

(c) To find E(X5 | X3 = 1, X0 = 2), we condition on the starting state X0 = 2 and the state at time step 3, X3 = 1. Given this condition, we can calculate the expected value of X5, which represents the expected state at time step 5.

To compute this expectation, we can use the Markov property, which states that the future behavior of the chain depends only on its current state. Since X3 = 1 is known, we only need to consider the possible transitions from state 1 to other states according to the transition probability matrix P. By following these transitions, we can calculate the probability of reaching each state at time step 5 and then compute the expected value of X5 accordingly.

By evaluating the probabilities and the corresponding states, we can find the expected value E(X5 | X3 = 1, X0 = 2) for the given random walk with absorbing barriers.

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The relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean is (b) The 95% C.I. is more precise in estimating a mean than the 90% C.I.

You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval.

The upper and lower numbers of a range with a 95% confidence interval (CI) of the mean are determined from a sample. This range describes potential possibilities for the mean because the actual population mean is unknown. Hence, the 95% C.I. is more precise in estimating a mean than the 90% C.I.

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The percent change in tuition at FSU from $85/credit hour to $147/credit hour is approximately 72.94%.

To calculate the percent change, you can use the formula:
Percent Change = [(New Value - Old Value) / Old Value] × 100
In this case, the old value is $85/credit hour and the new value is $147/credit hour.
Percent Change = [($147 - $85) / $85] × 100 = ($62 / $85) × 100 ≈ 72.94%

The tuition at FSU has increased by approximately 72.94% over the four-year period.

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Answer:

D. \(\displaystyle No\:Solution\)

Explanation:

The absolute value of an integer is NEVER negative, hence, your answer. ON THE OTHER HAND, these are the only exceptions:

\(\displaystyle -6 = -|3[-2]| \\ -6 = -|3[2]|\)

The negative absolute value of an integer however, IS negative.

I hope you are capable of differentiating between the two, and as always, I am joyous to assist anyone at any time.

Answer:

8 cups of water

Step-by-step explanation:

63/7=9

72/9=8

the least buckling load for the strut is determined by Euler's formula, which predicts a larger buckling load than the Rankine formula for the same boundary conditions and material properties. Therefore, for this situation, Euler's formula is preferable as it gives a more conservative estimate.

According to the Euler formula, the least buckling load (Pcr) of a column can be computed as

\(Pcr = π²EI / L²\)

where Pcr is the critical or least buckling load, E is the modulus of elasticity, I is the moment of inertia of the column cross-section about its axis of buckling, and L is the length of the column.

The strut's I cross-section has cross-sectional values of 610 x 229 x 113 (mm x mm x kg/mm).

Its weaker axis is its Z axis (i.e., the axis perpendicular to the 610 mm face) and its stronger axis is its Y axis (i.e., the axis perpendicular to the 229 mm face).

As a result, the moment of inertia of the strut about its weaker axis can be computed as

IZ = (610 x 229³) / 12 - (533 x 113³) / 12 = 6.47 x 10¹⁰ mm⁴

And the moment of inertia of the strut about its stronger axis isIY = (229 x 610³) / 12 = 9.35 x 10⁸ mm⁴

When the strut is pinned on both ends and buckles about its stronger axis, it has a buckling factor of 1/2 (as opposed to 1 for a fixed-fixed end strut).

As a result, the Rankine constant for a column that is fixed at both ends is 1/6400, so the Rankine constant for a column that is pinned at both ends is 1/4 of that, or 1/25600.

Using the same values as before and the Rankine formula, the least buckling load for the strut when buckling about its weaker axis is:

Pcr,z = (π² x 210 x 6.47 x 10¹⁰) / (10²)² x (1/25600) = 0.357 MN (to three significant figures)

And the least buckling load for the strut when buckling about its stronger axis is

:Pcr,y = (π² x 210 x 9.35 x 10⁸) / (10²)² x (1/25600) = 25.5 kN (to three significant figures)

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The type of error that explains the variability in the results between groups is "random error."Explanation:Random error is the variability between the groups' results due to the imprecision of the measuring instrument or technique.

It is caused by minor differences in the experimental conditions that are unpredictable and can not be controlled or accounted for in the experiment. Random error can lead to imprecise results that fluctuate from the main answer, which means that it is not biased towards one particular direction.The other type of error that is commonly known is "systematic error" which is characterized by consistent errors that occur in a specific direction due to the method or instrument used.

Systematic error is due to the inaccuracy of the measuring instrument or incorrect experimental design, and it can affect the accuracy of the main answer. Mistakes or human errors, on the other hand, are due to human error, such as incorrect calculations or transcriptions, and are not part of the sources of errors.

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A posted speed limit of 55 mph means that: You may drive 55 mph only under favorable conditions.

Speed limits on road traffic, as used basically to set the legal maximum speed at which vehicles are permitted to utilize on a given stretch of road.

Now generally, speed limits are normally indicated on traffic signs reflecting the maximum allowable speed in kilometers per hour (km/h) or eevn miles per hour (mph). They are primarily set by the legislative bodies of national or provincial governments and then enforced by law enforcement agencies. This suggests that speed limits varies from road to road and is even absent in some certain areas.

Now, in this question we are told that the posted speed limit is 55 mph. Thus, from our definitions of speed limits above it is clear that A posted speed limit of 55 mph means that: You may drive 55 mph only under favorable conditions.

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Answer:

Step-by-step explanation:

Attached are the formula. (Ignore the point slope formula not needed)

For second part, just know that m= slope and b = y intercept in the slope-intercept formula. Just plug those in for each of those, I will do one for you and you try the rest ok

Slope = 1/3 and y-intercept = -1

Slope intercept formula is y = mx + b

y = 1/3 x + (-1)

y= 1/3 x -1

Now you try the rest.

The inequality that satisfies the number of hours of volunteer work that saul could complete each month to meet his goal is 21 hours.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Different types of inequalities are represented by a variety of notations, including:

The symbol a <  b indicates that a is smaller than b.

When a > b is used, it indicates that an is bigger than b.

Given,

Hours Saul plans to volunteer in the 9-month period = 225 hours

Also,

Hours of volunteering he has already completed = 36 hours

=> Number of hours left = 225 - 36 =189 hours

Number of months= 9

=> Minimum number of hours he has to volunteer per month

=> \(\frac{Number of hours left}{Number of months}\)

=>\(\frac{189}{9}\\ 21 hours\)

=>Minimum number of hours saul has to volunteer per month ≥ 21 hours

Therefore, The number of hours of volunteer work that saul could complete each month to meet his goal is 21 hours.

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Answer:

65⁰

Step-by-step explanation:

When light comes into contact with a surface, the angle of reflection equals the angle of incidence.

Answer:

x = - \(\frac{1}{6}\)

Step-by-step explanation:

the x- intercept is the value of x where the line crosses the x- axis

on the x- axis the y- coordinate of any point is zero

let y = 0 in the equation and solve for x

y = 6x + 1 , then

0 = 6x + 1 ( subtract 1 from both sides )

- 1 = 6x ( divide both sides by 6 )

- \(\frac{1}{6}\) = x ← is the x- intercept

Answer:

 \(x = \frac{1}{6}y-\frac{1}{6}\)

Step-by-step explanation:

Find the x-intercept of the line with equation y=6x +1

y = 6x + 1, solve for x

y = 6x + 1 subtract 6x from both sides:

y - 6x = 6x + 1 - 6x

y - 6x =  1

subtract y from both sides:

y - 6x - y =  1 - y

- 6x =  1 - y

divide both sides by -6:

- 6x/-6 =  (1 - y)/-6

x = -1/6 + 1/6 y

rearrange left side:

\(x = \frac{1}{6}y-\frac{1}{6}\)

Answer:

hope this helps :)

Step-by-step explanation:

20−3x=5

Subtract 20 from both sides.

20-3x-20=5-20

⇒-3x=-15

divide both sides by 3

⇒-3x/-3=-15/-3

⇒x=5

Answer:

\( \sf \: d) \: x = 5\)

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 20 - 3x = 5

Then the value of x will be,

→ 20 - 3x = 5

→ -3x = 5 - 20

→ -3x = -15

→ 3x = 15

→ x = 15 ÷ 3

→ [ x = 5 ]

Hence, the value of x is 5.

The required area and circumference of circle A are 1,134.57feet² and 119.43 feet.

All points in a plane that are at a specific distance from a specific point, the center, form a circle.

In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

So, the area and circumference of circle A:

d = the circumference of circle B

r = radius of circle A

r = 2d - 3

Diameter of circle A = 2 x (2d - 3) = 4d - 6

By figuring out d, we may find the diameter of circle B.

4d - 6 + d = 49

5d = 55

d = 11

Diameter of circle A = 4(11) - 6 = 38

Radius of circle A = 38/2 = 19 feet

Area of a circle = πr²

22/7 x 19² = 1,134.57 feet²

Circumference of a circle = πD

22/7 X 38 = 119.43feet

Therefore, the required area and circumference of circle A are 1,134.57feet² and 119.43 feet.

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Given the figure of a circle

As shown the radius of the circle = r = 5 ft

so, the answer will be:

Area = 78.5 ft^2

Circumference = 31.4 ft

The highest level of the corporate social responsibility pyramid is philanthropic responsibility.

The corporate social responsibility (CSR) pyramid is a framework that categorizes the various levels of social responsibility that companies can demonstrate. It is often depicted as a pyramid with four distinct levels, with each level building upon the previous one. The highest level of the CSR pyramid is philanthropic responsibility.

The four levels of the CSR pyramid are:

Economic Responsibility: This is the foundation of the pyramid and represents a company's obligation to be profitable and contribute to the economy by providing goods, services, and employment opportunities.

Legal Responsibility: The next level involves a company's compliance with laws and regulations. It signifies that a company should operate within the legal framework and fulfill its legal obligations.

Ethical Responsibility: This level goes beyond legal compliance and requires a company to conduct its business in an ethical and moral manner. It involves behaving responsibly and doing what is right, even if it is not explicitly required by law.

Philanthropic Responsibility: The highest level of the CSR pyramid is philanthropic responsibility. It represents a company's voluntary efforts to contribute to society and make a positive impact through charitable donations, community involvement, and social initiatives. Philanthropic responsibilities are often seen as going above and beyond what is expected or required of a company.

The highest level of the corporate social responsibility pyramid is philanthropic responsibility. It signifies a company's voluntary actions to contribute to society and make a positive impact through charitable donations, community involvement, and social initiatives. While economic, legal, and ethical responsibilities are important, philanthropic responsibility represents a company's commitment to giving back and making a difference in the communities it operates in.

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Answer:

2006

Step-by-step explanation:

Trust

Stochastic processes in finance are modeled using a formula such as the Geometric Brownian Motion equation, which is used to predict the random variations in asset prices and inform investor decisions.

Stochastic processes in finance are processes that are randomly determined, with the outcomes being uncertain. These processes are used to model financial markets, and are useful for forecasting future price movements. These processes are usually modeled using a formula, such as the Geometric Brownian Motion (GBM) equation:

dS = μSdt + σSdz

Where dS is the change in the price of an asset over a short time period, μ is the drift term (expected rate of return), S is the current price of the asset, dt is the time period, σ is the volatility, and dz is a random variable.

This equation is used to model the random variations of an asset’s price, and can be used to predict future price movements. By understanding the GBM equation and its parameters, investors can make more informed decisions when trading financial instruments.

Stochastic processes in finance are modeled using a formula such as the Geometric Brownian Motion equation, which is used to predict the random variations in asset prices and inform investor decisions.

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Complete question

What is the Geometric Brownian Motion equation and how is it used in stochastic processes in finance?

To find the area of a circle, you can use the formula:

area = πr^2

where "r" is the radius of the circle.

In this case, the radius of the circle is 14 cm, so the area of the circle is:

area = π * 14^2

= π * 196

= approximately 300.96 cm^2

The units of the answer are square centimeters (cm^2).

Answer:

32 minutes

Step-by-step explanation:

all you have to do is know that the unit rate is 4 so multiply 8 and 4 to get 32

Answer:

32 minutes

Step-by-step explanation:

8 times 4 is 32.

Step-by-step explanation:

x=10

y=24

r=√10²+24²=√100+576=√676=26

sin = y/r = 24/26

cos = x/r =10/26

tan=y/x = 24/10

csc = r/y=26/24

sec= r/x = 26/10

tan = x/y = 10/24

Answer:

correct / incorrect / incorrect

Step-by-step explanation:

5a - 8 + 2a² + 2a - 1 ← collect like terms

= 2a² + 7a - 9 ← correct

-------------------------------------

b² + 6b - 4 - (3b + b²) ← distribute parenthesis by - 1

= b² + 6b - 4 - 3b - b² ← collect like terms

= 3b - 4 ≠ 2b² + 3b - 4

---------------------------------------

9c - 4c² - (2c² + c) ← distribute parenthesis by - 1

= 9c - 4c² - 2c² - c ← collect like terms

= - 6c² + 8c ≠ - 6c² + 10c

Answer:

correct

incorrect

incorrect

Step-by-step explanation:

\(\begin{aligned}(5a-8)+(2a^2+2a-1)&=5a-8+2a^2+2a-1\\& = 2a^2+5a+2a-8-1\\ & = 2a^2+7a-9\end{aligned}\)

\(\implies (5a-8)+(2a^2+2a-1)=2a^2+7a-9\quad\textsf{is correct}\)

---------------------------------------------------------------------------------------

\(\begin{aligned}(b^2+6b-4)-(3b+b^2) &=b^2+6b-4-3b-b^2\\ & = b^2-b^2+6b-3b-4\\& = 3b-4\end{aligned}\)

\(\implies (b^2+6b-4)-(3b+b^2)=2b^2+3b-4\quad\textsf{is incorrect}\)

---------------------------------------------------------------------------------------

\(\begin{aligned}(9c-4c^2)-(2c^2+c) &=9c-4c^2-2c^2-c\\ & = -4c^2-2c^2+9c-c\\& = -6c^2+8c\end{aligned}\)

\(\implies (9c-4c^2)-(2c^2+c)=-6c^2+10c\quad\textsf{is incorrect}\)

Volume of a pyramid is calculated using the same basic formula as that of a cone: volume = (1/3) × base area × height, where height is the distance between the base and the apex. Then the height is 6 feet.

Using the equation volume = base area height / 3, one may calculate the volume of a regular square pyramid. Keep in mind that the base area is equal to the base edge length squared.

A polygonal base and an apex come together to form a polyhedron known as a pyramid. Volume of a pyramid is calculated using the same basic formula as that of a cone: volume = (1/3) × base area × height, where height is the distance between the base and the apex.

The volume of a square pyramid exists found by multiplying the area of the base by the height divided by 3.

32 = 4² × h/3

32 = 16 × h/3

Multiply both sides by 3

96 = 16 × h

Divide both sides by 16

H = 96/16

H = 6

Therefore, the height is 6 feet.

The complete question is:

Find the height of a square pyramid that has a volume of 32 cubic feet and a base length of 4 feet.

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Applying a subtraction operation, it is found that his new ERA was of 3.17.

ERA is a baseball concept, but understanding of baseball is not relevant to this question.

One year, a professional baseball pitcher had a 3.91 ERA. The next year, it was 0.74 points lower, hence it was given by the subtraction of 3.91 and 0.74, that is:

ERA = 3.91 - 0.74 = 3.17.

His new ERA was of 3.17.

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To find the production level that maximizes profit, we need to determine the point where the revenue and cost functions intersect.

The revenue function is given by R(x) = x * p(x), where p(x) represents the demand function. The profit function is defined as P(x) = R(x) - C(x).

First, let's find the revenue function. Since p(x) = 2900 - 7x, we can express the revenue function as R(x) = x * (2900 - 7x) = 2900x - 7x^2.

Now, we can substitute the cost and revenue functions into the profit equation and simplify it as follows:

P(x) = R(x) - C(x)

    = (2900x - 7x^2) - (18000 + 500x - 2.2x^2 + 0.004x^3)

    = -0.004x^3 + 2.2x^2 + 2400x - 18000

To find the production level that maximizes profit, we need to find the critical points of the profit function by taking its derivative and setting it equal to zero:

P'(x) = -0.012x^2 + 4.4x + 2400

Solving P'(x) = 0, we can find the production level that maximizes profit.

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