how to find the intervals of increasing and decreasing

Maximize Z = -2x1 + x2 - 4x3 + 3x4 subject to the following constraints:

x1 + x2 + x3 + 2x4 + s1 = 4,

-x1 + x3 + x4 - s2 = -1,

2x1 + x2 + s3 = 2,

and x1 + 2x2 + x3 + 2x4 = 2, where x1, x2, x3, x4, s1, s2, s3 ≥ 0.

To reformulate the given problem in the standard form of a linear programming model, we need to convert all the inequalities into equations and express all variables as non-negative.

The standard form of a linear programming problem is as follows:

Maximize (Z) = c1x1 + c2x2 + c3x3 + c4x4

Subject to:

a11x1 + a12x2 + a13x3 + a14x4 = b1

a21x1 + a22x2 + a23x3 + a24x4 = b2

a31x1 + a32x2 + a33x3 + a34x4 = b3

an1x1 + an2x2 + an3x3 + an4x4 = bn

x1, x2, x3, x4 >= 0

Now let's reformulate the given problem:

Maximize (Z) = -2x1 + x2 - 4x3 + 3x4

Subject to:

x1 + x2 + x3 + 2x4 <= 4

-x1 + 0x2 + x3 + x4 >= -1

2x1 + x2 + 0x3 + 0x4 <= 2

x1 + 2x2 + x3 + 2x4 = 2

x1, x2, x3, x4 >= 0

The reformulated linear programming problem in standard form is as follows:

Maximize (Z) = -2x1 + x2 - 4x3 + 3x4

Subject to:

x1 + x2 + x3 + 2x4 + s1 = 4

-x1 + x3 + x4 - s2 = -1

2x1 + x2 + s3 = 2

x1 + 2x2 + x3 + 2x4 = 2

x1, x2, x3, x4, s1, s2, s3 >= 0

Note: The reformulated problem includes slack variables s1, s2, and s3 to convert the inequalities into equations, and all variables are non-negative.

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Answer:

12 cm ,13cm 14cm is the correct answer

Answer:

c) The vertical asymptotes are x = (-5 + √(13))/4 and x = (-5 - √(13))/4. To find them, set the denominator equal to zero and solve for x.

d) There are no holes in the function.

e) The zeros are x = 0, x = 2, and x = -3. To find them, set the numerator equal to zero and solve for x.

f) The slant asymptote is y = x + 2 - (3.5x + 1.5)/(2x^2 + 5x + 3). To find it, use long division to divide the numerator by the denominator. To find the slant asymptote of the given rational function, we use long division to divide the numerator by the denominator. The quotient of the division gives the equation of the slant asymptote.

g) The domain is (-∞, (-5 - √(13))/4) U ((-5 + √(13))/4, ∞). To find it, set the denominator not equal to zero and solve for x. To find the domain of the given rational function, we set the denominator not equal to zero and solve for x. The domain is all real numbers except the values of x that make the denominator equal to zero.

I hope this helps you! I'm sorry if it's wrong! If you need more help, ask me! :]

Answer:

the unit rate is  6.375 meters per second.

Step-by-step explanation:

51 meters ÷ 8

——————————-

8 seconds ÷ 8

=    6.375 meters

——————————

      1 second

6.375

51 / 8

8÷ 8

6.375 meters per second

Answer:

a.

Step-by-step explanation:

you add 2 & 3 ... you get 4. then you add 2 & 4 ... you get 6.

Part A:What is the probability of getting a red jellybean on the first draw?

Given information: Red jellybeans = 12  Yellow jellybeans = 8  Green jellybeans = 4   Total jellybeans = 24                           The probability of getting a red jellybean on the first draw is:

Probability of getting a red jellybean=Number of red jellybeans/Total jellybeans=12/24=1/2=0.5

Decimal: P(1st Red)=0.5 Percent: P(1 st Red )=50%

Part B: Let's say you did get a red jellybean on the first draw.

What is the probability that you will then get a green on the second draw?

Now, the total number of jellybeans is 23, since one red jellybean has been taken out. The probability of getting a green jellybean is: Probability of getting a green jellybean=Number of green jellybeans/Total number of jellybeans=4/23=0.174 Decimal: P(2nd Green | 1st Red )=0.174 Percent: P(2nd Green | 1st Red )=17%

Part C: If you had gotten a yellow on the first draw, would your answer to Part B be different?

Yes, because there is only 1 rotten egg yellow jellybean and if it were chosen in the first draw, it would not be returned back to the container. Therefore, the total number of jellybeans would be 23 for the second draw, and the probability of getting a green jellybean would be:

Probability of getting a green jellybean=Number of green jellybeans/Total number of jellybeans=4/23=0.174

Thus, the answer would be the same as Part B.

Part D: What is the conditional probability of the dependent event "red then green?"

Given that one red jellybean and one green jellybean are selected: Probability of the first jellybean being red is 1/2

Probability of the second jellybean being green given that the first jellybean is red is 4/23

Probability of "red then green" is calculated as follows: Probability of red then green=P(Red) × P(Green|Red)= 1/2 × 4/23 = 2/23  Decimal: P(1st Red and 2nd Green )=2/23  Percent: P(1st Red and 2nd Green )=8.70%

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A road is 6 degrees inclined after 4900 feet of travel. The driver's increasing in altitude is 509.6

Given that,

A road is 6 degrees inclined after 4900 feet of travel.

We have to find the driver's increasing in altitude.

In a right angle triangle,

According to the definition of a right triangle, a triangle is referred to as a right-angled triangle or simply a right triangle if one of the angles is a right angle (90°). Triangle ABC is a right triangle in the illustration, consisting of the base, altitude, and hypotenuse. The significant side of a right triangle is the hypotenuse, which is the longest side and sits in opposition to the triangle's right angle.

Sinθ=Altitude/Hypotenuse

Sinθ×Hypotenuse=Altitude

Altitude=Sin6°×4900

Altitude=0.104×4900

Altitude=509.6

Therefore, The driver's increasing in altitude is 509.6

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Answer:

D

Step-by-step explanation:

f(x) = x-4

f(3.2) = -3.2-4

= -7.2

Answer:

44

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

4d+6=

you substitute 3 for d

4(3)+6=

12+6=

18

Answer:

4 x 3 + 6 = 18

Step-by-step explanation:

4 x 3 = 12

12 + 6 = 18

Answer:

13

Step-by-step explanation:

3h - j

3(8) - 11

24 - 11

13

Answer:

The answer to your problem is, D. 1/20

Step-by-step explanation:

Just how to divide the fractions:

= \(\frac{1}{4}\) x \(\frac{1}{5}\)

= \(\frac{1 * 1}{4 * 5}\)

= \(\frac{1}{20}\)

Thus the answer to your problem is, \(\frac{1}{20}\)

The c is equal to half of the definite integral of the function over the interval [0, 2].

To determine c such that f(c) is the average value of the function on the interval [0, 2], we can use the formula for the average value of a function:

avg = 1/(b-a) * ∫(a to b) f(x) dx

In this case, a = 0 and b = 2, so the formula becomes:

avg = 1/2 * ∫(0 to 2) f(x) dx

We want to find the value of c such that f(c) = avg, so we can set these two expressions equal to each other and solve for c:

f(c) = avg
f(c) = 1/2 * ∫(0 to 2) f(x) dx

We can then use calculus to solve for c by finding the derivative of both sides with respect to c and setting them equal to each other:

f'(c) = 1/2 * (f(2) - f(0))

Solving for c gives us:

c = (1/2) * ∫(0 to 2) f(x) dx

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Answer:

Trillion is a 1 with 12 zeros after it, and it looks like this: 1,000,000,000,000.

Step-by-step explanation:

Answer:

1000000000000

quadrillions

Step-by-step explanation:

Answer:

The area of rectangle WXYZ is 175.36 square inches. To find the area, you multiply the length (10.8 inches) by the width (16.2 inches). 10.8 x 16.2 = 175.36.

Answer:

B

Step-by-step explanation:

Students may not truthfully reply because they fear it will affect their grade.

Answer: 4x + 29

Step-by-step explanation: add the like terms together.

Answer:

39 inches

Step-by-step explanation:

the triangle has all equal angles

this means it is equilateral and this also means all the sides are equal

so take 2 sides and set them equal to each other to find x

21 - x = x + 5

now solve

add x to both sides

21 = 2x + 5

subtract 5 to both sides

16 = 2x

divide everything by 2

8 = x

now flip it

x = 8

plug this is to one of the equations and multiply that by 3

8 + 5 = 13

13 * 3 = 39

that is the perimeter

The answer is 3.65 x 10^8. To add and subtract values expressed in scientific notation, we need to ensure that the exponents of the powers of 10 are the same.

Let's solve the given expression step by step:
\(\((6.15 \times 10^8) - (2.5 \times 10^7) = (0.615 \times 10^9) - (0.25 \times 10^9)\)\)First, we can convert the given numbers to scientific notation by moving the decimal point to the left of the first non-zero digit:
\(\[ 0.615 \times 10^9 = 6.15 \times 10^8 \]\\ 0.25 \times 10^9 = 2.5 \times 10^8 \]\)

Now we have the same exponent (8) for both values. To subtract, we can directly subtract the coefficients:

\(\((6.15 \times 10^8) - (2.5 \times 10^7) = (6.15 - 2.5) \times 10^8 = 3.65 \times 10^8\)\)

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Tenemos un simple problema algebraico.

Encontraremos que la cantidad que la fábrica pagó es $6,694,410.00

La información dada es:

Se compran 37 camionetas.

Cada camioneta cuesta $180,930.00

Entonces la cantidad total que la fábrica paga es 37 veces $180,930.00, que es:

37*$180,930.00 = $6,694,410.00

Concluimos en que el total que paga la fábrica es $6,694,410.00

Si quieres aprender más puedes leer.

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The range of x are;

1. x < -30

2. x > 8

3. x > 15

4. x < -2

A relationship between two expressions or values that are not equal to each other is called 'inequality.

1. -130 > 50x +20

-130-20> 50x

-150 > 50x

-150/50 > x

-30 > x

x < -30

2. -8(x-3) < -40

-8x +24< -40

collect like terms

-8x < -64

x > -64/-8

x > 8

3. 2x - 22 > 8

collect like terms

2x > 30

divide both sides by 2

x > 30/2

x > 15

4. -35 < -5(x+9)

-35 < -5x -45

collect like terms

10 < -5x

-2 > x

x < -2

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The critical value of t with df as 7 is 2.36, and the critical value of t with df as 102 is 2.62

In a hypothesis test, the critical value is a value that is used to decide whether to accept the null hypothesis or not. It is based on the level of significance that was selected, which is the highest likelihood that a Type I error could occur.

a)

On referring to the t-distribution table, which is statistical software, or a calculator to find the critical value of t for a 95% confidence interval with degrees of freedom (df) = 7. The two-tailed confidence level of 0.95 is the essential value. We discover that the crucial value of t for a 95% confidence interval with df = 7 is roughly 2.365 using a t-distribution table or program.

b)

The t-distribution table, statistical software, or a calculator are used in a similar manner to estimate the critical value of t for a 99% confidence interval with df = 102. The crucial value is equal to the 0.99 two-tailed confidence level. The crucial value of t for a 99% confidence interval with df = 102 is roughly 2.62, according to a t-distribution table or computer programme.

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An opinion poll survey based on a sample of a small section of people is likely to provide the most accurate results.

An opinion poll, often known as a poll or survey, is a human research survey of the general public from a specific sample. By asking a series of questions and extending generalizations into ratios or confidence intervals, opinion polls are often created to represent the opinions of a population. A person who conducts polls is referred to as a pollster.

An opinion poll is a survey that samples a tiny portion of the population in an effort to forecast election outcomes or gauge popular sentiment toward various concerns.

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Given:

The expression is

\((1-2g+4h)\cdot 5\)

To find:

The equivalent expression.

Solution:

Distributive property of multiplication over addition is

\(a(b+c)=ab+ac\)

Where, a, b and c are real numbers.

We have,

\((1-2g+4h)\cdot 5\)

Using distributive property, we get

\(=(1)\cdot 5+(-2g)\cdot 5+(4h)\cdot 5\)

\(=5-10g+20h\)

Therefore, the expression \(5-10g+20h\) is equivalent to the given expression.

Answer:

5-10g+20h

Step-by-step

Please give Brainliest :)

The following values are as follows: a) Mean = 0.6, b) standard deviation = 0.073 and c) Probability is 0.0855

a) As the number of samples is large enough which is up to 30 then the mean of the average number of moths in 30 traps is given as 0.6, given from the central limit theorem.

b) The population deviation divided by the square root of the sample size gives the standard deviation value.

standard derivation = σ/ \(\sqrt{n}\) = 0.4 / \(\sqrt{30}\) = 0.4/ 5.477 = 0.073

c) The probability that an approximately normally distributed data with the standard deviation, σ, with a sample size of n is greater than a number, x, and a mean, μ, is given by

1 - P (X < x)= P (X > x)

= 1 - P(z< x- µ/ σ/\(\sqrt{n}\))

Thus, given that the mean is 0.6 and the standard deviation is 0.4, the probability that the average number of moths in 30 traps is greater than 0.7 is given by:

1 -P (X - 0.7) = P (X > 0.7)

= 1 - P(z < \(\frac{0.7-0.6}{0.073}\)) = 1 - P(z < 1.369)

= 1 - 0.91455 = 0.0855

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Answer:

Image result for Use the Hypotenuse Theorem

The Pythagoras theorem, also known as the Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle. Or, the sum of the squares of the two legs of a right triangle is equal to the square of its hypotenuse.

Step-by-step explanation:

Answer:

400

Step-by-step explanation:

the volume of a pyramid with a square base is \(\frac{lwh}{3}\) so the volume is 12*10*10 divided by 3, which is 1200/3, or 400

Answer:

23 should have been subtracted from, not added to, both sides of the equation.

Answer:

4 bags

Step-by-step explanation:

lxw

12x10=120

30x4=120

l=length

w=width

Answer:

Step-by-step explanation:

Step one:

given data

Cost of skateboard= $120

if she has $25 at hand then she will need 120-25= $95 to balance up for the board.

Step two:

We are told that she will sell each book for $5

then for her to realize $95 she has to sell

95/5=19

therefore she has to sell a minimum of 19 books

the equation is

let the number of books be b

b>=19