What is the range in interval notation of the function graphed below?

To set up the artificial variable LP (Phase I LP) for the given problem, we introduce an artificial variable, LP, to the objective function with a coefficient of 1. The artificial variable is used to identify infeasible solutions.

To set up the artificial variable LP (Phase I LP), we modify the objective function as follows:

Maximize Z = 4x1 + 7x2 + x3 + LP

The artificial variable LP is introduced to the objective function with a coefficient of 1. This allows us to track its value during the iterations.

The initial constraints remain the same:

2x1 + 3x2 + x3 = 20

3x1 + 4x2 + x3 + x4 = 40

8x1 + 5x2 + 2x3 - x5 = 70

The initial basic variables (BV) are the slack variables corresponding to the equality and inequality constraints, namely, x3 and x4. The artificial variable LP is initially a non-basic variable.

The initial artificial variables' basic variable (BVB) values are set to the right-hand side values of the constraints:

x3 = 20

x4 = 40

The initial artificial variable LP's value is set to 0.

Next, the artificial variable LP is selected as the entering variable, as it has a positive coefficient in the objective function. To determine the leaving variable, we perform the ratio test using the ratios of the right-hand side values and the entering column values (coefficients of LP) for the respective constraints.

The leaving variable is determined based on the minimum ratio, ensuring that the corresponding row represents a valid pivot element. If no valid pivot element is found, the problem is infeasible.

This completes the setup of the artificial variable LP (Phase I LP) without performing a complete pivot. Further steps would involve applying the simplex method and iteratively pivoting to find the optimal solution or identify infeasibility.

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Question 1 True or False: A sector of a circle with a measure of 72 and radius of 12 cm has an arc length of about 15cm. True O False

Step-by-step explanation:

its false

The given statement about the sector of the circle is true.

A circle is a shape or a curve in a plane that has a fixed distance, called the radius, from a given point, called the centre. A circle is also the set of all points that are equidistant from the centre.

Given that we need to check whether a sector of a circle with a measure of 72° and radius of 12 cm has an arc length of about 15cm, or not,

Arc length = central angle / 360° × 2π × radius

= 72/ 360° × 2(3.14) × 12

= 0.2 × 6.28 × 12

= 15.072

≈ 15

Therefore, yes the sector of a circle with a measure of 72° and radius of 12 cm has an arc length of about 15cm.

Hence, the given statement about the sector of the circle is true.

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3√64 × 2^-1

= 4 × 1/2

= 2

The answer is 2.

Please do mark me Brainliest

Answer:

1.1 gigabytes

Step-by-step explanation:

Let us represent:

The number of gigabytes = g

Under his cell phone plan, Owen pays a flat cost of $67.50 per month and $4 per gigabyte. He wants to keep his bill at $71.90 per month.

The Equation is given as:

$71.90 = $67.50 + $4 × g

71.90 = 67.50 + 4g

71.90 - 67.50 = 4g

4.4 = 4g

x = 4.4/4

x = 1.1 gigabytes

Therefore, the number of gigabytes of data Owen can use while staying within his budget is 1.1 gigabytes

Answer: 3.6

Step-by-step explanation:

4x+64.5=78.9

-64.5 -64.5

4x/4=14.4/4

X=3.6

The gradient, evaluated at the starting point is x = -4 cos(x) cos(V2/2y)

y = -4 sin(x) sin(V2/2y)

We have the function: \(f(x,y) = 3 + x^2/8 + y^2/8 - sin(x) cos(V2/2y)\)

To find a minimum of this function, we need to find where the gradient of the function is equal to zero. The gradient of f is a vector of partial derivatives:

\(∇f(x,y) = [∂f/∂x, ∂f/∂y]\)

Taking the partial derivative of f with respect to x, we get:

\(∂f/∂x = x/4 - cos(x) cos(V2/2y) V2/4y\)

Taking the partial derivative of f with respect to y, we get:

\(∂f/∂y = y/4 + sin(x) sin(V2/2y) V2/4y^2\)

Therefore, the gradient of f is:

\(∇f(x,y) = [x/4 - cos(x) cos(V2/2y) V2/4y, y/4 + sin(x) sin(V2/2y) V2/4y^2]\)

Now, we need to evaluate the gradient at the starting point x0 = [phi/3, phi/2V2]. Substituting these values into the gradient, we get:

\(∇f(phi/3, phi/2V2) = [phi/12 - cos(phi/3) cos(1/2), phi/8 + sin(phi/3) sin(1/2)]\)

To find the minimum, we need to set the gradient equal to zero:

∇f(x,y) = [0,0]

Solving for x and y, we get:

x = -4 cos(x) cos(V2/2y)

y = -4 sin(x) sin(V2/2y)

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Answer:

pic?

Step-by-step explanation:

Answer:

155°

Step-by-step explanation:

x + 25° = 180° {Being linear pair }

x = 180° - 25°

Therefore x = 155°

Hope it will help :)

Answer:

155⁰

Step-by-step explanation:

Total angle on a straight line = 180⁰

: 25⁰ + x⁰ = 180⁰

x⁰ = 180⁰ - 25⁰

x⁰ = 155⁰

The statement is true. If we take any two distinct prime numbers, and the number "1", these numbers will always be pairwise relatively prime.

Two numbers are said to be pairwise relatively prime if their greatest common divisor (GCD) is equal to 1. In this case, since we are considering distinct prime numbers, their GCD will always be 1 since prime numbers have no common factors other than 1 and themselves. Therefore, any two distinct prime numbers will be relatively prime.

Similarly, when we consider the number "1", it is relatively prime to any other number because its only divisor is 1. Hence, when "1" is paired with any prime number, the GCD will be 1.

In summary, whether we consider two distinct prime numbers or pair them with the number "1", the resulting numbers will always be pairwise relatively prime.

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Answer:

2 ounces

\(0.125*16=2\)

Multiply mass by 16 to find.

Answer:

true

Step-by-step explanation:

bc my brain is right ( BTW i got my dad to check :>)

Yes, it can be concluded at a 0.01 level of significance that there is a linear correlation between the two variables.

The following is a solution to the given question. The weight of a child riding a bike and the rolling distance achieved after going down a hill without pedaling is given by the data. The correlation coefficient between the two variables is to be tested to conclude if there is a linear correlation between the two variables at a 0.01 level of significance.

Linear correlation between the two variables A correlation coefficient, r, is used to determine if two variables have a linear correlation. A value of r=1 indicates a perfect positive correlation, while a value of r=-1 indicates a perfect negative correlation. A value of r=0 indicates no correlation between the two variables.To find the correlation coefficient, we use the following formula:

\($r = \frac{n\sum xy - \sum x\sum y}{\sqrt{(n\sum x^2 - (\sum x)^2)(n\sum y^2 - (\sum y)^2)}}$\)

Where

Weight, \($x$\)  Rolling Distance \($y$59 2683 4397 4956 20103 6587 4488 4891 4252 3963 3371 39100 4989 55103 5399 4274 3375 3089 30102 40103 3399 3386 3785 37\)

We need to find n,

\($\sum x$\) \($\sum y$\) \($\sum x^2$\)\($\sum y^2$\)

\(\sum xy$.n=30$\\ \sum x=2792$$\\ \sum y=1129$$\\ \sum x^2=221506$$\\ \sum y^2=86223$$\\ \sum xy=106883$r = 0.91\)

Correct to two decimal places.

Decision RuleWe have to check if the value of r lies in the critical region for a 0.01 level of significance. The value of r that separates the critical region from the non-critical region is found using the following formula:

\($$r_c = \frac{1}{\sqrt{n-2}}$$\)

Where n is the sample size.

Substituting the values, we get

\($$r_c = \frac{1}{\sqrt{30-2}} = 0.366$$\)

The critical region is when r is greater than 0.366 or less than -0.366.

Conclusion The value of r (0.91) is greater than the critical value (0.366). Hence, we conclude that there is a linear correlation between the two variables at a 0.01 level of significance. Therefore, the answer is: Yes, it can be concluded at a 0.01 level of significance that there is a linear correlation between the two variables.

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True. in an assignment a(:) = b, the number of elements in a and b must be the same.

In MATLAB, the assignment statement a(:) = b is used to assign the elements of b to the elements of a in a column-wise fashion. For this to work, the number of elements in a and b must be the same. If the number of elements in b is less than that of a, then the remaining elements of a will retain their previous values. If the number of elements in b is greater than that of a, then an error will occur.

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The amount of snow that Gabriella would have on her lawn t hours of snow melting is; S(t) = 12.5 - 0.5t

The snow started melting at a rate of 0.5 inches per hour and it is known that 3 hours  after the storm ended, the depth of snow was down to 11 inches.

Snow melted in 3 hours = 0.5 * 3 = 1.5 inches

Thus;

The Initial depth of snow = 11 + 1.5 inches = 12.5 inches.

Now, depth of snow on Gabriella's lawn = Initial depth - 0.5(Number of hours)

Let S(t) be the depth of snow on  Gabriella's lawn, in inches, t hours after the snow stopped falling.

Thus; S(t) = 12.5 - 0.5t

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Answer:

4

Step-by-step explanation:

4-2=2

Answer:

4-2=2

Step-by-step explanation:

The quadratic equation given the points (6,0), (-1,0), and (7,4).

The correct answer is h(x) = 1/2(x + 1)(x - 6).

To find the quadratic equation given the points (6,0), (-1,0), and (7,4), we can use the general form of a quadratic equation, which is \(h(x) = ax^2 + bx + c.\)

First, let's substitute the coordinates of the given points into the equation to create a system of equations:

For the point (6,0):

\(0 = a(6)^2 + b(6) + c ---- (1)\)

For the point (-1,0):

\(0 = a(-1)^2 + b(-1) + c ---- (2)\)

For the point (7,4):

\(4 = a(7)^2 + b(7) + c ---- (3)\)

We now have a system of three equations with three unknowns (a, b, c). We can solve this system to find the values of a, b, and c.

Solving the system of equations (1), (2), and (3), we find:

a = 1/2

b = -3/2

c = 0

Thus, the quadratic equation that satisfies the given points is:

h(x) = 1/2(x + 1)(x - 6).

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Answer:

C(C^3 + 8C^2 -3C -7)

Step-by-step explanation:

(-3C^4-5C^2-7C)+(4C^4+8C^3+2C^2)  

(-3C^4 +4C^4)+8C^3 + ( -5C^2 +2C^2)  -7C  [Combine like terms]

C^4 + 8C^3 -3C^2 -7C                                     [Simplify]

C(C^3 + 8C^2 -3C -7)                                   [Isolate 1C from the rest]

The  six different iterated triple integrals for the volume of the tetrahedron cut from the first octant by the plane 6x + 3y+ 2z = 8 are ,

Triple integrals are functionally equivalent to double integrals. Triple integrals can be converted into  iterated integrals.

The only trick, as with double integrals, is determining the limits on the iterated integrals. (Drawing in three dimensions is more difficult.)

The triple integral represents W's actual mass. Triple integrals are iterated functions with three variables. Triple integrals are iterated functions with three variables. We are now integrating our function over a three-dimensional figure with volume, rather than a given area.

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Answer:

I can only answer b but I hope it helps

B = £75,400

Explanation:

10% is £6500

6 % is £3900

=£10,400

+the original pay

=£75,400

That is her new salary

Answer:

7x

Step-by-step explanation:

(8x+5)- (x+5)

8x+5-x-5

8x -x(1x)

7x

The measure of the length of the arc of the circle is s = 7.74 inches

Given data ,

The formula for calculating the arc length of a circle is given by:

s = r * θ

where:

s = arc length

r = radius of the circle

θ = angle in radians

Given that the radius of the circle is 8.6 inches and the angle measure is 0.9 radians

s = 8.6 * 0.9

s ≈ 7.74

Hence , the arc length is s = 7.74 inches

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Considering that y is between x and z, we have that:

We consider that y is between x and z, hence the length of the segment is given by:

xz = xy + yz

The separate lengths are given as follows:

Hence:

4k + 38 = 3k - 2 + 7k + 4.

4k + 38 = 10k + 2

6k = 36

k = 6.

Hence the length of yz is given by:

yz = 7k + 4 = 7(6) + 4 = 42 + 4 = 46 units.

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Answer:

the number can be 12

1 x 12 = 12

2 x 6 = 12

3 x 4 = 12

the width of the previous image is 9.5mm.

     The widthh can be defined as the horizontal measurement or distance measured from side to side.

       In geometry, the shorter side of an object is frequently referred to as its "width". For instance, both of the given rectangles are identical rectangles, but one of them has been rotated to demonstrate that the shorter side of the rectangle is referred to as its width.

In the given problem,

         if the width of the previous image is x,

                            4x=38

                        ⇒x=9.5mm

So, the width of previous image is 9.5mm.

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The  valid license plates are possible = 676,000 possibilities

In mathematics, there are two alternative methods for dividing up a collection of components into subsets: combination and permutation. The subset's components can be arranged in any sequence when used together. The subset's components are given in a permutation in a certain order.

There is no prohibition on using the same letters or numbers more than once, therefore all 26 letters of the alphabet and all 10 numerals are permissible choices.

There are 26 options if the initial answer is A:

AA, AB, AC,AD,AE ...................................... AW, AX, AY, AZ.

There are 26 options if the initial answer is B:

BA, BB, BC, BD, BE .........................................BW, BX,BY,BZ

So,

The first letter can be one of 26 options, and the second letter can be one of 26 options. There are a variety of 2 letter combinations, including:

26 x 26 = 676

For the three digits, the same holds true.

The first, second, and third options each have ten options available:

10  × 10 × 10 = 1000

Thus, there are several options for a license plate with two letters and three digits:

26 x 26 x 10  × 10 × 10 =  676,000 possibilities.

The  valid license plates are possible = 676,000 possibilities.

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Answer:

91in^2

Step-by-step explanation:

First, add 11 and 15:   11 + 15 = 26

Second, divide it by 2: 26/2 = 13

Third, multiply it by the height: 13 * 7 = 91in^2

Answer:

83.2

Step-by-step explanation:

The pk\(_b\) of given acid conjugate base is 9.74 if k\(_a\) of the same acid is equal to 5.57×10⁻⁵

The Bronsted-Lowry corrosive base hypothesis incorporates the ideas of form acids and form bases. At the point when a corrosive separates into its particles in water, it loses a hydrogen particle. The species that is shaped is the corrosive's form base.

A more broad definition is that a form base is the base part, X-, of a couple of mixtures that change into one another by acquiring or losing a proton. The form base can acquire or retain a proton in a synthetic response. The form corrosive gives the proton or hydrogen in the response.

In a corrosive base response, the substance response is:

Corrosive + Base ⇌ Form Base + Form Corrosive

We know very well that from equilibrium state theories that  pk\(_b\) +pk\(_a\) =14

where  pk\(_a\) = - log( k\(_a\) )

So, we have k\(_a\) =5.57×10⁻⁵

Taking log of  k\(_a\) ,we get

=>pk\(_a\)= -log(5.57×10⁻⁵)

Using properties of logarithm, log(a × b)=log(a)+log(b)

=>pk\(_a\)= -log(5.57) -log(10⁻⁵)

=>pk\(_a\)= -0.745 +5

=>pk\(_a\)=4.25

Therefore, from above written formula, we get

=>4.25+pk\(_b\)=14

=>pk\(_b\)=14-4.25

=>pk\(_b\)=9.74

Hence, pk\(_b\) value is 9.74

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Answer: 115 degrees

Step-by-step explanation:

Pretty vague question but with the info given im guessing that your looking for the last angle in the triangle which is 115 since all angles in a triangle must add up to 180