Write the dual of following problems: Maximize Z = 7X1 + 5X2 Subject to: X1 + 2X2 ≤ 6 4X1 + 3X2 ≤ 12 X1 , X2 ≥ 0 brainly

The distance of the point P to the plane is 42/√629 units. The solution has been obtained by using vectors.

What are vectors?

An item with both magnitude and direction is said to contain a vector. An object's motion from one point to another is described by a vector.

We are given three points Q, R and S. So, we will find equation of the plane defined by the three points.

Vector RQ = < 5, 1, -4 >  and RS = < 7, 6, -7>  and their cross product

RQ x RS = < 5, 1, -4 > x < 7, 6, -7> = < 17 , 7, 23>  = n  

This is a vector normal to the plane.

So, the equation of the plane is 17x + 4y + 18z = 139

The distance is calculated using

⇒d = (|A·Mx + B·My + C·Mz + D| )/(√A² + B² + C²)

⇒d = (|-17·3 + (-4)·1 + (-18)·7 + 139|)/((-17)² + (-4)² + (-18)²)

⇒d = 42/√629

Hence, the distance is 42/√629 units.

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Answer:

Step-by-step explanation:

The number of Dr. Pepper cans are 39.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Julia bought a total of 52 cans of Dr. Pepper and Sprite.

There were three times as many cans of Dr. Pepper as Sprite.

Let number of sprite cans be x.

Then, the number of Dr. Pepper cans will be 3x.

Now, x+3x=52

4x=52

x=13

So, 3x=39

Therefore, the number of Dr. Pepper cans are 39.

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Applying the triangle proportionality theorem, QR = 17½.

The triangle proportionality theorem states that when a line is constructed parallel to one side of a triangle and intersects the remaining two sides at two different points, the two sides of the triangle will be divided in equivalent proportions.

Therefore:

SQ/PS = TQ/TR

SQ = 5

PS = 2

TQ = ?

TR = 5

Plug in the values:

5/2 = TQ/5

Cross multiply:

2TQ = 25

TQ = 25/2

TQ = 12½.

QR = TQ + TR

QR = 12½ + 5

QR = 17½

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The graph of the points on a coordinate plane is added as an attachment

From the question, we have the following parameters that can be used in our computation:

(0.5, -1.5) and (3,5) on the coordinate plane

The description of the points are:

Using the above as a guide, we have the graph as an attachment

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The required cost of the dinner not including sales tax was $34.28.

A sales tax is a fee that is paid to the government when specified goods and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing authority.

To find out how much the dinner cost before sales tax, we need to subtract the sales tax amount from the total cost.

We know that the sales tax rate is 8%. To find the sales tax amount, we can multiply the total cost by 8% (or 0.08):

Sales tax = 0.08 * $37.26 = $2.98

To find the cost of the dinner before sales tax, we can subtract the sales tax amount from the total cost:

Cost before sales tax = $37.26 - $2.98 = $34.28

Therefore, the cost of the dinner not including sales tax was $34.28.

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The equation of the line given by the coordinates (-8, 3) and (-6, 0) is 2y = -3x -18.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Hence, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = (y2 - y1) / (x2 - x1)

The coordinates of the points are:

(-8, 3) and (-6, 0)

The slope of the line is given as:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates we have:

m = (0 - 3)/ (-6 + 8)

m = -3/2

Using the point slope form:

y - y1 = m (x - x1)

Substituting the values of slope and coordinates we have:

y - 3 = -3/2(x + 8)

2(y - 3) = -3(x + 8)

2y - 6 = -3x -24

2y = -3x -18

Hence, the equation of the line given by the coordinates (-8, 3) and (-6, 0) is 2y = -3x -18.

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Ans:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps! :)

Answer:

z = -37/50

Step-by-step explanation:

Now we have to,

→ Find the required value of z.

The equation is,

→ 51z - 21 = z - 58

Then the value of z will be,

→ 51z - 21 = z - 58

→ 51z = z - 58 + 21

→ 51z = z - 37

→ 51z - z = -37

→ 50z = -37

→ [ z = -37/50 ]

Hence, value of z is -37/50.

The x-coordinate of P is given as follows:

x = 4.

The x-coordinate of P is obtained applying the proportions in the context of this problem.

The partition ratio is 2:4, hence the equation to obtain the coordinates is given as follows:

P - A = 2/6(B - A)

P - A = 1/3(B - A).

Then the x-coordinate of P is obtained as follows:

x - 10 = 1/3(-8 - 10)

x - 10 = -6

x = 4.

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Answer: No, the graph of y = x² + 2 is not a straight line. The graph is a parabola that opens upwards and has its vertex at (0, 2).

A straight line is defined by a linear equation, which is an equation that can be written in the form y = mx + b, where m and b are constants. In this equation, the coefficient of x (m) represents the slope of the line, and the constant term (b) represents the y-intercept. A straight line has a constant slope, which means that the rate of change of y with respect to x is constant.

In the case of y = x² + 2, the coefficient of x (x) is not a constant, but rather a variable, which means that the slope of the line changes as x changes. The graph of y = x² + 2 is a parabolic shape that opens upwards and has its vertex at (0, 2). The slope of the graph is not constant, but rather increases as x increases. This means that the graph does not represent a straight line, but rather a parabolic curve.

Step-by-step explanation:

The volume of the pyramid is 400 cubic cm and the surface area is

340 sq cm.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces.

The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.

The volume of a pyramid is = (1/3)×l×w×h and the surface area of a pyramid is (1/2)×PL + B, where P = perimeter of the base, L = height, and

B = area of the base.

Therefore, The volume is =  (1/3)×10×10×12 cubic cm.

= 1200/3 cubic cm.

= 400 cubic cm

And, The total surface area is,

= (1/2)[2(10 + 10)×12 + (10×10) sq cm.

= 240 + 100 sq cm.

= 340 sq cm.

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Step-by-step explanation:

you have to be careful when typing questions and particularly formulae and expressions here. automatic text conversion has the habit of transforming e.g. fractions into one line divisions without any brackets.

what your wrote here :

575,000/1 + 4000e^-T = 575,000 + 4000e^-T

that cannot be the function.

I am sure it must be

F(T) = 575,000/(1 + 4000e^-T)

right ?

I am basing the rest of my answer on that assumption.

how many people became ill, when the outbreak began ? that means T = 0.

F(0) = 575,000/(1 + 4000e^-0) =

= 575,000/(1 + 4000×1) =

= 575,000/(4001) = 143.7140715... ≈ 144 people

6 weeks after the outbreak

F(6) = 575,000/(1 + 4000e^-6) =

= 575,000/(1 + 4000/(e^6)) =

= 575,000/(1 + 9.915008707...) =

= 575,000/10.915008707... =

= 52,679.75642... ≈ 52,680 people

limit t -> infinity

F(infinity) = 575,000/(1 + 4000e^-infinity) =

= 575,000/(1 + 4000/(e^infinity)) =

= 575,000/(1 + 0) = 575,000 people

The error in the expression 4 + 2x - 1/2(10 - 4x) is the missing parentheses.

Parentheses are a sort of punctuation mark that is used to separate or distinguish content inside a phrase. They frequently assist to clarify the meaning of a statement by adding information. Parentheses can also be used to denote a break or to divide items in a list.

Error in the given question: Missing parentheses

Corrected expression: 4 + 2x - 1/2(10 - 4x)

The problem may be fixed by ensuring that the proper syntax is used when declaring variables. If the variable is a string, for example, it should be stated as "var myVariable ='string value';". If it is an integer, define it like "var myVariable = 42;".

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Answer:

-2x^4+4x^3+8x

Step-by-step explanation:

please check the answer given

EFGH is a square as all its sides are equal and all its angles are right angles.

Let's start by considering the sides. We know that AE = BF = CG = DH, and we also know that the opposite sides of a square are parallel and equal in length. Therefore, we can say that:

AE = DH (opposite sides of square ABCD)

BF = AE (opposite sides of square ABFE)

CG = BF (opposite sides of square BCGF)

DH = CG (opposite sides of square CDHG)

Thus, we have shown that all four sides of EFGH are equal in length, and so EFGH may be a square.

Now, let's consider the angles. Since AE and BF are opposite sides of a square, we know that angle AEB = angle BFA = 90 degrees. Similarly, we can show that angle BFC = angle CGD = angle DHE = 90 degrees.

Next, we observe that E, F, G, and H are midpoints of the sides of square ABCD. Therefore, we can say that:

EF || AB, and EF = 1/2 * AB

FG || BC, and FG = 1/2 * BC

GH || CD, and GH = 1/2 * CD

HE || DA, and HE = 1/2 * DA

Since opposite sides of a square are parallel, we can also say that:

EF || GH, and EF = GH

FG || HE, and FG = HE

Now, we have two pairs of parallel sides with equal lengths, which means that opposite angles are equal. Therefore, we can say that:

angle FEG = angle GHE (corresponding angles)

angle EFG = angle HEF (corresponding angles)

Combining these with the right angles we established earlier, we have shown that all four angles of EFGH are right angles, and so EFGH is a square.

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Answer:

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

Let the number of pizzas be x.

The average cost per pizza is:

If we need the average cost be at most $3.50, we need an inequality:

This is translated as:

The blanks are:

The value of the length of  hypotenuse when base length is  11cm and angle is 24°:  12.04 cm

Trigonometry is a branch of mathematics, which deals with the study of right angle triangles. Trigonometry is concerned with specified functions of angles and their applications to calculations.

There are 6 commonly used functions in trigonometry with their name and abbreviations-

sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), cosecant (cosec)

Given that,

The length of hypotenuse = x

The length of base =  11 cm

The angle = 24°

It is known that,

cosФ = base/hypotenuse

         = 11/x

cos24° = 11/x

x = 11/cos24°

  = 12.4

Therefore, the length of the hypotenuse is approximately 12.04cm.

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The requried graph with the x-axis labeled a number of side dishes and the y-axis labeled cost in dollars and a line going from point [0,5.25] through point [3, 9.75]. Option C is correct.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
Calculate the slope of the given relation in the table, using any two of the ordered pair,
m = 11.25 - 8.25 / 4 - 2
m = 3/2
m = 1.5

Now calculate the slope in each option, the slope of any option matches with m = 1.5 then that will be the required graph, so the slope of the graph mentioned in option C matches with m = 1.5.

Thus, Option C is the required answer.

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The probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is given by the equation P = 9/17

The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.

Given data ,

Let the probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 be P

Now , the equation will be

The fraction of doctors who are general practitioners be n ( A ) = 7/17

The fraction of doctors who are under the age of 45 n ( B ) = 4/17

And ,

The fraction of doctors who are both n ( A ∩ B ) = 2/17

Now , from the set theory formula ,

n(A∪B) = n(A) + n(B) - n(A⋂B)

And , probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B )

Substituting the values in the equation , we get

Probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B ) = ( 7 / 17 ) + ( 4/17 ) - ( 2/17 )

On simplifying the equations , we get

Probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B ) = 9/17

Hence , the probability is 9/17

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Answer:

the perimeter of the polygon is 36 feet.

Step-by-step explanation:

The perimeter of a polygon is the sum of the lengths of all its sides. In this case, you have three sides with lengths of 14 ft, 15 ft, and 7 ft. To find the perimeter, simply add these lengths together:

Perimeter = 14 ft + 15 ft + 7 ft

Perimeter = 36 ft

So the perimeter of the polygon is 36 feet.

The value of x in the proportion 1650 = x(156.25) is 10.56

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

Given the proportion:

1650 = x(156.25)

We are required to solve for x. To find x, divide both sides of the equation by 156.25:

1650 / 156.25 = x(156.25) / 156.25

x =  1650 / 156.25

x = 10.56

The value of x is 10.56

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The measure of sinx from the trigonometry is 7/25

Given the following trigonometry

tan x = 7/24

Since tan theta = opposite/adjacent

Determine the hypotenuse

h^2 = 7^2 + 24^2

h^2 = 49 + 576
h^2 = 625

h = 25

The value of sin x will be given as:

sinx = opposite/hypotenuse

sinx = 7/25

Hence the exact value of sinx where sinx>0 is 7/25

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Answer:

  5/4

Step-by-step explanation:

You want the product abc when 5x^-2y^(3/2)/√(25xy^4) is written as ax^by^c.

The applicable rules of exponents are ...

  [tex]a^ba^c=a^{b+c}\\\\\dfrac{1}{\sqrt{a}}=a^{-\frac{1}{2}}\\\\(a^b)^c=a^{bc}[/tex]

Using these rules, the expression can be simplified to ...

  [tex]\dfrac{5x^{-2}y^{\frac{3}{2}}}{\sqrt{25xy^4}}=(5x^{-2}y^{\frac{3}{2}})(5^2xy^4)^{-\frac{1}{2}}=(5x^{-2}y^{\frac{3}{2}})(5^{2(-\frac{1}{2})}x^{-\frac{1}{2}}y^{4(-\frac{1}{2})})\\\\=5^{1-1}x^{-2-\frac{1}{2}}y^{\frac{3}{2}-2}\\\\=1\cdot x^{-\frac{5}{2}}y^{-\frac{1}{2}}[/tex]

From this last expression, we determine ...

The product of the values of interest is ...

  abc = (1)(-5/2)(-1/2)

  abc = 5/4

The minimum length of the box to hold the smaller mirror is 10 inches for largest mirror fits in a box that is 18 inches wide by 20 inches long her smaller mirror.

What is proportion ?

In mathematics, proportion refers to the equality of two ratios. Two ratios are said to be proportional if they have the same relative size, meaning they represent the same relationship between quantities.

For example, if we have two ratios, such as 2/3 and 4/6, they are proportional because they represent the same relationship between two quantities. We can say that 2 is to 3 as 4 is to 6, and we can simplify both ratios by dividing the numerator and denominator of each by their greatest common factor, which in this case is 2.

Since the smaller mirror is similar in proportion to the larger mirror, the ratio of their corresponding sides is the same. Therefore, the width of the smaller box is half of the width of the larger box (9 inches is half of 18 inches).

To find the minimum length of the smaller box, we need to use the same ratio of sides. The length of the larger box is 20 inches, so the length of the smaller box should be half of 20 inches, which is 10 inches.

Therefore, the minimum length of the box to hold the smaller mirror is 10 inches.

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The conclusion is that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

The test statistic for this hypothesis test can be calculated as follows:

t = (μ1 - μ2) / sqrt(s1^2 / n1 + s2^2 / n2)

where:

μ1 = mean bumper repair cost for small pickups ($1090)

μ2 = mean bumper repair cost for small utility vehicles ($485)

s1 = standard deviation of bumper repair cost for small pickups ($403)

s2 = standard deviation of bumper repair cost for small utility vehicles ($382)

n1 = sample size for small pickups (5)

n2 = sample size for small utility vehicles (8)

Plugging in the values, we get:

t = (1090 - 485) / sqrt(403^2 / 5 + 382^2 / 8) = 4.36

Next, we need to find the critical value for a two-tailed test at a significance level of 0.10 using a t-distribution table or using a t-distribution calculator. Since the degrees of freedom (df) for a Welch's t-test are unequal, the critical value can be approximated using the degrees of freedom formula:

df = ((s1^2 / n1) + (s2^2 / n2))^2 / (((s1^2 / n1)^2) / (n1 - 1) + ((s2^2 / n2)^2) / (n2 - 1))

Plugging in the values, we get:

df = ((403^2 / 5) + (382^2 / 8))^2 / (((403^2 / 5)^2) / (5 - 1) + ((382^2 / 8)^2) / (8 - 1)) = 9.57

Using a t-distribution table or calculator, we find the critical value for a two-tailed test at a significance level of 0.10 and df = 9.57 is ±1.833.

Since the calculated t-value (4.36) is greater than the critical value (1.833), we reject the null hypothesis and conclude that there is evidence to suggest that the mean bumper repair cost is greater for small pickups than for small utility vehicles at a significance level of 0.10.

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Answer:(4,-1)

Step-by-step explanation: The vertex is the highest point of the parabola (curved line). The vertex is the point where the parabola crosses its axis of symmetry.

The vertical asymptotes of y = 6tan(0.2x) is [tex]\:x=\frac{\pi }{0.4}+\frac{\pi }{0.2}n[/tex]

From the question, we have the following parameters that can be used in our computation:

y = 6tan(0.2x)

The equation is a trigonometry function

The best way to determine the vertical asymptotes is with the use of a graphing tool

Using the above as a guide, we have the following:

From the graphing tool, we have

[tex]\:x=\frac{5\pi }{2}+\frac{\pi }{0.2}n[/tex]

This gives

[tex]\:x=\frac{\pi }{0.4}+\frac{\pi }{0.2}n[/tex]

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A triangle has three sides, three angles, and three vertices (also known as corners).

A triangle is a geometric shape that consists of three line segments that connect three non-collinear points.

Each of these line segments is called a side of the triangle. The three points where these sides meet are called the vertices (singular: vertex) of the triangle.

The triangle also has three interior angles formed by its sides. These angles are located inside the triangle, and their sum is always equal to 180 degrees.

In summary, a triangle is defined by its three sides, three angles, and three vertices.

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The number 7.787887888 is option (C) not a rational number, it has a pattern which is predictable, but not repeating

The given number is 7.787887888

The rational numbers is a number that can be expressed as the p/q format, where p and q are integers and p will not be equal to zero. So the rational number is the ratio of the two integers.

Here the given number is 7.787887888.

So this is an non terminating number

But here we can see that there is a pattern which is predictable but its not repeating

Therefore, it is not a rational number ,but it has a pattern which is predictable, but not repeating

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