• The two rectangles below are similar.1096What is the value of x?O 15O 30O 5.45O 6.7ok

The optimal solution for the given linear programming model is:

max z = 38

when x1 = 5, x2 = 10, x3 = 0

To solve the given linear programming model using the simplex algorithm, we start by converting the inequalities into equations and introducing slack variables. The initial tableau is constructed with the coefficients of the decision variables and the right-hand side constants.

Next, we apply the simplex algorithm to iteratively improve the solution. By performing pivot operations, we move towards the optimal solution. In each iteration, we select the pivot column based on the most negative coefficient in the objective row and the pivot row based on the minimum ratio test.

After several iterations, we reach the optimal tableau, where all the coefficients in the objective row are non-negative. The optimal solution is obtained by reading the values of the decision variables from the tableau.

In this case, the optimal solution is z = 38 when x1 = 5, x2 = 10, and x3 = 0. This means that to maximize the objective function, the decision variables x1 and x2 should be set to 5 and 10 respectively, while x3 is set to 0.

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Answer:

6 weeks

Step-by-step explanation:

18x 6 = 108

116+108=223

Answer:

6 weeks

Step-by-step explanation:

First, if the bike is $223 and if Jennifer has 115 saved, then you have to do 223 - 115 which gets you 108.

Second, if you need $108, and you make $18 every week, then you would do 108/18 which gets you 6.

Therefore, it would take Jennifer 6 weeks to buy the bike.

Hope this helps!

Given:

Arc(AB) = 78 degrees

Measure of angle CMD = 106 degrees

To find:

The measure of arc CD.

Solution:

Secant intersection theorem: If two secant of a circle intersect each other inside the circle, then the intersection angle is the average of intercepted arcs.

Using secant intersection theorem, we get

\(m\angle CMD=\dfrac{1}{2}(Arc(AB)+Arc(CD))\)

\(106^\circ=\dfrac{1}{2}(78^\circ+Arc(CD))\)

Multiply both sides by 2.

\(212^\circ=78^\circ+Arc(CD)\)

\(212^\circ-78^\circ=Arc(CD)\)

\(134^\circ=Arc(CD)\)

Therefore, the measure of arc CD is 134 degrees and the correct option is C.

The preliminary sample size is undefined since the projected misstatement is zero.

In determining the appropriate sample size for testing inventory valuation using MUS, the following steps are taken;

Given that the population has 2,620 inventory items valued at $12,625,000 and the tolerable misstatement is $500,000 at a 10% ARIA, we can calculate the preliminary sample size using the formula;

Preliminary sample size = (Confidence Factor2 × Tolerable Misstatement)/Projected misstatement.

Considering that no misstatements are expected in the population, the projected misstatement will be zero.

Thus; the Preliminary sample size = (2.31 × 500,000)/0. Preliminary sample size = (2.31 × ∞) / 0. The preliminary sample size is undefined.

In conclusion, the preliminary sample size is undefined since the projected misstatement is zero.

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Step-by-step explanation:

Susan message=34.66

Frank message=27.6

Dan message=28

Answer:

54.06 + 33 + 29.4 = 116.46

Step-by-step explanation:

Hope This Helps

If the average salary of several of the groups was close to $51,000 then least likely to be the average salary of another one of the groups are equal to $41,000.

Random groups of teachers are = 30

If the average salary of several of the groups was close to equal to = $51,000

The mean, or average, salary is the amount derived by adding two or more salary values and dividing the sum by the number of values.

So we can write,

The average wage is known to be close to $41,000

$41,000 < $51,000

Therefore,

The average salary of another one of the groups are equal to $41,000.

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Using permutations, the 20 number different ways can the two positions be filled if each position can only be filled by one person.

According to the question,

Five people are applying for the positions of president and treasurer.

A permutations is an arrangement in a definite order of a number of objects taken some or all at a time.

\(P(n,r)=nP_{r} = \frac{n!}{(n-r)!}\)

In order to find the number different ways can the two positions be filled if each position can only be filled by one person we can find using permutations

\(5P_{2} = \frac{5!}{(5-2)!}\)

= \(\frac{120}{3*2}\)

=20

Hence, using permutations, the 20 number different ways can the two positions be filled if each position can only be filled by one person.

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Answer: Is a plane figure with at least 3 straight sides and angles, and typically five or more sides.

Step-by-step explanation:

Answer:

20, 21 and 22 are composite numbers

Step-by-step explanation:

20 is divisible by 2 4 5 and 10

21 is divisible by 3 and 7

22 is divisible by 2 and 11

Answer:

\(\frac{5}{12}\)

Step-by-step explanation:

\(\frac{5}{9}\) × \(\frac{3}{4}\) = \(\frac{15}{36}\)

HCF of 15,36 = 3

\(\frac{15}{36}\) ÷ \(\frac{3}{3}\) = \(\frac{5}{12}\)

Answer:

Three times the sum of x and seven plus ten

Step-by-step explanation:

Just did this test

The probability that an employee selected at random earns more than $50,000 per year, given that they are a college graduate, is 66.7%.

The probability of an employee being a college graduate is 20%, and the probability of an employee earning more than $50,000 per year is 25%. The probability of an employee being a college graduate and earning more than $50,000 per year is 15%.

The probability that an employee selected at random earns more than $50,000 per year, given that they are a college graduate, can be calculated using Bayes' theorem. Bayes' theorem states that the probability of an event A given an event B is equal to the probability of event A and event B happening divided by the probability of event B happening.

In this case, event A is an employee earning more than $50,000 per year, and event B is an employee being a college graduate. The probability of event A and event B happening is 15%. The probability of event B happening is 20%.

Therefore, the probability of event A given event B is 15% / 20% = 0.75 = 66.7%.

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Answer:

if we assume that

tan = opp/adj

then we can find the hypotenus by using phytagoras law

h² = o² + a²

h² = (m-1)² + (2√m)²

h² = m² - 2m + 1 + 4m

h² = m² + 2m + 1

then we factorized become

h² = (m + 1)²

h = m+1

so for sin x = opp/hyp = (m-1)/(m+1)

hope this can help you.

Answer:

4.95

Step-by-step explanation:

The volume of the rectangular prism is 16.2 ft³.

The volume of any object defined the capacity of it, how much it can hold something is called its volume.

Given is rectangular prism, we need to find the volume of the same,

So, we know that the volume of a rectangular prism is the product of its dimensions.

V = length × width × height.

\(V = 1\frac{1}{5} \times 4\frac{1}{2} \times 3\)

\(V = \frac{6}{5} \times \frac{9}{2} \times 3\)

V = 162/10

V = 16.2

Hence, the volume of the rectangular prism is 16.2 ft³.

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Theorem 5.6.1 states that any partially ordered set of size mn has either a chain of size m or an antichain of size n.

To prove this theorem, we can use induction on m.

Base Case: When m = 1, the partially ordered set has n elements, which can be viewed as an antichain of size n or a chain of size 1.

Inductive Hypothesis: Assume that any partially ordered set of size (m-1)n has either a chain of size m-1 or an antichain of size n.

Inductive Step: Consider a partially ordered set P of size mn. We choose an element p in P, and consider the two sets:

A = {x ∈ P : x < p}

B = {x ∈ P : x > p}

Note that p cannot be compared to any element in A or B, since otherwise, we would have either a chain of length m or an antichain of length n. Therefore, p is not contained in any chain or antichain of P.

Now, we can apply the inductive hypothesis to the sets A and B. If A has a chain of size m-1, then we can add p to the end of that chain to get a chain of size m. Otherwise, A has an antichain of size n-1, and similarly, B has either a chain of size m-1 or an antichain of size n-1. If both A and B have antichains of size n-1, then we can combine them with p to get an antichain of size n.

Therefore, in all cases, we have either a chain of size m or an antichain of size n, as required. This completes the proof of Theorem 5.6.1.

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The properties of the quadratic equation y=-3x^2+6x+17 is Axis of symmetry - x=1, Vertex (maximum) - (1,20), Parabola opens downwards and the end behaviour is x→∞,y→-∞, x→-∞, y→-∞.

What is a quadratic equation?

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax^2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

The quadratic equation in the general form can be written as -

y=-3x^2+6x+17

Here, a=-3

b=6

c=17

An imaginary straight line known as the axis of symmetry divides a shape into two identical sections, making one part the mirror image of the other.

Here, the axis of symmetry is x=1.

The vertex of the equation is at the maximum or the lowest point of the parabola.

So, after plotting the graph the maximum point is (1,20).

The leading coefficient of the equation is -3, which is less than zero.

So, the parabola formed by the quadratic equation opens downwards and forms a upside-down U shaped parabola.

According to the equation has an even degree and the graph of  the parabola is leading towards negative infinity.

Therefore, it can be denoted as x→∞,y→-∞, (right end down) and as x→-∞, y→-∞ (left end down).

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Answer:

1. n ≥ -1

2. n < -25/3

Step-by-step explanation:

Answer:

5.9

Step-by-step explanation:

The distance between a point A and a point B is A-B.  (4.5) - (-1.4) is the same as 4.5 + 1.4 so your answer is 5.9

Answer:

Step-by-steDistance between

(

−

4.5

,

−

4.5

)

and  

(

3.5

,

3.5

)

 is

8

√

2p explanation:

Hence distance between

(

−

4.5

,

−

4.5

)

and

(

3.5

,

3.5

)

is given by

√

(

3.5

−

(

−

4.5

)

)

2

+

(

3.5

−

(

−

4.5

)

)

2

=

√

8

2

+

8

2

=

√

64

+

64

=

√

128

=

√

8

2

×

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2

The Exact number of \($$P_{9,2}$$\) is \(72\)

The Exact number of \($$C_{7,5} $$\) is \(21\)

An exact number is a value that is known with complete certainty. In other words, an exact number has zero uncertainty and an infinite number of significant figures. An exact number cannot be simplified or reduced.

Examples of exact numbers included counted numbers, defined units, and defined unit conversions. Many exact numbers are integers, but some are decimals. Here are specific examples.

Here we have to compute \($P_{9,2}$\) means

\(P_{1,5} & =\frac{7 !}{(7-5) !}\)

\(P_{9,2} & =\frac{9 !}{(9-2) !}\)

\(=\frac{9 !}{7 !}=\frac{9 \times 8 \times 7 !}{7 !}\)

\(P_{9,2} & =7 \times 8=72\)

Hence \($P_{9,2}$\) \(=72\)

Here we have to compute \($C_{7,5}$\) means

Combination \($(7,5)$\)

\($$\begin{aligned}& \left(\begin{array}{l}7 \\5\end{array}\right)=\frac{7 !}{(7-5) ! 5 !}=\frac{7 * 6 * 5 !}{2 ! * 5 !} \\& =\frac{7 * 6}{2 * 1}=21\end{aligned}$$\)

Hence

\($$C_{7,5}=21$$\)

Therefore, the Exact number of P9,2. is 72 and C7,5. is 21.

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Answer:

2. \(\frac{1}{2}x+125=450\)

Step-by-step explanation:

We can use x to mean the number not known. Let's start by using \(\frac{1}{2}\) of a number which would be \(\frac{1}{2}x\) because the number here is signified by x. Then you would add 125 to that answer which would be shown by \(\frac{1}{2}x+125\). All of it equals 450, so it would be written as \(\frac{1}{2}x+125=450\)

2) BA and CD are parallel (segments that are collinear with parallel segments are parallel)

3) CDAB is a parallelogram (a quadrilateral with two pairs of parallel sides is a parallelogram)

4) ∠B is congruent to ∠D (opposite angles of a parallelogram are congruent)

5) m∠B = m∠D (congruent angles)

6) m∠D=115° (transitive property)

7) m∠EDA=65° (linear pair)

8) m∠EAD=65° (base angle of an isosceles triangle)

9) m∠E = 50° (sum of angles in a triangle)

Answer:

(y+1)^3

Step-by-step explanation:

(y+1)^5-2

(y+1)^3

Answer:

y1=-1,y2=0

Step-by-step explanation:

the 1 and two are both below the y :) hope this helps

The orthocenter of the ΔABC is ( -1,5 ).

In a right triangle, the orthocenter is the polygonal vertex of the right angle. When the triangle's vertices and orthocenter are joined, any point becomes the orthocenter of the other three points, according to Carnot (Wells 1991). These four locations thus form an orthocentric system.

Given the  co-ordinates A( -3,3 ), B( -1,7 ) and C( 3,3 ).

To find the orthocenter using below steps:

1. First, we find the equations of AB and BC.

The general form of a line is y = mx + b

where m is the slope and b is the y-intercept.

Using the formula of slope given \($m =\frac{y_2 - y_1}{x_2 - x_1}\)  , we will find the slope of AB and BC.

Now, slope of AB is m = (7-3/-1 + 3)  

i.e. m = (4/2) = 2

Putting this 'm' in the general form and using the point B(-1, 1), we get the y-intercept as,

y = mx + b

1 = 2 × (-1) + b

i.e. b = 3.

So, the equation of AB is y = 2x + 3.

Also, slope of BC is m=(3-7/3+1)  i.e. m=-4/4 i.e. m--1

Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,

y = mx + b i.e. 1 = (-1) × (-1) + b i.e. b = 0.

So, the equation of BC is y = -x.

2. We will find the slope of line perpendicular to AB and BC.

When two lines are perpendicular, then the product of their slopes is -1.

So, slope of line perpendicular to AB is \(m*2=-1\)  i.e. m = -1/2

So, slope of line perpendicular to BC is  i.e.\(m*-1=-1\) i.e. m = 1.

3. We will now find the equations of line perpendicular to AB and BC.

Using the slope of line perpendicular to AB m=-1/2 i.e.  and the point opposite to AB

i.e. C(3, 3), we get,

y = mx + b

i.e. \(3=-1/2*3+b\)  

i.e. b = 9/2

So, the equation of line perpendicular to AB is

\(y=-x/2+9/2\)

Again, using the slope of line perpendicular to BC i.e. m = 1 and the point opposite to BC

i.e. A( -3,3 ), we get,

y = mx + b

i.e. 3 = 1 × -3 + b

i.e. b = 6.

So, the equation of line perpendicular to BC is y = x+6

4. Finally, we will solve the obtained equations to find the value of (x, y).

As, we have y = x + 6 and  y = -x/2 + 9/2

This gives, y = -x/2 + 9/2 → x + 6

y = -x/2 + 9/2

simplifying the above equation, we get

2x + 12 = -x + 9

3x = -3

x = -1.

So, y = x + 6

simplifying the above equation, we get

y = -1 + 6

y = 5.

The value of x = -1 and y = 5.

Hence, the orthocenter of the ΔABC is ( -1,5 ).

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Answer:

15πcm

Step-by-step explanation:

2πr = circumference

radius = 0.075m = 7.5cm

Circumference = 7.5X2π

15π cm

The expression of the league fee is an algebraic expression

The expression that represents the league fee is 14x

The expression is given as:

14x + 20(2y + ) 5z + 10

The expression is not properly stated;

Only the league fee can be deducted from the given expression.

From the question, we understand that there are 14 players in total

i.e you (1) and (13) others

This means that the total league fee for the 14 players is:

Total = 14 * League fee for each player.

One of the terms of the expression is 14x.

So, we have:

14 * League fee for each player. = 14x

Hence, the expression that represents the league fee is 14x

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Answer:

the first one is about 8

the second one is about 13

Step-by-step explanation:

By algebra properties and trigonometric formulas, the trigonometric expression (tan x - 1) / (tan x + 1) is equivalent to (1 - cot x) / (1 + cot x).

In this problem we find a trigonometric expression, whose equivalent expression is found both by algebra properties and trigonometric formulas. First, write the entire expression:

(tan x - 1) / (tan x + 1)

Second, use trigonometric formulas:

(1 / cot x - 1) / (1 / cot x + 1)

Third, use algebra properties and simplify the resulting expressions:

[(1 - cot x) / cot x] / [(1 + cot x) / cot x]

(1 - cot x) / (1 + cot x)

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