Solve the following LP using M-method [10M]
Maximize z=x₁ + 5x₂
Subject to 3x₁ + 4x₂ ≤ 6
x₁ + 3x₂ ≥ 2,
X1, X₂, ≥ 0.

The positions of the keys in a hash table of size n = 7 has been determined and the collisions are resolved by linear probing.

To determine the positions of the keys in a hash table of size n=7 and insert them into the hash table while resolving collisions by linear probing, we need to first apply a hash function that maps the keys to a specific position in the table. Let's assume that we use the simple mod function as the hash function: h(key) = key % 7.
Using this hash function, the keys will be mapped to the following positions in the hash table:
- 34 -> h(34) = 6
- 78 -> h(78) = 1
- 93 -> h(93) = 2
- 5 -> h(5) = 5
- 74 -> h(74) = 4
- 81 -> h(81) = 4
We can see that two keys, 74 and 81, are mapped to the same position in the table (position 4). This is called a collision. To resolve collisions using linear probing, we simply look for the next available position in the table and insert the key there.
Starting from the position of the collision (position 4), we check the next positions in the table sequentially until we find an empty position. The keys will be inserted into the following positions:
- 34 -> position 6
- 78 -> position 1
- 93 -> position 2
- 5 -> position 5
- 74 -> position 4 (original position)
- 81 -> position 5 (next available position after collision)
Therefore, the final hash table with the keys inserted using linear probing will look like this:
0 | |
1 |78|
2 |93|
3 | |
4 |74|
5 |5|
6 |34|

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Answer:

(d + 1) (2d + 9)

Step-by-step explanation:

2d² + 11d + 9

First, we rewrite 11d as 2d + 9d, we have the equation:

2d² + 2d + 9d + 9

We group them, so the equation will be

(2d² + 2d) + (9d + 9)

Factor out the GCF of each group

2d (d + 1) + 9 (d + 1)

Factor the polynomial by factoring out the greatest common factor, d+1

(d + 1) (2d + 9)

So, the answer is (d + 1) (2d + 9)

(X+3)(5-x)≤0

Therefore, collecting like terms,

x+3 ≤ 0

x ≤ -3

OR 5 - × ≤ 0

-x ≤ -5

Dividing both sides by -1,

x ≥ 5

We conclude that the absolute value of the given fraction is 7/10 = 0.7

Remember that the absolute value function works as follows:

Now we want to find the absolute value of a given fraction, which is 7/10.

First, we want to see if we can simplify this fraction, but we can see that the numerator is a prime number, and it is not a factor of the denominator, thus, the fraction is already in its simplest form. We also can see that it is larger than zero, then using the above rule we can write the absolute value as.

|7/10| = 7/10

We conclude that the absolute value of the given fraction is 7/10 = 0.7

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The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

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Step-by-step explanation:

For a polynomial of the form

a

x

2

+

b

x

+

c

, rewrite the middle term as a sum of two terms whose product is

a

⋅

c

=

6

⋅

−

12

=

−

72

and whose sum is

b

=

−

1

.

−

1

out of

−

x

.

6

x

2

−

(

x

)

−

12

Rewrite

−

1

as

8

plus

−

9

6

x

2

+

(

8

−

9

)

x

−

12

Apply the distributive property.

6

x

2

+

8

x

−

9

x

−

12

Factor out the greatest common factor from each group.

Tap for more steps...

2

x

(

3

x

+

4

)

−

3

(

3

x

+

4

)

Factor the polynomial by factoring out the greatest common factor,

3

x

+

4

.

(

3

x

+

4

)

(

2

x

−

3

)

147.5 times 14 = 2065

And they want an estimate so just round the 147.5 to 150.0 and the 14 to a 15 and your answer is 2250

Estimate : 2250

Actual answer is : 2065

If you have any questions comment under this post

Have a wonderful day<3

Answer:

C. (-5,1)

Explanation:

One point in the pre-image has the coordinates (-3, 7)

The translation rule is given below:

Therefore, the coordinates of its image will be:

The correct choice is C.

There are infinitely many solutions to an equation with two variables.

We know that an equation is a mathematical statement that contains equal symbol between two mathematical expressions.

In this question need to solve  an equation with x and y in one equation.

Consider an equation with two variables: 5x + y = 8

If we solve given equation for x then it would be,

5x + y = 8

5x + y - y = 8 - y

5x/5 = (8 - y)/5

x = (8 - y)/5

for any arbitrary real value value of y we can find the value of x.

This means there are infinitely many solutions.

If we solve given equation for y then it would be,

5x + y = 8

5x + y - 5x = 8 - 5x

y = 8 - 5x

for any arbitrary real value value of x we can find the value of y.

Therefore, an equation with two variables has infinitely many solutions.

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Looking at the given diagram,

angle 9x - 1 and angle y - 20 are linear pairs. they lie on a straight line. The sum of the angles on a straight line is 180 degrees. It means that

9x - 1 + y - 20 = 180

y = 180 + 1 + 20 - 9x

y = 201 - 9x equation 1

Also, angle 5x - 15 and angle y - 20 are vertically opposite angles. Vertically opposite angles are equal. It means that

5x - 15 = y - 20 equation 2

Substituting equation 1 into equation 2, it becomes

5x - 15 = 201 - 9x - 20

Collecting like terms, it becomes

5x + 9x = 201 - 20 + 15

14x = 196

x = 196/14

x = 14

y = 201 - 9x = 201 - 9 * 14

y = 201 - 126

y = 75+

The statement which are true for triangle LMN are :

1 ) The angle at vertex L is acute.

2) The angle at vertex N is acute.

What is obtuse angle ?

An obtuse angle is defined as an angle measuring less than 180 degrees and greater than 90 degrees. Examples of obtuse angle degrees include 165°, 135°, 110°, 179°, 91°, etc., which lie between 90° and 180°.

Here, it is given that triangle LMN has an obtuse angle at vertex M that is :

The angle formed by vertex L and N will be acute angle that is less then 90 degrees as to satisfy the triangle law of addition (all sum of all the angles of a triangle is 180 degree).

Therefore, option A and D are correct.

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Answer:  1, 2 and 5

Step-by-step explanation:

Analyzing Obtuse Triangles
see picture

Main Answer:The correct answer is "equality of three or more population means."

Supporting Question and Answer:

What is the purpose of the one-way analysis of variance (ANOVA) test?

ANOVA helps to assess whether these differences are statistically significant by comparing the variation between the groups to the variation within the groups.

Body of the Solution:The one-way analysis of variance (ANOVA) is used to test for" the equality of three or more population means". ANOVA compares the variation between the groups (due to differences in means) to the variation within the groups (due to individual differences within each group) to assess whether the observed differences in means are statistically significant. Therefore, the correct answer is:

"equality of three or more population means."

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Answer:

7 terms

Step-by-step explanation:

There is a common ratio between consecutive terms, that is

r = 10 ÷ 2 = 50 ÷ 10 = 5

This indicates the sequence is geometric with nth term

\(a_{n}\) = a₁ \(r^{n-1}\)

where a₁ is the first term and r the common ratio

Here a₁ = 2 and r = 5, then equating to 31250 and solving for n

2 × \(5^{n-1}\) = 31250 ( divide both sides by 2 )

\(5^{n-1}\) = 15625 = \(5^{6}\)

Since bases on both sides are equal, both 5, equate exponents

n - 1 = 6 ( add 1 to both sides )

n = 7

That is there are 7 terms in the sequence

Answer:

ueidicjfkfktitorr*rtt

28

Answer:

A

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse h is equal to the sum of the squares on the other 2 sides, that is

h² = 20² + 20² = 400 + 400 = 800 ( take the square root of both sides )

h = \(\sqrt{800}\) ≈ 28 in ( to the nearest whole number )

The range of the function y = x² - 1 is {- 1, 0, 3}.

Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x  is defined.

Given, A function y = x² - 1.

The set of domains is  {- 2, - 1, 0, 1, 2}.

The set of co-domain is {3, 0, - 1, 0, 3}.

We know range ⊆ codomain.

Therefore, The range is {- 1, 0, 3}.

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Answer:

Option B

Step-by-step explanation:

Let 'x' represents the number of miles traveled and 'y' represents the total cost of of the taxi ride.

Cost of ride with a rate of $2.25 per mile = $2.25x

Since, service charge of the taxi = $3 for first mile

Total cost of the ride = 2.25x + 3

Equation for the cost of the ride will be,

y = 2.25x + 3

Since, farthest distance that the taxi can travel = 35 miles

That means value of x may vary between x = 0 to x = 35 (including x = 25)

Therefore, domain for the situation will be,

0 < x ≤ 35

Option B will be the answer.

Answer:

Step-by-step explanation:

The first one is Crosses the axis at (1, 0). The second one is Crosses the axis at (−4, 0). The third one is touching the axis at (−5, 0).

To graph the function g(x) = (x - 5)² - 9, shift the graph of f(x) = x²

5 units right and 9 units down

Step-by-step explanation:

Let us revise the translation

1. If the function f(x) translated horizontally to the right by h units, then

   its image is g(x) = f(x - h)

2. If the function f(x) translated horizontally to the left by h units, then

   its image is g(x) = f(x + h)

3. If the function f(x) translated vertically up by k units, then its image

   is g(x) = f(x) + k

4. If the function f(x) translated vertically down by k units, then its image

   is g(x) = f(x) - k

∵ f(x) = x²

∵ g(x) = (x - 5)² - 9

∴ g(x) = f(x - 5)² - 9

∴ h = 5 ⇒ 5 units right

∴ k = -9 ⇒ 9 units down

∴ f(x) translated 5 units to the right

∴ f(x) translated 9 units down

To graph the function g(x) = (x - 5)² - 9, shift the graph of f(x) = x²

5 units right and 9 units down

The graph of g(x) = -1/5(x + 5)² - 2 is plotted making use of the points it passes.

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

The given function is g(x) = -1/5(x + 5)² - 2.

In order to plot its graph, consider following values of x and y as follows,

For x = 0,

g(x) = -1/5(0 + 5)² - 2

      = -7

For x = -5,

g(x) = -1/5(-5 + 5)² - 2

      = -2

Now as the given function has its degree as 2, it is parabolic.

Thus, its graph can be drawn as follows,

Hence, the graph of the given function is drawn clearly.

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Answer:

x=7+1/2

Step-by-step explanation:

 We move all terms to the left:

3(x+4.5)-(36.)=0

We add all the numbers together, and all the variables

3(x+4.5)-36=0

We multiply parentheses

3x+13.5-36=0

We add all the numbers together, and all the variables

3x-22.5=0

We move all terms containing x to the left, all other terms to the right

3x=22.5

x=22.5/3

x=7+1/2

Answer:

he can rolled upto 70 times when he roled in 35 time

Answer:

20 Players

Step-by-step explanation:

Total Amount of Money: $2412.50

First the team rented us a bus for $1072.50

Subtract the bus from the total

$2412.50 - $1072.50 = $1340

Total Amount of Money after bus: $1340

From there we need to find the max number of players that can go.

The budget cost for each player is $67.

So we divide the remaining money by $67 to find the number of players that can go.

$1340/$67 = 20 Players.

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Yes, the given set of numbers can be the measures of the sides of a triangle. The triangle is acute.

By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.

6.2 + 13.8 > 20

13.8 + 20 > 6.2

20 + 6.2 > 13.8

Hence, these set of numbers can be the measures of the sides of a triangle.

According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:

acute if \(a^{2} + b^{2} < c^{2}\)

obtuse if  \(a^{2} + b^{2} > c^{2}\)

right if  \(a^{2} + b^{2} = c^{2}\)

∴The longest side is 20.

Hence, a = 6.2, b = 13.8 and c = 20;

Consider \(a^{2} + b^{2}\)  :

= \(6.2^{2} + 13.8^{2}\)

= 228.88.

Now consider \(c^{2}\) :

= \(20^{2}\)

= 400.

Thus,  \(a^{2} + b^{2} < c^{2}\).

Hence, the triangle is acute.

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The test score is 91.5.

z-score:

A z-score is the number of standard deviations from the mean value of the reference population.

Here we have to find the test score.

Mean(μ) = 90

Standard deviation(б) = 15

z-score = 0.1

Formula for z-score:

z = X - μ / б

Now putting the values in the equation:

0.1 = X - 90 / 15

1.5 = X - 90

X = 91.5

Therefore the test score is 91.5.

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It seems there is an error in the given vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ as it does not have a component along the y-axis. Please double-check the vector field or provide the correct vector field to proceed with the calculation.

To compute the flux of the vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ through the surface S given by y=x^2+z^2, with 0≤y≤16, x≥0, z≥0, oriented toward the xz-plane, we can use the surface integral.

The surface integral of a vector field F⃗ over a surface S is given by the formula:

∬S F⃗ · dS = ∬S F⃗ · (n⃗ dS)

where F⃗ is the vector field, dS is the differential area vector, and n⃗ is the unit normal vector to the surface.

In this case, the surface S is given by y=x^2+z^2, with 0≤y≤16, x≥0, z≥0. We can parameterize this surface as:

r(x, z) = xi⃗ + yj⃗ + zk⃗ = xi⃗ + (x^2+z^2)j⃗ + zk⃗

To find the normal vector n⃗ to the surface, we can take the cross product of the partial derivatives of r(x, z) with respect to x and z:

n⃗ = ∂r/∂x × ∂r/∂z

= (1i⃗ + 2xj⃗) × (0i⃗ + 2zj⃗)

= -2xz i⃗ + 2zj⃗ + 2xk⃗

Now, we can calculate the flux:

∬S F⃗ · (n⃗ dS) = ∬S (3(x+z)i⃗ + 2j⃗ + 3zk⃗) · (-2xz i⃗ + 2zj⃗ + 2xk⃗) dS

= ∬S (-6x^2z - 4xz + 6xz^2 + 6xz) dS

= ∬S (-6x^2z + 2xz + 6xz^2) dS

To evaluate this integral, we need to determine the limits of integration for x, y, and z.

Since the surface is defined by 0≤y≤16, x≥0, z≥0, we have:

0 ≤ y = x^2 + z^2 ≤ 16

Simplifying the inequality, we get:

0 ≤ x^2 + z^2 ≤ 16

From this, we can see that x and z both range from 0 to 4.

Now, we can evaluate the flux:

∬S (-6x^2z + 2xz + 6xz^2) dS = ∫∫ (-6x^2z + 2xz + 6xz^2) dA

where dA is the differential area.

Integrating over the limits 0 ≤ x ≤ 4 and 0 ≤ z ≤ 4, we can calculate the flux.

However, it seems there is an error in the given vector field F⃗ = 3(x+z)i⃗ + 2j⃗ + 3zk⃗ as it does not have a component along the y-axis. Please double-check the vector field or provide the correct vector field to proceed with the calculation.

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Divide each term in the bracket by 4:

=  

3

x

−

2

Explanation:

Multiplying by  

1

4

is the same as dividing by 4. - You are finding a quarter of something.

To find a quarter of the bracket, divide each coefficient by 4.

You will get two unlike terms so you will not be able to simplify them.

This is the reason why you cannot simplify inside the original bracket either.

Step-by-step explanation:

The probability that an individual bottle contains less than 2.03 liters is approximately 0.0668, or 6.68%. If a sample of 4 bottles is selected, the probability that the sample mean amount contained is less than 2.03 liters can be calculated using the Central Limit Theorem and is approximately 0.0014, or 0.14%.

For the first part, to find the probability that an individual bottle contains less than 2.03 liters, we need to calculate the z-score and use the standard normal distribution table. The z-score is given by (X - μ) / σ, where X is the value (2.03 liters), μ is the mean (2.05 liters), and σ is the standard deviation (0.025 liters). Substituting the values, we have (2.03 - 2.05) / 0.025 = -0.08. Looking up the z-score in the standard normal distribution table, we find the corresponding probability to be approximately 0.4662. However, since we are interested in the probability that the amount is less than 2.03 liters, we need to consider the area to the left of the z-score, which is 0.5 - 0.4662 = 0.0338. Therefore, the probability is approximately 0.0338 or 3.38%.

For the second part, to find the probability that the sample mean amount contained is less than 2.03 liters for a sample of 4 bottles, we can use the Central Limit Theorem. The Central Limit Theorem states that for a large enough sample size, the sample mean will be approximately normally distributed, regardless of the shape of the population distribution. In this case, the sample mean would have the same mean (2.05 liters) but a reduced standard deviation (0.025 / √4 = 0.0125 liters). Again, we calculate the z-score using the same formula and find it to be (-0.08 - 0) / 0.0125 = -6.4. Looking up this z-score in the standard normal distribution table, the probability is extremely small and approaches 0. Therefore, the probability that the sample mean amount contained is less than 2.03 liters is approximately 0.0014 or 0.14%.

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We can drag the particles in mass/grams measurement to the corresponding descriptions as follows:

1.  1.6744 × 10⁻²⁴: Two electrons and 0ne proton

2. 5.021 × 10⁻²⁴: Two protons and one neutron

3. 5.0224 × 10⁻²⁴: One proton and two neutrons

4. 3.3484  × 10⁻²⁴: One electron, one proton, and one neutron

To match the measurements to the descriptions first note that one neutron is 1.6749 × 10⁻²⁴. One proton is equal to  1.6726 × 10⁻²⁴ and one electron is equal to  9.108 × 10⁻²⁸.

To obtain the right combinations, we have to add up the particles to arrive at the constituents. So, for the figure;

1.6744 × 10⁻²⁴, we would

Add 2 electrons and one proton

= 2(9.108 × 10⁻²⁸) + 1.6726 × 10⁻²⁴

= 1.6744 × 10⁻²⁴

The same applies to the other combinations.

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