which primal constraints are active at dual optimal solution when primal constraints are inequalities

Answer:

Step-by-step explanation:

Divide by 35

c = 37/35

or

c= 1.05714286

or c = 1 and 2/35

Answer:

q=5/18 decimal form is 0.27

Step-by-step explanation:

Here is the completed two-column proof:

Given: ZA and B are complementary angles. ZB and ZC are complementary angles.

Reasons Statements

Given ZA + B = 90° and ZB + ZC = 90°

Definition of complementary angles |

ZA = 90° - B and ZB = 90° - ZC

Substitution property of equality |

90° - B = 90° - ZC

Subtraction property of equality |

ZA = ZC

Angles that have equal measure are congruent |

ZAZC

Complementary angles are a pair of angles that add up to 90 degrees. In other words, when you have two complementary angles, the sum of their measures is always 90 degrees. Each angle in a pair of complementary angles is said to be the complement of the other angle.

For example, if you have one angle that measures 30 degrees, its complement would measure 60 degrees, because 30 + 60 = 90. Similarly, if you have an angle measuring 45 degrees, its complement would be 45 degrees as well, because 45 + 45 = 90.

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Answer and Explanation:

The number 18 is a rational number. Rational numbers are those that result when one integer is divided by another.

answer:

_____________________________________

the ratio 18 is as a faction: 18/100

and as a percent: 18%

_____________________________________

a ratio of a number and 18 as a faction: 18/24

and as a percent: 75%

my number is: 24

_____________________________________

explanation:

hope this helped <3 also if wouldn't mind could you pls give me brainliest? (im trying to level up) thanks! :)

Answer:

\(f(x) = - 8 \\ \\ - 7x - 1 = - 8 \\ \\ - 7x = - 8 + 1 \\ \\ - 7x = - 7 \\ \\ 7x = 7 \\ \\ x = \frac{7}{7} \\ \\ x = 1\)

Answer:

3x - 1 = 4x - 10

-1 = x - 10

9 = x

Step-by-step explanation:

10-1=4x-3x

9=X

this is the answer with steps

Answer:

A. 42 \(u^{2}\)

Step-by-step explanation:

The area of the figure is length × width. The length of the figure is 7 units, and the width is 6 units.

Finding the area:

length × width

= 7 × 6

= 42 \(u^{2}\)

The frequency of A allele after a single generation of mutation can be found as follows: Frequency of A allele after a single generationp(A) = p(A) x (1 - m) + q(a) x m

where,
m = mutation rate = 10^-6p(A) = frequency of A allele in initial generation = 0.75q(a) = frequency of a allele in initial generation = 0.25Thus,p(A) = 0.75 x (1 - 10^-6) + 0.25 x 10^-6 = 0.74999925

And the frequency of a allele will beq(a) = 1 - p(A) = 1 - 0.74999925 = 0.25000075

Therefore, the frequency of the A and a alleles in the next generation will beA: 0.74999925 and a: 0.25000075.

This is option D.

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Answer:

Step-by-step explanation:

an (the nth term ) = a1 + d(n - 1)

=  6 + 3(n - 1).

a17 = 6 + 3(17-1)

= 6 + 48

= 54.

Answer:

26

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

This is quite some trial and error question.

Based on the question, the numbers we can use are 1,3,5,7 and 9.

We will start with the middle digit first.

Since the question has stated it is 3 times the last digit, the number has to be in multiples of 3.

So we are left with: 3 and 9.

Then, the question also states the middle digit is 4 more than the first digit. See, its a digit, so the value cannot be less than 1 (odd numbers only and no negative values), so if we subtract 4 to the middle digit to find the first, it should still be a Positive Single numerical value.

3 - 4 = -1

9 - 4 = 5

Therefore, this middle digit is = 9.

Since we know the middle digit = 9

The first digit will be 9 - 4 = 5

The whole value is now 593.

(a) The smallest positive value of n for which a simple graph on n vertices and 2n edges can exist is 3. An example of such a graph for the smallest n is a triangle, where each vertex is connected to the other two vertices.

In this case, we have 3 vertices and 2n = 2 * 3 = 6 edges, which satisfies the condition.

To determine the smallest positive value of n, we need to consider the conditions for a simple graph:

1. Each vertex must be connected to at least one other vertex.

2. There should be no multiple edges between the same pair of vertices.

3. There should be no self-loops (edges connecting a vertex to itself).

Considering these conditions, we start by trying with the smallest possible n, which is 3. We construct a graph with 3 vertices and connect each vertex to the other two vertices, resulting in a triangle. This graph satisfies the conditions and has 2n = 2 * 3 = 6 edges.

(b) To prove that G is connected, we will use a proof by contradiction.

Assume that G is not connected, meaning it has two or more components. Let's consider two distinct components, C1 and C2.

Since G has at most two components, each component can have at most 10 vertices (20 vertices / 2 components). Let's assume C1 has x vertices and C2 has y vertices, where x + y ≤ 20.

Now, let's consider two vertices u and v, where u belongs to C1 and v belongs to C2. According to the given condition, deg(u) + deg(v) > 19.

Since deg(u) represents the degree of vertex u, it means the number of edges incident to vertex u. Similarly, deg(v) represents the degree of vertex v.

In C1, the maximum possible degree for a vertex is x - 1 (since there are x vertices, each connected to at most x - 1 other vertices in C1). Similarly, in C2, the maximum possible degree for a vertex is y - 1.

Therefore, deg(u) + deg(v) ≤ (x - 1) + (y - 1) = x + y - 2.

But according to the given condition, deg(u) + deg(v) > 19. This contradicts the assumption that G has at most two components.

Hence, our assumption that G is not connected is false. Therefore, G must be connected.

In conclusion, if a simple graph G has 20 vertices, at most two components, and every pair of distinct vertices satisfies the inequality deg(u) + deg(v) > 19, then G is connected.

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Answer:

below

Step-by-step explanation:

a) 1/6 * 1/6 = 1/36 = 2,78%

b) 3/6 * 3/6 = 1/4 = 25%

c) 6/6 * 1/6 = 16,67%

d) 6/6 * 5/6 = 83,33%

Answer:

Lucy is 5(m+3)=65

Soling is 5m-3=65

Kyan is 5m+3=65

Daniel is 5(m-3)=65

Step-by-step explanation:

Answer:

Lucy: 1

Solign: 3

Kyan: 2

Daniel: 4

Step-by-step explanation:

Answer:

I think it is B but i'm not 100% sure.

Step-by-step explanation:

In this scenario, the position of 0 represents the surface of the river. The value of 0 is the reference point or the baseline from which we measure the depth of objects in the river.

If the rock is 7 feet below the surface of the river, its position can be recorded as -7 feet, indicating that it is 7 feet below the reference point or the surface of the river.

the position of 0 represents the surface of the river, and any positive value represents a position above the surface of the river, while any negative value represents a position below the surface of the river.

what is surface?

In mathematics and geometry, a surface is a two-dimensional object that can be represented as a subset of three-dimensional Euclidean space. More generally, a surface can be defined as a continuous, two-dimensional manifold, which means that it is a topological space that locally resembles Euclidean space.

A surface can take on many forms, such as a plane, a sphere, a cylinder, a cone, or a torus. In general, surfaces can be classified based on their properties, such as their curvature, smoothness, and boundary conditions.

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Probability of each of the following is,

(a) 0.24, (b) 0.20 and (c) 0.56

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

(a) From the table,

Probability that exactly 1 of the trucks are not working at any point in time  = P(x = 1) = 0.24.

(b) Probability that fewer than 1 of the trucks are not working at any point in time is the probability that no trucks are working at any point of time.

P(x < 1) = P(x = 0) = 0.20

(c) Probability that more than 1 of the trucks are not working at any point in time is the combined probability that 2, 3 and 4 trucks are working.

P(x > 1) = P(x = 2) + P(x = 3) + P(x = 4)

           = 0.17 + 0.06 + 0.33

           = 0.56

Hence each of the values of the probability is found.

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The center of mass lies on the x-axis, at a distance of 4/3 units from the origin.

To find the total mass of the lamina, we need to integrate the density function rho(x,y) over the region of the lamina:

m = ∫∫ rho(x,y) dA

where dA is the differential element of area in polar coordinates, given by dA = r dr dtheta. The limits of integration are 0 to 2 in both r and theta, since the lamina occupies the disk x^2 + y^2 ≤ 4 in the first quadrant.

m = ∫(θ=0 to π/2) ∫(r=0 to 2) 3r^3 (r dr dθ)

 = ∫(θ=0 to π/2) [3/4 r^5] (r=0 to 2) dθ

 = (3/4) ∫(θ=0 to π/2) 32 dθ

 = (3/4) * 32 * (π/2)

 = 12π

So the total mass of the lamina is 12π.

To find the center of mass, we need to find the moments Mx and My and divide by the total mass:

Mx = ∫∫ x rho(x,y) dA

My = ∫∫ y rho(x,y) dA

Using polar coordinates and the density function rho(x,y)=3(x^2+y^2), we get:

Mx = ∫(θ=0 to π/2) ∫(r=0 to 2) r cos(theta) 3r^3 (r dr dtheta)

  = ∫(θ=0 to π/2) 3 cos(theta) ∫(r=0 to 2) r^5 dr dtheta

  = (3/6) ∫(θ=0 to π/2) 32 cos(theta) dtheta

  = (3/6) * 32 * [sin(π/2) - sin(0)]

  = 16

My = ∫(θ=0 to π/2) ∫(r=0 to 2) r sin(theta) 3r^3 (r dr dtheta)

  = ∫(θ=0 to π/2) 3 sin(theta) ∫(r=0 to 2) r^5 dr dtheta

  = (3/6) ∫(θ=0 to π/2) 32 sin(theta) dtheta

  = (3/6) * 32 * [-cos(π/2) + cos(0)]

  = 0

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Answer:

This is a classic example of the mark and recapture method to estimate population size. The estimated population size can be calculated using the formula:

N = (M * n) / m

where N is the estimated population size, M is the number of individuals marked and released in the first sample (200 in this case), n is the total number of individuals captured in the second sample (450 in this case), and m is the number of marked individuals recaptured in the second sample (25 in this case).

Plugging these values into the formula gives us an estimated population size of:

N = (200 * 450) / 25 = 3600

So, based on this method, the estimated fish population in the pond is 3600.

Step-by-step explanation:

The estimated fish population of the pond is 3600, obtained through the mark and recapture method - a common technique in ecology for estimating an animal population.

In this problem, we will use a method called the mark and recapture method, which is a common technique in ecology for estimating an animal population. The idea is that the proportion of marked individuals in the population is equivalent to the proportion of marked individuals in a subsequent smaller sample.

To apply this method to the given problem, we use the formula: (First capture * Second capture) / Number of marked recaptures. So, to estimate the fish population, we substitute the given numbers into the formula: (200 * 450) / 25 = 3600. Therefore, the estimated total fish population in the pond is 3600.

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The probability that at least 9 customers ordered an item from the value menu is 0.927​.

What is the simple definition of probability?

A probability is a number that expresses the possibility or likelihood that a specific event will take place.

                           In addition to being expressed as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and and 1.

Subtract the preceding probability from 1 to get the likelihood of 9 to 14 people ordering out from value menu.

The likelihood is 1 x 0.073 = 0.927.

Therefore, the probability that at least 9 customers ordered an item from the value menu is 0.927.

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The equation relating x, y, and z is:

z = 0.5 * x * y.

In the given problem, the relationship between x, y, and z can be expressed by the equation z = k * x * y, where k represents the constant of proportionality. By substituting the values of x = 4 and y = 5, when z is equal to 10, we can determine the value of the constant of proportionality, k, and further define the relationship between the variables.

To find the constant of proportionality, we substitute the known values of x = 4, y = 5, and z = 10 into the equation z = k * x * y. This gives us the equation 10 = k * 4 * 5. By simplifying the equation, we have 10 = 20k. To isolate k, we divide both sides of the equation by 20, resulting in k = 0.5. Therefore, the equation relating x, y, and z is z = 0.5 * x * y, meaning that z is directly proportional to the product of x and y with a constant of proportionality equal to 0.5.

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Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

It should be no mystery that amounts deposited get added to bank balance, and amounts withdrawn by any means get subtracted. Regarding the balance in the bank, a debit card withdrawal is equivalent to a cheque withdrawal.

Regarding the balance in the bank, a debit card withdrawal is equivalent to a cheque withdrawal. The debit card withdrawal differs from a check in the check register in that there is no check number (and frequently no transaction number) connected to it.

initial transaction

$100 is deposited to open the account. The starting balance is that sum.

two-way transaction

You must calculate the tax on the purchases for this issue. Normally, the store would take care of that for you, and you would write a check to cover the debt. The sum owed in this case is...

Rounding up from $43.82 to 45.5728 is 45.57.

Instead of calculating the tax individually and then adding it to the original amount, it is more convenient to use a multiplier to determine the amount with tax. You should be aware that the purchase price multiplied by 100% plus 4% equals 104%, or 1.04 times the price.

As a withdrawal, this $45.57 is deducted from the prior transaction's $100 total, resulting in a new balance of $54.43.

third action

This is a straightforward withdrawal, therefore $46.43 is obtained by deducting the sum from the prior balance.

As previously said, there is no transaction number connected to this. It can occasionally be helpful to keep track of which debit card is being used if you have several debit cards that are taking money out of the account. The final four digits of the card number are used to identify transactions on my bank statement.

Fourth action

You must calculate the payroll deposit amount for this problem. That would typically be handled for you by your employer, along with any deductions for taxes, insurance, union dues, or employee purchases. The sum deposited in this case is...

Hourly rate times 40 equals $9.75, which equals $390.

The previous value is increased by this deposit, making the new balance $436.43.

In most cases, the coupon is applied to transactions including coupons before the tax is calculated. The fact that the purchase amounts are combined should be obvious. (You can calculate the total when there are numerous items at the same price using repeated addition or multiplication; most people find multiplication to be simpler.)

The purchase from the bike shop is arguably the most difficult. The total of the values in brackets is...

$180.00 + 14.95 + 8.95 = 203.90

Then, the 15% discount is applied.

Rounding up to 30.59 from 0.15 x $203.90 = 30.585

Taking this out of the previous amount* yields (before taxes)...

$203.90 -30.59 = $173.31

The amount subject to tax can then be calculated using the same multiplier described above:

Round to $180.24 using the formula: amount with tax = $173.31 x 1.04 = $180.24

* Talk about the 15% discount

As with additional tax, you can calculate the discount using a multiplier:

100% - 15% = 85% . . . 0.85 times as much

The result of applying this multiplier to the number 203.90 is 173.315, which is typically rounded up to 173.32. But this figure results from a discount that is rounded to the nearest half cent (30.585). The discounted amount, 173.315, is rounded down to 173.31 if the discount is rounded up. The intricacy of applying a multiplier to discounts is there.

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Answer:

7/20

Step-by-step explanation:

first of all you have to put the two fractions on the same denominators

1/4 (multiply by 5) and you will get 5/20

2/5(multiply by 4) and you will get 8/20

we have to add 5/20 and 8/20 that gives us 13/20

13/20 is the amount he drank

20/20 - 13/20 =7/20

7/20 is the amount of water left that Charlie has left

Answer: at the end of year 9 the car value would be $9963,5

Step by step:

Every year you lose 6.30% of the last value, so from the last year's value you take out another 6.3%.

every year the formula is the same, so based on first year it would be:

$17896 * (100%-6.3%) = $17896 * 93.5% = $16768.6

year 1 17896,0 6,30%

year 2 16768,6 6,30%

year 3 15712,1 6,30%

year 4 14722,3 6,30%

year 5 13794,8 6,30%

year 6 12925,7 6,30%

year 7 12111,4 6,30%

year 8 11348,4 6,30%

year 9 10633,4 6,30%

end of year 9    =     9963,5