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Alona [7]
3 years ago
6

True or False: If we have an integer primal solution with cost C and a fractional dual solution with cost at least C/2, the size

of the vertex cover corresponding to the primal solution is at most twice the size of the smallest vertex cover. Briefly justify your answer
Mathematics
1 answer:
maria [59]3 years ago
3 0

Answer:

True

Step-by-step explanation:

The size of the vertex cover is atleast twice the size of the maximum edge. Vertex must contain atleast one vertex from the matched edge. Vertex are never the strong dual solutions of each other.

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A student usually saves $20 a month. He would like to reach a goal of saving $350 in 12 months. The student writes the equation
elena-14-01-66 [18.8K]

Answer:

Step-by-step explanation:

350=12(x+20)

(divide both sides by 12)

29.1667=x+20

(subtract 20 from both sides)

x=9.16667

X (9.17) is the additional amount of money the student must save each month in order to reach his goal.

3 0
2 years ago
Consider the line y = x – 4. A line parallel to the graph of the line would have a slope of . A line perpendicular to the graph
kotykmax [81]

Answer:

A. 1

B. -1.

Step-by-step explanation:

We have been given an equation of a line y=x-4.

A. We know that slope of parallel lines is always equal,

We can see that slope of our given line is 1, therefore the slope of the line parallel to our given line would be 1.

B. We know that the product of slopes of two perpendicular lines is -1.

Let m represent slope of perpendicular to our given line, then:

m\times 1=-1

m=-1

Therefore the slope of the line perpendicular to our given line would be -1.

4 2
2 years ago
Read 2 more answers
The function A(b) relates the area of a trapezoid with a given height of 10 and
Natali [406]

Answer:

B(a)=\frac{a}{5} -7

Step-by-step explanation:

The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.

y = height * ( ( unknown base value ( b ) + 7 ) / 2 ),

y = 10 * ( ( b + 7 ) / 2 )

Now switch the positions of y and b -

b = 10 * ( ( y + 7 ) / 2 ) or b=\frac{\left(y+7\right)\cdot \:10}{2} - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,

y+7=\frac{a}{5},

y^{-1}=\frac{a}{5}-7 = B(a)

Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7

8 0
2 years ago
Adam and his sister Beatrice combined their allowance of $7 each so they could buy a movie for $12 they bought $1 containers of
Fittoniya [83]
14 - 12 = 2 dollars left over to buy containers. They each got one container each.
8 0
2 years ago
Read 2 more answers
In a survey of 2065 adults in a certain country conducted during a period of economic uncertainty, 63 % thought that wages paid
LenKa [72]

Answer:

a) D.The interpretation is flawed. No interval has been provided about the population proportion.

b) D.The interpretation is flawed. The interpretation indicates that the level of confidence is varying.

c) A.The interpretation is reasonable.

d) C.The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other intervals, which is not true.

Step-by-step explanation:

(a) We are 95 % confident 63 % of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low. Is the interpretation reasonable?

D.The interpretation is flawed. No interval has been provided about the population proportion.

The sample proportion alone will not give us any confidence in estimating the true proportion of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low.

We need a 95% confidence interval to claim that the true proportion is within this interval. In this case, as the margin of error is 4%, the 95% CI is 59% and 67%.

(b) We are 91 % to 99 % confident 63 % of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low. Is the interpretation reasonable?

D.The interpretation is flawed. The interpretation indicates that the level of confidence is varying.

The confidence is set at a fixed value and from that value the confidence interval is estimated. It still uses the sample proportion instead of the confidence interval to estimate the true proportion.

(c) We are 95 % confident the proportion of adults in the country during the period of economic uncertainty who believed wages paid to workers in industry were too low was between 0.59 and 0.67. Is the interpretation reasonable?

A.The interpretation is reasonable.

It uses the right sample data and interpret correctly the meaning of the confidence interval.

(d) In 95 % of samples of adults in the country during the period of economic uncertainty, the proportion who believed wages paid to workers in industry were too low is between 0.59 and 0.67. Is the interpretation reasonable?

C.The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other intervals, which is not true.

This confidence interval is an estimation about the parameter of the population. It doesn't give information to estimate the sampling distribution, as it only has information of one specific sample.

6 0
3 years ago
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