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irina [24]
2 years ago
9

Is the statement ""For every natural number n ≥ 1 there exists a directed graph of n vertices for which every vertex has an inde

gree equal to its outdegree"" TRUE or FALSE?
Mathematics
1 answer:
Semenov [28]2 years ago
5 0

Answer:

The given statement is false.

Step-by-step explanation:

Reason

let D be a directed graph with 'n' no of vertices and 'E' edges.

where 'n'=1.  thus D =(n,E).

In degree: in directed graph the number of incoming edges on a vertex is known as indegree.

it is denoted as deg ⁺(n).

And now we know that in a directed graph

if deg ⁻(n)= deg ⁺(n) for each vertex n.

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In a large city, 46% of adults support the local football team building a new stadium. If a poll is taken from a random sample o
Sveta_85 [38]

Answer: 0.46, 0.056, the distribution is approximately normal

Step-by-step explanation: The shape is approximately normal since the expected number of successes equals 36.8 and the expected number of failures equals 43.2 are both larger than 10

7 0
2 years ago
What is the slope of the segment shown for a staircase with 10-inch treads and 7.75-inch risers? As you walk up (or down) the st
s2008m [1.1K]

The formula for slope is

Slope = Rise / Run = Risers / Treads

Slope = 7.75 in /10 in = 0.775

The slope Is 0.775.

The vertical distance is not continuous, thus it is discrete. A discrete function only allows certain points in the interval. When you walk up or down the stairs, the vertical distances are not continuous because of the treads. You cannot stay also mid-air, so it should be discrete. An example of a continuous function would be when you walk up or down an inclined plane. 

8 0
2 years ago
A brochure from the department of public safety in a northern state recommends that motorists should carry 12 items (flashlights
scoray [572]

Answer:

Mean = 6.07

Median = 7

Mode = 7

Step-by-step explanation:

Given

Data: 5\ 3\ 7\ 8\ 0\ 1\ 0\ 5\ 12\ 10\ 7\ 6\ 7\ 11\ 9

n = 15

Solving (a): The mean

Mean is calculated as:

Mean = \frac{\sum x}{n}

This gives:

Mean = \frac{5+ 3+ 7+ 8+ 0+ 1+ 0+ 5+ 12+ 10+ 7+ 6+ 7+ 11+ 9}{15}

Mean = \frac{91}{15}

Mean = 6.07

Solving (b): The median

Sort the data in ascending order:

Data: 5\ 3\ 7\ 8\ 0\ 1\ 0\ 5\ 12\ 10\ 7\ 6\ 7\ 11\ 9

Sorted: 0\ 0\ 1\ 3\ 5\ 5\  6\ 7\ 7\ 7\ 8\ 9\ 10\ 11\ 12

The median is:

Median = \frac{n + 1}{2}th

Median = \frac{15 + 1}{2}th

Median = \frac{16}{2}th

Median = 8th    

The 8th item on the sorted dataset is 7; So:

Median = 7

Solving (c): The mode

Mode = 7

Because it has a frequency of 3 (more than any other element of the dataset).

6 0
2 years ago
An online furniture store sells chairs for $200 each and tables for $600 each. Every day, the store can ship a maximum of 32 pie
wolverine [178]

Answer:

If the minimum 13 chair were sold , then the minimum number of Table sold is 14

Step-by-step explanation:

Given as :

The cost of each chair = $ 200

The cost of each table = $ 600

The total number of furniture sold per day = 32

The minimum amount of selling per day = $ 12000

Let the total number of chair = C

The total number of table = T

So , according to question

C + T = 32         .......1

200 C + 600 T = 12000         .......2

Solving eq 1 and 2

200 C + 600 T = 12000

200 × ( C + T ) = 32 × 200

I.e 200 C + 200 T = 6400

or, ( 200 C + 600 T ) - ( 200 C + 200 T ) = 12,000 - 6400

Or, 400 T =  5600

∴  T = \frac{5600}{400}

I.e T = 14

Put The value of T in eq 2

So, 200 C + 600 × 14 = 12000

or , 200 C + 8400 = 12,000

Or, 200 C = 12000 - 8400

Or, 200 C = 3600

∴   C = \frac{3600}{200}

I.e C = 18

The number of chair sold is 18

If the number of chair sold is 13 ,

Then the min number of table sold = 200 × 18 + 600 T = 12000

i.e 600 T = 12000 - 3600

or, 600 T = 8400

∴   T = \frac{8400}{600}

I.e T = 14

Hence if the minimum 13 chair were sold , then the minimum number of Table sold is 14 . Answer

5 0
2 years ago
Becky is an experienced swimmer. The table contains data on her times in the 100-meter freestyle event for each year over the pa
Sauron [17]
Correlation coefficient (r) = [nΣxy - (Σx)(Σy)] / [sqrt(nΣx^2 - (Σx)^2)sqrt(nΣy^2 - (Σy)^2)]
Σx = 21 => (Σx)^2 = 21^2 = 441
Σy = 671 => (Σy)^2 = 671^2 = 450,241
Σx^2 = 1 + 4 + 9 + 16 + 25 + 36 = 91
Σy^2 = 98^2 + 101^2 + 109^2 + 117^2 + 119^2 + 127^2 = 75,665
Σxy = 1(98) + 2(101) + 3(109) + 4(117) + 5(119) + 6(127) = 2,452
r = [6(2,452) - 21(671)] / [sqrt(6(91) - 441)sqrt(6(75,665) - 450,241)] = 621/sqrt(105)sqrt(3749) = 0.99

option b is the correct answer.
5 0
2 years ago
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