Answer:
Contradiction
Step-by-step explanation:
Suppose that G has more than one cycle and let C be one of the cycles of G, if we remove one of the edges of C from G, then by our supposition the new graph G' would have a cycle. However, the number of edges of G' is equal to m-1=n-1 and G' has the same vertices of G, which means that n is the number of vertices of G. Therefore, the number of edges of G' is equal to the number of vertices of G' minus 1, which tells us that G' is a tree (it has no cycles), and so we get a contradiction.
Answer:
7
Step-by-step explanation:
21×1/3
21÷3=7
hope I've helped
Answer:
Step-by-step explanation:So we know x + y = 21 and 5x +10y = 165 We line them up in columns x + y = 21 5x +10y = 165 To eliminate the x variable, I'll multiply every element in the 1st equation by -5. -5x + -5y = -105 5x + 10y = 165 Now we combine (add) the equations, which eliminates x altogether. 5y = 60 ... y = 12 From there, x + 12 = 21 ... x = 21-12 ... x = 9 You should double check. Do 9 nickles and 12 dimes equal $1.65? A very important thing to remember using this method is to do the same thing to each element in the equation that you change! I hope that helps.
Answer:
1. x = 67.5
2. x = 2.5
3. x = 35.2
4. x = 2.0
5. x = 17.0
Step-by-step explanation:
Question 1
The proportion is set up in the form x/9 = 15/2. Multiply both sides by two to get rid of the two in the denominator on the right side. After doing so, multiply by 9 on both sides to get rid of the 9 in the denominator on the left:
2x/9 = 15
2x = 9(15)
Next solve for x:
2x = 135
x = 67.5
Question 2
The proportion is set up in the form 20/8.7 = 5.8/x. Multiply both sides by the second denominator, x, and then both sides by the first, 8.7. This will leave you with the work below:
20x/8.7 = 5.8
20x = 8.7(5.8)
Next, solve for x:
20x = 50.46
x = 2.523
Round to the nearest tenth:
x = 2.5
Question 3
The proportion is set up in the form 5/16 = 11/x. Multiply both sides by the second denominator, x, and then both sides by the first, 16. This will leave you with the work below:
5x/16 = 11
5x = 11(16)
Next, solve for x:
5x = 176
x = 35.2
Question 4
The proportion is set up in the form x/0.06 = 17/0.5. Multiply both sides by the second denominator, 0.5, and then both sides by the first, 0.06. This will leave you with the work below:
0.5x/0.06 = 17
0.5x = 17(0.06)
Next, solve for x:
0.5x = 1.02
x = 2.04
Round to the nearest tenth:
x = 2.0
Question 5
The proportion is set up in the form 29/x = 75/44. Multiply both sides by the second denominator, 44, and then both sides by the first, x. This will leave you with the work below:
29(44)/x = 75
29(44) = 75x
Next, solve for x:
1276 = 75x
x = 17.0133
Round to the nearest tenth:
x = 17.0
Answer:
2
Step-by-step explanation:
Given the data : 29, 2, 28, 30, 26, 31
Outlier ;
Lower :Q1 - (1.5 * IQR)
Upper : Q3 + (1.5 * IQR)
Q1 = Lower quartile ; Q3 = upper quartile ; IQR = Interquartile range
Using calculator :
Q1 = 26
Q3 = 30
IQR = (Q3 - Q1) = 30 - 26 = 4
Lower : 26 - (1.5 * 4) = 20
Upper : 30 + (1.5 * 4) = 36
Hence, the number in the given data which falls outside the range is 2