Answer:
1) 6r+7=13+7r —> 7r–6r=7–13 —> r = – 6
2) 13–4x=1–x —> 4x–x=13–1 —> 3x=12 —> x=12/3 —> x=4
3)–7x–3x+2=–8x–8 —> –8x+7x+3x=2+8 —> 2x=10 –> x= 10/2 –> x= 5
4)–8–x=x–4x —> –x–x+4x=8 —> 2X=8 —> x= 8/2 —> x= 4
5) –14+6b+7-2b=1+5b —> 5b +2b –6b = –14+7–1 —> b=–8
6) n+2=–14–n —> n+n=–14–2 —> 2n = –16 —> n = – 16/ 2 —> n = – 8
7) n – 3n = 14 –4n —> n –3n + 4n = 14 —> 2n = 14 —> n = 14/ 2 —> n = 7
8) 7a – 3 = 3 + 6a —> 7a – 6a = 3 + 3 —> a = 6
9) 3(1–3x ) =2(–4x+7) —> 3 –9x = –8x+14 —> 9x–8x = 3–14 —> x = –11
10) –10 +x+4–5 =7x –5 —> 7x–x = –10+4–5 +5 —> 6x = –6 —> x= –6/6 —> x = –1
11) –8n +4(1+5n)=–6n–14 —> –8n +4 + 20n = – 6n– 14
20n –8n +6n= –14 –4 —> 18n = – 18 —> n = –18/18 —> n = –1
12) –6n–20=–2n +4(1–3n) —> –6n –20 = – 2n +4 –12n —> 12n +2n –6n = 4 +20 —> 8n =24 —> n = 24/8 —> n =3
I hope I helped you^_^
Answer:
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Answer:
Step-by-step explanation:
From the given information:
a.
Compute 
:
b.
Compute P(A ∩ B)
P(A ∩ B) = P(A) +P(B) - P(A∪B)
P(A ∩ B) = 0.32 + 0.46 - 0.57
P(A ∩ B) = 0.21
Thus, since P(A ∩ B) ≠ 0, we can say that they are not mutually exclusive.
c.
P(A ∩ C) = P(A) +P(C) - P(A∪C)
P(A ∩ C) = 0.32 + 0.23 -0.55
P(A ∩ C) = 0
Thus, since P(A ∩ C) = 0, we can say that they are both mutually exclusive.
d. To determine P[(A ∪ B ∪ C)′]
i.e. none of the events occurring
Then :
P(B ∩ C) = 0.46 +0.23 -0.49
P(B ∩ C) = 0.20
Therefore:
P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∩ B ) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)
P(A ∪ B ∪ C) = 0.32 + 0.46 + 0.23 - 0.21 - 0 - 0.20 + 0
P(A ∪ B ∪ C) = 0.60
Using the findings from a qualitative study to develop a new quantitative survey is known as mixed integration.
Mixed integration is called the data collection and information classification system that includes both qualitative and quantitative processes as access mechanism to said data and information, that is, performing a mixed or dual analysis of the concepts being studied.
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