Answer:
0.172 ; 0.0884 ; 0.9115
Step-by-step explanation:
Proportion or those who feel secure, p = 0.45
Sample size, n = 8
Using the binomial distribution formula :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
A.) p(x = 5)
P(x =5) = 8C5 * 0.45^5 * 0.55^3
P(x = 5) = 56 * 0.0184528125 * 0.166375
P(x = 5) = 0.1719248540625
P(x = 5) = 0.172
B.) P(x > 5)
P(x > 5) = P(x = 6) + P(x = 7) + P(x = 8)
P(x > 5) = 0.0703 + 0.0164 + 0.0017
P(x > 5) = 0.0884
C.) P( ≤ 5) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5)
Using the binomial probability calculator to obtain a direct solution :
P( ≤ 5) = 0.9115
Answer:
Richard's cumulative GPA = 2.5
Step-by-step explanation:
Richard's cumulative GPA for 3 semesters was 2.0 for 42 credits.
Average = 2
Total credits = 42
Average = sum of terms/total no of terms
2 = sum of terms/42
sum of terms = 84 ....(1)
His fourth semester GPA was 4.0 for 14 course units
Average = 4
Total credits = 14
sum of terms = 56 .....(2)
Average for 4 semesters,
Hence, Richard's cumulative GPA for all 4 semesters is 2.5.
<h3><em>In AP form 2nd term - 1st term = 3rd term - 2nd term
</em></h3><h3><em>b²-a² = c²-b²
</em></h3><h3><em>b²+b² = c²+a²
</em></h3><h3><em>2b² = c²+a²
</em></h3><h3><em>
</em></h3><h3><em>Add 2ab+2ac+2bc on both sides
</em></h3><h3><em>
</em></h3><h3><em>2b²+2ab+2ac+2bc = a²+c²+ac+ac+bc+bc+ab+ab
</em></h3><h3><em>2b²+2ab+2ac+2bc = ac+bc+a²+ab+bc+c²+ab+ac
</em></h3><h3><em>2b²+2ab+2ca+2cb = ca+cb+a²+ab+cb+c²+ab+ac
</em></h3><h3><em>2(ba+b²+ca+cb) = (ca+cb+a²+ab) + (cb+c²+ab+ac)
</em></h3><h3><em>2((ba+b²)+(ca+cb)) = ((ca+cb)+(a²+ab)) + ((cb+c²)+(ab+ac))
</em></h3><h3><em>2(b(a+b)+c(a+b)) = (c(a+b)+a(a+b)) + (c(b+c)+a(b+c)) </em></h3><h3><em>2(b+c)(a+b) = (c+a)(a+b) + (c+a)(b+c)
</em></h3><h3><em>
</em></h3><h3><em>Divide whole by (a+b)(b+c)(c+a)</em></h3><h3><em></em></h3><h3><em>2/c+a = 1/b+c + 1/a+b</em></h3><h3><em>1/c+a + 1/c+a = 1/b+c + 1/a+b</em></h3><h3><em>1/c+a - 1/b+c = 1/a+b - 1/c+a</em></h3><h3><em></em></h3><h3><em>2nd term - 1st term = 3rd term - 2nd term
</em></h3><h3><em>Thus 1/b+c, 1/c+a, 1/a+b are in AP.</em></h3><h3><em></em></h3><h3><em>HOPE IT HELPS !!!</em></h3><h3><em>THANK YOU !!!</em></h3>
25.40
divide by 10 for 10%: 2.54
divide it by 2: 1.27
add 2.54 and 1.27: 3.81
add the 2 numbers together: 25.40+3.81= $29.21
Your answer is $29.21
