We have an equation: (5+b)/2= 5
⇒ 5+b= 5*2
⇒ 5+b= 10
⇒ b= 10-5
⇒ b= 5
Final answer: b=5~
Answer:
A), B) and D) are true
Step-by-step explanation:
A) We can prove it as follows:
B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that 
. Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then 
.
C) Consider 
. This set is orthogonal because 
, but S is not orthonormal because the norm of (0,2) is 2≠1.
D) Let A be an orthogonal matrix in 
. Then the columns of A form an orthonormal set. We have that 
. To see this, note than the component 
of the product 
is the dot product of the i-th row of 
and the jth row of 
. But the i-th row of is equal to the i-th column of . If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then 
E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.
In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set 
and suppose that there are coefficients a_i such that 
. For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then 
then 
.
Answer:
Therefore, the probability that at least half of them need to wait more than 10 minutes is <em>0.0031</em>.
Step-by-step explanation:
The formula for the probability of an exponential distribution is:
P(x < b) = 1 - e^(b/3)
Using the complement rule, we can determine the probability of a customer having to wait more than 10 minutes, by:
p = P(x > 10)
= 1 - P(x < 10)
= 1 - (1 - e^(-10/10) )
= e⁻¹
= 0.3679
The z-score is the difference in sample size and the population mean, divided by the standard deviation:
z = (p' - p) / √[p(1 - p) / n]
= (0.5 - 0.3679) / √[0.3679(1 - 0.3679) / 100)]
= 2.7393
Therefore, using the probability table, you find that the corresponding probability is:
P(p' ≥ 0.5) = P(z > 2.7393)
<em>P(p' ≥ 0.5) = 0.0031</em>
<em></em>
Therefore, the probability that at least half of them need to wait more than 10 minutes is <em>0.0031</em>.
Answer:
Step-by-step explanation:
STRENGTHS
1) Budget is a major pointer to a government's commitment in a particular sector. Money allocated for education versus the %GDP will definitely show if education is a priority for the government or not.
WEAKNESSES
1) The major player, (the citizens) is not the determinant in this measure.
2) Without knowing the actual number or estimate of those who would be captured in this budget it may be impossible to know if education was really the priority of the government. Let's say (X) number of persons will benefit from the education budget, if X is unknown then planning would be on assumptions.
3) Budget alone is not sufficient in determining the commitment of the government in a sector. Laws, policies as well play a huge role and in this research laws,and policies are not part of the determining indices.
Answer:
1.25a+4.4
Step-by-step explanation:
First add the variables (in this case the only variable is a) so it would be 1.5a+0.25-0.5a = 1.25a.
Then add the non variable numbers together which would be 4.7-0.3 = 4.4.
