Not necessarily.

and

may be linearly dependent, so that their span forms a subspace of

that does not contain every vector in

.
For example, we could have

and

. Any vector

of the form

, where

, is impossible to obtain as a linear combination of these

and

, since

unless

and

.
Answer:
28 hours
Step-by-step explanation:
Adena, Julius, and Tia volunteered to read to children at the public library.
Let us represent, the number of hours worked by
Adena = x
Julius = y
Tia = z
Julius worked two hours less than Tia.
y = z - 2
z = y + 2
Adena worked twice as many hours as Julius.
x = 2y
Altogether they worked 58 hours.
x + y + z = 58.... Equation 1
We substitute 2y for x and y + 2 for z in Equation 1
2y + y + y + 2 = 58
4y + 2 = 58
Collect like terms
4y = 58 - 2
4y = 56
y = 56/4
y = 14
We are the find the number of hours Adena worked which is represented by x
Note that:
x = 2y
y = 14, hence,
x = 2 × 14
x = 28 hours
Therefore, the number of hours Adena worked is 28 hours
Answer:
10 or x=10
Step-by-step explanation:
First we can combine like-terms.
8x+6=86
Then subtract 6 from both sides
8x=80
Divide by 8
x=10
Answer:
P(X>4)= 0.624
Step-by-step explanation:
Given that
n = 10
p= 0.5 ,q= 1 - p = 0.5
Two fifth of 10 = 2/5 x 10 =4
It means that we have to find probability P(X>4).
P(X>4)= 1 -P(X=0)-P(X=1)-P(X=2)-P(X=3)-P(X=4)
We know that





P(X>4)= 1 -P(X=0)-P(X=1)-P(X=2)-P(X=3)-P(X=4)
P(X>4)= 1 -0.0009 - 0.0097 - 0.043 - 0.117-0.205
P(X>4)= 0.624