Answer:
Possibility that the students selected are both girls = 31.25%
Step-by-step explanation:
It is given that
A science class have 5 girls and 3 boys in 7th grade
And 2 girls and 2 boys in the 8th grade
In 7th grade total students = 8
In 8th grade total students = 4
Total possibilities = 8 x 4 = 32
The teacher randomly selects a 7th grade and an 8th grade
The number ways a girl selected from 7th grade = 5c1 = 5
The number ways a girl selected from 8th grade = 2c1 = 2
Total possibilities = 5 x 2 = 10
Probability that the students selected are both girls =10 /32 = 31.25%
Answer:
The formula is not valid because the commutative property with respect to the matrix product operation is not fulfilled in the vector space of the real matrices.
Step-by-step explanation:
The formula is not valid because the commutative property with respect to the matrix product operation is not fulfilled in the vector space of the real matrices. That is, AB does not necessarily equal BA.
![A=\left[\begin{array}{ccc}1&0&0\\0&0&6\\0&8&0\end{array}\right] \\B=\left[\begin{array}{ccc}0&2&0\\6&0&0\\0&0&9\end{array}\right] \\(A -B) = \left[\begin{array}{ccc}1&-2&0\\-6&0&6\\0&8&-9\end{array}\right]\\\\(A + B) = \left[\begin{array}{ccc}1&2&0\\6&0&6\\0&8&9\end{array}\right]\\(A - B)(A + B) = \left[\begin{array}{ccc}-11&2&-12\\-6&36&54\\48&-72&-33\end{array}\right]\\A^2 - B^2 = \left[\begin{array}{ccc}-11&0&0\\0&36&0\\0&0&-33\end{array}\right]\\](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%5C%5C0%260%266%5C%5C0%268%260%5Cend%7Barray%7D%5Cright%5D%20%5C%5CB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%262%260%5C%5C6%260%260%5C%5C0%260%269%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%28A%20-B%29%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-2%260%5C%5C-6%260%266%5C%5C0%268%26-9%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%28A%20%2B%20B%29%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%262%260%5C%5C6%260%266%5C%5C0%268%269%5Cend%7Barray%7D%5Cright%5D%5C%5C%28A%20-%20B%29%28A%20%2B%20B%29%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-11%262%26-12%5C%5C-6%2636%2654%5C%5C48%26-72%26-33%5Cend%7Barray%7D%5Cright%5D%5C%5CA%5E2%20-%20B%5E2%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-11%260%260%5C%5C0%2636%260%5C%5C0%260%26-33%5Cend%7Barray%7D%5Cright%5D%5C%5C)
Given:
The cost function C(t) = 45t + 95 where t is the number of hours purchased
To Find:
The amount of money a customer pays more for using the service for 5 hours than for 3 hours
Solution:
A customer has to pay $90 more to use the service for 5 hours than for 3 hours.
Calculation:
First, we find the cost of using the service for 3 hours, i.e., at t=3. We do this by substituting t=3 in the cost function C(t) = 45t + 95
C(t) = 45(3) + 95 = 230
Thus the cost for using the service for 3 hours is $230.
Next, we find the cost of using the service for 5 hours, i.e., at t=5. We do this by substituting t=5 in the cost function C(t) = 45t + 95
C(t) = 45(5) + 95 = 320
Thus the cost for using the service for 5 hours is $320.
The difference in the two prices is $(320-230) = $90
So, a customer has to pay $90 more to use the service for 5 hours than for 3 hours.
Answer:
3x = 50 - 10y
Step-by-step explanation:
Here, x represents the number of 3 lb weights and y represents the number of 10 lb weights,
So, total weight of 3 lb weights = 3x
And, the weight of 10 lb weights = 10y
Total weight of all his weights = 3x + 10y
According to the question,
Total weight = 50 lb,
⇒ 3x + 10y = 50
Or 3x = 50 - 10y
Which is the required equation.
Second option is correct.
