Answer: the slope intercept form for this situation is y = 0.07x + 39
Step-by-step explanation:
The cell phone package charges $39 even if 0 minutes are used during the month. This means that the package has a constant charge of $39.
Each additional minute of talk time adds $0.07. Assuming x additional minutes of talk time is made, the total cost of x additional minutes of talk time would be
0.07x + 39
Let y represent the total cost of x additional minutes, then
y = 0.07x + 39
The equation for the slope intercept form is expressed as
y = mx + c
Where
m = slope
c = intercept.
Comparing with our equation,
The slope is 0.07 and the intercept is 39
Answer:
about 3 times
Step-by-step explanation:
8 X 5 = 40 dollars
88 divided by 40 is 2.2
Find a basis for the column space and rank of the matrix ((-2,-2,-4,1),(7,-3,14,-6),(2,-2,4,-2)(2,-6,4,-3))
Novosadov [1.4K]
Answer:
- B=\{\left[\begin{array}{c}-2\\-2\\-4\\1\end{array}\right], \left[\begin{array}{c}7\\-3\\14&-6\end{array}\right], \left[\begin{array}{c}2\\-2\\4\\-2\end{array}\right] \}[/tex] is a basis for the column space of A.
- The rank of A is 3.
Step-by-step explanation:
Remember, the column space of A is the generating subspace by the columns of A and if R is a echelon form of the matrix A then the column vectors of A, corresponding to the columns of R with pivots, form a basis for the space column. The rank of the matrix is the number of pivots in one of its echelon forms.
Let ![A=\left[\begin{array}{cccc}-2&7&2&2\\-2&-3&-2&-6\\-4&14&4&4\\1&-6&-2&-3\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D-2%267%262%262%5C%5C-2%26-3%26-2%26-6%5C%5C-4%2614%264%264%5C%5C1%26-6%26-2%26-3%5Cend%7Barray%7D%5Cright%5D)
the matrix of the problem.
Using row operations we obtain a echelon form of the matrix A, that is
![R=\left[\begin{array}{cccc}1&-6&-2&-3\\0&9&2&0\\0&0&-8&-21\\0&0&0&0\end{array}\right]](https://tex.z-dn.net/?f=R%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcccc%7D1%26-6%26-2%26-3%5C%5C0%269%262%260%5C%5C0%260%26-8%26-21%5C%5C0%260%260%260%5Cend%7Barray%7D%5Cright%5D)
Since columns 1,2 and 3 of R have pivots, then a basis for the column space of A is
![B=\{\left[\begin{array}{c}-2\\-2\\-4\\1\end{array}\right], \left[\begin{array}{c}7\\-3\\14&-6\end{array}\right], \left[\begin{array}{c}2\\-2\\4\\-2\end{array}\right] \}](https://tex.z-dn.net/?f=B%3D%5C%7B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-2%5C%5C-2%5C%5C-4%5C%5C1%5Cend%7Barray%7D%5Cright%5D%2C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D7%5C%5C-3%5C%5C14%26-6%5Cend%7Barray%7D%5Cright%5D%2C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%5C%5C-2%5C%5C4%5C%5C-2%5Cend%7Barray%7D%5Cright%5D%20%5C%7D)
.
And the rank of A is 3 because are three pivots in R.
I would say the answer would be B
Answer:
Sally's team found 50 balls
Step-by-step explanation:
300 balls are hidden.
300x30%x40%
=36 balls are yellow
Sally's team finds 20% of 36 and 80% of the white balls (300x30%-36).
20%x36+80%x(300x30%-36)
=7 (approximately or else they would've found 7.2 yellow balls) +80%x(90-36)
=7+43 (approximately)
=50
