Answer:
see explanation
Step-by-step explanation:
To multiply the vector by a scalar, multiply each of the elements by the scalar.
To add 3 vectors add the corresponding elements of each vector
2a + 3b + 4c
= 2![\left[\begin{array}{ccc}2\\3\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%5C%5C3%5C%5C%5Cend%7Barray%7D%5Cright%5D)
+ 3![\left[\begin{array}{ccc}-4\\1\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-4%5C%5C1%5C%5C%5Cend%7Barray%7D%5Cright%5D)
+ 4![\left[\begin{array}{ccc}3\\2\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C2%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}4\\6\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C6%5C%5C%5Cend%7Barray%7D%5Cright%5D)
+ ![\left[\begin{array}{ccc}-12\\3\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-12%5C%5C3%5C%5C%5Cend%7Barray%7D%5Cright%5D)
+ ![\left[\begin{array}{ccc}12\\8\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D12%5C%5C8%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}4-12+12\\6+3+8\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4-12%2B12%5C%5C6%2B3%2B8%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}4\\17\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%5C%5C17%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Answer:
Solution given:
length[l]=3x+7
breadth [b]=2x+3
we have
area of rectangle=l×b=(3x+7)(2x+3)
=6x²+14x+9x+21=6x²+23x+21 units ²
Answer:
(-1 (3 y + 17))/2
Step-by-step explanation:
Simplify the following:
y/4 - (1 + 3/4) y - 12 + 1/2 + 1 + 2
Put 1 + 3/4 over the common denominator 4. 1 + 3/4 = 4/4 + 3/4:
y/4 - 4/4 + 3/4 y - 12 + 1/2 + 1 + 2
4/4 + 3/4 = (4 + 3)/4:
y/4 - (4 + 3)/4 y - 12 + 1/2 + 1 + 2
4 + 3 = 7:
y/4 - 7 y/4 - 12 + 1/2 + 1 + 2
Put each term in y/4 - (7 y)/4 - 12 + 1/2 + 1 + 2 over the common denominator 4: y/4 - (7 y)/4 - 12 + 1/2 + 1 + 2 = y/4 - (7 y)/4 - 48/4 + 2/4 + 4/4 + 8/4:
y/4 - (7 y)/4 - 48/4 + 2/4 + 4/4 + 8/4
y/4 - (7 y)/4 - 48/4 + 2/4 + 4/4 + 8/4 = (y - 7 y - 48 + 2 + 4 + 8)/4:
(y - 7 y - 48 + 2 + 4 + 8)/4
Grouping like terms, y - 7 y - 48 + 2 + 4 + 8 = (y - 7 y) + (4 + 2 + 8 - 48):
((y - 7 y) + (4 + 2 + 8 - 48))/4
y - 7 y = -6 y:
(-6 y + (4 + 2 + 8 - 48))/4
4 + 2 + 8 - 48 = -34:
(-34 - 6 y)/4
Factor -2 out of -6 y - 34:
(-2 (3 y + 17))/4
The gcd of -2 and 4 is 2, so (-2 (3 y + 17))/4 = ((2 (-1)) (3 y + 17))/(2×2) = 2/2×(-(3 y + 17))/2 = (-(3 y + 17))/2:
Answer: (-1 (3 y + 17))/2
13/10 so 10/10=1
13-10=3
1 3/10 is 13/10 as a mixed number
hope that helps!
Answer:
Option D) significantly different from 24
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 24
Sample mean, 
= 25
Sample size, n = 16
Alpha, α = 0.05
Population standard deviation, σ = 2
First, we design the null and the alternate hypothesis
We use Two-tailed z test to perform this hypothesis.
Formula:
Putting all the values, we have
Now, 
Since,
The calculated z statistic does not lie in the acceptance region, we fail to accept the null hypothesis and reject it. We accept the alternate hypothesis.
Thus, it can be concluded that the mean age is
Option D) significantly different from 24
