Answer:
49
Step-by-step explanation:
- Try finding pattern of last two digits of 7 to the power of some numbers.
7^1=07
7^2=49
7^3=343
7^4= 2301
7^5= 16807
- so , the pattern is, 07,49,43,01
- so, if we start writing all numbers from 1 to 2018 , four number in each line, 2018 will fall in the second column.
- so it will have 49 as the last 2 digits [by seeing this pattern : 07,49,43,01 ]
Consider the contrapositive of the statement you want to prove.
The contrapositive of the logical statement
<em>p</em> ⇒ <em>q</em>
is
¬<em>q</em> ⇒ ¬<em>p</em>
In this case, the contrapositive claims that
"If there are no scalars <em>α</em> and <em>β</em> such that <em>c</em> = <em>α</em><em>a</em> + <em>β</em><em>b</em>, then <em>a₁b₂</em> - <em>a₂b₁</em> = 0."
The first equation is captured by a system of linear equations,

or in matrix form,

If this system has no solution, then the coefficient matrix on the right side must be singular and its determinant would be

and this is what we wanted to prove. QED
Hey I can help give me one moment .
Answer:
percentage change in weight ≈ 10%
Step-by-step explanation:
The dog weighed 48 kg after a diet and after an exercise program the dog had a weight of 43 kg. This means the dog loss weight since the dog weight decreased from an initial value of 48 kg to 43 kg. The decrease in weight can be calculate as
decrease in weight = original weight - new weight
original weight = 48 kg
new weight = 43 kg
decrease in weight = 48 - 43 = 5 kg
Since the weight decrease their will be a percentage decrease in weight.
% decrease = decrease in weight/original weight × 100
% decrease = 5/48 × 100
% decrease = 500/48
% decrease = 10. 42666666667
percentage change in weight ≈ 10%
This is not possible. Why not? Because the smallest the variance can get is 0.
Recall that 's' represents the standard deviation, so s^2 is the variance. It basically measures how spread out the values are. The higher the variance, the more spread out the data. You can think of it as "average distance from the mean". If the variance is 0, then all of the values are at the same point. So you could have a list like {2,2,2,2,2} which has variance 0. We cannot get any smaller variance than that. If your teacher insists all the values in the list are different, then the variance will be greater than 0.