Answer:
you got that
Step-by-step explanation:
wet wet wet
1). 16 Y= 164. ( then divided)
Y= 164 : 16
Y= 41 : 4
Y = 10 +1/4
2) 8z = 64. (then divided)
z= 64 :8
z= 8
3. D = A•B•C. ( divided)
D : A•B = C
C= D:AB
c. c= d divided by ab
Answer:
C
Step-by-step explanation:
mailing a check is the mechanical transport of a physical object representing a monetary amount for payment.
that act itself is not electronic.
at the end in today's times the final act to get the money from Elsa'a account into the account of the utility company will be most certainly electronic, but we don't know (it could still end up in the old fashioned way that somebody from the utility company goes with the check to their bank, cash that check in and then use that cash in some way). and Elsa would not be involved. for her the payment was manual, "mechanical", and not electronic.
Answer:
Step-by-step explanation:
The definite integral of a continuous function <em>f</em> over the interval [a,b] denoted by 
, is the limit of a Riemann sum as the number of subdivisions approaches infinity. That is,
where 
and 
To evaluate the integral
you must:
Find 
Find 
Therefore,
![\lim_{n \to \infty}\frac{2}{n} \sum_{i=1}^{n} 7(-2+\frac{2i}{n})^{2} +7(-2+\frac{2i}{n})\\\\\lim_{n \to \infty}\frac{2}{n} \sum_{i=1}^{n} 7[(-2+\frac{2i}{n})^{2} +(-2+\frac{2i}{n})]\\\\\lim_{n \to \infty}\frac{14}{n} \sum_{i=1}^{n} (-2+\frac{2i}{n})^{2} +(-2+\frac{2i}{n})](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%5Cfrac%7B2%7D%7Bn%7D%20%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%207%28-2%2B%5Cfrac%7B2i%7D%7Bn%7D%29%5E%7B2%7D%20%2B7%28-2%2B%5Cfrac%7B2i%7D%7Bn%7D%29%5C%5C%5C%5C%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%5Cfrac%7B2%7D%7Bn%7D%20%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%207%5B%28-2%2B%5Cfrac%7B2i%7D%7Bn%7D%29%5E%7B2%7D%20%2B%28-2%2B%5Cfrac%7B2i%7D%7Bn%7D%29%5D%5C%5C%5C%5C%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%5Cfrac%7B14%7D%7Bn%7D%20%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%20%28-2%2B%5Cfrac%7B2i%7D%7Bn%7D%29%5E%7B2%7D%20%2B%28-2%2B%5Cfrac%7B2i%7D%7Bn%7D%29)
![\lim_{n \to \infty}\frac{14}{n} \sum_{i=1}^{n} \frac{4i^2}{n^2}-\frac{6i}{n}+2\\\\\lim_{n \to \infty}\frac{14}{n}[ \sum_{i=1}^{n} \frac{4i^2}{n^2}-\sum_{i=1}^{n}\frac{6i}{n}+\sum_{i=1}^{n}2]\\\\\lim_{n \to \infty}\frac{14}{n}[ \frac{4}{n^2}\sum_{i=1}^{n}i^2 -\frac{6}{n}\sum_{i=1}^{n}i+\sum_{i=1}^{n}2]](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%5Cfrac%7B14%7D%7Bn%7D%20%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%20%5Cfrac%7B4i%5E2%7D%7Bn%5E2%7D-%5Cfrac%7B6i%7D%7Bn%7D%2B2%5C%5C%5C%5C%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%5Cfrac%7B14%7D%7Bn%7D%5B%20%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%20%5Cfrac%7B4i%5E2%7D%7Bn%5E2%7D-%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%5Cfrac%7B6i%7D%7Bn%7D%2B%5Csum_%7Bi%3D1%7D%5E%7Bn%7D2%5D%5C%5C%5C%5C%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%5Cfrac%7B14%7D%7Bn%7D%5B%20%5Cfrac%7B4%7D%7Bn%5E2%7D%5Csum_%7Bi%3D1%7D%5E%7Bn%7Di%5E2%20-%5Cfrac%7B6%7D%7Bn%7D%5Csum_%7Bi%3D1%7D%5E%7Bn%7Di%2B%5Csum_%7Bi%3D1%7D%5E%7Bn%7D2%5D)
We can use the facts that
![\lim_{n \to \infty}\frac{14}{n}[ \frac{4}{n^2}\cdot \frac{n(n+1)(2n+1)}{6}-\frac{6}{n}\cdot \frac{n(n+1)}{2}+2n]\\\\\lim_{n \to \infty}\frac{14}{n}[-n+\frac{2\left(n+1\right)\left(2n+1\right)}{3n}-3]\\\\\lim_{n \to \infty}\frac{14\left(n^2-3n+2\right)}{3n^2}](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%5Cfrac%7B14%7D%7Bn%7D%5B%20%5Cfrac%7B4%7D%7Bn%5E2%7D%5Ccdot%20%5Cfrac%7Bn%28n%2B1%29%282n%2B1%29%7D%7B6%7D-%5Cfrac%7B6%7D%7Bn%7D%5Ccdot%20%20%5Cfrac%7Bn%28n%2B1%29%7D%7B2%7D%2B2n%5D%5C%5C%5C%5C%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%5Cfrac%7B14%7D%7Bn%7D%5B-n%2B%5Cfrac%7B2%5Cleft%28n%2B1%5Cright%29%5Cleft%282n%2B1%5Cright%29%7D%7B3n%7D-3%5D%5C%5C%5C%5C%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%5Cfrac%7B14%5Cleft%28n%5E2-3n%2B2%5Cright%29%7D%7B3n%5E2%7D)
Thus,
Answer:
5 weeks
Step-by-step explanation:
To find the answer to this question we have to write an equation for both situation and put them equal to each other.
Let's write an equation for Joe:
12x + 100
Now, for Jessica
6x + 130
Next, put them equal to each other:
12x + 100 = 6x + 130
Solve:
12x + 100 = 6x + 130
6x + 100 = 130
6x = 30
x = 5
Therefore, it will take 5 weeks for Joe and Jessica to have the same amount of cards.
Check:
12(5) + 100 = 6(5) + 130
60 + 100 = 30 + 130
160 = 160
<em>I hope this helps!!</em>
<em>- Kay :)</em>
