Karmin will make $18.4 for working an hour after the increase.
Step-by-step explanation:
Step 1:
First, we need to determine how much Karmin made an hour.
Karmin's hourly rate ![= \frac{480}{30} = 16.](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B480%7D%7B30%7D%20%3D%2016.)
So Karmen made $16 every hour that she worked. She worked for 30 hours and earned $480.
She will get a 15% increase in her hourly rate this month.
Step 2:
We need to determine how much 15% of $16 is.
15% of $16 ![= \frac{15}{100} (16) = 0.15 (16)= 2.4.](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B15%7D%7B100%7D%20%2816%29%20%3D%200.15%20%2816%29%3D%202.4.)
So her 15% increase amounts to $2.4.
So the hourly rate for this month ![16 + 2.4 = 18.4.](https://tex.z-dn.net/?f=16%20%2B%202.4%20%3D%2018.4.)
So Karmin will make $18.4 for working 1 hour.
The manager already hired 9 people. Let
be the number of people he still can hire. Since these people will add to the 9 he already hired, when the hiring campaign will be over he will have hired
people. We know that he can't hire more than 14 people, so the number of people hired must be less than or equal to 14:
![9+x \leq 14](https://tex.z-dn.net/?f=%209%2Bx%20%5Cleq%2014%20)
If we subtract 9 from both sides, we have
![x \leq 14-9=5](https://tex.z-dn.net/?f=%20x%20%5Cleq%2014-9%3D5%20)
so, the manager can hire at most 5 other people
Please, use parentheses to enclose each fraction:
y=3/4X+5 should be written as <span>y=(3/4)X+5
Let's eliminate the fraction 3/4 by multiplying the above equation through by 4:
4[y] = 4[(3/4)x + 5]
Then 4y = 3x + 20
(no fraction here)
Let 's now solve the system
4y=3x + 20
4x-3y=-1
We are to solve this system using subtraction. To accomplish this, multiply the first equation by 3 and the second equation by 4. Here's what happens:
12y = 9x + 60 (first equation)
16x-12y = -4, or -12y = -4 - 16x (second equation)
Then we have
12y = 9x + 60
-12y =-16x - 4
If we add here, 12y-12y becomes zero and we then have 0 = -7x + 56.
Solving this for x: 7x = 56; x=8
We were given equations
</span><span>y=3/4X+5
4x-3y=-1
We can subst. x=8 into either of these eqn's to find y. Let's try the first one:
y = (3/4)(8)+5 = 6+5=11
Then x=8 and y=11.
You should check this result. Subst. x=8 and y=11 into the second given equation. Is this equation now true?</span>
Consecutive terms in an arithmetic sequence differ by a constant
![d](https://tex.z-dn.net/?f=d)
. So
![5k-1=2k+d](https://tex.z-dn.net/?f=5k-1%3D2k%2Bd)
![6k+2=5k-1+d](https://tex.z-dn.net/?f=6k%2B2%3D5k-1%2Bd)
![\implies\begin{cases}3k-d=1\\k-d=-3\end{cases}\implies k=2,d=5](https://tex.z-dn.net/?f=%5Cimplies%5Cbegin%7Bcases%7D3k-d%3D1%5C%5Ck-d%3D-3%5Cend%7Bcases%7D%5Cimplies%20k%3D2%2Cd%3D5)
Denote the
![n](https://tex.z-dn.net/?f=n)
-th term in the sequence by
![a_n](https://tex.z-dn.net/?f=a_n)
. Now that
![a_1=2](https://tex.z-dn.net/?f=a_1%3D2)
, we have
![a_n=a_{n-1}+5=a_{n-2}+2\cdot5=\cdots=a_1+(n-1)\cdot5](https://tex.z-dn.net/?f=a_n%3Da_%7Bn-1%7D%2B5%3Da_%7Bn-2%7D%2B2%5Ccdot5%3D%5Ccdots%3Da_1%2B%28n-1%29%5Ccdot5)
which means
Answer:
False
Step-by-step explanation:
10 jumbo jets