The solution is n = 5 and r = 4
Step-by-step explanation:
Given,
nCr : (n+1)Cr : (n+2)Cr = 1:3:7
To find the value of n and r.
Formula
nCr =
[ n! means = n.(n-1).(n-2)....3.2.1]
Now,
nCr : (n+1)Cr = 1:3 and (n+1)Cr : (n+2)Cr = 3:7
or,
:
= 1:3 or,
:
=
or,
×
=
or,
×
=
or,
=
or,
=
or, 3(n+1-r) = n+1 or, 7(n+2-r) = 3(n+2)
or, 3n+3-3r = n+1 or, 7n+14-7r = 3n+6
or, 2n-3r = -2 or, 4n-7r = -8
Now, by solving
2n-3r = -2 -----(1)
4n-7r = -8 -----(2) we will get n and r
Multiplying (1) by and then subtract with (2) we get,
2(2n-3r) - (4n-7r) = -4-(-8)
or, 4n-6r-4n+7r = 4
or, r = 4
From (1) we get,
2n = -2+3(4)
or, 2n = 10
or, n = 5
Hence,
n = 5 and r = 4
Answer: Total Cost = $200
Step-by-step explanation:
Given information
—————————-
Unit Price = $25 / 1 hr
$100 / 4 hr
Total Time = 8 hours
Derived formula from the given information
——————————————————————-
Total Cost = Unit Price × Total Time
Substitute values into the given formula
—————————————————————
Total Cost = (25) × (8)
Simplify by multiplication
—————————————-
Total Cost = $200
Hope this helps!! :)
Please let me know if you have any questions
<u>Answer:</u>
The range of the amount Veronica makes each hour if she can only work a total of 8 hours is 20 ≤ x ≤ 29.55
<u>Solution:
</u>
Let us assume that Veronica worked x hours
The starting pay is ![\$20](https://tex.z-dn.net/?f=%5C%2420)
Each hour increase is
So the function is ![f(x)=20(1.05)^{x}](https://tex.z-dn.net/?f=f%28x%29%3D20%281.05%29%5E%7Bx%7D)
Now if she works 8 hours, she will earn, ![= 20(1.05)^8](https://tex.z-dn.net/?f=%3D%2020%281.05%29%5E8)
![\Rightarrow 20\times1.477 = 29.55](https://tex.z-dn.net/?f=%5CRightarrow%2020%5Ctimes1.477%20%3D%2029.55)
So, the range will be 20 ≤ x ≤ 29.55
Step-by-step explanation:
x+(3x+10)=90
4x+10=90
4x=80
x=20 Ans
Explanation is in the file
tinyurl.com/wpazsebu