Answer:
y = 7
Step-by-step explanation:
we can substitute y for 7 in the equation to confirm that y = 7
7 + 4 = 2(7) - 3
7 + 4 = 14 - 3
11 = 14 - 3
11 = 11
(sorry if this is confusing but I hope it helped)
Answer:
19448 ways
70572902400 ways
Step-by-step explanation:
(a)
To arrange 17 books on a shelf from a possible we use the combination formula :
nCr = n! ÷ (n-r)!r!
17C10 = 17! ÷ 7! 10!
17C10 = 19448 ways
To arrange the books in alphabetical order :
2)
In question, 2, the order of arrangement matters ; hence, we use permutation ;
nPr = n! ÷ (n-r)!
17P10 = 17! ÷ (17 - 10)! = 17! ÷ 7!
17P10 = 70572902400
if we take 64 to be the 100%, how much is 6¼% off of it?
![\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 64&100\\ x&6\frac{1}{4} \end{array}\implies \cfrac{64}{x}=\cfrac{100}{6\frac{1}{4}}\implies \cfrac{64}{x}=\cfrac{\frac{100}{1}}{\frac{25}{4}}\implies \cfrac{64}{x}=\cfrac{100}{1}\cdot \cfrac{4}{25} \\\\\\ \cfrac{64}{x}=16\implies 64=16x\implies \cfrac{64}{16}=x\implies 4=x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{it had}}{64}-\stackrel{\textit{leakage}}{4}\implies \stackrel{\textit{remaining}}{60}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bccll%7D%20amount%26%5C%25%5C%5C%20%5Ccline%7B1-2%7D%2064%26100%5C%5C%20x%266%5Cfrac%7B1%7D%7B4%7D%20%5Cend%7Barray%7D%5Cimplies%20%5Ccfrac%7B64%7D%7Bx%7D%3D%5Ccfrac%7B100%7D%7B6%5Cfrac%7B1%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B64%7D%7Bx%7D%3D%5Ccfrac%7B%5Cfrac%7B100%7D%7B1%7D%7D%7B%5Cfrac%7B25%7D%7B4%7D%7D%5Cimplies%20%5Ccfrac%7B64%7D%7Bx%7D%3D%5Ccfrac%7B100%7D%7B1%7D%5Ccdot%20%5Ccfrac%7B4%7D%7B25%7D%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B64%7D%7Bx%7D%3D16%5Cimplies%2064%3D16x%5Cimplies%20%5Ccfrac%7B64%7D%7B16%7D%3Dx%5Cimplies%204%3Dx%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bit%20had%7D%7D%7B64%7D-%5Cstackrel%7B%5Ctextit%7Bleakage%7D%7D%7B4%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bremaining%7D%7D%7B60%7D)
X=41 Just S=ubract The 4 from 37 Then Subract X From X And Divide The Whole Thing By -1
Answer:
5817 Newtons.
Step-by-step explanation:
Total mass of the cage + the miners = 700 Kg which is a downward force of 700g N.
The net downward force = 700g - T where T is the tension (force) in the cable. The g = acceleration due to gravity = 9.81 m s-2.
We calculate the acceleration of the cage by using an equation of motion:
Distance = ut + 1/2 a t^2 where u = initial velocity , t = time and a = acceleration:
75 = 0(t) + 1/2 a (10^2)
50a = 75
a = 1.5 m s-2.
So using Newtons second law of motion
Force = mass * acceleration:
700*9.81 - T = 700 * 1.5
T = 700 * 9.81 - 700*1.5
= 5817 N.
