It is helpful to write them in different ways
some ways to write them are
1.fractions
2.decimals
3.squareroots (if applicable)
so it would be more helpful in an equation to leave 6/7 in fractional form if you are going to manipulate it more, because 0.857142857142... is much harder to keep track of than 6/7
and sometimes, they want a percent which is easier to convert to from decimal form than from fractinoal form so ex 0.857142857142...=85.7% vs 6/7 to percent
sometimes there will be square roots and they are easier if left like that ex
√2=1.4142135623...
it would be easier to leav it in square root
it depends on the equation you are trying to solve, because different forms have different pros and cons, some are easier to work with in a certain form but not in another, sometimes, you will need to change between multipule forms during the same problem
The solution will be: ![w>-1](https://tex.z-dn.net/?f=w%3E-1)
<em><u>Explanation</u></em>
The given inequality is: ![53w+13 < 56w + 16](https://tex.z-dn.net/?f=53w%2B13%20%3C%2056w%20%2B%2016)
First we will subtract
from both sides. So.....
![53w+13-56w](https://tex.z-dn.net/?f=53w%2B13-56w%3C16%5C%5C%20%5C%5C%20-3w%2B13%3C16)
Now we will subtract 13 from both sides. So.....
![-3w](https://tex.z-dn.net/?f=-3w%3C16-13%5C%5C%20%5C%5C%20-3w%3C3)
Then we need to divide both sides by -3. As here we are <u>dividing the inequality by a negative number, so we need to switch the inequality symbol</u>. So, we will get.......
![\frac{-3w}{-3}>\frac{3}{-3}\\ \\ w>-1](https://tex.z-dn.net/?f=%5Cfrac%7B-3w%7D%7B-3%7D%3E%5Cfrac%7B3%7D%7B-3%7D%5C%5C%20%5C%5C%20w%3E-1)
Thus, the solution will be: ![w>-1](https://tex.z-dn.net/?f=w%3E-1)
Answer: 154.4 Fahrenheit
Step-by-step explanation: 68°C = ( 68× 9 / 5 + 32 ) = 154.4°F
The initial cost is 189.69. It is marked up 30%.
By simple calculations,
Final cost of the tablet computer = Initial price + 30% of marked price
= 189.69 + (30/100 x 189.69)
This gives us the net value of 245.7. Hence the price of the computer after it's been marked up will be 245.7
SOLUTION
This is a binomial probability. For i, we will apply the Binomial probability formula
i. Exactly 2 are defective
Using the formula, we have
![\begin{gathered} P_x=^nC_x\left(p^x\right?\left(q^{n-x}\right) \\ Where\text{ } \\ P_x=binomial\text{ probability} \\ x=number\text{ of times for a specific outcome with n trials =2} \\ p=\text{ probability of success = }\frac{4}{24}=\frac{1}{6} \\ q=probability\text{ of failure =1-}\frac{1}{6}=\frac{5}{6} \\ ^nC_x=\text{ number of combinations = }^4C_2 \\ n=\text{ number of trials = 4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P_x%3D%5EnC_x%5Cleft%28p%5Ex%5Cright%3F%5Cleft%28q%5E%7Bn-x%7D%5Cright%29%20%5C%5C%20Where%5Ctext%7B%20%7D%20%5C%5C%20P_x%3Dbinomial%5Ctext%7B%20probability%7D%20%5C%5C%20x%3Dnumber%5Ctext%7B%20of%20times%20for%20a%20specific%20outcome%20with%20n%20trials%20%3D2%7D%20%5C%5C%20p%3D%5Ctext%7B%20probability%20of%20success%20%3D%20%7D%5Cfrac%7B4%7D%7B24%7D%3D%5Cfrac%7B1%7D%7B6%7D%20%5C%5C%20q%3Dprobability%5Ctext%7B%20of%20failure%20%3D1-%7D%5Cfrac%7B1%7D%7B6%7D%3D%5Cfrac%7B5%7D%7B6%7D%20%5C%5C%20%5EnC_x%3D%5Ctext%7B%20number%20of%20combinations%20%3D%20%7D%5E4C_2%20%5C%5C%20n%3D%5Ctext%7B%20number%20of%20trials%20%3D%204%7D%20%5Cend%7Bgathered%7D)
Note that I made the probability of being defective as the probability of success = p
and probability of none defective as probability of failure = q
Exactly 2 are defective becomes the binomial probability
![\begin{gathered} P_x=^4C_2\times\lparen\frac{1}{6})^2\times\lparen\frac{5}{6})^{4-2} \\ P_x=6\times\frac{1}{36}\times\frac{25}{36} \\ P_x=\frac{25}{216} \\ =0.1157 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P_x%3D%5E4C_2%5Ctimes%5Clparen%5Cfrac%7B1%7D%7B6%7D%29%5E2%5Ctimes%5Clparen%5Cfrac%7B5%7D%7B6%7D%29%5E%7B4-2%7D%20%5C%5C%20P_x%3D6%5Ctimes%5Cfrac%7B1%7D%7B36%7D%5Ctimes%5Cfrac%7B25%7D%7B36%7D%20%5C%5C%20P_x%3D%5Cfrac%7B25%7D%7B216%7D%20%5C%5C%20%3D0.1157%20%5Cend%7Bgathered%7D)
Hence the answer is 0.1157
(ii) None is defective becomes
![\begin{gathered} \lparen\frac{5}{6})^4=\frac{625}{1296} \\ =0.4823 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Clparen%5Cfrac%7B5%7D%7B6%7D%29%5E4%3D%5Cfrac%7B625%7D%7B1296%7D%20%5C%5C%20%3D0.4823%20%5Cend%7Bgathered%7D)
hence the answer is 0.4823
(iii) All are defective
![\begin{gathered} \lparen\frac{1}{6})^4=\frac{1}{1296} \\ =0.00077 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Clparen%5Cfrac%7B1%7D%7B6%7D%29%5E4%3D%5Cfrac%7B1%7D%7B1296%7D%20%5C%5C%20%3D0.00077%20%5Cend%7Bgathered%7D)
(iv) At least one is defective
This is 1 - probability that none is defective
![\begin{gathered} 1-\lparen\frac{5}{6})^4 \\ =1-\frac{625}{1296} \\ =\frac{671}{1296} \\ =0.5177 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%201-%5Clparen%5Cfrac%7B5%7D%7B6%7D%29%5E4%20%5C%5C%20%3D1-%5Cfrac%7B625%7D%7B1296%7D%20%5C%5C%20%3D%5Cfrac%7B671%7D%7B1296%7D%20%5C%5C%20%3D0.5177%20%5Cend%7Bgathered%7D)
Hence the answer is 0.5177