<h3>
Answer: Choice B) 3:1</h3>
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Explanation:
Consider a very small town of only 4 people.
If 1 person bikes to work, then 1/4 = 0.25 = 25% of the population commutes by bicycle. We see that the remaining 4-1 = 3 people don't travel by bike.
The odds against selecting someone who uses their bike to get to work is 3:1 which is why the answer is choice B
We list the number of people we don't want first, and then the number of people we do want (those who use a bike). A colon separates the two values to form the odds ratio.
We can say "3:1" as "3 to 1". It means we're 3 times more likely to select someone we don't want vs someone we do want. The odds are against the bike person which is why the value we don't want is listed first.
In contrast, if your teacher asked "what are the odds in favor of selecting someone who commutes by bicycle?" then the answer would be 1:3. We simply swap the positions of what we set up earlier.
Step-by-step explanation:
![\underline{ \underline{ \text{Given}}} :](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Cunderline%7B%20%5Ctext%7BGiven%7D%7D%7D%20%20%3A%20%20)
![\underline{ \underline { \text{To \: Find}}} :](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Cunderline%20%7B%20%5Ctext%7BTo%20%5C%3A%20Find%7D%7D%7D%20%3A%20)
![\underline{ \underline{ \text{Solution}}} :](https://tex.z-dn.net/?f=%20%5Cunderline%7B%20%5Cunderline%7B%20%5Ctext%7BSolution%7D%7D%7D%20%3A%20%20)
The new matrix obtained from a given matrix by interchanging it's rows and columns is called the transposition of matrix. It is denoted by
. Again , Interchange it's rows and columns in order to find ' A '.
![\tt{A = \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix}}](https://tex.z-dn.net/?f=%20%5Ctt%7BA%20%3D%20%5Cbegin%7Bbmatrix%7D%202%20%26%20%204%20%5C%5C%20%20-%204%20%26%203%20%5C%5C%20%5Cend%7Bbmatrix%7D%7D)
Now , LEFT HAND SIDE ( L.H.S )
![\tt{ {A}^{2} - 5A+ 22I}](https://tex.z-dn.net/?f=%20%5Ctt%7B%20%7BA%7D%5E%7B2%7D%20%20-%205A%2B%2022I%7D)
Here, I refers to identity matrix. A diagonal matrix in which all the elements of leading diagonal are 1 ( unit ) is called unit or identity matrix.
⟼ ![\begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} \times \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} - 5 \times \begin{bmatrix} 2 & 4 \\ - 4 & 3 \\ \end{bmatrix} + 22 \times \begin{bmatrix} 1 & 0 \\ 0 & 1\\ \end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D%202%20%26%20%20%204%20%5C%5C%20%20-%204%20%26%203%20%5C%5C%20%5Cend%7Bbmatrix%7D%20%5Ctimes%20%5Cbegin%7Bbmatrix%7D%202%20%26%20%204%20%5C%5C%20-%20%204%20%26%203%20%5C%5C%20%5Cend%7Bbmatrix%7D%20-%205%20%5Ctimes%20%5Cbegin%7Bbmatrix%7D%202%20%26%20%20%204%20%5C%5C%20%20-%204%20%26%203%20%5C%5C%20%5Cend%7Bbmatrix%7D%20%2B%2022%20%5Ctimes%20%5Cbegin%7Bbmatrix%7D%201%20%26%20%20%200%20%5C%5C%20%200%20%26%201%5C%5C%20%5Cend%7Bbmatrix%7D)
⟼ ![\begin{bmatrix} 2 \times 2 + 4 \times ( - 4)& 2 \times 4 + 4 \times 3 \\ - 4 \times 2 + 3 \times ( - 4) & - 4 \times 4 + 3 \times 3 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20& 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D%202%20%20%5Ctimes%202%20%2B%204%20%5Ctimes%20%28%20-%204%29%26%20%20%202%20%20%5Ctimes%204%20%2B%204%20%5Ctimes%203%20%5C%5C%20%20-%204%20%5Ctimes%202%20%2B%203%20%5Ctimes%20%28%20-%204%29%20%26%20%20-%204%20%20%5Ctimes%204%20%2B%203%20%5Ctimes%203%20%5C%5C%20%5Cend%7Bbmatrix%7D%20-%20%5Cbegin%7Bbmatrix%7D%2010%20%26%20%20%2020%20%5C%5C%20%20%20-%2020%26%2015%20%5C%5C%20%5Cend%7Bbmatrix%7D%20%2B%20%5Cbegin%7Bbmatrix%7D%2022%20%26%20%20%200%20%5C%5C%20%200%20%26%2022%20%5C%5C%20%5Cend%7Bbmatrix%7D)
⟼ ![\begin{bmatrix} 4 + ( - 16) & 8 + 12 \\ - 8 + ( - 12) & - 16 + 9 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D%204%20%2B%20%28%20-%2016%29%20%26%20%20%208%20%2B%2012%20%5C%5C%20%20%20-%208%20%2B%20%28%20-%2012%29%20%26%20%20-%2016%20%2B%209%20%5C%5C%20%5Cend%7Bbmatrix%7D%20-%20%5Cbegin%7Bbmatrix%7D%2010%20%26%20%20%2020%20%5C%5C%20%20%20-%2020%20%26%2015%20%5C%5C%20%5Cend%7Bbmatrix%7D%20%2B%20%5Cbegin%7Bbmatrix%7D%2022%20%26%20%20%200%20%5C%5C%20%200%20%26%2022%20%5C%5C%20%5Cend%7Bbmatrix%7D)
⟼ ![\begin{bmatrix} - 12 & 20\\ - 20& - 7 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}](https://tex.z-dn.net/?f=%20%20%5Cbegin%7Bbmatrix%7D%20-%2012%20%26%20%20%2020%5C%5C%20%20-%2020%26%20%20-%207%20%5C%5C%20%5Cend%7Bbmatrix%7D%20-%20%5Cbegin%7Bbmatrix%7D%2010%20%26%20%20%2020%20%5C%5C%20%20%20-%2020%20%26%2015%20%5C%5C%20%5Cend%7Bbmatrix%7D%20%2B%20%5Cbegin%7Bbmatrix%7D%2022%20%26%20%20%200%20%5C%5C%20%200%20%26%2022%20%5C%5C%20%5Cend%7Bbmatrix%7D)
⟼ ![\begin{bmatrix} - 22 & 0 \\ 0& - 22 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D%20%20-%2022%20%26%20%20%200%20%5C%5C%20%200%26%20%20-%2022%20%5C%5C%20%5Cend%7Bbmatrix%7D%20%20%2B%20%5Cbegin%7Bbmatrix%7D%2022%20%26%20%20%200%20%5C%5C%20%200%20%26%2022%20%5C%5C%20%5Cend%7Bbmatrix%7D)
⟼ ![\begin{bmatrix} - 22 + 22 & 0 + 0 \\ 0 + 0 & - 22 + 22 \\ \end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D%20%20-%2022%20%2B%2022%20%26%20%20%200%20%2B%200%20%5C%5C%20%200%20%2B%200%20%26%20%20-%2022%20%20%2B%2022%20%5C%5C%20%5Cend%7Bbmatrix%7D)
⟼ ![\begin{bmatrix} 0 & 0\\ 0 & 0 \\ \end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D%200%20%26%20%20%200%5C%5C%20%200%20%26%200%20%5C%5C%20%5Cend%7Bbmatrix%7D)
⟼ ![\sf{0}](https://tex.z-dn.net/?f=%20%5Csf%7B0%7D)
RIGHT HAND SIDE ( R.H.S ) : 0
L.H.S = R.H.S [ Hence , proved ! ]
Hope I helped ! ♡
Have a wonderful day / night ! ツ
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Answer:
60 meters
Step-by-step explanation:
Mrs. Kemp would have to walk 5 meters to the right to be 12 meters in front of Wesley. She'd then have to walk 12 meters in order to meet Wesley. 12 multiplied by 5 is 60. Hope that makes sense
33 is the closest number if talking about math but in the question 34 is the number closest to 6 in your question
Answer:
13 cases
Step-by-step explanation:
we know that
You have 1 case of soap bars
There are 150 bars in a case
You use 300 bars of soap per day ----> 2 cases per day
using proportion
Find how many cases do you need to order to have enough for 7 days
Let
x ----->the number of cases
2/1=x/7
x=2*7=14 cases
but remember that you have 1 case
so
you needed 14-1=13 cases