Answer:
The answer would be 9
Step-by-step explanation:
Step 1: Our output value is 30.
Step 2: We represent the unknown value with $x$.
Step 3: From step 1 above,$30=100\%$.
Step 4: Similarly, $x=30\%$.
Step 5: This results in a pair of simple equations:
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have
Step 7: Again, the reciprocal of both sides gives
Therefore, 30% of 30 is 9
Answer:
C. 52/289
Step-by-step explanation:
Ok so the total number of marbles is 6+4+2+5 (17).
The probability of picking an orange is 4/17 (because there are 4 orange blocks).
The probability of picking a block that isn't orange is 13/17.
Multiply those two numbers together, and you get: 52/289
Answer:
(B) A function is a relation in which each value of the input variable is
paired with at least one value of the output variable.
(D) The vertical line test may be used to determine whether a function
is one-to-one.
Both of these are incorrect/false statements
(I used these in my test on Apex and got both correct)
This means that if the question was reversed and asking about the statements are true, the answers would be:
(A) A sequence is a function whose domain is the set of natural
numbers.
(C) The horizontal line test may be used to determine whether a
function is one-to-one.
In order to multiply a matrix by another matrix, we multiply the rows in the first matrix by the columns in the other matrix (How this is done is shown below)
To determine the pairs of matrices that AB=BA, we will determine AB and BA for each of the options below.
For the first option
![A= \left[\begin{array}{cc}1&0&-2&1&\end{array}\right]; B= \left[\begin{array}{cc}5&0&3&2&\end{array}\right] \\](https://tex.z-dn.net/?f=A%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%26-2%261%26%5Cend%7Barray%7D%5Cright%5D%3B%20B%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%263%262%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
![AB= \left[\begin{array}{cc}(1\times5)+(0\times3)&(1\times0)+(0\times 2)&(-2\times5)+(1\times3)&(-2\times0)+(1\times2)&\end{array}\right]\\AB= \left[\begin{array}{cc}5+0&0+0&-10+3&0+2&\end{array}\right]\\AB = \left[\begin{array}{cc}5&0&-7&2&\end{array}\right] \\](https://tex.z-dn.net/?f=AB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%281%5Ctimes5%29%2B%280%5Ctimes3%29%26%281%5Ctimes0%29%2B%280%5Ctimes%202%29%26%28-2%5Ctimes5%29%2B%281%5Ctimes3%29%26%28-2%5Ctimes0%29%2B%281%5Ctimes2%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%2B0%260%2B0%26-10%2B3%260%2B2%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%26-7%262%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
and
![BA= \left[\begin{array}{cc}(5\times1)+(0\times-2)&(5\times0)+(0\times 1)&(3\times1)+(2\times-2)&(3\times0)+(1\times2)&\end{array}\right]\\BA= \left[\begin{array}{cc}5+0&0+0&3+-4&0+2&\end{array}\right]\\BA = \left[\begin{array}{cc}5&0&-1&2&\end{array}\right] \\](https://tex.z-dn.net/?f=BA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%285%5Ctimes1%29%2B%280%5Ctimes-2%29%26%285%5Ctimes0%29%2B%280%5Ctimes%201%29%26%283%5Ctimes1%29%2B%282%5Ctimes-2%29%26%283%5Ctimes0%29%2B%281%5Ctimes2%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%2B0%260%2B0%263%2B-4%260%2B2%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%26-1%262%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
∴ AB≠BA
For the second option
![A= \left[\begin{array}{cc}1&0&-1&2&\end{array}\right]; B= \left[\begin{array}{cc}3&0&6&-3&\end{array}\right] \\](https://tex.z-dn.net/?f=A%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%26-1%262%26%5Cend%7Barray%7D%5Cright%5D%3B%20B%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%266%26-3%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
![AB= \left[\begin{array}{cc}(1\times3)+(0\times6)&(1\times0)+(0\times -3)&(-1\times3)+(2\times6)&(-1\times0)+(2\times-3)&\end{array}\right]\\AB= \left[\begin{array}{cc}3+0&0+0&-3+12&0+-6&\end{array}\right]\\AB = \left[\begin{array}{cc}3&0&9&-6&\end{array}\right] \\](https://tex.z-dn.net/?f=AB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%281%5Ctimes3%29%2B%280%5Ctimes6%29%26%281%5Ctimes0%29%2B%280%5Ctimes%20-3%29%26%28-1%5Ctimes3%29%2B%282%5Ctimes6%29%26%28-1%5Ctimes0%29%2B%282%5Ctimes-3%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%2B0%260%2B0%26-3%2B12%260%2B-6%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%269%26-6%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
and
![BA= \left[\begin{array}{cc}(3\times1)+(0\times-1)&(3\times0)+(0\times 2)&(6\times1)+(-3\times-1)&(6\times0)+(-3\times2)&\end{array}\right]\\BA= \left[\begin{array}{cc}3+0&0+0&6+3&0+-6&\end{array}\right]\\BA = \left[\begin{array}{cc}3&0&9&-6&\end{array}\right] \\](https://tex.z-dn.net/?f=BA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%283%5Ctimes1%29%2B%280%5Ctimes-1%29%26%283%5Ctimes0%29%2B%280%5Ctimes%202%29%26%286%5Ctimes1%29%2B%28-3%5Ctimes-1%29%26%286%5Ctimes0%29%2B%28-3%5Ctimes2%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%2B0%260%2B0%266%2B3%260%2B-6%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%269%26-6%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Here AB = BA
For the third option
![A= \left[\begin{array}{cc}1&0&-1&2&\end{array}\right]; B= \left[\begin{array}{cc}5&0&3&2&\end{array}\right] \\](https://tex.z-dn.net/?f=A%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%26-1%262%26%5Cend%7Barray%7D%5Cright%5D%3B%20B%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%263%262%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
![AB= \left[\begin{array}{cc}(1\times5)+(0\times3)&(1\times0)+(0\times 2)&(-1\times5)+(2\times3)&(-1\times0)+(2\times2)&\end{array}\right]\\AB= \left[\begin{array}{cc}5+0&0+0&-5+6&0+4&\end{array}\right]\\AB = \left[\begin{array}{cc}5&0&1&4&\end{array}\right] \\](https://tex.z-dn.net/?f=AB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%281%5Ctimes5%29%2B%280%5Ctimes3%29%26%281%5Ctimes0%29%2B%280%5Ctimes%202%29%26%28-1%5Ctimes5%29%2B%282%5Ctimes3%29%26%28-1%5Ctimes0%29%2B%282%5Ctimes2%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%2B0%260%2B0%26-5%2B6%260%2B4%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%261%264%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
and
![BA= \left[\begin{array}{cc}(5\times1)+(0\times-1)&(5\times0)+(0\times 2)&(3\times1)+(2\times-1)&(3\times0)+(2\times2)&\end{array}\right]\\BA= \left[\begin{array}{cc}5+0&0+0&3+-2&0+4&\end{array}\right]\\BA = \left[\begin{array}{cc}5&0&1&4&\end{array}\right] \\](https://tex.z-dn.net/?f=BA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%285%5Ctimes1%29%2B%280%5Ctimes-1%29%26%285%5Ctimes0%29%2B%280%5Ctimes%202%29%26%283%5Ctimes1%29%2B%282%5Ctimes-1%29%26%283%5Ctimes0%29%2B%282%5Ctimes2%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%2B0%260%2B0%263%2B-2%260%2B4%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%261%264%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Here also, AB=BA
For the fourth option
![A= \left[\begin{array}{cc}1&0&-2&1&\end{array}\right]; B= \left[\begin{array}{cc}3&0&6&-3&\end{array}\right] \\](https://tex.z-dn.net/?f=A%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%26-2%261%26%5Cend%7Barray%7D%5Cright%5D%3B%20B%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%266%26-3%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
![AB= \left[\begin{array}{cc}(1\times3)+(0\times6)&(1\times0)+(0\times -3)&(-2\times3)+(1\times6)&(-2\times0)+(1\times-3)&\end{array}\right]\\AB= \left[\begin{array}{cc}3+0&0+0&-6+6&0+-3&\end{array}\right]\\AB = \left[\begin{array}{cc}3&0&0&-3&\end{array}\right] \\](https://tex.z-dn.net/?f=AB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%281%5Ctimes3%29%2B%280%5Ctimes6%29%26%281%5Ctimes0%29%2B%280%5Ctimes%20-3%29%26%28-2%5Ctimes3%29%2B%281%5Ctimes6%29%26%28-2%5Ctimes0%29%2B%281%5Ctimes-3%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%2B0%260%2B0%26-6%2B6%260%2B-3%26%5Cend%7Barray%7D%5Cright%5D%5C%5CAB%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%260%26-3%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
and
![BA= \left[\begin{array}{cc}(3\times1)+(0\times-2)&(3\times0)+(0\times 1)&(6\times1)+(-3\times-2)&(6\times0)+(-3\times1)&\end{array}\right]\\BA= \left[\begin{array}{cc}3+0&0+0&6+6&0+-3&\end{array}\right]\\BA = \left[\begin{array}{cc}3&0&12&-3&\end{array}\right] \\](https://tex.z-dn.net/?f=BA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%283%5Ctimes1%29%2B%280%5Ctimes-2%29%26%283%5Ctimes0%29%2B%280%5Ctimes%201%29%26%286%5Ctimes1%29%2B%28-3%5Ctimes-2%29%26%286%5Ctimes0%29%2B%28-3%5Ctimes1%29%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%2B0%260%2B0%266%2B6%260%2B-3%26%5Cend%7Barray%7D%5Cright%5D%5C%5CBA%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%260%2612%26-3%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Here, AB≠BA
Hence, it is only in the second and third options that AB = BA
and ![A= \left[\begin{array}{cc}1&0&-1&2&\end{array}\right]B= \left[\begin{array}{cc}5&0&3&2&\end{array}\right] \\](https://tex.z-dn.net/?f=A%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%26-1%262%26%5Cend%7Barray%7D%5Cright%5DB%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%260%263%262%26%5Cend%7Barray%7D%5Cright%5D%20%5C%5C)
Learn more on matrices multiplication here: brainly.com/question/12755004
Answer:
2.7 x 10^-7 :)
Step-by-step explanation: