Answer:
7 hours and 30 minutes
Step-by-step explanation:
If you start counting from 11:00 to 5:45 you get 7 hours
Answer:
18 nickels, 9 dimes, 6 quarters.
Step-by-step explanation:
Basically, I just made a money table and used it to get my equation, which is: 60x-30=330, to get how many quarters there are. Then, plug that in to the problem and you have your answer.
Answer:
x=-1/85; y=-283/85; z=2/17
Step-by-step explanation:
Using an algebraic method like elimination or substitution would take a lot of steps which could lead to mistake the calculations. In this case, I decided to use the Gaussian elimination. We can express the system in matrix form as follows:
![\left[\begin{array}{ccc}2&-4&6\\9&-3&1\\5&0&9\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}14\\10\\1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26-4%266%5C%5C9%26-3%261%5C%5C5%260%269%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D14%5C%5C10%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
To begin the calculations, we write the system in augmented matrix form and use the Gaussian elimination:
![\left[\begin{array}{ccccc}2&-4&6&|&14\\9&-3&1&|&10\\5&0&9&|&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D2%26-4%266%26%7C%2614%5C%5C9%26-3%261%26%7C%2610%5C%5C5%260%269%26%7C%261%5Cend%7Barray%7D%5Cright%5D)
By applying the Gaussian elimination, the final matrix is the following:
![\left[\begin{array}{ccccc}1&0&0&|&-1/85\\0&1&0&|&-283/85\\0&0&1&|&2/17\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7D1%260%260%26%7C%26-1%2F85%5C%5C0%261%260%26%7C%26-283%2F85%5C%5C0%260%261%26%7C%262%2F17%5Cend%7Barray%7D%5Cright%5D)
In order to verify the results, it´s enough to substitute the calculated values in the original equations to see if the equalities are correct. Here you can see the verification for all of the equations:

Using the <u>arrangements and the probability concept</u>, it is found that there is a 0.75 = 75% probability that the number formed is not divisible by 4.
- A probability is the <u>number of desired outcomes divided by the number of total outcomes</u>.
- The number of possible arrangements of n elements is given by

In this problem, there are 4 elements, hence
.
A number is a multiple of 4 if the <u>number composed by it's last 2 digits are multiples of 4</u>.
- Hence, the possible options for the last 2 digits are: 56, 68, 76.
- For each of them, there are
options for the first 2 digits, hence, there will be 2 x 3 = 6 multiples of 4.
The other 18 numbers formed are not divisible by 4, hence:

0.75 = 75% probability that the number formed is not divisible by 4.
For more on <u>arrangements and probabilities</u>, you can check brainly.com/question/24437717
Answer:
Step-by-step explanation:
if we're estimating ,we're going to round up to 8 since you can multiply that easier. 25 times 8 is 200 so estimation will be around 200