Answer:
the answer is 12 attendees
Step-by-step explanation:
Let a=the attendees & Let d=the cost
if the budget is $97 and the cost of the gala is represented by the equation d=7a+13, substitute the $97 for d
d=7a+13
97=7a+13
now take subtract 13 from both sides
97-13=7a+13-13
since the 13 cancels out on the right side it'll now read:
84=7a
to get a by itself you now divide 7 from both sides getting a by itself
84/7=7a/7
12=a
so the answer will be 12
Answer: 
Step-by-step explanation:
From the sports arena to Kristina's house = 
From the sports arena to Luke's house = 
Subtract Luke from Kristina

There's a confusing but easy way to solve this. However, I'm going to convert into improper fractions to make it easier.
To convert to improper fraction, take the whole number, multiply it by the denominator and add it to the numerator. All over the same denominator.


Subtract them.


Convert to mixed number by dividing.
65/10=6
60
----
5
The 6 is the whole number, 5 the numerator and 10 the denominator. Remember the negative sign that we had.

5 and 10 can be simplified
5/5=1
10/5=2
Our final answer would be:

Answer:
The probability of the system being down in the next hour of operation is 0.3.
Step-by-step explanation:
We have a transition matrix from one period to the next (one hour) that can be written as:
![T=\left[\begin{array}{ccc}&R&D\\R&0.7&0.3\\D&0.2&0.8\end{array}\right]](https://tex.z-dn.net/?f=T%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%26R%26D%5C%5CR%260.7%260.3%5C%5CD%260.2%260.8%5Cend%7Barray%7D%5Cright%5D)
We can represent the state that system is initially running with the vector:
![S_0=\left[\begin{array}{cc}1&0\end{array}\right]](https://tex.z-dn.net/?f=S_0%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5Cend%7Barray%7D%5Cright%5D)
The probabilties of the states in the next period can be calculated using the matrix product of the actual state and the transition matrix:

That is:
![S_1=S_0\cdot T= \left[\begin{array}{cc}1&0\end{array}\right]\cdot \left[\begin{array}{cc}0.7&0.3\\0.2&0.8\end{array}\right]= \left[\begin{array}{cc}0.7&0.3\end{array}\right]](https://tex.z-dn.net/?f=S_1%3DS_0%5Ccdot%20T%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5Cend%7Barray%7D%5Cright%5D%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.7%260.3%5C%5C0.2%260.8%5Cend%7Barray%7D%5Cright%5D%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.7%260.3%5Cend%7Barray%7D%5Cright%5D)
With the inital state as running, we have a probabilty of 0.7 that the system will be running in the next hour and a probability of 0.3 that it will be down.
Answer:
A) Gilligan can conclude that triangle ABC and triangle SDC are similar.
B) He can conclude that the distance is longer than the hypotenuses of the triangles.
Step-by-step explanation:
A) This is because they are the same shape and have proportionate sizes.
B) This is because if AB = 90 feet, he knows that the distance will be about the same length as the hypotenuses of the triangles.
Answer:
<h2>60</h2>
Step-by-step explanation:
