People: p
<span>men: 2/5 p </span>
<span>children: c </span>
<span>women: 3c </span>
<span>men: 2/5 p = c+45 </span>
<span>people = m+w+c = 2/5 p + 3c + c </span>
<span>so, p = 2/5 p + 4c </span>
<span>3/5 p = 4c </span>
<span>2/5 p = c+45 </span>
<span>c=27 </span>
<span>p=180 </span>
<span>180 people at the show. </span>
<span>so, women=81 </span>
<span>men=72 </span>
Answer:
230 were sold at the door
170 were sold in advance
Step-by-step explanation:
x=at door y=in advance
x+y=400
3x+2y=1030
y=-x+400
2y=-3x+1030
y=-3/2x+515
-x+400=-3/2x+515
x=230 y=170
Using the Fundamental Counting Theorem, it is found that for each case, the total number of outcomes is:
a) 60,466,176.
b) 5,961,600.
<h3>What is the Fundamental Counting Theorem?</h3>
It is a theorem that states that if there are n things, each with
ways to be done, each thing independent of the other, the number of ways they can be done is:
![N = n_1 \times n_2 \times \cdots \times n_n](https://tex.z-dn.net/?f=N%20%3D%20n_1%20%5Ctimes%20n_2%20%5Ctimes%20%5Ccdots%20%5Ctimes%20n_n)
Item a:
No restrictions, hence for each of the five characters, there are 36 outcomes, hence
.
Then, the possible number of passwords is:
![N = 36^5 = 60466176](https://tex.z-dn.net/?f=N%20%3D%2036%5E5%20%3D%2060466176)
Item b:
The letters and the digits have to be alternated, hence:
- Starting with a letter,
.
- Starting with a digit,
.
Then, the possible number of passwords is:
![N = 36^3 \times 10^2 + 10^3 \times 36^2 = 5961600](https://tex.z-dn.net/?f=N%20%3D%2036%5E3%20%5Ctimes%2010%5E2%20%2B%2010%5E3%20%5Ctimes%2036%5E2%20%3D%205961600)
To learn more about the Fundamental Counting Theorem, you can take a look at brainly.com/question/24314866
Answer:
w = - 16.06 or w = 2.06
Step-by-step explanation:
Given
w² + 14w - 33 = 0 ( add 33 to both sides )
w² + 14w = 33
To complete the square
add ( half the coefficient of the w- term )² to both sides
w² + 2(7)w + 49 = 33 + 49, that is
(w + 7)² = 82 ( take the square root of both sides )
w + 7 = ±
( subtract 7 from both sides )
w = - 7 ±
, that is
w = - 7 -
≈ - 16.06 or w = - 7 +
≈ 2.06
Answer:
d. y=
+3
Step-by-step explanation:
we see theres a point at (4,2) and if we plug 4 into the x, we get 2 for y