Length=2x
width=x
Perimeter of a rectangle=2(lenght)+2(width)
The first is to find out the measures of this rectangle, that is to say, you have to find the length and width of these rectangle.
We can suggest this equation:
24=2(2x)+2(x)
4x+2x=24
6x=24
x=24/6
x=4
2x=2(4)=8
The lenght will be 8 in, and the length will be 4 in.
The second; you have to calculate the area of this rectangle.
area of a rectangle= lenght x width
area=(8 in)(4 in)=32 in²
answer: the area of Marshall´s rectangular poster would be 32 in²
Answer:
52 tickets cost $10 and 18 tickets cost $12
Step-by-step explanation:
10x+12y=804. (1)
x+y=70. (2)
From (2)
x=70-y
Substitute x=70-y into (1)
10x+12y=804
10(70-y)+12y=804
700-10y+12y=804
700+2y=804
2y=804-700
2y=104
y=104/2
y=52
Recall
x+y=70
x+52=70
x=70-52
x=18
52 tickets cost $10 and 18 tickets cost $12
Answer:
The probability that at most 3 attempts are required to produce a craft item with satisfactory quality is 0.9375
Step-by-step explanation:
Let E be a random variable denoting the event that an artist makes a craft item with satisfactory level.
Then the random variable E follows a Geometric distribution.
A Geometric distribution is defined as the number of failures (<em>k</em>) before the first success.
The probability function of Geometric distribution is:
, <em>p</em> = Probability of success and <em>k</em> = 0, 1, 2, 3...
The probability of success is, <em>p</em> = 0.5 and the number of failures is, <em>k</em> = 3.
Compute the probability of at most 3 attempts before the first success is:
![P(X\leq 3) =P(X=3)+P(X = 2)+P(X=1) +P(X = 0)\\=[(1-0.5)^{0}*0.5]+[(1-0.5)^{1}*0.5]+[(1-0.5)^{2}*0.5]+[(1-0.5)^{3}*0.5]\\=0.9375](https://tex.z-dn.net/?f=P%28X%5Cleq%203%29%20%3DP%28X%3D3%29%2BP%28X%20%3D%202%29%2BP%28X%3D1%29%20%2BP%28X%20%3D%200%29%5C%5C%3D%5B%281-0.5%29%5E%7B0%7D%2A0.5%5D%2B%5B%281-0.5%29%5E%7B1%7D%2A0.5%5D%2B%5B%281-0.5%29%5E%7B2%7D%2A0.5%5D%2B%5B%281-0.5%29%5E%7B3%7D%2A0.5%5D%5C%5C%3D0.9375)
Therefore, the probability that at most 3 attempts are required to produce a craft item with satisfactory quality is 0.9375.
Answer:
Katherine will make minimum 8 playlists. Each playlist will contain 4 pop songs and 9 rock songs.
Step-by-step explanation:
We have been given that Katherine has 32 pop songs and 72 rock songs on her mp3 player. She is willing to organizing the songs into playlists such that there are equal number of pop songs and an equal number of rock songs into each playlist.
We can find the minimum number of playlists by finding GCF of the given two numbers.
We can write 32 = 2^5 and we can write 72 = 2^3*3^2
Therefore, GCF of the two numbers is 2^3 = 8.
Hence, she will be making total 8 playlists where each playlist will contain 4 pop songs and 9 rock songs.
$26.79
If you took 30% of 26.79 you get 8.037
Subtract: 26.79-8.037 = 18.753
