Answer:
![0.02](https://tex.z-dn.net/?f=0.02)
Step-by-step explanation:
we know that
The probability that a point chosen randomly inside the rectangle is in the triangle is equal to divide the area of the triangle by the area of rectangle
Let
x-----> the area of triangle
y----> the area of rectangle
P -----> the probability
![P=x/y](https://tex.z-dn.net/?f=P%3Dx%2Fy)
<em>Find the area of triangle (x)</em>
![A=(1/2)(5)(2)=5\ in^{2}](https://tex.z-dn.net/?f=A%3D%281%2F2%29%285%29%282%29%3D5%5C%20in%5E%7B2%7D)
<em>Find the area of rectangle (y)</em>
![A=18*12=216\ in^{2}](https://tex.z-dn.net/?f=A%3D18%2A12%3D216%5C%20in%5E%7B2%7D)
<em>Find the probability P</em>
![P=5/216=0.02](https://tex.z-dn.net/?f=P%3D5%2F216%3D0.02)
Answer:
Step-by-step explanation:
<R=<P=70degrees
<Q=180-70=110 degrees
Answer:
72
Step-by-step explanation:
Let the number of candies = n
Tracy ate = 1/3 of n = n/3 remaining 2n / 3
she gave 1/4 of the remainder to her friend = 1/4 of ( n - n/3) = 2n / 12
the new remainder = (2n / 3) - (2n / 12) = n /2
she and her mom then ate altogether = 30
and the brother took from 1 to five, the number he took = x
and she has 3 left
( n/2) - 30 - x = 3
n = 2 ( 33 + x)
now we know that the candies could not be broken and x is between 1 to 5
n = 2 (33 + 1), 2 (33+2), 2(33 +3), 2 (33+ 4) and 2 (33 + 5) this are the possible values of n, ( 68, 70, 72, 74, 76) and the multiple of 3 is 72
n therefore = 72
A = C (congruent angles)
Then: 4p+12 = 36
Solve for p
4p = 36 - 12
4p = 24
4p/4 = 24/4
p = 6
Answer is going to be A.
You probably mean either
![8\cdot2^x + 3 = 48](https://tex.z-dn.net/?f=8%5Ccdot2%5Ex%20%2B%203%20%3D%2048)
or
![8\cdot2^{x+3} = 48](https://tex.z-dn.net/?f=8%5Ccdot2%5E%7Bx%2B3%7D%20%3D%2048)
Write 8 = 2³, so that in the first interpretation,
![8\cdot2^x = 2^3 \cdot 2^x = 2^{x + 3}](https://tex.z-dn.net/?f=8%5Ccdot2%5Ex%20%3D%202%5E3%20%5Ccdot%202%5Ex%20%3D%202%5E%7Bx%20%2B%203%7D)
and in the second,
![8\cdot2^{x+3} = 2^3 \cdot 2^{x+3} = 2^{x + 6}](https://tex.z-dn.net/?f=8%5Ccdot2%5E%7Bx%2B3%7D%20%3D%202%5E3%20%5Ccdot%202%5E%7Bx%2B3%7D%20%3D%202%5E%7Bx%20%2B%206%7D)
Then in the first interpretation, we have
![2^{x + 3} + 3 = 48 \implies 2^{x + 3} = 45 \implies x + 3 = \log_2(45) \implies x = \log_2(45) - 3 \approx \boxed{2.492}](https://tex.z-dn.net/?f=2%5E%7Bx%20%2B%203%7D%20%2B%203%20%3D%2048%20%5Cimplies%202%5E%7Bx%20%2B%203%7D%20%3D%2045%20%5Cimplies%20x%20%2B%203%20%3D%20%5Clog_2%2845%29%20%5Cimplies%20x%20%3D%20%5Clog_2%2845%29%20-%203%20%5Capprox%20%5Cboxed%7B2.492%7D)
Otherwise, the second interpretation gives
![2^{x + 6} = 48 \implies x + 6 = \log_2(48) \implies x = \log_2(48) - 6 \approx -0.415](https://tex.z-dn.net/?f=2%5E%7Bx%20%2B%206%7D%20%3D%2048%20%5Cimplies%20x%20%2B%206%20%3D%20%5Clog_2%2848%29%20%5Cimplies%20x%20%3D%20%5Clog_2%2848%29%20-%206%20%5Capprox%20-0.415)