Answer:
The maximum height of the prism is 
Step-by-step explanation:
Let
x------> the height of the prism
we know that
the area of the rectangular base of the prism is equal to
so
-------> inequality A
------> equation B
-----> equation C
Substitute equation B in equation C
------> equation D
Substitute equation B and equation D in the inequality A
-------> using a graphing tool to solve the inequality
The solution for x is the interval---------->![[0,12]](https://tex.z-dn.net/?f=%5B0%2C12%5D)
see the attached figure
but remember that
The width of the base must be 
meters less than the height of the prism
so
the solution for x is the interval ------> ![(9,12]](https://tex.z-dn.net/?f=%289%2C12%5D)
The maximum height of the prism is
hi,
you must replace x by the number between parenthese.
I show you with the first one and let you do the second one
p(x) = 11x^5 -11x^4 - 5x^2 +15x-8
p(-4) = 11 (-4)^5 - 11 (-4)^4 -5(-4)² +15(-4) -8
p(-4) = 11 ( -1024- 256) - 5*16 -60-8
p(-4) = 11 ( -1280) -80-60-8
p(-4) = - 14080 - 148
p(-4) = - 14 228
Answer:
a = 1, b = 3.
Step-by-step explanation:
a + b = 4
a - b = -2 Adding to eliminate b:
2a = 2
a = 1
So 1 + b = 4
giving b = 3.
Answer:
the probability of getting exactly 2 fours is 0.16
Step-by-step explanation:
The probability of obtaining a number that is four = ¹/₆
The probability of obtaining a non 4 number = 1 - ¹/₆ = ⁵/₆
The number of ways 2 fours can be arrange in five numbers = ⁵C₂ = 10 ways
If the die is tossed five times, the probability of the events is calculated as;
P = 10 x (¹/₆)² x (⁵/₆)³
P = 10 x (¹/₃₆) x (¹²⁵/₂₁₆)
P = 10 x 0.02778 x 0.5787
P = 0.16
Therefore, the probability of getting exactly 2 fours is 0.16
