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
Step-by-step explanation:
making x subject in eq 1
x= (-1-9y)/-14
substituting the value of x in eq 2
17(-1-9y/-14)=7+9y
(-17-153y)/-14=7+9y
-17-153y=-98-126y
-17+98=153y-126y
81=27y
y=3
substituting this value of y in eq 1
-14x=-1-9(3)
-14x=-28
x=2
(x,y) = (2,3)
Answer:
Step-by-step explanation:
Hello!
The variable of interest, X: height of women at a college, has an approximately normal distribution with mean μ= 65 inches and standard deviation σ= 1.5 inches.
You need to look for the value of height that marks the bottom 20% of the distribution, i.e. the height at the 20th percentile of the normal curve, symbolically:
P(X≤x₀)= 0.20
To know what value of height belongs to the 20% of the distribution, you have to work using the standard normal distribution and then reverse the standardization with the population mean and standard deviation to reach the value of X. So the first step is to look for the Z-value that accumulates 20% of the distribution:
P(Z≤z₀)=0.20
z₀= -0.842
z₀= (x₀-μ)/σ
z₀*σ= (x₀-μ)
x₀= (z₀*σ)+μ
x₀= (-0.842*1.5)+65
x₀= 63.737 inches
I hope it helps!
Answer:
A. 45.77 kg
Step-by-step explanation:
The measurement with the smallest difference from 45.76 is 45.77 kg.
