Find the common factors of:(i) 24 and 28 (ii) 12 and 18 (iii) 36 and 48
1 answer:
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Answer:
Step-by-step explanation:
From the given question.
We can write the null hypothesis & the alternative hypothesis as:
Null hypothesis:
Alternative hypothesis:
From above, let's think about the type I error we could make and the type II error we could make.
<u>Type I error:</u>
The type I error at the null hypothesis showcases that the snow level is at 6 inches or below 6 inches, but we falsely concluded that the snow level is high above sea level.
<u>Type II error:</u>
Here, the snow level is literally above 6 inches, hence, we failed to conclude that the snow level is above 6 inches.
Thus, the consequences of the above analysis showcase that type II error has higher severe consequences because it may result in a situation that may endanger the passengers' safety.
Answer:
a) Each corral should be 33⅓ ft long and 25 ft wide
b) The total enclosed area is 1666⅔ ft²
Step-by-step explanation:
I assume that the corrals have identical dimensions and are to be fenced as in the diagram below
Let x = one dimension of a corral
and y = the other dimension
(a) Dimensions to maximize the area
The total length of fencing used is:
4x + 3y = 200
4x = 200 – 3y
x = 50 - ¾y
The area of one corral is A = xy, so the area of the two corrals is
A = 2xy
Substitute the value of x
A = 2(50 - ¾y)y
A = 100 y – (³/₂)y²
This is the equation for a downward-pointing parabola:
A = (-³/₂)y² + 100y
a = -³/₂; b = 100; c = 0
The vertex (maximum) occurs at
y = -b/(2a) = 100 ÷ (2׳/₂) = 100 ÷ 3 = 33⅓ ft
4x + 3y = 100
Substitute the value of y
4x + 3(33⅓) = 200
4x + 100 = 200
4x = 100
x = 25 ft
Each corral should measure 33⅓ ft long and 25 ft wide.
Step 2. Calculate the total enclosed area
The enclosed area is 50 ft long and 33⅓ ft wide.
A = lw = 50 × 100/3 = 5000/3 = 1666⅔ ft²
