Really none of the above.
A principal square root of a real number is a positive real number (or a positive real number times i, if you're up to complex numbers, but let's assume not.) It's not necessarily a positive integer, √2 being the obvious example.
Is √2 a positive fraction? We can write it as √2 / 1 so I suppose it is. It's certainly not a rational number. Even if we grant irrationals as fractions surely √0=0 isn't a positive fraction. So "always" isn't correct.
I'd go with none of the above, but if I had to choose I'd choose D.
Answer: 1) Let's simplify step-by-step.
x22(x+y)−y2
Distribute:
=(x22)(x)+(x22)(y)+−y2
=x23+x22y+−y2
Answer:
=x23+x22y−y2
2)Let's simplify step-by-step.
x4+x2y2+y4
There are no like terms.
Answer:
=x4+x2y2+y4
The surface area of the pyramid will be given as follows:
Area of triangles:
A=1/2×base×height
A=1/2×12×18
A=108 m²
Area of 6 triangles is given by:
A=108×6=648 m²
Area of the hexagon:
A=6×1/2×12×6√3
A=374.123m²
Total surface area:
SA=648+374.123
SA=1022.123 m²~1022 m²
Answer: C] 1022 m²
Let x = the width
then
2x = the length
:
The box dimensions: 2x by x by 4
Given the surface area:
2(2x*x) + 2(2x*4) + 2(x*4) = 220
:
4x^2 + 16x + 8x = 220
A quadratic equation:
4x^2 + 24x - 220 = 0
simplify, divide by 4
x^2 + 6x - 55 = 0
Factor
(x+11)(x-5) = 0
The positive solution is what we want here:
x = 5 ft is the width
then
2(5) = 10 ft is the length
:
Find the volume
10 * 5 * 4 = 200 cu/ft is the volume
Answer:
The statistic for this system of hypothesis is given by:
If the statistic is equal to 1 then that means 
and we don't have enough evidence to conclude that the two population variances and deviations are different.
Step-by-step explanation:
System of hypothesis
We want to test if the variation for a group1 is equal to another one 2, so the system of hypothesis are:
H0: 
H1: 
Calculate the statistic
The statistic for this system of hypothesis is given by:
If the statistic is equal to 1 then that means and we don't have enough evidence to conclude that the two population variances and deviations are different.
