12 is the square root of 144.
~Silver
Answer:
80 square feet
Step-by-step explanation:
You can split it into a rectangle and a triangle. The area of the rectangle would be 2 * 16 = 32 square feet.
Next, you need to find the height of the triangle. To do this, you can split the triangle into two right triangles and use the pythagorean theorem to find the height. The dimensions of one of the right triangle is 8 for one of the legs and 10 for the hypotenuse. Using the pythagorean theorem, 8^2 + b^2 = 10^2, which is 64 + b^2 = 100, so b^2 = 36 and b = 6. This means that the height is 6. Now, you find the area of the triangle and you get 16 * 6 / 2 = 48.
Adding the area of the rectangle and the triangle: 32 + 48 = 80
Not sure why that's not an answer choice, I'm fairly confident it's right.
Answer:
x=y=z=90.
Step-by-step explanation:
let the 3 numbers be x,y,z.
let s be sum
s=x+y+z
we need to maximize xy+yz+zx
or , xy + y(270-(x+y))+x(270-(x+y)) = P(x)
Use Lagrange's Multipliers
⇒ΔP= λΔS
⇒
⇒y=x
⇒\frac{x+z}{x+y} =1
⇒z=y
⇒x=y=z
⇒3x = 270
⇒x= 90
hence, x=y=z=90.
Answer:
Option b
Step-by-step explanation:
Given that For a particular course, the pass rate for the 16-week format is 59%. A team of faculty examine student data from 40 randomly selected accelerated classes and determine that the pass rate is 78%.
we have to find whether taking a class in a short-term format (8 weeks instead of 16 weeks) increase a student’s likelihood of passing the course
Since pass rate for 16 weeks is 59% we check whether for 8 weeks is more than this.
So correct null and alternative hypotheses for this research question
would be:
b.H0: p = 0.59; Ha: p > 0.59
Option b is right.
Answer:
A. 2x + 5(2x + 6) = 12x + 30
Step-by-step explanation:
Infinitely many solutions means the two sides of the equation will be equal to each other, so B and D can be eliminated. Distribute for A and C to check
A. 2x + 5(2x + 6) = 12x + 30
2x + 10x + 30 = 12x + 30
12x + 30 = 12x + 30
C. 2(x + 5) + 2 = 6x + 2(x + 2)
2x + 10 + 2 = 6x +2x + 4
2x + 12 = 8x + 4
You only get the same equation for A, therefore A is the correct answer
