Answer:
1.66
Step-by-step explanation:
Calculation to find the standard deviation for the random variable X of the number of students who work full time in samples of size
Using this formula
Standard deviation(X)=√np(1−p)
Where,
n represent the number of students=16
p represent the percentage of all students who work full time=22
Let plug in the formula
Standard deviation(X)=√16(0.22)(1−0.22)
Standard deviation(X)=√(3.52)(0.78)
Standard deviation(X)=√2.7456
Standard deviation(X)=1.656
Standard deviation(X)=1.66 (Approximately)
Therefore the standard deviation for the number of students who work full time in samples of size 16 will be 1.66
The formula of an area of a rectangle:
A = wl
We have l = w - 4 and A = 21.
Substitute:
w(w - 4) = 21 <em>use distributive property</em>
(w)(w) + (w)(-4) = 21
w² - 4w = 21 <em>subtract 21 from both sides</em>
w² - 4w - 21 = 0
w² - 7w + 3w - 21 = 0
w(w - 7) + 3(w - 7) = 0
(w - 7)(w + 3) = 0 ↔ w - 7 = 0 ∨ w + 3 = 0
w = 7 ∨ w = -3 < 0
l = w - 4 → l = 7 - 4 = 3
<h3>Answer: the length = 3 u.</h3>
If the angle in B is 45º, that means the angle in A is also going to be 45º, considering it's a right triangle, so AC and BC are they have the same length.
Then using Pythagoras, you'll get that

equals

.
Now, you know that AC=BC and that AB=24.
So you'll get

. You do the square root in both sides and you get that 2AC=24 and AC=12.
Now that you know that both AC and BC equal 12, you can find the area by just multiplying them and then diving them by 2. (The formula for the area of a triangle is half base multiplied by height, and in a right triangle, if a cathetus is the base, the other cathetus<span> will be the height)
And so the area is equal to 72.</span>
The correct answer is:
C. They are similar because the corresponding sides of kites KELY and BRAD all have the relationship 2:1.
Using the distance formula,

the lengths of the sides of BRAD are:

The lengths of the sides of KELY are:

Each side of KELY is twice the length of the corresponding side on BRAD. This makes the ratio of the sides 2:1 and the figures are similar.
Answer:
third side = 9
Step-by-step explanation:
Using Pythagoras' identity on the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
let the third side be x, then
x² + 40² = 41², that is
x² + 1600 = 1681 ( subtract 1600 from both sides )
x² = 81 ( take the square root of both sides )
x =
= 9
The third side is 9