X=8 i did mental math but 56x-16-x=424
+16 +16
55x=440
/55 /55
x=8
The answer, in short, is that the short leg equals 15 mm, the long leg equals 20 mm, and the hypotenuse equals 25mm. but if you'd like to see how I solved it, here are the steps.
-----------------------------
The Pythagorean theorem (also known as Pythagoras's Theorem) can be used to solve this. This theorem states that one leg or a right triangle squared plus the other side of that same triangle squared equals the hypotenuse of that triangle squared. To put it in equation form, L² + L² = H².
Let's call the longer leg B, the shorter leg A, and the hypotenuse H.
From the question, we know that A = B - 5, and H = B + 5.
So if we put those values into an equation, we have (B - 5)² + B² = (B + 5)²
Now, to solve. Let's square the two terms in parentheses first:
(B² - 5B - 5B + 25) + B² = B² + 5B + 5B + 25
Now combine like terms:
2B² -10B + 25 = B² + 10B + 25
And now we simplify. Subtract 25 from each side:
2B² - 10B = B² + 10B
Subtract B² from each side:
B² - 10B = 10B
Add 10B to each side:
B² = 20B
And finally, divide each side by B:
B = 20
So that's the length of B. Now to find out A and H.
A = B - 5, so A = 15.
H = B + 5, so H = 25.
And your final answer is A = 15mm, B = 20mm, and H = 25mm
Answer:
700 cm
Step-by-step explanation:
1 Meter is 100 Centimeters
The string would have to be 4 feet long to have a frequency of 400cps because each foot=100cps
Answer:
Poisson Distribution , P(x<2) = 0.1446
Step-by-step explanation:
This is a binomial distribution question with
sample space, n = 300
probability of diagnosed with ASD, p = 1/88 = 0.0114
probability of not diagnosed with ASD, q = 1 - p = 0.9886
Mean, m is given as np = 300 * 0.0114 = 3.42
variance, v = npq = 300 * 0.0114 * 0.9886 = 3.38101
standard deviation, s = square root of variance = 3.38101^(0.5) = 1.83875
This binomial distribution can be approximated as Poisson Distribution since
n > 20 and p < 0.05
For a Poisson Distribution
P(X = x) = [e^(-m) * m^(x)]/ x!
b) x = 2
P(X < 2) = P(X = 0) + P(X = 1)
using the z score table and evaluating, we obtain
P(x<2) = 0.1446
