Answer:
Options (D), (E) and (F) are the correct options.
Step-by-step explanation:
From the figure attached,
1). Angle 4 is the exterior angle of the given triangle having interior angles 1, 2 and 3.
Therefore, by the property of exterior angle,
∠4 = ∠1 + ∠2
2). Since ∠4 = ∠1 + ∠2,
Therefore, ∠4 will be greater than ∠1
Similarly, ∠4 will be greater than ∠2
Therefore, Options (D), (E) and (F) are the correct options.
By the Triangle Inequality Theorem, the sum of two sides should be greater than the length of the third side, while the difference of these two sides should be less than the length of this third side. Normally you would take the absolute value of the difference of these two side as you wouldn't know which is greater than the other!
The simplest way to prove whether these line segments can form a triangle, is by going against this theory. Let us prove that the line segment don't form a triangle. As you can see, adding 7 and 1 is greater than 1, respectively 7 and 7 is greater than 1. Thus -
<u><em>Solution = A. True</em></u>
As the problem states, to solve this, we are going to use the equation

where

is the loudness in dB

is the intensity of a sound

<span>is the minimum intensity detectable by the human ear
</span>
We know for our problem that

; we also now that the minimum intensity detectable by the human ear is

, so

. Lets replace those values in our equation to find

:


Qe can conclude that since the explosion is under 100dB, it does not violates the regulation of the town. We used tow physical values to calculate the answer: the intensity of the sound of the explosion,

, and the minimum intensity detectable by the human ear

.
Answer:
Simplifying
3n + 7 = 30
Reorder the terms:
7 + 3n = 30
Solving
7 + 3n = 30
Solving for variable 'n'.
Move all terms containing n to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + 3n = 30 + -7
Combine like terms: 7 + -7 = 0
0 + 3n = 30 + -7
3n = 30 + -7
Combine like terms: 30 + -7 = 23
3n = 23
Divide each side by '3'.
n = 7.666666667
Simplifying
n = 7.666666667
Step-by-step explanation:
Answer:
D. 0.1353
B. 0.0473
Step-by-step explanation:
For an exponentially distributed random variable, the cumulative distribution function is:

with parameter λ=2, then P(X≥1) is equal to:

D. 0.1353
with parameter λ=1.5, then P(2≤X≤4) is equal to
B. 0.0473