Answer: last option. 9.2
Step-by-step explanation:
The pythagoreon theorm tells us, a^2+b^2 = c^2. We can substitute these values, so 7^2 + 6^2 = x^2 => 49+36 = x^2 => root of 85. The root of 85 is 9.219 something so you can round 9.219 to 9.2.
Answer:
x° ≈ 77.6°
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationships between trig functions and triangle sides. Side CD is common to the triangle on the left and the one on the right, so we can consider relationships that might help us use that to find the answer.
In the triangle on the right, we need a relationship between CD and BD. These sides are opposite and adjacent to the given angle, so we can use the relation ...
Tan = Opposite/Adjacent
tan(38°) = CD/3.5
Multiplying by 3.5, we can find CD:
CD = 3.5·tan(38°)
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In the triangle on the left, we know sides CD and CA, the side opposite x° and the hypotenuse of that right triangle. This lets us use the sine relationship:
Sin = Opposite/Hypotenuse
sin(x°) = CD/2.8
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Using our value for CD, this becomes ...
sin(x°) = (3.5·tan(38°)/2.8)
sin(x°) = (5/4)tan(38°)
Using the inverse sine function, we can find x° to be ...
x° = arcsin(5/4·tan(38°)) ≈ 77.6°
The size of the angle marked x° is about 77.6°.
If an event occurs 0 times (out of 4, in this case) then it does not occur at least once. So we can find the probability of it not occurring and then subtract that value from 1.
So, what are the chances of it not occurring in 1 trip?
1−.37=.63
What about not occurring in 2 trips?
(1−.37)⋅(1−.37)=.63⋅.63=.3969
Now what about not occurring in 4 trips?
.63^4 = 0.15752961
We must subtract this value from 1
(recall that what we just calculated is the probability of it not occurring, so the probability of it occurring at least once is:
1−0.15752961 = .84247039
TLDR - In 4 trips the chance of a guest catching a cutthroat once in under 4 trips in 0.84.
A=bh
A=4(10)
A= 40 inches squared