Which expression is equivalent to √96
2 answers:
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Answer:
Step-by-step explanation:
Let X be the length of pregnancy.
X is N(268, 15)
a) Prob of pregnancy lasting 307 days or longer
= P(X>307) =
=0.5-0.4953
=0.0047
b) Lowest 2% is 2nd percentile
Z=-2.55
X score = 268-2.55(15)
= 229.75 days
If length of days >230 days then it is not premature.
Answer:
- sin θ ≈ -0.08667
- cos θ ≈ 0.99624
Step-by-step explanation:
Straightforward use of the inverse tangent function of a calculator will tell you θ ≈ -0.08678 radians. This is an angle in the 4th quadrant, where your restriction on θ places it. (To comply with the restriction, you would need to consider the angle value to be 2π-0.08678 radians. The trig values for this angle are the same as the trig values for -0.08678 radians.)
Likewise, straightforward use of the calculator to find the other function values gives ...
sin(-0.08678 radians) ≈ -0.08667
cos(-0.08678 radians) ≈ 0.99624
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<em>Note on inverse tangent</em>
Depending on the mode setting of your calculator, the arctan or tan⁻¹ function may give you a value in degrees, not radians. That doesn't matter for this problem. sin(arctan(-0.087)) is the same whether the angle is degrees or radians, as long as you don't change the mode in the middle of the computation.
We have shown radians in the above answer because the restriction on the angle is written in terms of radians.
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<em>Alternate solution</em>
The relationship between tan and sin and cos in the 4th quadrant is ...
That is, the cosine is positive, and the sign of the sine matches that of the tangent.
This more complicated computation gives the same result as above.
By using trigonometric relations, we will see that:
AC = 15.6 in
AB = 8.4 in.
<h3>How to get the measures of the other two sides of the right triangle?</h3>Here we have the right triangle where:
B = 90°
C = 40°
BC = 10 in.
Notice that is the adjacent cathetus to the angle C, then we can use the two relations:
- sin(a) = (adjacent cathetus)/(hypotenuse).
- tan(a) = (opposite cathetus)/(adjacent cathetus).
Where:
- hypotenuse = AC
- opposite cathetus = AB.
Then we will have:
sin(40°) = 10in/AC.
AC = 10in/sin(40°) = 15.6 in
tan(40°) = AB/10in
tan(40°)*10in = AB = 8.4 in.
So we can conclude that for the given right triangle we have:
AC = 15.6 in
AB = 8.4 in.
If you want to learn more about right triangles:
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