Tina's age is 4 years less than 3 times her niece's age. If her niece's age is x years, which of the following expressions best
2 answers:
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Answer:
A. 35 ft.
B. 35 ft
Step-by-step explanation:
Please see attached photo for diagram.
A. Determination of the diagonal using pythagorean theorem.
A square has all sides equal. Thus, the diagonal of the square can be obtained as follow:
Ist leg (L₁) = 25 ft
2nd leg (L₂) = 25 ft
Diagonal (d) =?
d² = L₁² + L₂²
d² = 25² + 25²
d² = 625 + 625
d² = 1250
Take the square root of both side
d = √1250
d = 35 ft
B. Determination of the diagonal using trigonometry.
Since all the sides in a square are equal, the angle between each leg will be 90°. Thus, the diagonal will bisect the angle between the two leg equally i.e
Angle between Diagonal and each leg = 90/2 = 45°
Finally, we shall determine the length of the diagonal. This can be obtained as follow:
Angle θ = 45°
Opposite = 25 ft
Hypothenus = d
Sine θ = Opposite / Hypothenus
Sine 45 = 25 / d
0.7071 = 25 / d
Cross multiply
0.7071 × d = 25
Divide both side by 0.7071
d = 25 / 0.7071
d = 35 ft
You have to use the Law of Cosines here, since there's no other way to solve this. it's not a right triangle, so you can't use the Pythagorean Theorem. The Law of Cosines will help us find the missing side length then we will have to use the Law of Sines to find another angle. Then after that we will use the Triangle Angle-Sum theorem to finish it off. Ready? The Law of Cosines to find side b is
and fill in the info we know, which is everything but the b. 
. Doing all that math gives us that side b = 40.9 or 41. Now the Law of Sines to find missing angle A or C. Let's find A. 
. That gives us that angle A is 29. Now use the fact that all triangles add up to 180 to get that angle C is 42. And you're done!
Answer:
a) p = 0.1808
b) Since 341.54 ≥ 10. Therefore the requirements for constructing a confidence interval for p is satisfied.
c) The interval is (0.1676, 0.194)
d) We are 90% confident that the population proportion of adult Americans who have donated blood in the past two years is between 0.1676 and 0.194
Step-by-step explanation:
Given that:
n = 2306 and x =417
a) Obtain a point estimate for the population proportion (p) is the ratio of sample successes to sample size.
Therefore: p = x / n = 417 / 2306 = 0.1808
p = 0.1808
b) requirements for constructing a confidence interval for p is given by:
np(1-p) ≥ 10
Therefore: np(1-p) = 2306(0.1808)(1 - 0.1808) = 341.54 ≥ 10
Since 341.54 ≥ 10. Therefore the requirements for constructing a confidence interval for p is satisfied.
c) c = 90% = 0.9
α = 1 - 0.9 = 0.1
α / 2 = 0.1 /2 = 0.05
From the probability table,
Margin of error (e) =
The boundaries are (p - e, p + e) = (0.1808 - 0.0132, 0.1808 + 0.0132) = (0.1676, 0.194)
The interval is (0.1676, 0.194)
d) We are 90% confident that the population proportion of adult Americans who have donated blood in the past two years is between 0.1676 and 0.194