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3 years ago

Determine whether the given measures can be the lengths of the sides of a triangle. write yes or no. explain. 9.2, 14.5, 17.1

Mathematics

2 answers:

viktelen [127]3 years ago

8 0

Answer with explanation:

If the length of three segments are, 9.2, 14.5 and 17.1 ,it can be sides of triangle if , Sum of two segments is greater than the third segment.

1.→ 9.2 +14.5=23.7 >17.1

2.→ 14.5 +17.1=41.6 > 9.2

3.→17.1 +9.2=26.3 >14.5

As, sum of any two segment is greater than third segment, so the following measurements can be the the lengths of the sides of a triangle.

Sergio039 [100]3 years ago

3 0

If the triangle has a angle of 90°, you can solved this exercise by applying the Pythagorean Theorem, which is:

h²=a²+b²
h=√(a²+b²)

h: It is the hypotenuse (The opposite side of the right angle and the longest side of the triangle).

a and b: They are the legs (The sides that form the right angle).

The result of h=√(a²+b²), should be 17.1 (The longest side given in the problem). So, let's substitute the values of the legs into the Pythagorean equation:

h=√(a²+b²)
h=√((9.2)²+(14.5)²)
h=17.1

Therefore, the answer is:

Yes, the given measures can be the lengths of the sides of a triangle.

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Answer:

The calculated value Z = 2.3084 > 1.96 at 5% level of significance

Null hypothesis is rejected

Alternative hypothesis is accepted

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Step-by-step explanation:

Step(i):-

Given the hotel takes a random sample of 223 guests. Out of this sample, 39 guests requested smoking rooms.

Sample proportion

p = x/n = 39/223 = 0.174

Given Population proportion 'P' = 0.24

Given random sample size 'n' = 223

Level of significance ∝ =0.05

The critical value Z₀.₀₅ = 1.96

Null Hypothesis (H₀) : P=0.24

Alternative Hypothesis (H₁) : P≠ 0.24

Step(ii):-

Test statistic

$Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }$

$Z = \frac{0.174-0.24}{\sqrt{\frac{0.24 X 0.76}{223} } }$

|Z| = | -2.3084|= 2.3084

The calculated value Z = 2.3084 > 1.96 at 5% level of significance

Null hypothesis is rejected

Alternative hypothesis is accepted

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2 years ago

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bonufazy [111]

Answer:

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Step-by-step explanation:

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Answer:

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