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2 years ago

Molly wants to put a fence around an area. The fence will follow the diagram of the triangle shown below.

Mathematics

1 answer:

IgorC [24]2 years ago

3 0

Molly would need 43 feet of fencing to fence the area.

Step-by-step explanation:

We can see that the area is in the form of a right-angled triangle. Since only two sides of the triangle is given, we could utilise Pythagoras theorem to our advantage to find out the third side.

In Δ ABC

AB² (base) + AC² (perpendicular) = BC² (hypotenuse)

Substituting the values of AB as 10 feet and BC as 18 feet

AC²= BC²- AB ²

∴AC²= 224

∴AC= 14.96 cm

Amount of fence required by molly would equal perimter of the area.

⇒The perimeter of the area would equal AB+BC+AC

⇒Summing up the values of AB, AC and BC

Perimeter= 10+14.96+18= 42.96 feet which is about 43 feet

Hence, Molly would require 43 feet of fencing.

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Two well-known aviation training schools are being compared using random samples of their graduates. It is found that 70 of 140

egoroff_w [7]

Answer:

Step-by-step explanation:

Given that two well-known aviation training schools are being compared using random samples of their graduates

Fly more academy 70 of 140

Blue Yonder 104 of 260

Combined pass = (70+104) out of (140+260)

a) Pooled proportion= $\frac{174}{400} \\=0.435$

b) H0: p1 = p2

Ha: p1 ≠p2

(two tailed test)

p difference= $\frac{70}{140} -\frac{104}{260} =0.10$

std error for difference (using pooled proportion) = $\sqrt{\frac{0.435*0.565}{400} } \\=0.0248$

Test statistic = p difff/std error = 4.034

c) Critical value for 0.05 is 1.96

d) p value is < 0.005

Since p < 0.05 our significant level we reject H0

There is significant difference between the two proportions.

8 0

2 years ago

In a certain community, eight percent of all adults over age 50 have diabetes. If a health service in this community correctly d

____ [38]

Complete question is;

In a certain community, 8% of all people above 50 years of age have diabetes. A health service in this community correctly diagnoses 95% of all person with diabetes as having the disease, and incorrectly diagnoses 10% of all person without diabetes as having the disease. Find the probability that a person randomly selected from among all people of age above 50 and diagnosed by the health service as having diabetes actually has the disease.

Answer:

P(has diabetes | positive) = 0.442

Step-by-step explanation:

Probability of having diabetes and being positive is;

P(positive & has diabetes) = P(has diabetes) × P(positive | has diabetes)

We are told 8% or 0.08 have diabetes and there's a correct diagnosis of 95% of all the persons with diabetes having the disease.

Thus;

P(positive & has diabetes) = 0.08 × 0.95 = 0.076

P(negative & has diabetes) = P(has diabetes) × (1 –P(positive | has diabetes)) = 0.08 × (1 - 0.95)

P(negative & has diabetes) = 0.004

P(positive & no diabetes) = P(no diabetes) × P(positive | no diabetes)

We are told that there is an incorrect diagnoses of 10% of all persons without diabetes as having the disease

Thus;

P(positive & no diabetes) = 0.92 × 0.1 = 0.092

P(negative &no diabetes) =P(no diabetes) × (1 –P(positive | no diabetes)) = 0.92 × (1 - 0.1)

P(negative &no diabetes) = 0.828

Probability that a person selected having diabetes actually has the disease is;

P(has diabetes | positive) =P(positive & has diabetes) / P(positive)

P(positive) = 0.08 + P(positive & no diabetes)

P(positive) = 0.08 + 0.092 = 0.172

P(has diabetes | positive) = 0.076/0.172 = 0.442

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2 years ago

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Dahasolnce [82]

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2 years ago

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mixer [17]

we have

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