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const2013 [10]
2 years ago
9

The director of health services is concerned about a possible flu outbreak at her college. She surveyed

Mathematics
2 answers:
IgorLugansk [536]2 years ago
6 0

Answer:

39/100

Step-by-step explanation:

The question asks to find the probability that a dormitory resident

chosen at random from this group has had a flu shot, given that he is male.

As for that, the first thing to do is to look at the column where it says male.

Male:

39-Had Flu Shot

12-Did not have Flu Shot

Since the question is asking for the total number of males who did get a flu shot, it would be 39.

Lastly, to find probability, you have to use part over whole. The part would be 39. The whole would be the number of people selected to be tested. Therefore, the whole would be 100. That is why the probability that a dormitory resident chosen at random from this group has had a flu shot, given that he is male would be 39/100.

nordsb [41]2 years ago
3 0

Answer:

I believe the answer is A.

Step-by-step explanation:

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The approximate area of the region bounded by the curves f(x) = x / √(x² + 1) and g(x) = x⁴ - x is approximately 0.806.

<h3>How to determine the approximate area of the regions bounded by the curves</h3>

In this problem we must use definite integrals to determine the area of the region bounded by the curves. Based on all the information given by the graph attached below, the area can be defined in accordance with this formula:

A = A₁ + A₂                                                                (1)

A₁ = ∫ [g(x) - f(x)] dx, for x ∈ [- 0.786, 0]                   (2)

A₂ = ∫ [f(x) - g(x)] dx, for x ∈ [0, 1.151]                       (3)

g(x) = x⁴ - x                                                               (4)

f(x) = x / √(x² + 1)                                                      (5)

Then, we proceed to find the integrals:

∫ g(x) dx = ∫ x⁴ dx - ∫ x dx = (1 / 5) · x⁵ - (1 / 2) · x²                          (6)

∫ f(x) dx = ∫ [x / √(x² + 1)] dx = (1 / 2) ∫ [2 · x / √(x² + 1)] dx = (1 / 2) ∫ [du / √u] = √u = √(x² + 1)                                                                                  (7)

And the complete expression for the integral is:

A = A₁ + A₂                                                                                      (1b)

A₁ = (1 / 5) · x⁵ - (1 / 2) · x² - √(x² + 1), for x ∈ [- 0.786, 0]               (2b)

A₂ = √(x² + 1) - (1 / 5) · x⁵ + (1 / 2) · x², for x ∈ [0, 1.151]                  (3b)

A₁ = 0.023

A₂ = 0.783

A = 0.023 + 0.783

A = 0.806

The approximate area of the region bounded by the curves f(x) = x / √(x² + 1) and g(x) = x⁴ - x is approximately 0.806.

To learn more on definite integral: brainly.com/question/14279102

#SPJ1

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