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In the Health ABC Study, 543 subjects owned a pet and 1977 subjects did not. Among the pet owners, there were 293 women; 975 of

True [87]

Answer:

The proportion of pet owners who were women is 0.540.

The proportion of non-pet owners who were women is 0.493.

Step-by-step explanation:

The data provided is summarized in the table below.

Pet Owners Non-Pet Owners TOTAL

Men 250 1002 1252

Women 293 975 1268

TOTAL 543 1977 2520

Denote the events as follows:

W = a subject is a women

P = a subject is a pet owner

The probability of an event, say E, is defined as the ration of the favorable outcomes of E to the the total number of outcomes of the experiment.

P (E) = n (E) ÷ N

Here,

n (E) = favorable outcome

N = total number of outcomes

(1)

The conditional probability of an event B given that another events A has already occurred is:

P (B | A) = n (A ∩ B) ÷ n (A)

Compute the probability of a pet owner being a women as follows:

P (W | P) = n (W ∩ P) ÷ n (P)

= 975 ÷ 1977

= 0.5396

≈ 0.540

Thus, the proportion of pet owners who were women is 0.540.

(2)

Compute the probability of a non-pet owner being a women as follows:

P (W | P') = n (W ∩ P') ÷ n (P')

= 293 ÷ 543

= 0.4932

≈ 0.493

Thus, the proportion of non-pet owners who were women is 0.493.

8 0

3 years ago

Find the value of each variable. Write the equation and solve showing ALL the work.

Anit [1.1K]

The angles must add up to 360 degrees, so we can set the sum of the interior angles equal to 360 and solve for x.

106 + 94 + 135 + x + (x + 5) = 360

Combine like terms:

340 + 2x = 360

2x = 20

x = 10

6 0

3 years ago

45/15 is an integer but not a whole number. Is that correct or incorrect? Can you explain the correct answer to me?

Minchanka [31]

Answer:

Incorrect.

Step-by-step explanation:

45/15 = 3.

It is an integer and a whole number.

7 0

3 years ago

Read 2 more answers

Cassie leaves Escanaba at 8:30 AM heading for Marquette on her bike. She bikes at a uniform rate of 12 miles per hour. Brian lea

exis [7]

Answer:

(D) 11: 00

Step-by-step explanation:

We have been given that Cassie leaves Escanaba at 8:30 AM heading for Marquette on her bike. Brian leaves Marquette at 9:00 AM heading for Escanaba on his bike.

This means that Cassie leaves 1/2 hour before Brian.

Since Cassie bikes at a uniform rate of 12 miles per hour, so distance covered in half hour would be half of 12 miles that is 6 miles.

Since total distance is 62 miles, so distance left between both at 9:00 Am would be $62-6=56$ .

We are told that Brian bikes at a uniform rate of 16 miles per hour and Cassie bikes at a uniform rate of 12 miles per hour, so distance traveled by both in one hour would be $16+12=28$ miles.

Let us divide 56 by 28 to find time taken to complete 56 miles.

$\frac{56}{28}=2$ .

Since it will take them 2 hours to cover 56 miles, therefore, they will meet 2 hours after 9:00 AM that is 11:00 AM.

3 0

4 years ago

How do you do both parts?

AnnZ [28]

Step-by-step explanation:

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

Divide top and bottom by 5.

f(x) = ⅕ / (1 + ⅕x)

f(x) = ⅕ / (1 − (-⅕x))

Write as a geometric series.

f(x) = ∑ₙ₌₀°° ⅕ (-⅕x)ⁿ

f(x) = ∑ₙ₌₀°° ⅕ (-1)ⁿ (⅕)ⁿ xⁿ

f(x) = ∑ₙ₌₀°° (-1)ⁿ (⅕)ⁿ⁺¹ xⁿ

Use ratio test:

lim(n→∞)│aₙ₊₁ / aₙ│< 1

lim(n→∞)│[(-1)ⁿ⁺¹ (⅕)ⁿ⁺² xⁿ⁺¹] / [(-1)ⁿ (⅕)ⁿ⁺¹ xⁿ]│< 1

lim(n→∞)│-1 (⅕) x│< 1

│x/5│< 1

│x│< 5

-5 < x < 5

If x = -5, ∑ₙ₌₀°° ⅕ (-1)ⁿ (⅕)ⁿ (-5)ⁿ = ∑ₙ₌₀°° ⅕ (1)ⁿ, which diverges.

If x = 5, ∑ₙ₌₀°° ⅕ (-1)ⁿ (⅕)ⁿ (5)ⁿ = ∑ₙ₌₀°° ⅕ (-1)ⁿ, which diverges.

The interval of convergence is therefore (-5, 5).

4 0

3 years ago