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2 years ago

Plese tell how to solve this

Mathematics

1 answer:

klasskru [66]2 years ago

8 0

Answer:

hope you understand the answers

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A recent survey by the American Cancer Society shows that the probability that someone is a smoker is P(S) = 0.19. It has also d

Rom4ik [11]

P(LC / S) = P(S intersect LC) / P(S)
P(S intersect LC) = P(S)*P(LC / S) = 0.19 * 0.158 = 0.03

8 0

2 years ago

Let f be defined by the function f(x) = 1/(x^2+9)

riadik2000 [5.3K]

(a)

$\displaystyle\int_3^\infty \frac{\mathrm dx}{x^2+9}=\lim_{b\to\infty}\int_{x=3}^{x=b}\frac{\mathrm dx}{x^2+9}$

Substitute x = 3 tan(t ) and dx = 3 sec²(t ) dt :

$\displaystyle\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\frac{3\sec^2(t)}{(3\tan(t))^2+9}\,\mathrm dt=\frac13\lim_{b\to\infty}\int_{t=\arctan(1)}^{t=\arctan\left(\frac b3\right)}\mathrm dt$

$=\displaystyle \frac13 \lim_{b\to\infty}\left(\arctan\left(\frac b3\right)-\arctan(1)\right)=\boxed{\dfrac\pi{12}}$

(b) The series

$\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}$

converges by comparison to the convergent p-series,

$\displaystyle\sum_{n=3}^\infty\frac1{n^2}$

$\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}$

converges absolutely, since

$\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}$

That is, ∑ (-1)ⁿ (n ² + 9)/eⁿ converges absolutely because ∑ |(-1)ⁿ (n ² + 9)/eⁿ| = ∑ (n ² + 9)/eⁿ in turn converges by comparison to a geometric series.

5 0

2 years ago

Which line is the best model for the data in the scatter plot?

tatyana61 [14]

1.Not Even
2.Even
3.Not Even
4.Not Even

7 0

2 years ago

For the expression y + 6-3 determine the coefficient for the variable term. (2 points)

aksik [14]

Answer:

The answer is 1.

Step-by-step explanation:

The number is usually in front of the variable, if there is no number, it is a 1.

6 0

2 years ago

A spinner with 10 equally sized slices is shown below. (3 slices are blue, 2 are yellow, and 5 are rec the probability that the

Ainat [17]

Answer:

1/2

Step-by-step explanation:

Blue + yellow = 3 + 2 = 5 out of 10 slices

5 out of 10 = 5/10 = 1/2

5 0

1 year ago

Plese tell how to solve this​

Plese tell how to solve this