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3 years ago

Use the table of integrals, or a computer or calculator with symbolic integration capabilities, to find the indefinite integral.

Mathematics

1 answer:

Dahasolnce [82]3 years ago

7 0

Answer:

Indefinite integral of the expression will be $16lnx+16x$

Step-by-step explanation:

We have given expression $I=\int( \frac{16}{\sqrt{x^2}}+16)dx=\int (\frac{16}{x}+16)dx$

We have to integrate this function

So I=\int( \frac{16}{\sqrt{x^2}}+16)dx=\int (\frac{16}{x}+16)dx=\int (16x^{-1}+16)dx

$I=\int (16x^{-1}+16)dx=16lnx+16x$

So indefinite integral of the expression will be $16lnx+16x$

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If I chose a number uniformly from the integers from 1 to 25, calculate the conditional probability that the number is a multipl

topjm [15]

Answer:

Step-by-step explanation:

If I choose a number from the integers 1 to 25, the total number of integers I can pick is the total outcome which is 25. n(U) = 25

Let the probability that the number chosen at random is a multiple of 6 be P(A) and the probability that the number chosen at random is is larger than 18 be P(B)

P(A) = P(multiple of 6)

P(B) = P(number larger than 18)

A = {6, 12, 18, 24}

B = {19, 20, 21, 22, 23, 24, 25}

The conditional probability that the number is a multiple of 6 (including 6) given that it is larger than 18 is expressed as P(A|B).

P(A|B) = P(A∩B)/P(B)

Since probability = expected outcome/total outcome

A∩B = {24}

n(A∩B) = 1

P(A∩B) = n(A∩B)/n(U)

P(A∩B) = 1/25

Given B = {19, 20, 21, 22, 23, 24, 25}.

n(B) = 7

p(B) = n(B)/n(U)

p(B) = 7/25

Since P(A|B) = P(A∩B)/P(B)

P(A|B) = (1/25)/(7/24)

P(A|B) = 1/25*25/7

P(A|B) = 1/7

<em>Hence the conditional probability that the number is a multiple of 6 (including 6) given that it is larger than 18 is 1/7</em>

7 0

3 years ago

Sripathi 10 years old than ragu. their total age is 100

Fiesta28 [93]

S = 10 + r

s + r = 100

Adding equations,

2s +r = 110 + r

2s = 110

s = 55

r = 45

8 0

3 years ago

The National Cancer Institute estimates that 3.65% of women in their 60s get breast cancer. A mammogram can typically identify c

masha68 [24]

Answer:

39.17% probability that a woman in her 60s who has a positive test actually has breast cancer

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

$P(B|A) = \frac{P(B)*P(A|B)}{P(A)}$

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Positive test.

Event B: Having breast cancer.

3.65% of women in their 60s get breast cancer

This means that $P(B) = 0.0365$

A mammogram can typically identify correctly 85% of cancer cases

This means that $P(A|B) = 0.85$

Probability of a positive test.

85% of 3.65% and 100-95 = 5% of 100-3.65 = 96.35%. So

$P(A) = 0.85*0.0365 + 0.05*0.9635 = 0.0792$

What is the probability that a woman in her 60s who has a positive test actually has breast cancer?

$P(B|A) = \frac{0.0365*0.85}{0.0792} = 0.3917$

39.17% probability that a woman in her 60s who has a positive test actually has breast cancer

7 0

3 years ago

Please help i have no clue what to do <br> i suck at math

beks73 [17]

The first one is 63.9 and the second should be 116.1

3 0

3 years ago

A prop for the theater club’s play is constructed as a cone topped with a half- sphere. What is the volume of the prop? Round yo

san4es73 [151]

The volume of the prop is calculated to be 1,875.6 cubic cm.

Step-by-step explanation:

Step 1; The prop consists of a cone and a half-sphere on top. We will have to calculate the volumes of the cone and the half-sphere separately and then add them to obtain the total volume.

Step 2; The volume of a cone is determined by multiplying $\frac{1}{3}$ with π, the square of the radius (r²) and height (h). Here we substitute π as 3.14. The radius is 8 cm and the height is 12 cm.

The volume of the cone = $\frac{1}{3}$ × 3.14 × 8 × 8 × 12 = 803.84 cubic cm.

Step 3; The area of a half-sphere is half of a full sphere. The volume of a sphere is given by multiplying $\frac{4}{3}$ with π and the cube of the radius (r³). Here the radius is 8cm. We take π as 3.14.

The volume of a full sphere = $\frac{4}{3}$ × 3.14 × r³ = $\frac{4}{3}$ × π × 8³ = 2,143.5733 cubic cm.

The volume of a half-sphere = $\frac{ 2,143.5733}{2}$ = 1,071.7866 cubic cm.

Step 4; The total volume = The volume of the cone + The volume of the half sphere,

The total volume = 803.84 cubic cm + 1,071.7866 cubic cm = 1,875.6266 cubic cm. By rounding this off to the nearest tenth we get 1,875.6 cubic cm.

4 0

4 years ago