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2 years ago

If r=1 and 0=5pie/3, what is the approximate arc length?

Mathematics

1 answer:

Masja [62]2 years ago

4 0

Answer:

5.236 units

Step-by-step explanation:

The relation between r, θ and arc length ( l ) is,

l = rθ

l = 1 * 5π / 3

( The value of π = 3.14 approximately )

5π = 5 x 3.14 = 15.7

l = 1 * 5π / 3

= 5π / 3

= 15.7/3

l = 5.236 units

Note : -

Arc length is denoted by " l ".

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Suppose that bugs are present in 1% of all computer programs. A computer de-bugging program detects an actual bug with probabili

lawyer [7]

Answer:

(i) The probability that there is a bug in the program given that the de-bugging program has detected the bug is 0.3333.

(ii) The probability that the bug is actually present given that the de-bugging program claims that bugs are present on both the first and second tests is 0.1111.

(iii) The probability that the bug is actually present given that the de-bugging program claims that bugs are present on all three tests is 0.037.

Step-by-step explanation:

Denote the events as follows:

B = bugs are present in a computer program.

D = a de-bugging program detects the bug.

The information provided is:

$P(B) =0.01\\P(D|B)=0.99\\P(D|B^{c})=0.02$

(i)

The probability that there is a bug in the program given that the de-bugging program has detected the bug is, P (B | D).

The Bayes' theorem states that the conditional probability of an event E given that another event X has already occurred is:

$P(E|X)=\frac{P(X|E)P(E)}{P(X|E)P(E)+P(X|E^{c})P(E^{c})}$

Use the Bayes' theorem to compute the value of P (B | D) as follows:

$P(B|D)=\frac{P(D|B)P(B)}{P(D|B)P(B)+P(D|B^{c})P(B^{c})}=\frac{(0.99\times 0.01)}{(0.99\times 0.01)+(0.02\times (1-0.01))}=0.3333$

Thus, the probability that there is a bug in the program given that the de-bugging program has detected the bug is 0.3333.

(ii)

The probability that a bug is actually present given that the de-bugging program claims that bug is present is:

P (B|D) = 0.3333

Now it is provided that two tests are performed on the program A.

Both the test are independent of each other.

The probability that the bug is actually present given that the de-bugging program claims that bugs are present on both the first and second tests is:

P (Bugs are actually present | Detects on both test) = P (B|D) × P (B|D)

$=0.3333\times 0.3333\\=0.11108889\\\approx 0.1111$

Thus, the probability that the bug is actually present given that the de-bugging program claims that bugs are present on both the first and second tests is 0.1111.

(iii)

Now it is provided that three tests are performed on the program A.

All the three tests are independent of each other.

The probability that the bug is actually present given that the de-bugging program claims that bugs are present on all three tests is:

P (Bugs are actually present | Detects on all 3 test)

= P (B|D) × P (B|D) × P (B|D)

$=0.3333\times 0.3333\times 0.3333\\=0.037025927037\\\approx 0.037$

Thus, the probability that the bug is actually present given that the de-bugging program claims that bugs are present on all three tests is 0.037.

4 0

3 years ago

Bailey studies 3 days for her final exam in history. The first day she studied 1 1/2 hours on day 2 she studied 1/2 as long as s

borishaifa [10]

1st day: 1 1/2 hours
2nd day: half of first day = 1/2 * 1 1/2 hours
3rd day: 2 1/2 times as long as first day: 2 1/2 * 1 1/2 hours

1 1/2 + 1/2 * 1 1/2 + 2 1/2 * 1 1/2 =

= 3/2 + 1/2 * 3/2 + 5/2 * 3/2

= 3/2 + 3/4 + 15/4

= 6/4 + 3/4 + 15/4

= 24/4

= 6

Answer: She studied for 6 hours over the 3-day period.

5 0

4 years ago

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Trevor ran a hundred meter dash in 10.4 seconds what was his speed be in miles per hour at this rate round your answer to the ne

kicyunya [14]

(100 m / 10.4 sec) x (3600 sec/hr) x (mile/1609.344m) = 21.5 miles per hour

Rounded to the nearest whole number, that's 22 mph .

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3 years ago

Jimmy earns $9.25 per hour working at a local grocery store. If Jimmy earned $74 last week, which equation would be used to dete

Alekssandra [29.7K]

9.25h=74 you multiply h by 9.25

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4 years ago

Is Joon lee soo a girl or boy name???

blagie [28]

Answer:

Girl

Step-by-step explanation:

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3 years ago

If r=1 and 0=5pie/3, what is the approximate arc length?​

If r=1 and 0=5pie/3, what is the approximate arc length?