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3 years ago

What type of angles are ECH and FCG?

Mathematics

2 answers:

Darina [25.2K]3 years ago

5 0

ECH is an acute angle.

FCG is also an acute angle.

Elenna [48]3 years ago

5 0

Answer:

Vertical angles

Step-by-step explanation:

Vertical angles are angles formed by two intersecting lines, which the angles are facing the opposite direction. Also the angles are on the same vertice (point).

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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

Sam receives a weekly paycheck. Here’s a copy of one of his pay statements. If there are 4 paydays per month, what is Sam’s mont

Xelga [282]

In this problem, since we are trying to find Sam's monthly net income, we just need to multiply his weekly net income (which is after all the deductions come out) by how many times he gets paid! Because he gets paid 4 times, we just need to multiply $654.48 by 4! The you should get an answer of $2617.92, which is Sam's monthly net income!

7 0

3 years ago

What is the value of 8(x-3.7) if x=4.9?

Vsevolod [243]

Take 8 times 4.9 and 8 times 3.7, 8 times 4.9 is 39.2 and 8 times 3.7 is 29.6 now all you have to do is subtract them numbers from each other and it gives you the answer of 9.6

Answer: 9.6

7 0

3 years ago

Find the circumstances of the circle

Mkey [24]

The meaning of circumference is to find the distance around a circle or in other words perimeter by using the formula C=2πr or C=πd.

On this case it is asked you to find the circumference of a circle with a diameter of 3 meters, so you will use the formula C=2πr.

C=2πr
C=2(3.14)(3)
C=18.84 meters

The circumference of the given circle is 18.84 meters.

8 0

2 years ago

Margie pays $9.43, which includes 15%

andrew-mc [135]

Answer:

15% $1.41 $10.84

10.84

8 0

3 years ago