Nathan had an infection, and his doctor wanted him to take penicillin. because nathan’s father and paternal grandfather were allergic to penicillin, nathan has a 75% chance of having the same allergy. the doctor performed a skin test to see whether nathan would react to it. the test is 98% accurate. what is the probability that nathan is not allergic to penicillin and the test predicts it?

Probability that Nathan is not allergic to penicillin and the test predicts it is 24.5%.

Step-by-step explanation:

Since we have given that

Probability that Nathan having the same allergy that his father and paternal grandfather are prone to =75%

Probability that the test is accurate = 98%

We need to find that Nathan is not allergic to penicillin and the test predicts it.

So, probability that Nathan is not allergic = 100-75=25%

So, we will use "P(A∩B)=P(A)×P(B)"

here, A be the event that Nathan is not having allergy and B be the event that the test predicts it.

We are using the above formula because event A and B are independent events.

so, it becomes,

Hence,  probability that Nathan is not allergic to penicillin and the test predicts it is 24.5%.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.