**Question 1**

d). If a car is traveling 75 miles per hour, how

many feet will it travel in 10 seconds ?

e) . If a car is traveling 75 kilometers per hour,

how many meters will it travel in 10 seconds?

f) . A leaky faucet drips at the rate of 1 pint per

hour. How many gallons will drip in a 24 hour

day?

Question 2

How many seconds are there in a solar year (365.24 days), expressed in the correct number of Significant Figures? (60 seconds per minute, 60 min per hour, & 24 hours per day)

Question 3

Question 4

Answer to question 1

Answer to question 2

The above answers are incorrect. Here you want to use FIVE significant figures. The reason for this is because conversion factors do NOT get factored into the significant figure rules. Since even your question states “there are EXACTLY…..” you can assume that this is NOT limiting your significant figures (which makes sense, because seconds and minutes and hours are human-made time intervals.)

The year (the time it takes the earth to go around the sun) is NOT an interval that is made up arbitrarily by humans (hence why there is a decimal place in the conversion). THIS is your limiting factor, so your answer will have 5 significant figures.

3.1557×10^7

Answer to question 3

Answer to question 4

7) Here , X is a random variable which represents number of fair coins turns out to be head out of n=3 coins & probability of getting head on each coin is p=0.5.

Assuming cons are independently fliped .

Clearly , X~Binomial(n=3,p=0.5)

Then,probability mass function of X is ,

P(X=x)=^{n}C_{x}*p^{x}*(1-p)^{n-x}=^{3}C_{x}*0.5^{x}*0.5^{3-x };x=0,1,2,3

We have to find here the probability that we get exactly one head i.e. P(X=1).

Consider,

P(X=1)=^{3}C_{1}*0.5^{1}*0.5^{3-1}={3!/[1!*(3-1)!]}*0.5* 0.5^{2}={3*2*1/[1*2*1]}*0.5* 0.5^{2}=0.375

(8) There are 60 seconds in a minute.

Threre are 60 minutes in a hour.

Therefore,a hour contains 60*60=3600 seconds .

There are 24 hours in a day.

Therefore, hours contains 3600*24= 86400 seconds.