1. A) If you flip an unfair coin 100 times, and the probability for a coin to be heads is 0.4, then the number of heads you expect on average is:

B) If you flip an unfair coin 100 times, and the probability for a coin to be heads is 0.4, then the standard deviation for the number of heads is:

C) If you flip an unfair coin 2 times, and the probability for a coin to be heads is 0.4, then what is the probability to find exactly 1 heads?

D) If you flip an unfair coin 2 times, and the probability for a coin to be heads is 0.4, then what is the probability to find exactly 2 heads?

E) If you flip an unfair coin 10 times, and the probability for a coin to be heads is 0.4, then what is the probability to find exactly 2 heads?

F) Suppose that 20 molecules jump randomly in and out of a cell. Eventually, each molecule is independently distributed and has a probability 0.1 to be in the cell.

What is the variance of the count of these molecules inside of the cell?

a cart with a mass of 100 kg is traveling down a 5% grade. the coefficient of drag of the area is Cd = 0.05 based on a frontal area of 0.6 m^2. coefficient of friction for the wheels is mu = 0.0062. Find terminal velocity? assuming started at a standstill find distance to get to terminal velocity?

Assume that on a standardized test of 100 questions, a person has a probability of 80% of answering any particular question correctly. Find the probability of answering between 70 and 80 questions, inclusive. (Assume independence, and round your answer to four decimal places.)

P(70 ≤ X ≤ 80) =

Assume the population mean IQ is 100 with a standard deviation of 15. A sample of 25 students recently took an IQ test in which their average score was 108. If another sample of 25 students was selected, what is the probability that that sample would have a mean greater than 108?

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
A) If one person are randomly selected, find the probability the IQ score is greater than 112.
B)If one person are randomly selected, find the probability the IQ score is less than 95.
C)If one person are randomly selected, find the probability the IQ score is between 97 and 110.
D) If 16 people are randomly selected, find the probability the IQ score will be less than 95.

A sled with mass 100 kg moves in a straight line on a horizontal surface as it is being pulled by a force 250 N at an angle of 35° with the direction of motion. A force of friction of 30 N acts on the sled. At one point in its path, its speed is 3.0 m/s; after it has traveled a distance d beyond this point, its speed is 8.0 m/s.

1. Use the work-energy theorem to find the total work done on the sled?

B. Find the distance d traveled by the sled.

Suppose you have a sample of with 100 mCi of 82Sr. When will the activity of 82Rb reach over 99% of the activity of 82Sr? min You currently have 7 submissions for this question. Only 10 submission are allowed. You can make 3 more submissions for this question. Help: Since the daugther's half-life is much smaller than the parent's half-life, the daugther reaches the parent's activity only asymptotically over several half-lives. Activity of daugther after n half-lives = (1/2)n. You need to find the value of n such that ARb/ASr>=0.99. Note: You do not have to find the exact time when ARb/ASr=0.99. Instead find the smallest value of the integer n such that, after n half-lives ARb/ASr>=0.99. 3) How much daughter activity will there be after 20 minutes? mCi You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 4) How much daughter activity (Question 1) will there be after 20 days? mCi

assume that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.

Find the probability that a randomly selected person has an IQ score less than 115.

Find the probability that a randomly selected person has an IQ score greater than 118.

Find the probability that a randomly selected person has an IQ score between 88 and 112.

a.) If 5 ml of 0.1 NaOH (a strong base) is added to 100 ml of 0.05 phosphate buffer (phosphoric acid- H3PO4), pH 7.1, what is the resulting pH? (Ignore the volume change). Clearly identify the appropriate acid and conjugate base and determine their concentration in the final solution. b.) What would the resulting pH be if instead you added 5 ml of 0.25 M HCl? (Ignore the volume change) *Please show your work and steps to understand*