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Four point charges are placed at the four corners of a square that is 30 cm on each side. Find the potential at the center of the square if two of the four charges are +2μC and the other two are -2μC.
With Complete Solution
Answer the following questions.
1. Describe briefly the different allied fields of genetics
2. Draw a Time Line of genetics specifying important highlights from 1950’s to present.
Assignment to work on:
1. What is genetics?
2. Allied branches of genetics.
3. Importance of studying genetics.
Eric runs a bicycle repair business and employs a single worker, Vanessa. He charges $6 to repair a flat tire. Vanessa's marginal product is given by 𝑇=1.5−𝐿
100 where 𝐿
L is the number of hours she works in a day and 𝑇
T is the number of additional tires that she repairs.
Suppose Eric currently pays Vanessa $8.25 per hour. How many hours changing tires, per day, should Eric have Vanessa work?
In an exchange economy, there are two people, A and B, and two goods, 𝑥1and 𝑥2. Their respective utility functions and endowments are
𝑢𝐴(𝑥𝐴1,𝑥𝐴2)=min{𝑥𝐴1,2𝑥𝐴2}
𝑢𝐵(𝑥𝐵1,𝑥𝐵2)=𝑥𝐵1+𝑥𝐵2
𝜔𝐴=(9,19)
𝜔𝐵=(9,0)
Note: The As and Bs in the equations above are not powers but rather superscripts to indicate each agent.
The minimum and maximum possible amounts of 𝑥𝐴2 on the contract curve are
Minimum 𝑥𝐴2
Maximum 𝑥𝐴2=
The minimum and maximum possible amounts of 𝑥𝐴1 on the contract curve are
Minimum 𝑥𝐴1=
Maximum 𝑥𝐴1=
a) A manufacturer has developed a new shing line, which the company claims has mean breaking strength of 15 kilograms with a standard deviation of 0.5 kilograms. To test the claim, a random sample of 50 lines will be tested. The rejection region to be used is de ned to be \bar{X} < 14:9.i) State the null and alternative hypotheses.
ii) Find type I error probability, "\\alpha" ,
iii) Evaluate "\\beta" or the alternative "\\mu" = 14.8.
iv) Evaluate power function for the alternative "\\mu" = 14.8.
b) Suppose that we wish to test the hypothesis H0 : "\\mu" = 68 kg versus H1 : "\\mu" > 68 kg, for weights of male students at a certain college, using "\\alpha" = 0.05 level of signifi cance, when it is known that "\\sigma" = 5.
i) Find the sample size required if the power of the test is to be 0.95
when the true mean is 69 kg.
ii) For what values of \bar{X} will the null hypothesis be rejected?P(-3.10<z<1 90)
P(z>2.92)
Two spherical obejcts have masses of 3.2 ×10^6 kg and 6.5×10^4 kg.The gravitational attraction between them is 75 N.How far apart are their centers?
b) two types of engines, A and B, were compared. Gas mileage, in miles per gallon, was measured. 50 experiments were conducted using engine type A and 75 experiments were done with engine type B. The gasoline used and other conditions were held constant. The average gas mileage was 36 miles per gallon for engine A and 42 miles per gallon for engine B. Find a 95% con dence interval on "\\mu"B - "\\mu"A, where "\\mu"B and "\\mu"Aare true mean gas mileages for engines A and B, respectively. population standard deviations are 6 and 8 for engines A and B, respectively. What can you conclude?
#339914 on Dec 2023