14ezra2003

Copper, 1.04 g is dissolved in nitric acid, to produce copper(II) nitrate, which when reacted with NaOH and heated, produces 1.19 g of copper oxide, which is isolated and dried. What is the percent yield for the production of copper oxide?

Answer to the nearest integer without the % sign (example: 74)

Let's start by solving for p and q using the given equations:

 

Given:

x = va(sinu + cosv)

y = va(cosu - sinv)

z = 1 + sin(u - v)

 

To find p and q, we need to eliminate u and v from the equations. Here's how we can do it:

 

1. Square both sides of the first equation:

x^2 = v^2a^2(sinu + cosv)^2

 

2. Square both sides of the second equation:

y^2 = v^2a^2(cosu - sinv)^2

 

3. Add the squared equations together:

x^2 + y^2 = v^2a^2(sinu + cosv)^2 + v^2a^2(cosu - sinv)^2

 

4. Expand and simplify the equation:

x^2 + y^2 = v^2a^2(sin^2u + 2sinucosv + cos^2v) + v^2a^2(cos^2u - 2sinvcosu + sin^2v)

 

5. Combine like terms:

x^2 + y^2 = v^2a^2(sin^2u + cos^2u + sin^2v + cos^2v) + 2v^2a^2(sinucosv - sinvcosu)

 

6. Simplify further using trigonometric identities:

x^2 + y^2 = v^2a^2 + 2v^2a^2(sin(u + v))

 

7. Now, let's look at the equation for z:

z = 1 + sin(u - v)

 

8. Square both sides of the equation:

z^2 = (1 + sin(u - v))^2

 

9. Expand and simplify the equation:

z^2 = 1 + 2sin(u - v) + sin^2(u - v)

 

10. Substitute the value of z from the original equation:

z^2 = 1 + 2sin(u - v) + sin^2(u - v)

 

11. Simplify further:

z^2 = 1 + 2sin(u - v) + (1 - cos^2(u - v))

 

12. Simplify even more:

z^2 = 2 - cos^2(u - v) + 2sin(u - v)

 

13. Rearrange the equation:

cos^2(u - v) = 2 - z^2 - 2sin(u - v)

 

14. Substitute the value of sin(u - v) from the equation derived in step 6:

cos^2(u - v) = 2 - z^2 - 2v^2a^2

 

15. Take the square root of both sides:

cos(u - v) = ±√(2 - z^2 - 2v^2a^2)

 

16. Now, let's find sin(u - v) using the equation derived in step 6:

sin(u - v) = (x^2 + y^2 - v^2a^2) / (2va^2)

 

17. Substitute the values of cos(u - v) and sin(u - v) into the equation for x:

x = va(sinu + cosv)

 

18. Substitute the values of sin(u - v) and cos(u - v) into the equation for y:

y = va(cosu - sinv)

 

19. Simplify the equations further and solve for p and q:

p = arcsin((x - y) / (2va))

q = arccos((x + y) / (2va))

 

These are the values of p and q based on the given equations. Please note that there may be other solutions or constraints depending on the specific values of x, y, z, v, and a.

7) The time it takes for a statistics professor to grade an exam is normally distributed with a mean of 9.7 minutes and a standard devation of 1.9 minutes. There are 50 students in the professor's class. What is the probabilty that more than 8 hours are needed to grade all of the exams? (Report your answer to 4 decimal places.)

8) The daily productivity of a factory worker is normally distributed with a mean of 100 units and a standard deviation of 22 units. What is the probability that  the average number of units produced in one day by 9 randomly selected workers is less than 90 units? (Report your answer to 4 decimal places.)

9) A coffee shop in a large office building provides coffee for the occupants in the building. The coffee shop manager has determined that the mean number of cups of coffee an employee consumes in a day is 2 with a standard deviation of 0.9. A new business that has located in the building intends to have 150 new employees. What is the probability that the new employees will consume more than 285 cups of coffee per day? (Report your answer to 4 decimal places.)

10) The number of hamburgers consumed per month by undergraduate students is normally distributed with a mean of 8.5 and a standard deviation of 1.75. What is the probability that in a random sample of 28 students more than 231 hamburgers are consumed? (report your answer as a decimal to 4 decimal places) 

 

11) A pharmaceutical manufacturer of aspirin claims that the proportion of headache sufferers who get relieve with two aspirins is 66%. What is the probability that in a random sample of 250 headache sufferers, more than 70% obtain relief? (Report your answer to 4 decimal places.)

12) Using the aspirin problem above, what if the probability if the sample is increased to 1000? (Report your answer to 4 decimal places.)

please explain how to do this in excel along with the answers.