Explain why an increase in sample size will reduce the probability of a type II error, but such an increase will not impact the probability of a type I error.
Support your reasoning using a scholarly source.
Category: Mathematics
Math Problems
Computer services revenue $25,307 Net income $18,833 Current liabilities $ 875
Net sales (of goods) 18,693 Quick asset 90,924 total liabilities 875
Total sales and revenue 44,000 Current assets 95,568 total equity 119,393
Cost of goods sold 14,052 total assets 120,268
1. Compute the gross margin ratio (both with and without services revenue) and net profit margin ratio (round the percent to one decimal).
2 Compute the current and acid-test ratios (round to one decimal).
3. Compute the debt and equity ratios (round the percent to one decimal).
4. What percent of its assets are current? What percent are long-term? Round percent to one decimal.
Understanding of probability
Have you ever wondered about the likelihood of an event occurring? Whether it’s the odds of your favorite football team winning on Sunday or how much you pay for car insurance, probability concepts can play a role in making those determinations.
Respond to the following questions in a minimum of 200 words:
Consider a situation that you might need to use your understanding of probability to make an informed decision.
What sorts of information would you collect?
How might you use what you have learned about probability to determine a course of action?
What are the possible benefits and limitations of this approach?
Application of Prime Numbers in Cryptography: A Review on RSA Algorithm
Rivest, Shamir and Adleman (RSA) algorithm is one of the most well-known public key cyptosystem algorithms. Although it’s been in use for a long time, a few fruitful attacks have been designed to break it due to the way its derived.
The algorithm’s security is primarily based on the difficultly of factoring the prod uct of two chosen large numbers. The RSA public key algorithm uses one key for encryption and another key for decryption and the choice of these keys should be handled delicately. Many analysts have presented ways to improve the efficiency and resis tance of the RSA algorithm. In this paper, we conceal the values of the publicly communicated parameters of public key, namely the encryption key and common modulus, from the public. The implementation of this concept makes use of two separate algorithms and randomly selecting between them using a random number generator.
The choice is communicated to the receiver so they know the proper algorithm to use. Lastly, we will followa quicker implementation of the modular exponentiation technique used in RSA encryption and decryption.
Real world Situations
Write and solve each equation from the given word problem on a blank sheet of paper. Write your answers in a complete sentence on this page. Show Your Work
1.) Maria combines her 39 seashells with Jacob’s seashells for a total of 173 seashells. Find how many seashells Jacob had before the collections were combined.
2.) The gym teacher divided a class into four teams with 7 students per team. How many students are in the class?
3.) An emergency plumber charges $65 as a call-out fee plus an additional $75 per hour. He arrives at a house at 9:30 and works to repair a water tank. If the total repair bill is $196.25, at what time was the repair completed?
4.) To convert temperatures in Fahrenheit to temperatures in Celsius, take the temperature in degrees Fahrenheit, subtract 32, and then divide the result by 1.8. This gives the temperature in degrees Celsius. Write an equation that shows the conversion process.
4a.) Convert 50 degrees Fahrenheit to degrees Celsius.
4b.) Convert 25 degrees Celsius to degrees Fahrenheit.
5.) Jasmin’s dad, Andrew, is planning a surprise birthday party for her. He will hire a bouncy castle, and will provide party food for all the guests. The bouncy castle costs $150 for the afternoon, and the food will cost $3 per person. Andrew has a budget of $300. Write an equation and use it to determine the maximum number of guests he can invite.
6.) The speed of a body is the distance it travels per unit of time. That means that we can also find out how far an object moves in a certain amount of time if we know its speed: we use the equation “distance = time x speed” Shanice’s car is traveling 10 miles per hour slower than twice the speed of Brandon’s car. She covers 93 miles in 1 hour 30 minutes. How fast is Brandon driving?
7.) The electrical current, I (amps), passing through an electronic component varies directly with the applied voltage, V (volts), according to the relationship V=I⋅R where R is the resistance measured in Ohms (Ω).
a. A scientist is trying to deduce the resistance of an unknown component. He labels the resistance of the unknown component x Ω. The resistance of a circuit containing a number of these components is (5x+20) Ω. If a 120 volt potential difference across the circuit produces a current of 2.5 amps, calculate the resistance of the unknown component.
8.) A factory manager is packing engine components into wooden crates to be shipped on a small truck. The truck is designed to hold sixteen crates, and will safely carry a 1200 lb cargo. Each crate weighs 12 lbs empty. How much weight should the manager instruct the workers to put in each crate in order to get the shipment weight as close as possible to 1200 lbs?
9.) The lifespan of a guinea pig is 6 years less than that of a giraffe. The lifespan of a tiger is 4 times that of the guinea pig. If the total lifespan of the animals is 30 years, calculate the longevity for the giraffe.
10.) Danielle baked macaroni for her children for which she used up 1/9 th of a jug of milk. She also poured 20.5 ounces of milk into a bowl of cornflakes. If 25.5 ounces of milk remain in the jug, how much milk did the jug originally contain?
11.) Katrina’s uncle loaned her $1200 to buy a computer. Katrina plans to pay her uncle $75 per month until the loan is paid off. How many months will it take Katrina to pay back the money?
12.) A medical center is planning to hire a total of 54 nurses and CNAs (Certified Nursing Assistants). If the center needs twice as many CNAs as nurses, how many of each should they hire?
13.) A company is ordering 350 t-shirts to sell at a fundraiser. The company wants to order the same number of large size t-shirts as medium size t-shirts, but only half as many small t-shirts. How many of each size should they order?
14.) The perimeter of the triangle shown to the right is 26 inches. Determine the length of each side of the triangle. The three sides of triangle lenght are 3x, x, and 2x+8
Combinations and permutations
Applications of Counting Techniques
In this unit, you have seen the differences between combinations and permutations as well as how to calculate the results for each type of counting application. For example, say you would like to form a focus group on improving your software with individuals who took an initial survey. How many different three-person focus groups can be formed from the 20 people who originally took the survey? (Combination problem)
If you want your three-person focus group to have one person serve as the spokesperson for the group, one person as the notetaker, and one person as the timekeeper, how many different focus groups can you form with these three positions, drawing from the total group of 20 people? (Permutation problem)
Post 1: Initial Response
Compose a counting question that applies either the combination or permutation formula (i.e., focus the development of your question to draw upon one of these two counting techniques, specifically). Please include the following information:
Provide a description of the situation, including how many people or items you may select from in total (n) and how many will make up the outcome (r).
Clearly state the counting question which can be addressed based on this situation.
Identify the counting technique required to answer the question and show the steps for determining the solution.
Express the solution in a complete, narrative sentence, tying in some of the original context from the situation you described above to clearly communicate your result.
Understanding Functions
Required Resources
Read/review the following resources for this activity:
• Assignments
o The Vertical Line Test and Graphs of Functions
o Graph a Quadratic Equation
o Radical Functions
Initial Post Instructions
In the real world, functions are mathematical representations of input-output situations. A vending machine is one such example. The input is the money combined with the selected button. The output is the product.
Here is another example: The formula for converting a temperature from Fahrenheit to Celsius is a function expressed as:
C = (5/9)(F – 32), where F is the Fahrenheit temperature and C is the Celsius temperature. If it is 77 degrees Fahrenheit in Phoenix Arizona, then what is the equivalent temperature on the Celsius thermometer? Our input is 77. C = (5/9)(77 – 32)
C = (5/9)*(45)
C = 25
The equivalent temperature is 25 degrees Celsius.
To complete the Discussion activity, please do the following:
Choose your own function or choose from the list below and then provide a unique example of a function and evaluate the function for a specific input (like the example above).
Arm length is a function of height.
The circumference of a circle is a function of diameter.
The height of a tree is a function of its age.
The length of person’s shadow on the ground is a function of his or her height.
Weekly salary is a function of the hourly pay rate and the number of hours worked.
Compound interest is a function of initial investment, interest rate, and time.
Supply and demand: As price goes up, demand goes down.
Understanding Functions
Required Resources
Read/review the following resources for this activity:
• Assignments
o The Vertical Line Test and Graphs of Functions
o Graph a Quadratic Equation
o Radical Functions
Initial Post Instructions
In the real world, functions are mathematical representations of input-output situations. A vending machine is one such example. The input is the money combined with the selected button. The output is the product.
Here is another example: The formula for converting a temperature from Fahrenheit to Celsius is a function expressed as:
C = (5/9)(F – 32), where F is the Fahrenheit temperature and C is the Celsius temperature. If it is 77 degrees Fahrenheit in Phoenix Arizona, then what is the equivalent temperature on the Celsius thermometer? Our input is 77. C = (5/9)(77 – 32)
C = (5/9)*(45)
C = 25
The equivalent temperature is 25 degrees Celsius.
To complete the Discussion activity, please do the following:
Choose your own function or choose from the list below and then provide a unique example of a function and evaluate the function for a specific input (like the example above).
Arm length is a function of height.
The circumference of a circle is a function of diameter.
The height of a tree is a function of its age.
The length of person’s shadow on the ground is a function of his or her height.
Weekly salary is a function of the hourly pay rate and the number of hours worked.
Compound interest is a function of initial investment, interest rate, and time.
Supply and demand: As price goes up, demand goes down.
Understanding Functions
Required Resources
Read/review the following resources for this activity:
• Assignments
o The Vertical Line Test and Graphs of Functions
o Graph a Quadratic Equation
o Radical Functions
Initial Post Instructions
In the real world, functions are mathematical representations of input-output situations. A vending machine is one such example. The input is the money combined with the selected button. The output is the product.
Here is another example: The formula for converting a temperature from Fahrenheit to Celsius is a function expressed as:
C = (5/9)(F – 32), where F is the Fahrenheit temperature and C is the Celsius temperature. If it is 77 degrees Fahrenheit in Phoenix Arizona, then what is the equivalent temperature on the Celsius thermometer? Our input is 77. C = (5/9)(77 – 32)
C = (5/9)*(45)
C = 25
The equivalent temperature is 25 degrees Celsius.
To complete the Discussion activity, please do the following:
Choose your own function or choose from the list below and then provide a unique example of a function and evaluate the function for a specific input (like the example above).
Arm length is a function of height.
The circumference of a circle is a function of diameter.
The height of a tree is a function of its age.
The length of person’s shadow on the ground is a function of his or her height.
Weekly salary is a function of the hourly pay rate and the number of hours worked.
Compound interest is a function of initial investment, interest rate, and time.
Supply and demand: As price goes up, demand goes down.
Understanding Functions
Required Resources
Read/review the following resources for this activity:
• Assignments
o The Vertical Line Test and Graphs of Functions
o Graph a Quadratic Equation
o Radical Functions
Initial Post Instructions
In the real world, functions are mathematical representations of input-output situations. A vending machine is one such example. The input is the money combined with the selected button. The output is the product.
Here is another example: The formula for converting a temperature from Fahrenheit to Celsius is a function expressed as:
C = (5/9)(F – 32), where F is the Fahrenheit temperature and C is the Celsius temperature. If it is 77 degrees Fahrenheit in Phoenix Arizona, then what is the equivalent temperature on the Celsius thermometer? Our input is 77. C = (5/9)(77 – 32)
C = (5/9)*(45)
C = 25
The equivalent temperature is 25 degrees Celsius.
To complete the Discussion activity, please do the following:
Choose your own function or choose from the list below and then provide a unique example of a function and evaluate the function for a specific input (like the example above).
Arm length is a function of height.
The circumference of a circle is a function of diameter.
The height of a tree is a function of its age.
The length of person’s shadow on the ground is a function of his or her height.
Weekly salary is a function of the hourly pay rate and the number of hours worked.
Compound interest is a function of initial investment, interest rate, and time.
Supply and demand: As price goes up, demand goes down.