please, help me

This question is from mathematical reasoning class

2. Let A and B be two finite sets. Let BA denote the set of all functionsfrom A to B.(a) Prove that IBAI = IBI’A’ (b) Let I C BA denote the subset of all injective functions from A tcB. Show that I|=n(n—l)…(n—m+l),wheren: |B| andm: |A|.

The gestation time for human babies is assumed to be normally distributed with a mean of 278 days and a standard deviation of 12 days. What happens to the standard deviation of the sampling distribution of the sample mean as n increases?

Hello, would this be considered a polynomial? It is a real life situation for a polynomial and it goes like this:

Harold opens a savings account with a 24% interest rate compounded yearly. What is the saving accounts annual percentage yield rounded to the nearest tenth? 

The polynomial would go like this.

(1+0.24-:12)^(12)-1 and yield an answer of 

.26824179

So the APY would be 26.82%, 26.8% when it is rounded to the nearest tenth.

A manufacturer has learned that, by pricing a phone at $125, sales will reach 85 phones per week. Raising the price to $200 will cause the sales to fall to 42 per week. Let y be the number of phones sold per week at the prices of x dollars each. Write a linear equation that relates the number of phones sold per week, y, to the price x.

A lamina occupies the region inside the circle x2 + y2 = 10y but outside the circle x2 + y2 = 25. Find the center of mass if the density at any point is inversely proportional to its distance from the origin.

n a 6 acre apple orchard, it is decided to plant 20 or more trees per acre. If 20 trees are planted per acre then each mature tree will yield 300 apples per year. For each additional tree planted per acre, the number of apples produced by each tree decreases by 12 per year. Express the total number of apples A produced per year in terms of the number n of trees per acre.

Fine grains of beach sand are assumed to bespheres of radius 38.5 µm. These grains aremade of silicon dioxide which has a density of2600 kg/m3.What is the mass of each grain of sand?Answer in units of kgConsider a cube whose sides are 0.824 m long.How many kg of sand would it take for thetotal surface area of all the grains of sand toequal the surface area of the cube?Answer in units of kg

Austin rented a truck for one day. There was a base fee of $14.95, and there was an additional charge of 76 cents for each mile given. Austin had to pay $149.47 when he returned the truck. For how many miles did he drive the truck?

URGENT I need help on the following question:

You ask the production team to make some candles for the sale. The team is not sure how many they can produce in your short time frame, so they ask for an acceptable range for how many of each candle they should make. Use your costs and recommended retail prices to create linear programming model to show the BeeSwaks executives possible profits for selling certain numbers of each type of candle during this promotion. Decide on the constraints for the numbers of candles made for the sale and explain your reasoning for these constraints. Graph the feasible region and find maximum and minimum profits.

Info: The retail price must be greater than the cost. I suggest setting the retail price for both the Brick and the Egyptian candles at $5.

Teacher Hints:

1. Writes a linear programming model that is accurate with their recommendations: Think about the cost of each candle and what you set for the retail price. How much profit does each candle make? Create objective function to find the total profit from selling a number of each candle. Also determine constraints for the number of candles requested from the factory. Keep in mind that it is a small sale and production time is limited. Think about the customers in the area where you will sell the candles. Do you think one of the models would sell better than the other? 
2. Correctly graphs the feasible region.: Graph the lines based on your model. Because the factory manager asked for a range of each, you should have a closed feasible region. 
3. Correctly finds the maximum profit.: Find the coordinates of the vertices of the feasible region. Find the pair that gives the greatest result.
4. Correctly finds the minimum profit.: Find the coordinates of the vertices of the feasible region. Find the pair that gives the smallest result. 

Leave a comment if you need additional information

Part A. SPSS AssignmentIn this exercise, you are playing the role of a researcher that is testing new medication designed to improve cholesterol levels. When examining cholesterol in clinical settings, we look at two numbers: low-density lipoprotein (LDL) and high-density lipoprotein (HDL). You may have heard these called “good” (HDL) and “bad” (LDL) cholesterol. For LDL, lower numbers are better (below 100 is considered optimal. For HDL, 60 or higher is optimal. 

In this experiment, the researcher is testing three different versions of the new medication. In data file “Activity 12.sav” you will find the following variables: group (0=control, 1=Drug A, 2=Drug B, 3=Drug C), LDL, and HDL (cholesterol numbers of participants after 12 weeks). 

Using a MANOVA, try to ascertain which version of the drug (A, B or C) shows the most promise. Perform the following analyses, and paste the SPSS output into your document.

1. Exploratory Data Analysis.
   1. Perform exploratory data analysis on the relevant variables in the dataset. When possible, include appropriate graphs to help illustrate the dataset.
   2. Give a one to two paragraph write up of the data once you have done this.
   3. Create an APA style table that presents descriptive statistics for the sample.
2. Perform a MANOVA. Using the “Activity 12.sav” data set perform a MANOVA. “Group” is your fixed factor, and LDL and HDL are your dependent variables. Be sure to include simple contrasts to distinguish between the drugs (group variable). In the same analysis, include descriptive statistics, and parameter estimates. Finally, be certain to inform SPSS that you want post-hoc test to help you determine which drug works best.
   1. Is there any statistically significant difference in how the drugs perform? If so, explain the effect. Use the post hoc tests as needed.
   2. Write up the results using APA style and interpret them.

Data set has been attached to post.

Due : June 1, 2019 by 12pm EST