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ax+by+c=0.ax+by+c=0.

Let (s′,t′)(s′,t′) be the reflection of the point (s,t)(s,t) in ℓℓ. Find a formula that computes the coordinates of (s′,t′)(s′,t′) if one knows the numbers s,t,a,bs,t,a,b and cc. Your formula should depend on the variables s,t,a,bs,t,a,b and cc. It should work for arbitrary values of s,t,a,bs,t,a,b and cc as long as (a,b)≠(0,0)(a,b)≠(0,0). Its output should be a point.

Given a normal distribution with mu equals 100 and sigma equals 10 comma complete parts​ (a) through​ (d). cumulative standardized normal distribution table.

a. What is the probability that Upper X greater than 80​?

The probability that Upper X greater than 80 is . ​(Round to four decimal places as​ needed.)

b. What is the probability that Upper X less than 95​?

The probability that Upper X less than 95 is . ​(Round to four decimal places as​ needed.)

c. What is the probability that Upper X less than 85 or Upper X greater than 110​?

The probability that Upper X less than 85 or Upper X greater than 110 is . ​(Round to four decimal places as​ needed.)

d. 80​% of the values are between what two​ X-values (symmetrically distributed around the​ mean)?

80​% of the values are greater than nothing and less than . ​(Round to two decimal places as​ needed.)

Investment advisors agree that​ near-retirees, defined as people aged 55 to​ 65, should have balanced portfolios. Most advisors suggest that the​ near-retirees have no more than​ 50% of their investments in stocks.​ However, during the huge decline in the stock market in​ 2008, 23​% of​ near-retirees had 85​% or more of their investments in stocks. Suppose you have a random sample of 10 people who would have been labeled as​ near-retirees in 2008. Complete parts​ (a) through​ (d) below.

a. What is the probability that during 2008 none had 85​% or more of their investment in​ stocks? The probability is . ​(Round to four decimal places as​ needed.)

b. What is the probability that during 2008 exactly one had 85​% or more of his or her investment in​ stocks? The probability is . ​(Round to four decimal places as​ needed.)

c. What is the probability that during 2008 two or fewer had 85​% or more of their investment in​ stocks? The probability is . ​(Round to four decimal places as​ needed.)

d. What is the probability that during 2008 three or more had 85​% or more of their investment in​ stocks? The probability is . ​(Round to four decimal places as​ needed.)

A doctor has scheduled two appointments, one at 1pm and the other at 1:30pm. The amount of time the doctor spends with the patient is a constant 20 minutes plus a random amount of time which is distributed as exponential with mean 8 minutes. Assume that both patients will be on time for their appointments.

1. What is the chance the doctor will be late for her 1:30 appointment because she spends more than 30 minutes with her 1pm appointment?
2. On average, how long will the 1:30 appointment be at the doctor’s office?

The time the 1:30 appointment spends in the office is the sum of 3 parts: the random waiting time W, the constant 20 minutes of examination time and the additional random examination time T.

We seek E[W + 20 + T] = E[W] + 20 + E[T]

To determine the E[W], condition on whether or not the 1:00pm appointment is still going on at 1:30pm.

Explanations with answers please

In your own words, explain what an outlier is.

Question 2: Use the following information to complete Exercises 3 – 5: A political scientist took a pool of the political attitudes of the students in one of his classes. Students were asked to rate, on a scale from 1 to 11, “What is your overall political attitude?”, where 1 = extremely liberal and 11 = extremely conservative. The following frequency analysis resulted: (1.5 points)

4. Compute the values that define the following percentiles:

a. 25^th             b. 50^th             c. 57^th             d. 75^th    

What is the interquartile range of the data in #4?

6. Compute the exact percentile ranks that correspond to the following scores:

a. 3            b. 5            c. 7            d. 9

1. Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $67, $95, and $133, respectively. The production requirements per unit are as follows:

   	Number of Fans	Number of Cooling Coils	Manufacturing Time (hours)
   Economy	1	1	8
   Standard	1	2	12
   Deluxe	1	4	14

   For the coming production period, the company has 300 fan motors, 340 cooling coils, and 2000 hours of manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows:

   Max	67E	+	95S	+	133D
   s.t.
   	1E	+	1S	+	1D	≤	300	Fan motors
   	1E	+	2S	+	4D	≤	340	Cooling coils
   	8E	+	12S	+	14D	≤	2000	Manufacturing time
   E, S, D ≥ 0

   The sensitivity report is shown in the figure below.

   Optimal Objective Value =      17380.00000
   		Variable		Value		Reduced Cost
   		E		180.00000		0.00000
   		S		0.00000		9.00000
   		D		40.00000		0.00000
   		Constraint		Slack/Surplus		Dual Value
   		Fan motors		80.00000		0.00000
   		Cooling coils		0.00000		7.00000
   		Manufacturing time		0.00000		7.50000

   		Variable		Objective Coefficient		Allowable Increase		Allowable Decrease
   		E		67.00000		9.00000		8.10000
   		S		95.00000		9.00000		Infinite
   		D		133.00000		135.00000		15.75000
   		Constraint		RHS Value		Allowable Increase		Allowable Decrease
   		Fan motors		300.00000		Infinite		80.00000
   		Cooling coils		340.00000		231.42860		90.00000
   		Manufacturing time		2000.00000		480.00000		810.00000

   1. Identify the range of optimality for each objective function coefficient. If there is no limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place.
      

      	Objective Coefficient Range
      Variable	lower limit	upper limit
      E
      S
      D

   2. Suppose the profit for the economy model (E) is increased by $6 per unit, the profit for the standard model (S) is decreased by $2 per unit, and the profit for the deluxe model (D) is increased by $4 per unit. What will the new optimal solution be? If required, round your answers to three decimal places. If your answer is zero, enter "0".
      

      Optimal Solution
      E
      S
      D

      
      If required, round your answer for Total Profit to two decimal places.
      
      Total Profit: $  
      
   3. Identify the range of feasibility for the right-hand-side values. If there is no limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place.
      

      	Right-Hand-Side-Range
      Constraints	lower limit	upper limit
      Fan motors
      Cooling coils
      Manufacturing time

   4. If the number of manufacturing time available for production is increased by 500, will the dual value for that constraint change?
      
      
      • Yes
      • No
      because the allowable increase for manufacturing time is without changing the optimal solution.

The number of victories (W), earned run average (ERA), runs scored (R), batting average (AVG), and on-base percentage (OBP) for each team in the American League in the 2012 season are provided in the following table. The ERA is one measure of the effectiveness of the pitching staff, and a lower number is better. The other statistics are measures of effectiveness of the hitters, and higher numbers are better for each of these.

Develop a regression model that could be used to predict the number of victories based on the ERA.

Develop a regression model that could be used to predict the number of victories based on the runs scored.

Develop a regression model that could be used to predict the number of victories based on the batting average.

Develop a regression model that could be used to predict the number of victories based on the on-base percentage.

Which of the four models is better for predicting the number of victories?

Develop a regression model that could be used to predict the number of victories based on the ERA, runs scored, batting average, on-base percentage

Develop the best regression model that can be used to predict the number of victories

Discuss the accuracy of the regression model you developed in section g, and the significance of independent variables

Distinguish between random and assignable variation. Discuss the relevance of each to measuring quality of care and to the design and evaluation of quality improvement initiatives.

NCAA rules require the circumference of a softball to be 12 ± 0.125 inches. A softball manufacturer bidding on an NCAA contract is shown to meet the requirements for mean circumference. Suppose that the NCAA also requires that the standard deviation of the softball circumferences not exceed 0.05 inch. A representative from the NCAA believes the manufacturer does not meet this requirement. She collects a random sample of 25 softballs from the production line and finds that s = 0.076 inch. The Anderson-Darling test of normality gives a P-value of 0.632. Is there enough evidence to support the representative’s belief (i.e., that the standard deviation of circumferences exceeds 0.05 inch) at the α = 0.01 level of significance?

On a separate sheet of paper, write down the hypotheses (H₀ and H_a) to be tested.

Conditions:
The conditions for the χ² ("chi-square") test for standard deviations  (are / are not) satisfied for this data.

Rejection Region:
To test the given hypotheses, we will use a (left / right / two) -tailed test.  
The appropriate critical value(s) for this test is/are _____.  (Report your answer exactly as it appears in Table VII. For two-tailed tests, report both critical values in the answer blank separated by only a single space.)

Suppose approximately 80% of all marketing personnel are extroverts, whereas about 70% of all computer programmers are introverts. (For each answer, enter a number. Round your answers to three decimal places.) (a) At a meeting of 15 marketing personnel, what is the probability that 10 or more are extroverts? What is the probability that 5 or more are extroverts? What is the probability that all are extroverts? (b) In a group of 4 computer programmers, what is the probability that none are introverts? What is the probability that 2 or more are introverts? What is the probability that all are introverts?

An urn contains 6 red balls and 4 green balls. Three balls are chosen randomly from the urn, without replacement.

(a) What is the probability that all three balls are red? (Round your answer to four decimal places.)

(b) Suppose that you win $20 for each red ball drawn and you lose $10 for each green ball drawn. Compute the expected value of your winnings.

For this assignment, use data from W1 Assignment.

Compute a t-test comparing males' and females' heights. You must determine which type of t-test to compute.

Move your output into a Microsoft Word document and write a one-paragraph, APA-formatted interpretation of the results.

Participant ID   Age   Sex   Height   Year in college  
1   18   f   60   freshman  
2   17   f   61   freshman  
3   18   f   62   freshman  
4   18   f   63   freshman  
5   23   f   66   freshman  
6   25   m   65   freshman  
7   22   m   66   freshman  
8   21   m   68   freshman  
9   37   m   69   freshman  
10   32   m   72   freshman  
11   19   f   70   sophomore  
12   20   f   60   sophomore  
13   33   f   61   sophomore  
14   22   f   60   sophomore  
15   23   f   65   sophomore  
16   20   m   67   sophomore  
17   21   m   67   sophomore  
18   22   m   65   sophomore  
19   27   m   70   sophomore  
20   29   m   71   sophomore  
21   20   f   61   junior  
22   21   f   63   junior  
23   33   f   64   junior  
24   37   f   64   junior  
25   24   f   65   junior  
26   24   m   68   junior  
27   26   m   67   junior  
28   31   m   69   junior  
29   28   m   70   junior  
30   33   m   64   junior  
31   21   f   63   senior  
32   23   f   66   senior  
33   28   f   67   senior  
34   29   f   68   senior  
35   52   f   62   senior  
36   43   m   72   senior  
37   32   m   70   senior  
38   28   m   69   senior  
39   29   m   67   senior  
40   40   m   65   senior  

What proportion of college students plan to major in Business? You survey a random sample of 250 first-year college students, and you find that 57 of these students indicate they plan to pursue a major in Business. Use this information to construct a 90% confidence in order to estimate the population proportion of college students who plan to major in Business.

The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Here are data for beak heat loss, as a percent of total body heat loss from all sources, at various temperatures in degrees Celsius. [Note: The numerical values in this problem have been modified for testing purposes.]

The equation of the least-squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature is: (Use decimal notation. Enter the values of the intercept and slope rounded to two decimal places. Use the letter ? to represent the value of the temperature.)

y^=

Use the equation of the least‑squares regression line to predict beak heat loss, as a percent of total body heat loss from all sources, at a temperature of 2525 degrees Celsius. Enter your answer rounded to two decimal places.

beak heat as a percent of total body heat loss=beak heat as a percent of total body heat loss= ?%

What percent of the variation in beak heat loss is explained by the straight-line relationship with temperature? Enter your answer rounded to two decimal places.

percent of variation in beak heat loss explained by the equation=percent of variation in beak heat loss explained by the equation= ?%

Find the correlation ?r between beak heat loss and temperature. Enter your answer rounded to three decimal places.

?=