Which equation represents the selling price, s, in dollars, of an item originally priced p dollars after a markdown of 30%? As = 0.3p s= 0.7p © p = 0.3s Dp= 0.7s (b) Part B Complete the table below to show pairs of solutions to the equation in Part A.
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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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- Suppose Laura, a facilities manager at a health and wellness company, wants to estimate the difference in the average amount of time that men and women spend at the company's fitness centers each week. Laura randomly selects 15 adult male fitness center members from the membership database and then selects 15 adult female members from the database. Laura gathers data from the past month containing logged time at the fitness center for these members. She plans to use the data to estimate the difference in the time men and women spend per week at the fitness center. The sample statistics are summarized in the table. Population Populationdescription Population mean(unknown) Samplesize Sample mean(min) Sample standarddeviation (min) 11 male μ1 n=15 x¯1=137.7 s=51.7 22 female μ2 n=15 x¯2=114.6 s=34.2 df=24.283 The population standard deviations are unknown and unlikely to be equal, based on the sample data. Laura plans to use the two-sample ?-t-procedures to estimate the…A college bookstore must order books two months before each semester starts. They believe that the number of books that will ultimately be sold for any particular course is related to the number of students registered for the course when the books are ordered. They would like to develop a bestfitting line to predict how many books to order. From past records, the bookstore obtains the number of students registered, X, and the number of books actually sold for a course, Y , for 12 different semesters.A scatterplot of the data along with the best fitting line is presented below. a. The correlation between the two variables is r = .89. Calculate and interpret the value of r2.b. The equation for the best fitting line is Y = 9.30 + 0.673X. Explain and interpret the value of 9.30.c. How many books should the store order for a class of 50 students? Would you trust this prediction?A company wants to plan production for the ensuing year so as to minimize thecombined cost of production and inventory storage. In each quarter of the year, demand isanticipated to be 65, 80, 135 and 75 respectively. The product can be manufactured duringregular time at a cost of Php 16 per unit produced, or during overtime at a cost of Php 20 perunit. The given table below shows data pertinent to production capacities. The cost of carryingone unit in inventory per quarter is Php 2. The inventory level at the beginning of the firstquarter is zero.
- Assume that you have collected cross-sectional data for average hourly earnings (ahe), the number of years of education (educ) and gender of the individuals (you have coded individuals as "1" if they are female and "0" if they are male; the name of the resulting variable is DFemme). Having faced recent tuition hikes at your university, you are interested in the return to education, that is, how much more will you earn extra for an additional year of being at your institution. To investigate this question, you run the following regression: ahe= -4.58 + 1.71×educ N = 14,925, R2 = 0.18, SER = 9.30 a. Interpret the regression output. b. Being a female, you wonder how these results are affected if you entered a binary variable (DFemme), which takes on the value of "1" if the individual is a female, and is "0" for males. The result is as follows ahe= = -3.44 - 4.09×DFemme + 1.76×educ N = 14,925, R2 = 0.22, SER = 9.08 Does it make sense that the standard error of the regression decreased…Customers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.a. Calculate the average utilization of the bakery serverFor each item, identify the type of data (quantitative - discrete, quantitative - continuous, or qualitative) used to describe a response. Number of correct answers on a quiz Brand of smart phones Students attitude towards Statistics Most-watched television show 5. Number of tickets sold to a concert
- A study of the relation between the rate of reproduction in Drosophila (fruit flies) bred in bottles and the density of the mated population found that the number of imagoes(sexually mature adults) per mated female per day (y) can beapproximated bylog y = 1.54 - 0.008x - 0.658 log x,where x is the mean density of the mated population (measuredas flies per bottle) over a 16-day period. Source: Elements ofMathematical Biology.a. Show that the above equation is equivalent toy = 34.711.01862-xx-0.658.b. Using your answer from part a, find the number of imagesper mated female per day when the density isi. 20 flies per bottle;ii. 40 flies per bottle.c. Using your answer from part a, find the rate of change inthe number of imagoes per mated female per day with respect to the density when the density isi. 20 flies per bottle;ii. 40 flies per bottleAssume that the fire caused construction to slow down and caused a reduction in efficiency in completing the building. Estimate the number of labor hours needed to complete the building if there were no slow down related to the fire. Assume that the relationship that existed between HOURS and FLRCOM and FLRCOMSQ before the fire would have continued to exist to the completion of the building had the fire not occurred. Estimate the extra labor hours traceable to the fire.A company is keen on investing in expanding its market penetration in Africa opening an on-line shop to new potential African clients. For this reason, the company wants to understand the level of digital divide, measured by the total number of internet users in relation to total population, as a function of clients’ personal characteristics. Considering the following analysis based on a survey conducted in two main markets, Nigeria and Kenya, we have the following information to estimate the digital divide: Age: respondent’s age from 25 to 55 years old. Gender: 1 female, 0 male. Education level measured as years of schooling. Region: Kenya =1, Nigeria =0. As part of their work they have produced the following linear regression. How well does the model “describe/explain” the digital divide? How would you improve the model? Is the model statistically significant?
- A company is keen on investing in expanding its market penetration in Africa opening an on-line shop to new potential African clients. For this reason, the company wants to understand the level of digital divide, measured by the total number of internet users in relation to total population, as a function of clients’ personal characteristics. Considering the following analysis based on a survey conducted in two main markets, Nigeria and Kenya, we have the following information to estimate the digital divide: Age: respondent’s age from 25 to 55 years old. Gender: 1 female, 0 male. Education level measured as years of schooling. Region: Kenya =1, Nigeria =0. As part of their work they have produced the following linear regression. Comment on the statistical significance, relative strength and direction of the relationships between the dependent variable and the independent variablesA company is keen on investing in expanding its market penetration in Africa opening an on-line shop to new potential African clients. For this reason, the company wants to understand the level of digital divide, measured by the total number of internet users in relation to total population, as a function of clients’ personal characteristics. Considering the following analysis based on a survey conducted in two main markets, Nigeria and Kenya, we have the following information to estimate the digital divide: Age: respondent’s age from 25 to 55 years old. Gender: 1 female, 0 male. Education level measured as years of schooling. Region: Kenya =1, Nigeria =0. As part of their work they have produced the following linear regression. How well does the model “describe/explain” the digital divide? How would you improve the model? Is the model statistically significant? Can we conclude that education definitely impacts on the digital divide? Justify your answer from a theoretical point…Q9: Assume that a researcher wants to estimate the proportion of “A” grade scorers in STAT101 course for the population of SEU students in 2020. Assume also that the proportion of “A” grade scorers in 2020 is not known. How many SEU students must be surveyed from STAT101 course in order to be 90% confident and the margin of error should not exceed two percentage points? (Given zα/2 = 1.64). 1- 1821 2- 1781 3- 1618 4- 1681