Advanced Placement (AP) : asked on kaylaelaine18

25.07.2020

1. The rate at which people enter a movie theater on a given day is modeled by the function S defined by S(t) = 80 -12 cos 6 The rate at which people leave the same movie theater is modeled by the function R defined by r(t) = 12eKo + 20. Both S (t) and r(t) are measured in people per hour and these functions are t valid for 10 < t < 22. At time t = 10, there are no people in the movie theater.(Problems are in the Picture and I need help)

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08.07.2023, solved by verified expert

Rajat Thapa

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Mathematics, DAV Post Graduate College

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Hi there!

To find the total amount of people that have ENTERED by t = 20, we must take the integral of the appropriate function.

Evaluate using a calculator:

To solve, we can find the total amount of people that have entered of the interval and subtract the total amount of people that have left from this value.

In other terms:

We can evaluate using a calculator (math-9 on T1-84):

If:

Then:

Evaluate at t = 20:

This means that at t = 20, there is a NET DECREASE of people at the movie theater of around 20.823 (21) people per hour.

To find the maximum, we must use the first-derivative test.

Set S(t) - R(t) equal to 0:

Graph the function with a graphing calculator and set the function equal to y = 0:

According to the graph, the graph of the first derivative changes from POSITIVE to NEGATIVE at t ≈ 17.78 hours, so there is a MAXIMUM at this value.

Thus, at t = 17.78 hours, the amount of people at the movie theater is a MAXIMUM.

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Advanced Placement (AP)

1. The rate at which people enter a movie theater on a given day is modeled by the function S defined by S(t) = 80 -12 cos 6 The rate at which people leave the same movie theater is modeled by the function R defined by r(t) = 12eKo + 20. Both S (t) and r(t) are measured in people per hour and these functions are t valid for 10 t 22. At time t = 10, there are no people in the movie theater.(Problems are in the Picture and I need help)

Step-by-step answer

P Answered by Master

Hi there!

To find the total amount of people that have ENTERED by t = 20, we must take the integral of the appropriate function.

$\text{Amount that entered} = \int\limits^{20}_{10} {S(t)} \, dt \\\\ = \int\limits^{20}_{10} {80 - 12cos(\frac{t}{5})} \, dt$

Evaluate using a calculator:

$= 899.97 \approx \boxed{900\text{ people}}$

To solve, we can find the total amount of people that have entered of the interval and subtract the total amount of people that have left from this value.

In other terms:
$\text{Amount of people} = \int\limits^{20}_{10} {S(t)} \, dt - \int\limits^{20}_{10} {R(t)} \, dt$

We can evaluate using a calculator (math-9 on T1-84):

$\text{\# of people} = \int\limits^{20}_{10} {80-12cos(\frac{t}{5})} \, dt - \int\limits^{20}_{10} {12e^{\frac{t}{10}}+20} \, dt$

$= 899.97 - 760.49 = 139.47 \approx \boxed{139 \text{ people}}$

If:
$P(t) = \int\limits^t_{10} {S(t) - R(t)} \, dt$

Then:

$\frac{dP}{dt} = P'(t)= \frac{d}{dt}\int\limits^t_{10} {S(t) - R(t)} \, dt = S(t) - R(t)$

Evaluate at t = 20:

$S(20) = 80 - 12cos(\frac{20}{5}) = 87.844\\\\R(20) = 12e^{\frac{20}{10}} + 20 = 108.669$

S(20) - R(20) = 87.844 - 108.669 = -20.823

This means that at t = 20, there is a NET DECREASE of people at the movie theater of around 20.823 (21) people per hour.

To find the maximum, we must use the first-derivative test.

Set S(t) - R(t) equal to 0:

$80 - 12cos(\frac{t}{5}) - 12e^{\frac{t}{10}} - 20 = 0\\\\60 - 12(cos(\frac{t}{5}) + e^{\frac{t}{10}})= 0$

Graph the function with a graphing calculator and set the function equal to y = 0:

According to the graph, the graph of the first derivative changes from POSITIVE to NEGATIVE at t ≈ 17.78 hours, so there is a MAXIMUM at this value.

Thus, at t = 17.78 hours, the amount of people at the movie theater is a MAXIMUM.

Advanced Placement (AP)

Jennifer is interested in training two of her new puppies to participate in agility competitions. one of the puppies, sasha, was given a treat each time she more closely approximated the behavior that jennifer wanted from her. then she got a treat every third time she completed the entire behavior correctly. the other puppy, rosie, was exposed to a harsh sound whenever she did the wrong behavior. in the chart, jennifer kept track of the number of correctly completed behaviors for each puppy, in order to know which one will be best for competition.

Step-by-step answer

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the answer is below

Explanation: The independent variable is the experimental factor which is manipulated and the variable whose effects are being studied. The dependent variable is a variable that could change due to the independent variable. The independent variable is the different ways that Jennifer treats her puppies in order to bring them closer to what she wants in the agility competition. The dependent variable is how they puppies perform each day.

Behavioral shaping is a conditioning procedure where the reinforcers guide behavior toward closer and closer approximations of a desired behavior. Jennifer guided Sasha closer and closer to completing a behavior correctly, thus utilizing shaping in order to bring the puppy closer to what she wanted.

Advanced Placement (AP)

You should present a cogent argument based on your critical analysis of the questions posed, using appropriate psychological terminology. it is not enough to answer a question by merely listing facts. dr. aguilera conducts psychological research that examines factors associated with college student academic performance. she administered a survey to 127 participants from her university’s student subject pool. in the survey, she asked students to report their current college grade point average (gpa). dr. aguilera also asked questions about sleeping,

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Answer Part A:

1. There is a significant negative relationship between anxiety and academic performance, described as:

a. Subjects with lower anxiety scores have higher current GPAs, or;

b. Subjects who have lower current GPAs have higher anxiety scores.

Explanation:

We can tell that the two variables (anxiety and academic performance) have a negative relationship from its correlation coefficient (-.64). The negative sign shows the relationship, while the statistical significance (p < .01 or p < .05) shows whether there is a relationship or not.

Remember, the power of the correlation (as represented by the number 0.64) does not tell you whether a relationship actually happens or not. It can, however tell the strength of a relationship. A .64 is usually described as moderate to strong, depending on which reference you are using.

Also remember that this is not causation - we do not know which variable causes changes at the other. This is why it is possible to describe the relationship with either option (A) or (B). It is preferable to use a neutral sounding one such as the one stated above: By only saying that there is a negative relationship between the two variables.

2. There is no relationship between hours sleeping per night and academic performance.

Explanation:

A correlation coefficient of 0.00 means that there is no relationship between two variables. The closer a correlation coefficient to 0, the less likely do the variables have a relationship with one another.

Answer Part B:

1. It contributes to the interpretation of the findings by discussing whether:

(1) The measurement used is appropriate for the research conducted,

(2) There are any limitations from the current method of measurement.

Explanation:

The operational definitions in the study are not explicitly stated, but we can come to our own conclusions from the description of the study. They are:

Academic performance is the current GPA as reported by the research subjects.

Anxiety is the anxiety score summed from the research subjects' responses to the anxiety scale.

Interpretation is usually done during the discussion part of a research journal, after the statistical results have been reported. Discussing operational definitions would help determine whether the right measurement is used. Is the method free of biases? For example, Dr. Aguilera used a 5-point scale to measure the student's anxiety levels; there is a possibility of central tendency bias occurring.

2. Cohort effects may contribute to a possible bias over the result of the research. The variations in both anxiety levels and GPA may not be due to each other's influences, but perhaps instead caused by other age-related experience variables such as social media use.

Explanation:

Cohort effects are defined as a condition shared with same-aged groups of people which affected the result of the research. It is a form of bias, when it is not controlled. Dr. Aguilera's study is at risk of being affected with this since her research subjects are all university students.

In the study, we saw that Dr. Aguilera measured social media use, however, she did not seem to control this variable. It is possible that the variation in anxiety is moderated by social media, which then affects the subjects' GPA.

Advanced Placement (AP)

Truisms are statements presented as facts that are supposed to be self-evident or understood through common sense. some truisms, such as yogi berra’s quip that you can observe a lot by watching, seem quite true. other truisms, however, such as a penny saved is a penny earned, may no longer be as valid today as they once were. identify a truism that you have heard or read many times that is worth defending, qualifying, or challenging. compose a thesis statement that you might use for an essay arguing your position on why the truism is worth defending,

Step-by-step answer

P Answered by PhD

“ nothing succeeds like success “
(sorry I don’t have anything else for you but I hope that helps)

Advanced Placement (AP)

The average sale price (online) for four year old harley davidson touring motorcycles is approximately normally distributed with a mean of $14,000 and a standard deviation of $4,000. a) molly has saved up $15,000 to spend on a motorcycle. what proportion of the available motorcycles of this type can she afford? b) what is the 30th percentile for the prices of motorcycles of this type? c) show that a motorcycle priced at $25,000 would be considered an outlier by the 1.5 x iqr rule.

Step-by-step answer

P Answered by Master

The proportion of the available motorcycles that Molly can afford is 60%.

The 30th percentile for the motorcycle is $11920

It should be noted that $25,000 is considered an outlier because it is greater than $24792

Since, mean, μ = $14,000 and standard deviation, σ = $4,000, the standard variable Z or x = $15,000 will be:

Z = (x - μ)/σ

Z = (15000 - 14000)/4000

Z = 0.25

We then check the table and see that it implies that Molly can buy 60% of the available motorcycles.

The 30th percentile for the prices of motorcycles of this type corresponds to a value of Z = -0.52. This will then be:

x = μ + Z*σ

x = 14000 + (-0.52) × 4000

x = $11920

Lastly, the third quartile value when added to 1.5 x IQR will be equal to:

= 16698 + (1.5 × 5396) = $24792

Therefore, $25,000 is considered an outlier because it is greater than $24792

Read related link on:

link

The average sale price (online) for four year old harley davidson touring motorcycles is approximate

Advanced Placement (AP)

Abusiness journal reports that the probability that internet users in the united states will use a mobile payment app is 0.60. the journal claims this indicates that out of 5 randomly selected internet users, 3 will use the mobile payment app. is this business journal interpreting the probability correctly?

Step-by-step answer

P Answered by PhD

Yes, the business journal is interpreting the probability correctly, because 3 out of 5 randomly selected Internet users that will use the mobile payment application, means that, 3/5, or 0.6 of probability. That is exactly the probability reported by the business journal.

Explanation:

Probability that Internet users in the United States will use a mobile payment app is 0.60.

Advanced Placement (AP)

3. A team of programmers is trying to determine the efficiency of a piece of code. They run the code with inputs of different sizes and also record the number of iterations through the core block of code. The data is recorded in the table below.

Step-by-step answer

P Answered by PhD

The algorithm's runtime has been divided into two main categories are given below.

Explanation:

Polynomial runtime would be defined as almost any run time that doesn't even improve quicker than n^k

, including fixed time ( n^0

), logarithmic time (log2{n}), linear ( n^1

), quadratic ( n^2

), as well as another polynomial of higher degrees (such as n^3

). The runtime that grows more than n^k

and contains exponential time including such ( 2^n

), factorial time (n!), or anything else is super polynomial runtime.It seems it is perceived that polynomial runtime seems to be rational as well as super polynomial growth in order are rendered irrational. It is not necessarily ideal to have a polynomial run time, but it's least theoretically possible.

Then maybe we can easily see by the information collected that perhaps the algorithm is increasing at either the frequency of 20×n. At which, across every iteration, n seems to be the input dimension. This suggests that perhaps the runtime specified seems to be of a polynomial category, therefore means that even this technique executes within a rational period.

Advanced Placement (AP)

(a) Describe the importance of phenotypic variation in louse body color among individuals in a population of lice. (b) Justify the decision of the researchers to hold lighting conditions constant in their experiment.

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Explanation:

Advanced Placement (AP)

Include correctly labeled diagrams, if useful or required, in explaining your answers. A correctly labeled diagram must have all axes and curves clearly labeled and must show directional changes. If the question prompts you to “Calculate,” you must show how you arrived at your final answer. Zeetopia and Freshland are two small tropical islands that use the same amounts of resources to produce mangoes and coconuts as shown in the table below. Coconuts (in tons) Mangoes (in tons) Zeetopia 50 60 Freshland 50 30 (a) Which island has an absolute advantage

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Answer:

(a) Which island has an absolute advantage in producing coconuts? Explain.
No island has absolute advantage in producing coconuts because both Zeetopia and Freshland can produce equal number of coconuts (50 each).

(b) Which island has a comparative advantage in producing coconuts? Explain.
Freshland has a comparative advantage in producing coconuts. Freashland's opportunity cost of producing coconuts (30/50 = 0.6 mangoes) is lower than Zeetopia's 60/50 = 1.2 mangoes). So, Freshland has a comparative advantage in producing coconuts

(c) Assume Zeetopia and Freshland decide to specialize according to their comparative advantages and 1 ton of coconuts is exchanged for 1 ton of mangoes. Are specialization and trade under these terms beneficial to both Zeetopia and Freshland? Explain.

Yes, the terms of trade (1 ton of coconut = 1 ton of mangoes) are beneficial for both islands.
For Zeetopia, opportunity cost of 1 ton of coconut is1.2 tons of mangoes (60/50 = 1.2). So, when it specializes in mangoes, it should get 1 ton of coconut for less than 1.2 tons of mangoes (or, it should give up less than 1.2 tons of mangoes to obtain 1 ton of coconuts). So, 1 ton of coconut = 1 ton of mangoes is beneficial for Zeetopia.
Similarly, the opportunity cost of 1 ton of coconuts for Freshland is 0.6 tons of mangoes. So, when it specializes in coconuts, it should get more than 0.6 tons of mangoes in return for 1 ton of coconuts. So, 1 ton of coconut = 1 ton of mangoes is beneficial for Freshland.

(d) The graph:
A biologist is growing bacteria for a lab experiment. There are 10 mg of bacteria in a controlled en

A biologist is growing bacteria for a lab experiment. There are 10 mg of bacteria in a controlled en

(e) Point X is unattainable for Freshland but feasible and inefficient for Zeetopia.

Advanced Placement (AP)

The distribution of the amount of water used per wash cycle, in gallons, by a particular brand of dishwasher during a wash cycle is approximately normal with mean 4 gallons and standard deviation 0.2 gallon. Which of the following is closest to the probability that more than 3.75 gallons are used for any wash cycle?

Step-by-step answer

P Answered by PhD

There is a probability of 89.44% that more than 3.75 gallons are used for any wash cycle.

The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

$z=\frac{x-\mu}{\sigma} \\\\Where\ x\ is\ raw \ score,\mu=mean,\sigma=standard\ deviation\\\\\\Given\ that\ \mu=4,\sigma=0.2:For\ x3.75\\\\z=\frac{3.75-4}{0.2}=-1.25\\\\$