Numerade

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Evaluate the integral $$ \int \sin^4 x \cos^2 x dx. $$

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Question 2 1 pts Paleoanthropologists have to make inferences about behavior based on the fossil and material culture remains found. You excavate a site and find animal bones with cut marks on them; these cut marks occur on top of carnivore tooth markings. What is your interpretation? There is not enough information to make an inference. This site represents scavenging by hominins. The fossil hominins have sexual dimorphism. This site represents hunting by hominins.

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3. Let $T: \mathbb{R}^3 \to \mathbb{R}^3$ be defined by $T\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} x + y + 3z \\ 2x + 3y + 6z \\ 3x + 3y + 10z \end{bmatrix}$ Find an input $\begin{bmatrix} x \\ y \\ z \end{bmatrix}$ such that $T\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}$ When solving this problem, convince me that you understand “$T(\vec{x}) = A\vec{x}$”, “$A\vec{x} = \vec{b}$”, and the steps required to find $A^{-1}$ for a $3 \times 3$ matrix $A$

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1. Explain the meaning of a point estimate and a confidence interval. What is the procedure to construct a confidence interval for a parameter using Statcrunch? 2. Explain what the statements below mean: a) A Rasmussen Reports national survey of 1000 adult Americans found that 18% dreaded Valentine's Day. The margin of error for the survey was 4.5 percentage points with 95% confidence. b) A Gallup poll of 547 adults Americans employed full or part time asked, "Generally speaking, would you say your commute to work is - very stressful, somewhat stressful, not that stressful at all?" Gallup reported that 24% of American workers said that their commute was "very" or "somewhat" stressful. The margin of error was 4 percentage points with 95% confidence. 3. Why do polling companies often survey 1060 individuals when they wish to estimate a population proportion with a margin of error 3% with 95% confidence? 4. Explain the procedure for testing a hypothesis using the P-value approach? What is the criterion for judging whether to reject the null hypothesis? 5. What does the level of significance represent in a test of hypothesis? 6. Explain the difference between "accepting" and "not rejecting" a null hypothesis. 7. Compare and contrast type I error and type II error. Give an example.

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(5 points) Find the area bounded by the graphs of equations.\\ $y = \frac{x}{e^{x/4}}$, $y = 0$, $x = 0$, $x = 1$

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A study was conducted to determine if a 6-week course on setting a budget changes financial self-efficacy. The researchers believe that the more experience people have with sticking to a budget, it will change their money management abilities. A sample of individuals was selected to participate in the 6-week budgeting program (n = 64). A week before training, financial self-efficacy was measured for each participant using a scale with scores from 0 to 100. Participants then completed the budgeting program, and after 6-weeks their financial self-efficacy using the same scale was measured again. The following results were provided: • ΣD = 80 • SS = 504 Determine whether the results indicate a significant change in financial literacy after the budgeting program. (There is no prior research to indicating the result would likely be in a certain direction.) Use an alpha .05, level of significance. To receive full credit provide the hypotheses (words or notation), critical boundary, standard error, t-score and decision including notation, decision and an explanation. Calculate and interpret Cohen’s d (even if not significant).

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Armidale Company Ltd (ACL) manufactures Special-purpose machines (SPMs) and functions with two operational divisions, AFN and BFN. In the case of Division AFN, Direct Labor (DL) cost is the basis on which manufacturing overhead (MOH) costs are allocated to SPMs. In the case of Division BFN, Direct Labor (DL) hours is the basis on which manufacturing overhead (MOH) costs are allocated to SPMs. ACL's 2021 books contain the following additional information: Budgeted Information/Data Division AFN Division BFN Direct labor cost $2,496,000 $4,275,000 Direct labor hours 249,600 450,000 Manufacturing overhead costs $3,120,000 $2,565,000 Job No. BXM, completed during 2021, details are appended in the following table: Actual Information/Data Division AFN Division BFN Direct materials (DM) used in production/requisitioned $237,000 $485,800 Direct labor cost $344,000 $388,000 Direct labor hours 43,000 38,000 Required: Work out the following: a) The budgeted (i.e. predetermined) rate for Division AFN at which MOH costs are allocated to jobs completed during 2021. b) The budgeted (i.e. predetermined) rate for Division BFN at which MOH costs are allocated to jobs completed during 2021. c) The total amount of MOH cost allocated to Job BXM. d) The per cost of output produced under job BXM if ACL produced 3,500 units under Job BXM.

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5.32 Determine the capitalized cost of a permanent roadside historical marker that has a first cost of $78,000 and a maintenance cost of $3500 once every 5 years. Use an interest rate of 8% per year. 5.33 The Golden Gate bridge is maintained by 38 painters and 17 ironworkers (who replace corroding steel and rivets). If the painters get an average wage of $120,000 per year (with benefits) and the ironwork- ers get $150,000 per year, what is the capitalized cost today of all the future wages for bridge maintenance at an interest rate of 8% per year?

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Let z = x + iy. Find in terms of x and y: R(z/z), S(1/z^2)

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Exercise 11-31 (Algorithmic) (LO. 8) Noah Yobs, who has $82,600 of AGI (solely from wages) before considering rental activities, has $74,340 of losses from a real estate rental activity in which he actively participates. He also actively participates in another real estate rental activity from which he has $41,300 of income. He has other passive activity income of $26,432. a. What amount of rental loss can Noah use to offset active or portfolio income in the current year? b. Compute Noah's AGI on Form 1040 [pages 1 and 2; also complete Schedule 1 (Form 1040)] for the current year. Use the minus sign to indicate a loss. Form Department of the Treasury-Internal Revenue Service (99) 1040 U.S. Individual Income Tax Return 2018 OMB No. 1545-0074 IRS Use Only Filing status: Single Married filing jointly Married filing separately Head of household Qualifying widow(er) Your first name and initial Noah Your standard deduction: If joint return, spouse's first name and initial Last name Vobs Your social security number 123-45-6789 Someone can claim you as a dependent You were born before January 2, 1954 You are blind Last name Spouse standard deduction: Someone can claim your spouse as a dependent Spouse was born before January 2, 1954 Spouse is blind Spouse itemizes on a separate return or you were dual- status alien Home address (number and street). If you have a P.O. box, see instructions. Spouse's social security number Full-year health care coverage or exempt (see inst.) Presidential Election Campaign (see inst.) You Spouse If more than four dependents, see inst. and \checkmark here (4)/ if qualifies for (see inst.) Apt. no. City, town or post office, state, and ZIP code. If you have a foreign address, attach Schedule 6. Dependents (see instructions): (2) Social security number (3) Relationship to you

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miguel -ngel s.