Scenario 1 A group of researchers has recently collected data to investigate whether or not different kinds of performance feedback influences flow (a state of intense task absorption). In particular, they are interested in testing whether or not flow differs when participants are given feedback that is either positive or negative. The researchers have computed descriptive statistics, but are asking you to test the difference between groups. Positive Feedback: n = 30, M = 3.64, s = 0.40 Negative Feedback: n = 31, M = 3.21, s = 0.35

Identify the IV (and its levels) and the DV, and conduct a hypothesis test (including all steps) using the appropriate t-test (α = 0.05).

Scenario 2 A speech therapist developed a new technique for resolving stuttering in children and adolescents that involves use of a distractor to reduce speech-related anxiety. He recruited 8 current clients of his clinic to participate in a simple study. Each participant’s speech was assessed without the technique (pre-test control) and again while using the technique (post-test). The number of stutters were counted in each assessment, and the data are reported below. Does the therapist’s new technique appear to be working?

Identify the IV (and its levels) and the DV, and conduct a hypothesis test (including all steps) using the appropriate t-test (α = 0.01). Client 1 2 3 4 5 6 7 8 Pre-test 4 6 4 7 7 3 3 4 Post-test 4 5 5 4 2 2 3 1

You have three types of a sand/salt/beet juice mixture for preparing the roads for different kinds of storm conditions. The first type (A) is 25% sand, 10% salt, and 65% beet juice. The second type (B) is 10% sand, 50% salt, and 40% beet juice. The third type is 70% sand, 15% salt, and 15% beet juice (C). For the storm that is coming, we need a mixture that will be 40% sand, 25% salt, and 35% beet juice (D). Find how much of each type should be combined to obtain this mixture. Write the system of equations that represents this problem and the translation of that system into a matrix.

(PLEASE TYPE THE ANSWERS)

create your own example of a misleading statistic about Apple Explain the context of the data, the source of the data, the sampling method that you used (or would use) to collect the data, and the (misleading) conclusions that would be drawn from your example.

Sales Mix and Break-Even Sales Data related to the expected sales of laptops and tablets for Tech Products Inc. for the current year, which is typical of recent years, are as follows: Products Unit Selling Price Unit Variable Cost Sales Mix Laptops $190 $130 30% Tablets 520 240 70% The estimated fixed costs for the current year are $269,640. Required: 1. Determine the estimated units of sales of the overall (total) product, E, necessary to reach the break-even point for the current year. units 2. Based on the break-even sales (units) in part (1), determine the unit sales of both laptops and tablets for the current year. Laptops: units Tablets: units 3. Assume that the sales mix was 70% laptops and 30% tablets. Determine the estimated units of sales of the overall product necessary to reach the break-even point for the current year. units Why is it so different? The break-even point is higher in this scenario than in part (1) because the sales mix is weighted more heavily toward the product with the lower contribution margin per unit of product.

A mass of 50 g stretches a spring 1.568 cm. If the mass is set in motion from its equilibrium position with a downward velocity of 50 cms, and if there is no damping, determine the position u of the mass at any time t. Enclose arguments of functions in parentheses. For example, sin(2x). Assume g=9.8 ms2. Enter an exact answer. u(t)= m When does the mass first return to its equilibrium position? Enter an exact answer. t=

Use the simplex method to solve the following problem. Find y1 ≥ ​0, y2 ≥ ​0, and y3 ≥ 0 such that

2 y1 + 7 y2 + 3 y3 ≤ 11​,

2 y1 + 14 y2 + 8 y3 ≥ 1010​,

and

w = 12 y1 + 42 y2 + 59 y3 is minimized.

The minimum value w = ___ occurs when y1 = ___​, y2 = ___​, and y3 = ___.

​(Simplify your​ answers.)

An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation.

1. Compute b₁ and b₀ (to 1 decimal).
   b₁  
   b₀  
   
   Complete the estimated regression equation (to 1 decimal).
   ŷ =  +  x
   
2. What is the variable cost per unit produced (to 1 decimal)?
   
   
3. Compute the coefficient of determination (to 3 decimals). Note: report r² between 0 and 1.
   r² =  
   
   What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)?
   %
   
4. The company's production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation (to the nearest whole number)?
   $

Discrete Math.

Problem 1.

Consider the statement: “If an animal is an rhinoceros, then it has a horn.”

(a) Write down the CONVERSE of this statement.

(b) Write down the CONTRAPOSITIVE of this statement

Problem 2.

Let x be a positive real number.

Using the definition of rational number, write a proof by contraposition of the following:

If x is irrational, then √ x + 6 is also irrational.

Problem 3

Let n be an integer. Using the definition of odd/even number, write a proof of the following: n is even if and only if 2n 2 + 5n + 7 is odd.

"Quadratic equations were totally useless in solving problems necessary to the running of the Roman Empire." Give arguments for and against this statement

Let f: X→Y and g: Y→Z be both onto. Prove that g◦f is an onto function

Let f: X→Y and g: Y→Z be both onto. Prove that f◦g is an onto function

Let f: X→Y and g: Y→Z be both one to one. Prove that g◦f is an one to one function

Let f: X→Y and g: Y→Z be both one to one. Prove that f◦g is an one to one function

Prove that any two groups with one element are isomorphic.

Prove that any two groups with two elements are isomorphic.

Prove that any two groups with three elements are isomorphic.