At the beginning of the school year, Priscilla Wescott decided to prepare a cash budget for the months of September, October, November, and December. The budget must plan for enough cash on December 31 to pay the spring semester tuition, which is the same as the fall tuition. The following information relates to the budget:

a. Prepare a cash budget for September, October, November, and December. Enter all amounts as positive values except cash decrease which should be indicated with a minus sign.

b. Are the four monthly budgets that are presented prepared as static budgets or flexible budgets?

c. What are the budget implications for Priscilla Wescott?

Priscilla can see that her present plan sufficient cash. If Priscilla did not budget but went ahead with the original plan, she would be $ at the end of December, with no time left to adjust.

Children playing in a playground on the flat roof of a city school lose their ball to the parking lot below. One of the teachers kicks the ball back up to the children as shown in the figure below. The playground is 5.50 m above the parking lot, and the school building's vertical wall is

h = 6.90 m

high, forming a 1.40 m high railing around the playground. The ball is launched at an angle of

θ = 53.0°

above the horizontal at a point

d = 24.0 m

from the base of the building wall. The ball takes 2.20 s to reach a point vertically above the wall. (Due to the nature of this problem, do not use rounded intermediate values in your calculations—including answers submitted in WebAssign.)

a) Find the speed (in m/s) at which the ball was launched.

(b) Find the vertical distance (in m) by which the ball clears the wall.

(c)Find the horizontal distance (in m) from the wall to the point on the roof where the ball lands.

(d)What If? If the teacher always launches the ball with the speed found in part (a), what is the minimum angle (in degrees above the horizontal) at which he can launch the ball and still clear the playground railing? (Hint: You may need to use the trigonometric identity

sec²(θ) = 1 + tan²(θ).)

(e)What would be the horizontal distance (in m) from the wall to the point on the roof where the ball lands in this case?

A school principal is interested in assessing the performance of her students on the Totally Oppressive Standardized test (TOST). She selects a simple random sample of 16 of her students and finds the following set of test scores:

Assume that the sample is drawn from a population with a standard deviation σ = 7.20.

a. (1 point) What is the mean test score for the sample of students?

13

b. (4 points) Calculate and write a sentence to interpret the 95% confidence interval for the mean test score.

c. (3 points) Calculate and write a sentence to interpret the 99% confidence interval for the mean test score.

13 - 2.58 * (1.8) 13 + 2.58 * (1.8)= 8.3,17.6????

d. (4 points) Explain why the margin of error for the 95% confidence interval in question (b) is smaller than the margin of error for the 99% confidence interval in question (c).

Suppose that the daily consumption of Pepsi in ounces by a high school student is normally distributed with mean = 13.0 ounces and variance = 2.0 ounces. The daily amount consumed is independent of other days except adjacent days where the covariance is -1.0. If the student has two six-packs of 16 ounce Pepsi bottles, what is the probability that some Pepsi remains at the end of two-weeks ?

At the beginning of the school year, Craig Kovar decided to prepare a cash budget for the months of September, October, November, and December. The budget must plan for enough cash on December 31 to pay the spring semester tuition, which is the same as the fall tuition. The following information relates to the budget:

a. Prepare a cash budget for September, October, November, and December. Use the minus sign to indicate cash outflows, a decrease in cash or cash payments.

b. Are the four monthly budgets that are presented prepared as static budgets or flexible budgets?

c. What are the budget implications for Craig Kovar?

Craig can see that his present plan   sufficient cash. If Craig did not budget but went ahead with the original plan, he would be $   at the end of December, with no time left to adjust.

The weight (in pounds) for a population of school-aged children is normally distributed with a mean equal to 138 ± 23 pounds (μ ± σ).Suppose we select a sample of 100 children (n = 100) to test whether children in this population are gaining weight at a 0.05 level of significance.

• Part (a)

  What are the null and alternative hypotheses?

  H₀: μ = 138
  H₁: μ < 138

• H₀: μ = 138

• H₁: μ ≠ 138    

• H₀: μ ≤ 138

• H₁: μ > 138

• H₀: μ ≤ 138
  H₁: μ = 138

• Part (b)

  What is the critical value for this test?

• Part (c)

  What is the mean of the sampling distribution?
  lb

• Part (d)

  What is the standard error of the mean for the sampling distribution?
  lb

A random selection of students at a school were chosen at random and how long they spent eating compared to how many calories they consumed was recorded as the following:

1. Make a scatterplot for the data

2. Find the LSRL

3. Describe the slope and the y-intercept, do they make sense?

4. Create a Residual Plot for the data

5. Create a 95% confidence interval for the slope of the line

A random selection of students at a school were chosen at random and how long they spent eating compared to how many calories they consumed was recorded as the following:

1. Make a scatterplot for the data

2. Find the LSRL

3. Describe the slope and the y-intercept, do they make sense?

4. Create a Residual Plot for the data

5. Create a 95% confidence interval for the slope of the line

A school is conducting optimization studies of the resources it has. One of the principal concerns of the Director is that of the staff. The problem he is currently facing is with the number of guards in the "Emergencies" section. To this end, he ordered a study to be carried out that yielded the following results:

Time Minimum number of guards required
O to 4 40
4 to 8 80
8 to 12 100
12 to 16 70
16 to 20 120
20 to 24 50

Each guard, according to Federal labor law, must work eight consecutive hours per day. Formulate the problem of hiring the minimum number of guards that meet the above requirements, as a Linear programing model.