Math Answers

A local high school needs to hire several cafeteria workers and bus drivers. Cafeteria workers earn R13 800

per month and bus drivers earn R17 250 per month. The school board gave the school permission to spend

no more than R345 000 on the salaries per month, but must hire more than 15 people.

Let B represent the number of bus drivers hired.

Let C represent the number of cafeteria workers hired.

For every bus driver hired there must be at least two cafeteria workers hired. The number of cafeteria

workers must at most be three more than twice the number of bus drivers.

Write a system of linear inequalities that the school could use to determine the number of cafeteria workers

and bus drivers they can hire

x - 3y + 6z = 21

3x + 2y - 5z = - 30

2x - 5y + 2z = -6

The sum of values of x

x, y

y, and z

z of the solution is

During the pandemic, online ordering of groceries and household supplies was offered by many stores as an accommodation for shoppers who preferred not to visit crowded stores in person. An online grocery shopping service claims that its mean delivery time is less than 120 minutes with a population standard deviation of 30 minutes. A random sample of 49 orders is delivered with a mean of 100 minutes. At the 95% confidence level, is there enough evidence to support the claim? Assume the data are normally distributed. Use the critical value method and respond to the prompts below.

A random sample of 30 households was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) was recorded for each household in the sample for the March quarter of 2020. The average usage was found to be 375kWh. In a very large study in the March quarter of the previous year it was found that the standard deviation of the usage was 85kWh. Assuming the standard deviation is unchanged and that the usage is normally distributed provide an expression for calculating a 99% confidence interval for the

mean usage in the March quarter of 2020

Solve for the determinant in the equation below(10marks)

1.7.1

"\\begin{matrix}\n 4 & -3 & 2 \\\\\n 1 & 2 &-2 \\\\\n 2 & -1 & -4\\\\\n\n\\end{matrix}"

1.7.2.

"\\begin{matrix}\n 2 & -2 & 1 \\\\\n 2 & 2 & 1\\\\\n 4 & 1 & 3 \\\\\n\\end{matrix}"

A fair coin tossed 400 times.If X is the number of heads obtained, find the expected value and variance of X

1.5 Solve the equation below using Inverse method (10 marks)

"\\begin{bmatrix}\n 1 & 3 & 0 \\\\\n 0 & 0.5 & 1\\\\\n0.05 & 0 & 1\\\\\n\n \\end{bmatrix}" "\\begin{bmatrix}\n x \\\\\n y\\\\\nz\\\\\n\\end{bmatrix}" ="\\begin{bmatrix}\n 4 \\\\\n 1\\\\\n3\\\\\n\\end{bmatrix}"

Using a Truth table, determine the value of the compound proposition(10marks)

((𝑝 ∨ 𝑞) ∧ (￢𝑝 ∨ 𝑟)) → (𝑞 ∨ 𝑟).

How many positive integers less than 1000 have at least one decimal digit equal to 9?

Solve for the determinant in the equation below. (10)

1.7.1.

4 −3 2

1 2 −2

2 −1 −4

1.7.2

2 −2 1

2 2 1

4 1 3