Question 1-

Part 1 - MI LTIPL E CHOICE QUETIONS

1) The domain of f(x) = 4/x³-8 f(t) is:

(a) All real numbers except 0.

(b) All real numbers except 2.

(c) All real numbers except 3.

(d) All real numbers.

2) The slope of the line 5y + 3x - 6 = 0 is:

(a) 3/5  

(b) -3/5

(c) 6/5

(d) -6/5

3) If log₃x = 3, then x =

(a) 125

(b) 1/4

(c) 27

(d) -4

4) If ln(3^x) = 4.394449, then x=

(a) -2.7 

(b) 3      

(c) 4      

(d). 5

5) An interest rate of 5% compounded quarterly corresponds to an effective rate of:

(a ) 61.04%

(b) 6.14%

(c) 5.90%

(d) 5.09%

Part 2-

(a) Differentiate: f(w) = w-5/w⁵

(b) Find: ∫(3√u + (1/√u)) dx

Question 2-

Part 1-

You have a friend who amortises a Loan of $250,000 mortgage for 30 years for a new property, obtained at the rate of 6.0% compounded monthly. Find:

(a) The monthly payment,

(b) The interest in the first payment,

(c) The principal repaid in the first payment

Part 2-

If the coefficient matrix of the system is invertible, solve the system by using the inverse matrix:

3x+y = 5

3x-y = 7

Part 3-

The demand equation for a manufacturer's product is p = 500 - 2q², where p is the price per unit for q units. Find the marginal revenue function.

Question 3-

Part 1-

A local store is doing market research about the characteristics of their customers who are parents to guide its season sales promotion. Information from 700 parents about the number of children in the family and whether they buy organic fruits is included d n the table below:

(a) What proportion of customers in this sample has more than one child?

(b) What proportion of customers in this sample buy organic finks and has only one child?

(c) What proportion of customers in this sample buy organic fruits or has only one child?

(d) Given the customer selected buys organic fruits, what is the probability that the customer only has one child?

Part 2-

The time it takes to prepare a sandwich at -Delicious Fast Food is normally distributed with a mean of 4.2 minutes and a standard deviation of 1 minute

(a) What is the probability that it will take at Least 5 minutes to prepare a sandwich?

(b) Above what time are 95% of the sandwiches prepared?

Question 4-

Part 1-

A convenience store wants to estimate the average number of soft drink cans that are sold daily. The number of cans sold daily is assumed to be normally distributed for each day with a standard deviation of 12. A sample of 16 days had a sample mean of 74 soft drink cans. This information %US used pa calculate an interval estimate for the population mean between 70 and 78 cans. What is the level of confidence of this interval?

Part 2- MULTIPLE CHOICE-

A media comp aw wards co use the number of minutes a commercial is broadcasted on TV (X) to predict the number of sales (Y). Data comprising 1,000 brands using commercials was used to fit the model:

E(Y) = β₀ + β₁X

The results of the simple linear regression were:

Y^{^}i = 500 + 20X_i

1) Interpret the estimate β₀, the Y-intercept of the line.

(a) For every minute extra the commercial is broadcasted, it is expected an increase in sales by 20 units on average.

(b) Atom 95% of minutes broadcasted fail within 500 of the least squares line.

(c) Companies will sell at leap 500 units.

(d) There is no practical interpretation.

2) Interpret the estimate β₁, the slope of the line.

(a) Number of minutes a commercial is broadcasted and sales are non-related variables.

(b) Companies will sell at least 500 units.

(c) For every minute extra the commercial is broadcasted, it is expected an increase in sales by 20 units on average.

(D) There is no practical interpretation.

3) If the two-tail p-value for testing β₁ is 0.01, interpret this p-value for testing whether β₁ exceeds 0.

(a) Number of minutes a commercial is broadcasted is a poor predictor of sales.

(b) For every additional minute a commercial is broadcasted, it is expected an increase in sales by 20 units on average.

(c) There is insufficient evidence (at α = 0.101) to conclude that minutes a commercial is broadcasted (X) is a useful linear predictor of sales (Y).

(d) There is sufficient evidence (at α = 0.05) to conclude that minutes a commercial is broadcasted (X) is a useful linear predictor of sales (Y).