Math Answers

Prove the statement by contraposition, if a product of two positive real numbers is greater

than 100, then at least one of the numbers is greater than 10.

For all integers n and m, if n − m is even then n^3 − m^3

is even.

The average reading performance of grade 6 pupils was found to be 80 words per minute. A random sample of 20 students from three sections took the reading test and found to have an average speed of 74 words with a standard deviation of 8 words per minute. Can we say that the students performance is below the standard when tested at 0.05 level of significance?

Are the following vectors linearly independent?

1. (1, 2), (-2, 4)
2. (0, 0, 1), (0, 1, 1), (1, 1, 1)
3. (1, 2), (1, 3), (1, 1)
4. (1, 2, 3), (2, 3, 4)
5. (0, 1, 2), (2, 0, 1), (0, 0, 1), (3, 2, 1)

The local electric company uses the following method for computing monthly electric bills for one class of customers. A monthly service charge of $5 is assessed for each customer. In addition, the company charges $0.095 per kilowatt hour. If c equals the monthly charge stated in dollars and k equals the number of kilowatt hours used during a month:

(a) Determine the function which expresses a customer's monthly charge as a function of the number of kilowatt hours.

(b) Use this function to compute the monthly charge for a customer who uses 850 kilowatt hours. 

An aptitude test for selecting officers in a bank was conducted on 1000 candidates. The average score is 42 and the standard deviation of scores is 24. Assuming normal distribution for the scores, find the number of candidates whose scores exceeds 58.

A string is stretched and fastened to two points x = 0 and x = l apart. Motion is started by

displacing the string into the form y = k(lx − x2

) from which it is released at time t = 0. Find

the displacement of any point on the string at a distance of x from one end at time t.

Hint: From this problem, we have the following boundary conditions:

y(0,t) = 0 for all t > 0

y(l,t) = 0 for all t > 0

∂y

∂t

(x, 0) = 0 (initial velocity is zero)

y(x, 0) = k(lx − x2

)

Find the value of m for which lim x->infinity

(x+1)(2x-3)(2-3x)/(4-x+mx³) exists.

The lateral edge of a pyramidal church spire is 61 ft. Each side of the

octagonal base is 22 ft. What will be the cost of painting the spire at

$0.025 a square foot?

Bluereef real estate agent wants to form a relationship between the prices of houses, how many bedrooms, House size in sq ft and Lot Size in sq ft. The data pertaining to 100 houses were processed using MINITAB and the following is an extract of the output obtained: The regression equation is 𝑃𝑟𝑖𝑐𝑒 = 𝛽 + 𝜙𝐵𝑒𝑑𝑟𝑜𝑜𝑚 + 𝛾𝐻𝑜𝑢𝑠𝑒 𝑆𝑖𝑧𝑒 + 𝜆𝐿𝑜𝑡 𝑆𝑖𝑧𝑒 Predictor Coef SE Coef T P Constant 37718 14177 2.66 ** Bedrooms 2306 6994 0.33 0.742 House Size 74.3 52.98 * 0.164 Lot Size -4.36 17.02 -0.26 0.798 S= 25023 R-Sq=56.0% R-Sq(adj)=54.6% Source DF SS MS F P Regression 3 76501718347 25500572782 *** **** Residual Error 96 60109046053 626135896 Total 99 a) Write out the regression equation. [1] b) Fill in the missing values *, **, *** and ****. [6] d) Is 𝛾 significantly different from -0.5? [4] e) Perform the F test at the 1% level, making sure to state the null and alternative hypotheses. [4] f) Give an interpretation to the term “R-sq” and comment on its value .