Math Answers

Determine whether W = {(x, y,z) | x + y + z + 1 = 0, x, y,z ∈ R} a subspace of R³ or

not?

A point particle is travelling in a circular path with variable speed. If its

velocity at time t seconds is v = (2t + 1)θˆ:

a. What is the tangential component of acceleration at any time t ?

b. What is the centripetal acceleration at any time t ?

c. What the acceleration of the particle at any time t? Your answer should

look like a = acentriˆr + atan ˆθ, where acentri and atan are scalars which

represent the centripetal and tangential components, respectively, of

the total acceleration a.

Find the limit f(x),if it exists.sketch the graph of f(x).

Limit x approaching zero f(x),where f(x)=2-x,x less than or equal zero,. x+2, x>0

Explain the usefulness of central limit theorem in solving problems involving sampling

Three lottery tickets for first, second, and third prizes

Two of the five (5) foreign automobiles from an overseas shipment have slight paint blemishes. If an agency receives three (3) of these automobiles at random, list the elements of the sample space 𝑆 using the letters B and N for “blemished” and “non-blemished”, respectively. For each sample point, assign a value 𝑥 of the random variable 𝑋 representing the number of automobiles purchased by the agency with paint blemishes.

Three lottery tickets for first, second, and third prizes are drawn from a group of 45 tickets

the mean weight of baggage of 25 passengers from USA bound for the Philippines is 31.8 kilos with a variance of 16. test the claim that the population mean baggage weight is equal to 30 kilos at 0.01 level of significance. Assume that the population is normally distributed. The t value is 2.492

paul is standing at the top of an escalator and lily is standing at the bottom. Their vertical distance is 4.5 m and the angle of elevation of paul from lily is 20 degrees. Find the horizontal distance between them

2. Average Senior High School annual cost of tuition fee for all private schools last year was Php43,700. A random sample of costs this year for 45 private schools indicated that the sample mean was Php45,800 and a sample standard deviation was Php5,600. At 0.01 level of significance, is there sufficient evidence to conclude that the cost increased? Solution: Step 1: State the hypothesis. 𝐻0: _____________________________________________________________ 𝐻1: _____________________________________________________________ Step 2: The level of significance and critical region. 𝛼 = ________ and the 𝑧𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙 = __________ Step 3: Compute for the value of one sample t test. 𝑧𝑐𝑜𝑚𝑝𝑢𝑡𝑒𝑑 = _______ Step 4: Decision Rule. ________________________________________________________________ ___________________________________. Step 5: Conclusion: _______________