Math Answers

1. Find the domain of the function 𝑓(𝑥)=ln(−2𝑥2−𝑥−6)+√𝑥2−1.

2. Find the inverse function of the function 𝑓(𝑥)=𝑥2−4𝑥+5,𝑥∈〈3,4⟩. Find the domain and the range of the inverse function.

3. Construct the tangent line to the graph of the function 𝑓(𝑥)=4𝑥⋅√𝑥−2⋅√𝑥 which is parallel to the line 𝑦=𝑥.

4. Find the maximal intervals of monotonicity of the function 𝑓(𝑥)=𝑒𝑥+3𝑥2+2𝑥+6.

5. Find the integral ∫6⋅𝑥3⋅𝑒𝑥2+2𝑑𝑥.

6. Find the general solution of the differential equation 𝑥2+1+𝑦′⋅cos(𝑦)=0. 

The owner of the drug store chain has 100 drugstore that that sell flexcoslow, a surgical mask that prevents a person from catching liquid droplets of viruses. His operation manager said that the average drugstore in his chain sell 12 boxes of the flexcoslow a day with a standard deviation of 2 boxes. To find out if this is true, the owner randomly selected 10 store and found that the mean is 15 boxes with a standard deviation of 1box.

N= ,n=

"\\mu" =

"\\sigma" ^{2 =}

X=

s=

Let f : R → R be defined by f(x) = (x3 + 1)/2

a. Prove that f is bijective

b. Determine f -1 (x) and f o f o f -1

The average age of public jeepneys plying in Metro Manila is 15 years. Assume that the standard deviation is 8 years. If a random sample of 25 public jeepneys is chosen, Find the probability that the mean of jeepneys ages is between 12 and 19.

This item is 10 points. A population consists of the five measurements 1, 5, 3, 8, and 10 . Suppose samples of size 2 are drawn from this population. 

Compute and find the following:

1) Find the variance of the population.

2) Find the variance of the sampling distribution. 

The average age of public jeepneys plying in Metro Manila is 15 years. Assume that the standard deviation is 8 years. If a random sample of 25 public jeepneys is chosen, Find the probability that the mean of jeepneys ages is between 12 and 19.

Kaitlyn is flipping a coin two times, and records the result of each flip. Which of the sets below is the entire sample space?

{HH,TT,HT,TH}

What is the probability of obtaining heads twice?

What is the probability of obtaining heads exactly once?

What is the probability of obtaining heads at least once?

What is the probability of obtaining no heads?

Suppose that the mean stopping time of a particular model of car moving at 40 mph is listed

as 1.8 seconds, with a standard deviation of 0.25 seconds. A random sample of 12 cars obtains a

standard deviation of 0.35 seconds. Test the claim that o = 0.25 seconds at the 0.05 level of significance

Suppose that a survey of 500 randomly selected registered voters are asked whether they voted in

the last presidential election and that 49% said that they had. We wish to test the claim at the a = 0.05 level of

significance that more than 50% of registered voters voted in the last presidential election.

An element with mass 140 grams decays by 21.6% per minute. How much of the element is remaining after 20 minutes, to the nearest 10th of a gram?