Math Answers

Tell whether if the following piecewise function is a continuous at a given point or not. (SHOW THE SOLUTION).

1. at x = 4

x + 1 if x < 4

(x - 4)² + 3 if x ≥ 4

Tell whether if the following piecewise function is a continuous at a given point or not. (SHOW THE SOLUTION).

1. at x = 4

x + 1 if x < 4

(x - 4)² + 3 if x ≥ 4

2. at x = 0

1/x if x ≤ -1

x² - 2 if x > -1

3. at x = 5

x² - 3 if x ≥ 5

4x + 2 if x < 5

if a population has a mean of 28.6 what is the mean of the sampling distribution of its means

CONTINUITY AT A POINT

A. Tell weather if the following is a continuous or discontinuous at a given point.

1. f(x) = 3x² + 2x + 1 at x = -2

2. f(x) = 1/x-2 at x = 2

3. f(x) = x-1/x² -1 at x = 1

4. f(x) = log (x² - 3) at x = 2

5. f(x) = 9x² - 1 at x = 1

Determine the given and compute the test statistic of the problem below using Central Limit Theorem, and construct the rejection region for each.

A company claimed that their N95 face mask has a mean filtration efficiency rate of 95%. A group of student researcher wanted to verify this claim. They bought and tested 40 of their N95 face masks. They found out that the average filtration efficiency rate of these face mask was 90% with a standard deviation of 4%. Test the claim at 5% level of significance and assume that the population is approximately normally distributed.

The probabilities that a surgeon operates on 3, 4, 5, 6, or 7 patients in any one day are 0.15, 0.20,0.25,0.20, 0.20, respectively.

43.) What is the mean that a surgeon operates on patients in any one day?

 a. 5.0             b. 5.1              c. 5.2              d. 5.3              e. 5.4

44.) What is the variance of the given problem?

 a. 1.76           b.1.77             c. 1.78            d. 1.79            e. 1.80

45.) What is the standard deviation of the given problem?

 a. 1.33           b. 1.35            c. 1.37            d. 1.36            e. 1.34

State the null and alternative hypothesis for each statement.

1. The average age of bus drivers in metro manila is 39 years old.

Ho : _______________

Ha: _______________

Show that if 5/3< 2x< 11/3, then x∈{y∈R such that |y- 4/3| < 1/2}.

Check whether the sequence (an), where

an = 1/ (n+1) + 1/(n+2) +....+1/(2n) is convergent or not

From a committee of 10 people,

1. In how many ways can we choose a chairperson, a vice-chairperson, and a secretary, assuming that one person cannot hold more than one position?

2. In how many ways can we choose a subcommittee of 3 people?

3. Find the number of combinations of 13 objects taken 8 at a time.

4. How many 5-card hands will have 3 aces and 2 kings?

5. Serial numbers for a product are to be made using 2 letters followed by 3 numbers. If the letters are to be taken from the first 8 letters of the alphabet with no repeats and the numbers are taken from the 10 digits (0-9) with no repeats, how many serial numbers are possible?

6. A company has 7 senior and 5 junior officers. An ad hoc legislative committee is to be formed. In how many ways can a 4-officer committee be formed so that it is composed of

a. Any 4 officers?

b. 4 senior officers?

c. 3 senior officers and 1 junior officer?

d. 2 senior officers and 2 junior officers?

e. At least 2 senior officers?