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2. How many 4 letter words can be created, if repetitions are allowed?
3. How many three digit numbers can be formed?
4. How many words (of any number of letters) can be formed from GAME?
5. How many 3-digit, 4-digit, or 5-digit numbers can be made using the digits of 46723819?
6. How many numbers between 999 and 9999 are divisible by 5 and have no repeated digits?
7. How many ways can you order the letters in KEYBOARD if K and Y must always be kept together?
8. How many ways can 4 rock, 5 pop, and 6 classical albums be ordered if all albums of the same genre must be kept together?
9. In how many ways can the letters from the word EDITOR be arranged if vowels and consonants alternate positions?
10. If 8 boys and 2 girls must stand in line for a picture, how many line-up’s will have the girls separated from each other?
A manufacturing firm claims that each water bottle they produce contains an average of 300 mL of water with a standard deviation of 1.2 mL. A random sample of 20 water bottles showed an average volume of 301.4 mL. if the t-value in the test is 3.14 and the critical values are ±2.861, what is the appropriate decision conclusion in the hypothesis testing?
According to a student conducted by the grade 12 students P155 is the average monthly expense for cellphone loads of high school students in their province. A statistics student claims that this amount has increased since January of this year. do you think his claim is acceptable if a random sample of 50 students has an average monthly expense of P165 for cellphone loads? Using 5% level of significance, assume that a population standard deviation is P52
Choose a variable that you will forecast using ARIMA Modelling and describe the importance of that variable
2. An association of City Mayors conducted a study to determine the average number of times a family went to buy necessities in a week. They found that the mean is 4 times in a week. A random sample of 20 families were asked and found a mean of 5 times in a week and a standard deviation of 2. Use 5% significance level to test that the population mean is not equal to 5. Assume that the population is normally distributed
3. A $1000 investment as interest a 4% per year, compounded quarterly How long will it take to double the value of the investment?
4. if $4000 is invested for 10 years, what annual interest rate, compounded semi-annually, would double the money?
How much do you need to deposit at the end of each quarter imo an account paying 83%a compounded quarterly if you want to have $5000 in 5 years?
Find the volume of the solid by revolving the astroid x⅔+y⅔=a⅔ along x axis
A medical expert claims that 80% of recovered COVID-19 patients have produced antibodies against the virus. To verify this, 1,000 recovered patients were tested and found that 823 of them have antibodies for the corona virus. Is this enough evidence to support the claim? Use 𝑎 = 0.01.
A politician claims that he will get at least 70% of the votes. Out of 300 randomly sampled registered voters, 200 said they will vote for the said politician. Test the claim using 0.10 level of significance.
