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A manufacturer of tires claim that their tire has a mean life of at least 50,000kms. A random sample of 28 of these tires is tested and the sample mean is 33,000kms. Assume that the population standard deviation is 3,000kms and the lives of the tires are approximately normally distributed.
1. ∫ (𝑥²+5)³ 2𝑥𝑑𝑥
2. ∫ 12𝑥² √4𝑥³ + 7𝑑𝑥
3. ∫ √2𝑥³+7 𝑥²𝑑𝑥
4. ∫ 5𝑥√1 + 4𝑥²
5. ∫(3𝑥² − 4𝑥 + 2)² (3𝑥 − 2)𝑑𝑥
Convert (1−i)/2 into trigonometric form
In a recent survey a researcher claimed that on average filipino teenagers watch k-dramas for 3.5 hours daily is the claim correct if a random sample of 50 filipino teenagers showed a mean of 2.8 hours with a standard deviation of 0.9 hours? use 99% confidence level
An aeroplane flies at a ground velocity (i.e. velocity relative to the ground) of 300 km/h N 30o W, in a wind blowing at a velocityof 50 km/h N 20o E. What is the velocity (speed and direction)of the plane relative to the ground? (Use a calculator and round the speed)
to the nearest km/h, and the corresponding angle to the nearest degree.)
A plane leaves an airport with a bearing of S41W. After traveling 24 miles, the plane turns and travels on a bearing of N49W for 32 miles. At that time, what's the bearing of the plane from the airport?
A group of students got the following scores in a test: 6,9,13,16,18,21. Consider sample size of size 3 that can be drawn from this population.
A. List all the possible samples and the corresponding mean.
B. Construct the samplong distribution of the sample means.
C. Compute for the mean and standard deviation of the sampling distribution of the sample means.
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
CREDIT CARDS
1) How much interest is due on an unpaid credit card balance of $1047.28 at a rate of 21.25% for 27 days?
2) How much interest is due on an unpaid credit card balance of $2111.67 at a rate of 18.5% for 5 months?
3) Adam has an unpaid credit card balance of $765.43 that charges an interest rate of 19.75%. If his payment was due on September 23, how much interest will he owe on October 14? Hint: September has 30 days.
4) Debbie has an unpaid credit card balance of $568.93. Her credit card company charges 24% per year, counting each day that an amount is owed. If she did not pay anything on July 10, her due date, how much does she owe on her next statement date, August 2? July has 31 days.
5) Stuart has an unpaid credit card balance of $268.67. What is his minimum payment if his credit card company charges an interest rate of 18.25%, and Stuart must pay 3% or $25, whichever is greater?
SIMPLE INTEREST
Match each variable with a value by placing the correct letter on each line.
Variable Value
a) principal ____ 280 days
b) interest ____ 1.95%
c) interest rate ____ $2000
d) term ____ $29.92
e) Using the values above, calculate whether the interest earned is the correct amount.
f) What is the total value of this investment?
2) Calculate the amount of simple interest earned in each of the situations.
a) principal = $1500 interest rate = 2.5% term = 5 years
b) principal = $3245 interest rate = 7.5% term = 3 years
c) principal = $500 interest rate = 11% term = 9 years
3) Peter invested $1860 for 10 months at a rate of 3.8%. How much interest did he earn?
5) Mike invested $4040 for 3 years and earned $410. What interest rate was this invested at?
6) How many months does it take to earn $180 in interest on an investment of the principal is $5000 and the interest rate is 2%?
#331389 on Nov 2022