Math Answers

7. Manila, the most populous city, has approximately 4.12x10^7 people

living in it. The population of the entire National Capital Region (NCR) is

approximately 3.1X10^8 people. About how many times greater is the

population of NCR than the population of Manila?

8. A box contains 5.125X10^4 thumb tucks. The mass of each thumb tuck is

8.1X10^-6 kilograms. What is the combined mass of the thumb tucks in

the box?

9. A microscope is set so it makes an object appear 4.3X10^3 times larger

than its usual size. A virus has a diameter of 2.7X10^-8 meter. How large

will the diameter of the virus appear when it is viewed under the

microscope?

10. 1.2 yottameter to yoctometer

Note: Assume that the population is infinite in this case and solve.

Problem: The scores of individual students on a national test have a normal distribution with mean 18.6 and standard deviation 5.9.At Federico Ramos Rural High School, 76 students took the test. If the scores at this school have the same distribution as national scores, what are the mean and standard deviation of the sample means for 76 students.

Table:

Steps Solution

1.Identify the given formation.

2.Find the mean of they sampling distribution. Use the property that Mx=M

3.find the standard deviation of the sampling distribution.

Consider a population consisting of 2,5,6,8, and 10. Suppose samples of size 2 are drawn from this population.

Q1.Compute the mean and the standard deviation of the population.

Q2. List all samples of size 5 and compute the mean for each sample.

Q3. Construct the sampling distribution of the sample means.

Q4. Calculate the mean of the sampling distribution of the sample means.

Q5. Calculate the standard deviation of the sampling distribution of the sample means.

The records of a certain hospital showed that the length of stay of its patients is normally distributed with a mean of 11.5 days and a standard deviation of 2 days. Find the standard score that corresponds to a hospital stay of 9 days.

Provide all detailed steps to find the limit of the following functions.

Lim x→∞ (e^4x - e^-2x) ÷ (ln(x+1)

c) Martin, Arop and Sam and went shopping at Kabale mega super market buying similar items. Martin bought one kilogram of sugar and one tin of blue band spending 6 shillings altogether. Arop bought bought 3 kilograms of maize flour and one tin of blue band spending 17 shillings altogether. Sam bought two kilograms of sugar, one kilogram of maize flour and 3 tins of blue band spending 15 shillings altogether. i) Express their purchases as equations ii) Using matrix method, find the cost of each kilogram of sugar, maize flour and a tin of blue band.

F(x) = 2x³ + cx² + 2x.

Suppose f is differentiable on R and has two roots. Show that f' has at least one root.

2. The growth in demand for computer hardware in a college is given by the equation t Q = )025.1(200 , where t is in months.

i) Calculate the demand when t = 0, 3, 6, 10 months.

ii) Calculate the time taken for the demand to increase to 300.

iii) Graph the demand for t = 0 to 30, hence confirm the answers to (i) and (ii).

A normally distributed data has a mean of 200 and a standard deviation of 20.What is the lowest value that belongs to the upper 10% of the distribution?

1. The demand for a product, in dollars, is P = 2000 - 0.2x - 0.01x²

Find the consumer surplus when the sales level is 250.

2.1. Find the area of the region that lies inside the circle r = 3sin(x)and

outside the cardioid r = 1+ sin(x).

2.2 Find the length of the cardioid r = 1+ sin(x)