Math Answers

Determine the length of the curve 𝑥 = 𝑦^2 /2 for 0 ≤ 𝑥 ≤ 1/2 . Assume 𝑦 positive.

Let a and b be two cardinal numbers. Modify Cantor’s definition of a < b to define a ≤ b. (Hint: Examine what happens if you drop condition (a) from Cantor’s definition of a < b.) 2. Prove that a ≤ a. 3. Prove that if a ≤ b and b ≤ c, then a ≤ c. 4. Do you think that a ≤ b and b ≤ a imply

a = b? Explain your reasoning. (Hint: This is not as trivial as it might look.)

The table below shows the frequency distribution for the variable level of satisfaction with nursing care by 475 women in the maternal health ward at hospital X.

Level of satisfaction. Frequency

Very satisfied. 121

Satisfied. 161

Neutral. 90

Dissatisfied. 51

Very dissatisfied. 52

(I) what measure of location can you established from this data?

(Ii) find the measure of location in (I)

(Iii) What measure of location is appropriate to describe the data set?

(Iv) Draw a pie chart and bar graph for the data and briefly interpret

The Burger Doodle restaurant franchises in Los Angeles are supplied from a central warehouse in Inglewood. The locations of the warehouse and its proximity, in minutes of travel time, to the franchises are shown in the following network: Trucks supply each franchise on a daily basis. Determine the shortest route from the warehouse at Inglewood to each of the nine franchises

"An employee at Infotech must enter product information into the computer. The employee may use a light pen that transmits the information to the PC along with the keyboard to issue Commands or fill out a bubble sheet and feed it to directly into the mainframe. Historically, we know the following probabilities: P(Light pen will fail) =0.025 P(PC keyboard will fail) =0.15 P(Light pen and PC keyboard will fail) =0.005 P(Mainframe will fail) =0.25 Data can be entered into the PC only if both the light pen and keyboard are functioning. Applying the concept of conditional probability , Solve the following (a) Chances of employee can use the PC to enter data? (b) Chance that either the PC fails or the mainframe fails? Assume they cannot both fail at the same time. "

For the two sample Ztest of testing difference of means, the value of test statistics is z=1.25 and the test is two tailed. The p-value for the above test is

A product designer is testing the tensile strength of a new synthetic fiber that will be used to produce cloth for women’s jackets. Strength is usually affected by the percentage of cotton used in the blend of materials for the fiber. An experiment is conducted with five levels of cotton content and replicated the experiment five times. The data are shown in the following Table 2.

Table 2

Cotton Weight (%)

Observations

15

7

7

15

11

9

20

12

17

12

18

18

25

14

19

19

18

18

30

19

25

22

19

23

35

7

10

11

15

11

Source

Sum of Squares

Treatment

475.76

Error

161.2

Identify the following items in this study.

Treatments

Dependant variable

Number of replications

Construct an analysis of variance (ANOVA) table.

Is there evidence to support the claim that cotton content affects the mean tensile strength? Use α = 0.05

Use the Fisher LSD method to make comparisons between the pairs of means. What conclusions can you draw?

When do you use an ANOVA test?

State the null hypothesis for a one-way ANOVA test if there are four groups.

There are five basic assumptions that must be fulfilled in order to perform a one-way ANOVA test. What are they?