Math Answers

Let V(x) denote the number of litres of fuel left in an aircraft’s fuel tank if it has flown x km. Suppose that V(x) satisfies the following differential equation: V (x) = −aV(x) − b. Here, the fuel consumption per km is a constant b > 0. The term −aV(x), with a > 0, is due to the weight of the fuel) a) solve the equation with v(0)=vo b) how many km,x,can the plane fly if it takes off with vo litres in the tank

Directions: Write a brief interpretation of the table below following the

suggested guidelines.

Table 1. Frequency and Percentage Distribution of Student's

Overall Performance in Pre-Calculus Pretest

Student's Overall Performance

Outstanding

Very satisfactory

Satisfactory

Unsatisfactory

Poor

Total

Frequency

2

15

33

50

Percentage

5

30

66

100

4. A survey of 100 students produced the following information: 30 speak English, 45 speak Hindi and 60 speak Marathi. It is found that 10 speak both. English and Hindi, 20 speak both Hindi and Marathi, 15 speak both English and Marathi and 5 speak all the three languages.

a) How many of these students speak none of the three languages ? b) How many of these students speak exactly two languages ?

The quality manager of a factory wants to determine the life expectancy for manufactured lamps of his factory and found the mean is 375 hours. The standard deviation of the population is 100 hours. A sample of 64 lamps showed a mean life time of 350 hours. At the 5% level, prove that the mean life expectancy is less than 375 hours. 

A university claims that the percentage of its graduates who fail to get a job after one year of graduation is less than 10%. A sample of 200 graduates from the university was randomly selected and found that 16 graduates fail to get a job after one year of graduation. Is there enough evidence to support the university's claim? Test at 5% significance level. 

The local government often faces the problem of not enough money to pay for the services that it provided. One way to deal is to raise the taxes and another way is to reduce services. When the local poll asked a random sample of 1200 residents, the results show that 52% favouring to raise taxes and 48% favouring to reduce services. Test whether the proportion of residents who choose to raise taxes is different from 50%. Test at 1% significance level. 

 The Pharmacy Department of Serdang Hospital reported that the average annual spending on medicines was different from RM838 per patient. A random sample of 60 patients was selected and found that the average annual spending on medicines was RM745 per patient with a standard deviation of RM300. (i) At the 5% level of significance, can the department report be rejected? (ii) Explain the Type I and Type II error in this test. 

A tower, 28.4ft high must be secured with a guy wire anchored 5ft. from the base of the

tower. What angle will the guy wire make with the ground?

To break even in a manufacturing​ business, income or revenue R must equal the cost of production C. The cost C to produce x skateboards is C=63+22x. The skateboards are sold wholesale for ​$25 ​each, so revenue R is given by R=25x. Find how many skateboards the manufacturer needs to produce and sell to break even.​ (Hint: Set the cost expression equal to the revenue expression and solve for​ x.)

Question content area bottom

Part 1

The manufacturer needs to produce and sell

enter your response here

skateboards to break even.

​(Simplify your​ answer.)

The average annual number of cigarettes smoked by an adult in some country continues to decline. For the years​ 2000-2009, the equation y=−94.2x+1555 approximates this data.​ Here, x is the number of years after 2000 and y is the average annual number of cigarettes smoked. Predict the average annual number of cigarettes smoked by an adult in this country in 2015. To do​ so, let  x=15 ​(since 2015−2000=15​) and find y.

The average annual number of cigarettes smoked by an adult in the country in 2015 is predicted to be

enter your response here

. ​(Simplify your​ answer.)