Math Answers

The following table relates to the tourist arrivals during 1990 to 1996 in Botswana:

Years:                    1990   1991    1992   1993  1994  1995  1996

Tourist’s arrivals:    18       20        23       25      24      28       30

Fit a straight line trend by the method of least squares and estimates the number of tourists that would arrives in the year 2000.

Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.2, P(F) = 0.1 and P(E n F) = 0.05. Compute.

a.      P(E u F)

b.     P(E^c n F^c)

c.      P(E n F)

C  Let A and B be event of a sample space S such that P (A) = 0.4, P (B) = 0.8 and P (AnB) =0.3 Find (a) P (A/B) (b) P (B/A)

a.     Suppose the correlation coefficient is 0.8 and number of observation is 62. What is the calculated test statistics? Is this significant correlation using a 1% level of significant?

A sample of blood pressure measurements is taken for a group of​ adults, and those values​ (mm Hg) are listed below. The values are matched so that 10 subjects each have a systolic and diastolic measurement. Find the coefficient of variation for each of the two​ samples; then compare the variation.

Systolic

116

126

158

96

156

122

117

134

125

118

Diastolic

79

77

76

53

88

89

58

66

72

84

The coefficient of variation for the systolic measurements is

enter your response here

​%.

A gumball machine contains 300 grape flavored balls, 400 cherry flavored balls, and 500 lemon flavored balls. What is the probability of getting 1 grape ball, 1 cherry ball, and 1 lemon ball if each ball was removed and then replaced before choosing the next from the machine?

What is the volume of the largest rectangular parallelepiped which can be inscribed in the ellipsoid x²/9+y²/16+z²/36=1? Show that the answer you get gives you the largest volume.(DO NOT USE LAGRANGE MULTIPLIERS)

The radius of a quarter circle is 3 meters. What is the quarter circle's perimeter?

Use 3.14 for ​𝜋.

a. When we cough, the trachea (windpipe) contracts to increase the velocity

of the air going out. This raises the questions of how much it should contract

to maximize the velocity and whether it really contracts that much when we

cough.

Under reasonable assumptions about the elasticity of the tracheal wall and

about how the air near the wall is slowed by friction, the average flow velocity

y can be modeled by the equation 𝑦 = 𝑐( 𝑟 , ,

0 − 𝑟)𝑟

2

𝑐𝑚/𝑠𝑒𝑐

𝑟0

2 < 𝑟 < 𝑟0

where 𝑟 is the rest radius of the trachea in centimeters and is a positive

𝑐

constant whose value depends in part on the length of the trachea. Show that

𝑦 is greatest when 𝑟 = (2/3)𝑟 that is, when the trachea is about

33%

contracted. The remarkable fact is that 𝑋 −ray photographs confirm that the

trachea contracts about this much during a cough.

b. Take 𝑟 to be and to be and graph over the interval .

0. 5 𝑐 1 𝑦 0 < 𝑟 < 0. 5

Compare what you see with the claim that 𝑦 is at a maximum when

𝑟 = (2/3)𝑟 .

How much Ione invest if she wants to have P19,640.62 at the end of 2.75 years at a bank that offers 11(1/4)% simple interest.