Archive for May, 2015

Problem 755

The  government, through a subsidy program, distributes 31,000,000. If each person or agency spends 65% of what is received, and 65% of this is spend, and so on, how much total increase in spending results from this government action?

 

Solution:-

 

The total increase in spending is given by infinite series shown below.

31,000,000 + 31,000,000 (0.65) + 31,000,000(0.65)2 + …..

Thus , the series is geometric. When -1 < r < 1, the sum of an infinite geometric series is given by S = \frac{a_{1}}{1-r}, where r is the common ratio and a1 is the first term of the geometric series.

To find the common ratio, choose a term the sequence (other than the first) and divide by the preceding term.

r = \frac{31,000,000(0.65)}{31,000,000}=0.65

Since -1 < 0.65 < 1 , the series has a sum.

Use the formula to find the sum of the infinite geometric series. Substitute 0.65 for r and 31,000,000 for a1.

S = \frac{a_{1}}{1-r}

= \frac{31,000,000}{1-0.65}

Simplify

S = \frac{31,000,000}{1-0.65}

=\frac{31,000,000}{0.35}

\approx 88,571,429

Therefore , the total effect on the economy will be approximately 88,571,429.

 

 

 

Problem 754

Add. Simplify by collecting like radical terms if possible, assuming that all expression under redicals represent nonnegative numbers.

\sqrt{605y-605} + \sqrt{5y-5}

 

Solution:-

 

\sqrt{605y-605} +\sqrt{5y+5}

= \sqrt{121(5y-5)+\sqrt{5y+5}

=\sqrt(121) \sqrt{5y-5}+ \sqrt{5y-5}

=11  \sqrt{5y-5} +\sqrt{5y-5}

= (11+1)\sqrt{5y-5}

=12\sqrt{5y-5}

 

Problem 753

a) Determine whether the function is linear, constant, or neither

y = \frac{x+3}{7}

 

Solution:-

 

Linear

 

b) Determine whether the function is linear, constant, or neither

y = x3 – x3 + 8

 

Solution:-

 

Neither

Problem 752

The distance traveled to 7 different swim meets are given below:

15,30,32,52,75,77

Find the median distance traveled.

 

Solution:-

 

52 miles

 

 

Problem 751

The paired data below consists of the temperature on randomly chosen days the amount of a certain kind plant grew (in millimeters).

Temp,x 62 76 50 51 71 46 51 44 79
Groth,y 36 39 50 13 33 33 17 6 16

 

 

 

Solution:-

 

y = .21x + 14.57

 

Problem 750

A 6-side die is rolled. Find P (3 or 5).

 

Solution:-

 

\frac{1}{3}

Problem 749

 

Find the probability of correctly answering the first 4 questions on a multiple choice test if random guesses are made and each question has 3 possible answers.

 

Solution:-

 

\frac{1}{81}

 

Problem 748

Find the probability of correctly answering the first 2 questions on a multiple choice test if random guesses are made and each question has 6 possible answers.

 

Solution:-

 

\frac{1}{36}

 

 

Problem 747

For the given function, find each of the following:

a)      Intercepts

b)      Vertex

c)       Maximum or minimum

d)      Range

 

Solution:-

 

a)      X – intercepts: 1,7; y-intercept: -7

b)      Vertex (4,9)

c)       Maximum: 9

d)      Y<= 9

Problem 746

For the given function, find each of the following:

a)      Intercept

b)      Vertex

c)       Maximum or minimum

d)      Range

g(x) = (x-1)2 – 4

 

Solution:-

 

a)      x – intercept:- 1,3; y – intercept: -3

b)      Vertex (1,-4)

c)       Minimum : -4

d)      y >= -4