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 = , 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 =

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 =

=

Simplify

S =

=

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.

+

Solution:-

+

= +

= +

=11 +

= (11+1)

=12

Problem 753

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

y =

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:-

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:-

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:-

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