## 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_{∞} = , where r is the common ratio and a_{1} 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 a_{1}.

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 = x^{3} – x^{3} + 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