## Archive for March, 2015

## A manufacturer has a steady annual demand for 22,638

A manufacturer has a steady annual demand for 22,638 cases of sugar. It costs $7 to store 1 case for 1 year, $33 in set up cost to produce each batch, and $20 to produce each case. Find the number of cases per batch that should be produced to minimize cost.

**Solution:-**

The manufacturer should produce 512 cases per batch.

## Problem 651

The time required to finish a test is normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes. What is the probability that a student will finish the test in less than 70 minutes?

**Solution:-**

84%

## Problem 650

The time required to finish a test is normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes. What is the z-Score for a student who finishes the test in 45 minutes?

**Solution:-**

z =

z =

z = -1.5

## Problem 649

Find the sum of the following infinite geometric series, if it exists.

**Solution:-**

S = , where r = common ratio (r ≤ 1) and a = first term.

a =

S =

S =

So the sum of the infinite geometric series 50/119

## Problem 648

Find the sum of the following infinite geometric series, if it exists.

**Solution:-**

S = , where r = common ratio (r ≤ 1) and a = first term.

a = , r = -1/8

S =

S =

So the sum of the infinite geometric series 4/9

## Problem 647

Find S15 for 1 + 1.5 + 2.25 + 3.375 + …

**Solution:-**

Sn =, Where a1 = first term , r = common ratio and n = finding term.

a1 = 1 , r = 1.5 , n = 15

S15 =

S15 = 873.79

So the value of S15 873.79

## Problem 646

Find S11 for 1 + 2 + 4 + 8 + …

**Solution:-**

Sn =

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r^{n} , Where a1 = first term , r = common ratio and n = finding term.

a1 = 1 , r = 2 , n = 11

S11 =

S11 = 2047

So the value of S11 2047

## Problem 645

Find the three geometric means between and 8.

**Solution:-**

t1= , t5 = 8

t5 =

8=

8*2 =

16 =

r = 2

In geometric sequence we have to find the next number by multiply last number to common ratio.

*2 = 1

1*2 = 2

2 * 2 = 4

So the three geometric means 1, 2, 4

## Problem 644

Find the three geometric means between 2 and 162.

**Solution:-**

t1=2

t5=162

162 =

81 =

r = 3

In geometric sequence we have to find the next number by multiply last number to common ratio.

2*3 = 6

6*3 =18

18*3 = 54

So the three geometric means 6, 18, 54

## Problem 643

Find the sixth term of a geometric sequence with t5 = 24 and t8 = 3.

**Solution:-**

t5 = 24 =

t8 = 3 =

Dividing one by the other

r =

t6 = = 12.

So the value of sixth term 12