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liq [111]
3 years ago
10

Yesterday, Sharon read 14 pages of a book. Today, she continued reading the book at the same speed. She read 10 pages in 35 minu

tes. How much time did she spend reading the book yesterday?
Mathematics
1 answer:
horrorfan [7]3 years ago
8 0

Answer:

Sharon spent a total of 49 minutes yesterday reading the book

Step-by-step explanation:

Step 1: Calculate the rate at which she reads

The total number of pages she reads at any given time interval can be expressed as;

T=P×m

where;

T=Total number of pages she reads

P=the rate at which she reads in number of pages per minute

m=total number of minutes she takes reading a book

In our case;

T=10 pages

P=p

m=35 minutes

replacing;

10=p×35

p=10/35

p=(10/35)

The rate at which she reads=(10/35) pages per minute

Step 2: Calculate the time she spent reading the book yesterday

Yesterdays variables are as follows;

T=14 pages

p=(10/35) pages per minute

m=unknown

replacing;

14=(10/35)×m

m=14×(35/10)

m=49

Sharon spent a total of 49 minutes yesterday reading the book

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Sample 1 = {1,1}, probablity = 1/9

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Sample 3 = {1,4}, probablity = 1/9

Sample 4 = {2,1}, probablity = 1/9

Sample 5 = {2,2}, probablity = 1/9

Sample 6 = {2,4}, probablity = 1/9

Sample 7 = {4,1}, probablity = 1/9

Sample 8 = {4,2}, probablity = 1/9

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==================================================

Part 2

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Sample 1 = {1,1}, xbar = 1

Sample 2 = {1,2}, xbar = 1.5

Sample 3 = {1,4}, xbar = 2.5

Sample 4 = {2,1}, xbar = 1.5

Sample 5 = {2,2}, xbar = 2

Sample 6 = {2,4}, xbar = 3

Sample 7 = {4,1}, xbar = 2.5

Sample 8 = {4,2}, xbar = 3

Sample 9 = {4,4}, xbar = 4

----------

Now let's list out each possible xbar value and its associated probability

xbar = 1, probability = 1/9

xbar = 1.5, probability = 2/9

xbar = 2, probability = 1/9

xbar = 2.5, probability = 2/9

xbar = 3, probability = 2/9

xbar = 4, probability = 1/9

note how the probabilities listed above add to 9/9 = 1.

Again a table is ideal to help organize the data.

==================================================

Part 3

To calculate the value of mu_x, we add up all the xbar values found in part 2, and divide by 9

(1+1.5+2.5+1.5+2+3+2.5+3+4)/9 = 2.333

So mu_x = 2.333 approximately

----------

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Luckily a calculator or spreadsheet can make quick work of this. You should get roughly 0.88192 as the standard deviation.

==================================================

Part 4

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The standard deviation of the population {1,2,4} is roughly 0.88191710368819 which matches with 0.88192 found earlier back in part 3.

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