A health research institute collects information from 20 individuals on the number of years they have spent smoking cigarettes, and their age of death. The data is summarized below: ∑x=1257
∑y^2=836
∑x^2=98823
∑y=116
∑(xy)=8249

Find the correlation coefficient (r):

The correlation coefficient of the health research institute data measures the relationship between the age and the years of the smokers

The correlation coefficient is 0.53

The correlation coefficient (r) is calculated as:

Using the given parameters, we have:

Evaluate the exponents

Evaluate the products

Evaluate the differences

Evaluate the product

Evaluate the root

Evaluate the quotient

Hence, the correlation coefficient is 0.53

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SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

The answer is in the image 

The answer is in the image 

The answer is in the image 

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76

The answer is in the image 

Given height of gymnasium is 5/6 height of 30 foot ball

therefore height of gymnasium=5/6 * 30

=25 feet

The solution is given below

The answer is in the image