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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The answer is in the image 

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

The solution is in the following image

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Approximately it is aqual to 1300kg

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

The answer is in the image