A poll commissioned by Friends of the Earth and conducted by the Mellman Group found that 72% of American voters are in favor a carbon tax. Suppose that six voters in the United States are randomly sampled and asked whether they favor a carbon tax. Determine the probability that the number answering in the affirmative is a. Exactly four. b. At least two

a

b

Step-by-step explanation:

From the question we are told that

    The proportion in favor of carbon tax is  

    The sample size is  n  = 6

Generally the distribution of poll  follows a binomial distribution  

i.e  

and the probability distribution function for binomial  distribution is  

Here C stands for combination hence we are going to be making use of the combination function in our calculators      

   Generally the probability that the number answering in the affirmative is  4 is mathematically represented as

=>    

   Generally the probability that the number answering in the affirmative is At least two is mathematically represented as

=>  

=>    

=>    

c. 65°

step-by-step explanation:

we are given a triangle with two known angles, 62° and 53°, while the third angle x is unknown and we are to find its value.

we know that the sum of angles in a triangle is equal to a total of 180 degrees. so we can write it as:

x + 62° + 53° = 180°

solving to find the value of x:

x = 180 - (62 + 53) = 65°

therefore, the value of x in this triangle is 65°.