Acoin is to be spun 25 times. let x be the number of spins that result in heads (h). consider the following rule for deciding whether or not the coin is fair: judge the coin to be fair if 8 ≤ x ≤ 17. judge the coin to be biased if either x ≤ 7 or x ≥ 18. a. what is the probability of judging the coin to be biased when it is actually fair?

0.0433

Step-by-step explanation:

Since we have a fixed number of trials (N = 25) and the probability of getting heads is always p = 0.05, we are going to treat this as a binomial distribution.

Using a binomial probability calculator, we find that the probability of obtaining heads from 8 to 17 times is 0.9567 given that the con is fair. The probability of obtaining any other value given that the coin is fair is going to be:

1 - 0.9567 = 0.0433

Since we are going to conclude that the coin is baised if either x<8 or x>17, the probability of judging the coin to be baised when it is actually fair is 4.33%

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

see explanation

step-by-step explanation:

a

(6r + 7) + (13 + 7r) ( remove brackets and collect like terms )

= 6r + 7 + 13 + 7r

= 13r + 20

b

remove brackets and collect like terms

13 - r - 1 + r

= 12 - r

c

remove brackets and collect like terms

= - 8 - r + 2r - 4

= - 12 + r

d

remove brackets and collect like terms

= 7r - - - 6r

[-   - = - - = - ]

= r -