58​% of U. S. adults have very little confidence in newspapers. You randomly select 10 U. S. adults. Find the probability that the number of U. S. adults who have very little confidence in newspapers is ​ (a) exactly​ five, (b) at least​ six, and​ (c) less than four. a) ​P(5)=
(b) ​P(x​≥6)=
​(c) ​P(x​<4)=

.216165788

.582225057

.417774943

Step-by-step explanation:

We need to use a binomial distribution here

A.

10C5*.58⁵*(1-.58)⁵= .216165788

B.

I honestly think the fastest way to solve this is adding the probabiblity of exactly 6,7,8,9,10

which means we write

10C6*.58⁶*(1-.58)⁴+10C7*.58⁷*(1-.58)³+10C8*.58⁸*(1-.58)²+10C9*.58⁹*(1-.58)+10C10*.58¹⁰= .582225057

C.

To solve this just take the compliment of answer B

1-.582225057= .417774943

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus