If you drew one card from a standard deck, would it be "significant" to draw a 5? answer the question, considering an event to be "significant" if its probability is less than or equal to 0.05.

It has been given to us that an event is considered to be "significant" if its probability is less than or equal to 0.05.

Thus, we have to find the probability of the event where a 5 is drawn from a standard deck of 52 cards.

We know that there are four cards of denomination 5 in a standard deck of 52 cards and thus the probability of the required event of drawing a 5 is as:

This is greater than the required 0.05 or in other words and thus, the asked event (that of drawing a 5) is not "significant".

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

the answer will be