Rosalie sleeps 8 hours the first night of finals week. Each night after, she stays up later to study and sleeps 75% as much as she did the previous night. How many total hours of sleep does she receive during the 4 nights of finals week? Do this without finding each night and adding for a total

she received 21.875 hours of sleep during the 4 nights.

Step-by-step explanation:

Rosalie is following a geometric sequence(GP) by having a common rate of sleep .

as 75% or 0.75%.

Formula for a sum in GP= , where a= first term, r = common ratio, n= number of terms.

Put a= 8, r=0.75 and n =4, we get

On simplifying we get

Sum =21.875 hours

Hence, she received 21.875 hours of sleep during the 4 nights.

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560