The article "a music key detection method based on pitch class distribution theory" (j. sun, h. li, and l. ma, international journal of knowledge-based and intelligent engineering systems, 2011: 165–175) describes a method of analyzing digital music files to determine the key in which the music is written. in a sample of 335 classical music selections, the key was identified correctly in 293 of them.

a. find a 90% confidence interval for the proportion of pieces for which the key will be correctly identified.
b. how many music pieces should be sampled to specify the proportion to within ±0.025 with 90% confidence?
c. another method of key detection is to be tested. at this point, there is no estimate of the proportion of the time this method will be identified correctly. find a conservative estimate of the sample size

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

step-by-step explanation:

because 1/3 is a fraction. we can tell because there is a divisor symbol between the 1 and the 3. if we were to add 2 fractions together, we would add the numerators, which is the number on top, but not the denominators, which is the number on the bottom

1/3+1/3=2/3

hope this !

4

step-by-step explanation:

im pretty sure it's 4 beacsue 8/2 equals 4

really really sorry if i'm

-12 -5(x + 4) = 3x

-12 - 5x - 20 = 3x

-12 - 20 - 5x = 3x

-32 - 5x = 3x

    + 5x   + 5x

-32 = 8x

8         8

- 4= x