Need to pass
consider u = {x|x is a negative real number}. which is an empty set?
a {x|x ∈ u and x has a negative cube root}
b {x|x ∈ u and x has a negative square root}
c{x|x ∈ u and x is equal to the product of a positive number and –1}
d {x|x ∈ u and x is equal to the sum of one negative and one positive number}

B={x|x ∈ U and x has a negative square root} is an empty set.

Step-by-step explanation:

let U={x|x is a negative real number}

A= {x|x ∈ U and x has a negative cube root}

It is not an empty set as it contains -1 ∈A such that

∈U . Hence A≠∅

B= {x|x ∈ U and x has a negative square root}

Let there exist some x∈U such that =negative square root of x

but x is a negative real number and its square root must be complex which does not belong to set of real numbers.

for example ,for x=-4∈U

∉set of real numbers.

C={x|x ∈ U and x is equal to the product of a positive number and –1}

C≠∅ as -8∈C such that 8×-1=-8.

D {x|x ∈ U and x is equal to the sum of one negative and one positive number}

D≠∅ as -1∉D such that -1=-5+4.

x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)

0 and 5 minutes

step-by-step explanation:

given that one morning eight buses arrive late by the number of minutes given below:

0 8 2 6 9 2 0 7 8

write these in ascending order

0   0 2 6 7 8 8 9

in the afternoon two more buses arrive at the bus stop say by x and y minutes late.

total number of buses = 10

median = average of 4th and 5th after arranging in ascending order

since 4th entry is 6, the values of x and y should be below 6

also given 0 is the mode so either x or y or both should be 0 because then only 0 gets the maximum frequency and hence mode

thus we have

0 0 0 2 6 7 8 8 9 and another unknown entry which is below 6.

since median is 3.5, we have the unknown entry to be 5 only because then only median =( 2+5)/2

thus the after noon buses were late by 0 and 5 minutes.