During the month of July, we only had 0.1573 inches of rain. What is this, rounded to the nearest thousandth? O 0.2 O 0.158 0.157 inches 0.16

The answer would be 0.157 Explanation: the 7 is in the thousandth place, the 7 would not round up to 8 because the number after the seven is 3. The number 3 is too small to round up a number, therefore 7 stays the same.

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

Where U = {x | x is a negative real number}.

Step-by-step explanation:

Given U = {x | x is a negative real number}.

This set can be written as

U = {-1, -2, -3, ..., -1000, ...}

Let us consider the options to see which one is an empty set.

(1) x has a negative cube root.

This is correct, as the cube root of any number in the set gives a negative value.

(-1)³ = -1 × -1 × -1 = -1

(-2)³ = -2 × -2 × -2 = -8

(-10)³ = -10 × -10 × -10 = -1000

and so on.

So, x ∈ {-1, -2, ..., -10, ...}

This is not an empty set, it is not the correct option.

(2) x has a negative square root.

This is incorrect, as the square root of any number in that set gives a positive value.

(-1)² = -1 × -1 = 1

(-2)² = -2 × -2 = 4

(-9)² = -9 × -9 = 81

and so on. This is the correct option as {x | x ∈ U and x has a negative square root} is an empty set.

(3) x is the product of one positive number and -1.

This is correct.

-1 = 1 × -1

-5 = 5 × -1

-15 = 15 × -1

and so on.

So, x ∈ {-1, -2, ..., -15, ...}This is not an empty set, it is not the correct option.

(4) x is the sum of one negative number and a positive number.

This is correct as

-1 = -2 + 1

-4 = -13 + 9

-50 = -55 + 5

and so on.

So, x ∈ {-1, -2, ..., -50, ...}This is not an empty set, it is not the correct option.