1. Use the laws of logic to show that ∀x(P(x) ∧ Q(x)) implies that ∀x Q(x) ∧ ∀x P(x).
2. Which of the following arguments are valid? Explain.
A. I have a student in my class who is getting an A. Therefore, John,
a student in my class is getting an A.
B. Every girl scouts who sells at least 50 boxes of cookies will get
a prize. Suzy, a girl scout, got a prize. Therefore Suzy sold 50 boxes
of cookies.

answer: no, but if it does it's a obvious pattern.

step-by-step explanation:

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4

in total they made   333.74 your welcome : d

mariah is studying the life cycle of the monarch butterfly. she must choose one stage in the cycle to present in science class: egg, caterpillar, chrysalis, or adult. she plans to make her choice randomly using a custom spinner divided into four sections. first, however, she spins the spinner 50 times to see the frequencies it generates.

stage times landed on

egg 10

caterpillar 12

chrysalis 15

adult 13

step-by-step explanation: