Answer:
See below
Step-by-step explanation:
Remember the notation and rules of quantifiers. ∀ is the universal quantifier and ∃ is the existential quantifier. To negate ∀x p(x) , write ∃x ¬p(x). To negate ∃x p(x) , write ∀x ¬p(x)
Part I:
A) None of life's problems have a simple solution.
B) All of life's problems have a simple solution.
C) Some of life's problems have a simple solution
D) All of life's problems have a simple solution (notice how the original statements in B and D mean exactly the same)
E) Some of life's problems do not have a simple solution.
Part II: Let x be a variable representing one of life's problems, y be a variable representing solutions, p(x):="x has a simple solution", and q(x,y):="y is a simple solution of x".
A) (∀x)(¬p(x)) or ¬(∃x)(p(x))
B) (∀x)(∃y)(q(x,y))
C) (∃y)(∀x)(q(x,y)). Note that the order of quantifiers is important. B) and C) have different meanings. In C) there is an universal solution of all problems, in B) each problem has its solution.
D) (∀x)(p(x))
E) Same as C)
Each would get 0.8 of a bag of popcorn (80%)
Answer: Fanuela walked 2.808 miles.
Step-by-step explanation:
If 3.9 = 100 and we need to work out what 72 is we can do this/
3.9 ÷ 10 = 0.39 which = 10
0.39 ÷ 10 = 0.039 which = 1
so with these calculations we can solve the problem.
To get the 70 in 72 we can do 0.39 x 7 (10 x 7) which = 2.73.
To get the remaining 2 in 72 we can do 0.039 x 2 (1 x 2) which = 0.078.
2.73 + 0.078 = 2.808.
Fanuela walked 2.808 miles.
Hope this helps! Feel free to ask any questions if you're still unsure.
Answer: (-0.61, 5.85) and (-2.72, 3.04)
<u>Step-by-step explanation:</u>
y = 2x² + 8x + 10
y = -x² - 2x + 5
Use substitution method to get: 2x² + 8x + 10 = -x² - 2x + 5
Move everything to one side and 0 on the other: 3x² + 10x + 5 = 0
Use the quadratic formula to solve for x: 
x₁ = -0.61 x₂ = -2.72
Next, input the x-values to solve for y:
y₁ = -x² - 2x + 5 y₂ = -x² - 2x + 5
= -(-0.61)² - 2(-0.61) + 5 = -(-2.72)² - 2(-2.72) + 5
= -0.37 + 1.22 + 5 = -7.40 + 5.44 + 5
= 5.85 = 3.04
Answer:
27
Step-by-step explanation:
15 + 12 = 27
Allie would have read 27 books in total after being in the book club for 12 months.
