A bag of popcorn contains 945 calories and serves 7.5 people. How many calories are in each serving?

(1.1.8 in the book) Let P be the proposition ’I bought a lottery ticket this weekend’ and Q be the proposition ’I won the millio

Karolina [17]

Answer:

~ is for negation

^ is for "and"

v is for "or"

=> for "if then"

<=> for "if and only if"

Step-by-step explanation:

(a) ~P (negation of P)

I didn't buy a lottery ticket this weekend.

(b) P v Q (P is in disjunction Q)

I have either bought a lottery ticket this weekend or won the million dollar jackpot.

(c) P => Q (Q is a consequence of P)

I won the million dollar jackpot because I bought a lottery ticket this weekend.

(d) P ^ Q (P is in conjunction with Q)

I bought a lottery ticket this weekend, and I won the million dollar jackpot.

(e) P <=> Q (P and Q are dependent on each other)

If only I had bought a lottery ticket this weekend, I would have won the million dollar jackpot.

(f) ~P => ~Q (negation of Q is a consequence of negation of P)

I didn't win the million dollar jackpot because I didn't buy a lottery ticket this weekend.

(g) ~P ^ ~Q (negation of P is in conjunction with negation of Q)

I neither bought a lottery ticket this weekend nor won the million dollar jackpot.

(h) ~P v (P ^ Q)

This is logically equivalent to (~P v P) ^ (~P v Q) (negation of P is in disjunction with P, and also with disjunction with Q), and can be best expressed as:

It didn't matter that I bought a jackpot ticket or not, I won the million dollar jackpot.

8 0

3 years ago

The regular price of a video game is $19.50 The store is having a 40% off sale.

Afina-wow [57]

A. The discount is 7.80 much

B. $11.7

7 0

3 years ago

I am having trouble with this problem. I need to find the lengths of this right triangle. How would you do this?

podryga [215]

You labeled the triangle wrong sides 'a' and 'b' are supposed to be the sides that make the right angle. the other side is called the hypotenuse which is the longest side which you should have labeled 'c'

so Pythagorean theorem says
a^2+b^2=c^2
so
(2x+1)^2+(11x+5)^2=(12x+1)^2
distribute
(4x^2+4x+1)+(121x^2+110x+25)=(144x^2+24x+1)
add like terms
125x^2+114x+26=144x^2+24x+1
subtract 125x^2 from both sides
114x+26=19x^2+24x+1
subtract 114x from both sides
26=19x^2-90x+1
subtract 26 from both sides
0=19x^2-90-25
factor
(x-5)(19x+5)=0
therefor x-5=0 and/or 19x+5=0
so
x-5=0 add 5 to both sides
x=5
19x+5=0
subtract 5 from both sides
19x=-5
divide both sides by 19
x=-5/19
since side legnths can't be negative, we can cross this solution out

so x=5
subtitute
1+2x
1+2(5)
1+10=11
side a=11

11x+5
11(5)+5
55+5=60
side b=60

12x+1
12(5)+1
60+1=60
side c=61
add them all up
side a+b+c=11+60+61=132=total legnth

5 0

2 years ago

Which of the following values when placed in the ten's place for the number 1_1 will make it a prime number?

Sloan [31]

The answer is 181.

Ans: 8

6 0

3 years ago

Read 2 more answers

A room with poor air quality has a particle concentration of 80 units. A fan removes 50% of the remaining particles each hour.

Eddi Din [679]

Answer:

20 units

Step-by-step explanation:

Initial particle concentration = 80 units

Particles removed each hour = 50% of the remaining particles

To find:

Particle concentration after 2 hours = ?

Solution:

Particles removed in 1 hour = 50% of remaining particles

i.e. Particles removed in 1 hour = 50% of initial concentration

Particles removed in 1 hour = 50% of 80 = 40

Particles removed in next 1 hour = 50% of remaining particles

i.e. Particles removed in next 1 hour = 50% of concentration after 1 hour

Particles removed in next 1 hour = 50% of 40 = 20

Total particles concentration removed in 2 hours = 40 + 20 = 60 units

Therefore, particle concentration after 2 hours = Initial concentration - Total particle concentration removed in 2 hours

= 80 - 60 = <em>20 units</em>

8 0

3 years ago