Answer:
1 plain pizza costs $10.50 and 1 pepperoni pizza costs $12.50
Step-by-step explanation:
Jack: 3x+2y= 58.5
Jill: 2x+4y=67
a) Multiply both equations so that one of the coefficients (number before the letter) are equal:
6x+4y=117
6x+12y=201
b) We can now easily subtract them to get:
(subtracted 6x) 4y=117 12y=201 (12y-4y and 201-117 next) 8y=84
c) Now we can divide 84 by 8 to get y=10.5, so now we can substitute it into any of the equations:
2x+(4*10.5)=67 --> 2x+42=67 -(subtract 42 from both sides)-> 2x=25 -(divide both side by 2)-> x=12.5.
d) To check if it works: 2(12.5)+4(10.5)=67 25+42=67 so it's correct.
V = LWH
6400 = (4W) * W * 4
1600 = 4W^2
400 = W^2
W = 20
L = 4(20)
L = 80
W = 20 ft
L = 80 ft
Answer:
the probability that a real emergency situation exists is 0.16 (16%)
Step-by-step explanation:
defining the event A= the alarm sounds ,we have
P(A)= probability that an emergency situation exists * probability that the alarm sounds given that an emergency situation exists + probability that a emergency situation does not exist * probability that the alarm sounds given that an emergency situation does not exist = 0.004* 0.95+ 0.996 * 0.02 = 0.02372
then if we use the theorem of Bayes for conditional probability and define the event E= a emergency situation exists , then
P(E/A)= P(E∩A)/P(A)= 0.004* 0.95/0.02372 =0.16 (16%)
where
P(E∩A)= probability that an emergency situation exists and the alarm sounds
P(E/A) = probability that an emergency situation exists given that the alarm has sounded
Answer:
1. -3x^2 + 13x + 5
2. 10y^2 - 7
Step-by-step explanation:
1. (7 + 4x - 8x^2) - (2 - 9x - 5x^2)
Combine Like Terms —›
(7) - (2) = 5
(4x) - (-9x) —› (4x) + (9x) = 13x
(-8x^2) - (-5x^2) —› (-8x^2) + (5x^2) = -3x^2
-3x^2 + 13x + 5
2. (2y^2 + 5xy - 8) - (5xy -1 - 10y^20)
(2y^2) - (-10y^2) —› (2y^2) + (10y^2) = 10y^2
(5xy) - (5xy) = 0
(-8) - (-1) —› (-8) + 1 = -7
10y^2 - 7
Answer:
Step-by-step explanation:
Assuming your original equation is
by the logarithm property 
this equation becomes
This means
Take the natural logarithm of both sides and get:
By the same lograthim property , the left side is modified:
which gives
or
