Answer:
89
Step-by-step explanation:
Given that,
During a promotional weekend, a state fair gives a free admission to every 179th person that enters the fair.
No of people attending the fair on Saturday is 8,633 amd No of people attending the fair on Sunday is 7,400.
We need to find the no of people that received a free admission over the two days.
Dividing 8,633 by 179 gives 48 as quotient and 41 as remainder. It means on Saturday 48 people entered for free.
Dividing 7,400 by 179 gives 41 as quotient and 61 as remainder. It means on Sunday 41 people entered for free.
Total no of people,
T = 48 + 41
T = 89
Hence, there are 89 people for free entries.
Answer: the cylindrical bottle contains 141.39 centimeters ^3 of water
Step-by-step explanation:
The bottle has the shape of a cylinder. This means the volume of the bottle will be calculated using the formula for calculating the volume of a cylinder. Formula for calculating the volume of a cylinder is
V = πr^2h
Radius, r = diameter of the cylindrical water bottle /2 = 4/2 = 2 centimeters
Height of cylindrical water bottle, h = 15 centimeters
Volume of cylindrical water bottle, V = 3.142 × 2^2 × 15
= 188.52 centimeters ^3
If he filled the water bottle 3/4 full of water, this means that the current volume of the water bottle is 3/4 × it's original volume.
= 3/4 × 188.52 = 141.39 centimeters ^3
X + y = 138
x - y = 88
--------------------------
x + y = 138
-x
y = -x + 138
--------------------------
-> substitute " -x + 138" into y
x- (-x+138) = 88
x + x - 138 = 88
2x - 138 = 88
+ 138
2x = 226
2x/2 = 226/2
x= 113
---------------------------
-> substitute "113" into x to get y
113 - y = 88
-113 -113
-y= -25
y = 25
---------------------------
Our final answers are the two numbers "113" and "25"
Note that the notation
is just another way of writing
. Here, we're simply taking the expression for f(x) and adding the expression for g(x) to it. Together, we have:
Which means that
And from there, it's just a matter of combining like terms to simplify.