Answer:
7 worms
Step-by-step explanation:
Let each can have x worms, so we can say
Luis has 4x worms
Diego has 3x + 2 worms
Cecil has 2x worms
Since, in total they have 65 worms, we can write and equation and solve:
4x + 3x + 2 + 2x = 65
9x + 2 = 65
9x = 63
x = 63/9
x = 7
There are 7 worms in each can.
The answer is: 3.91 inches .
___________________________________________
Note: Volume of cylinder: V = (base area) * (height);
in which: V = volume = 384 in.³ ;
h = height = 8 in. ;
Base area = area of the base (that is; "circle") = π r² ;
in which; "r" = radius;
___________________________________________
Solve for "r" :
___________________________________________
V = π r² * (8 in.) ;
384 in.³ = (8 in.) * (π r²) ;
___________________________________________
Divide EACH SIDE of the equation by "8" ;
___________________________________________
(384 in.³) / 8 = [ (8 in.) * (π r²) in.] / 8 ;
___________________________________________
to get:
___________________________________________
48 in.³ = (π r²) in.² * in. ;
___________________________________________
↔ (π r²) in.² * in. = 48 in.³ ;
___________________________________________
Rewrite this equation; using "3.14" as an approximation for: π ;
__________________________________________________
(3.14 * r²) in.² * in. = 48 in.³
_______________________________________
Divide EACH SIDE of the equation by:
"[(3.14)*(in.²)*(in.)]" ; to isolate "r² " on one side of the equation;
(since we want to solve for "r") ;
_____________________________________________________
→ [(3.14 * r²) in.² * in.] / [(3.14)*(in.²)*(in.)] = 48 in.³ / [(3.14)*(in.²)*(in.)] ;
__________________________________________________
→ to get: r² = 48/3.14 ;
________________________
→ r² = 15.2866242038216561 ;
_______________________________________
To solve for "r" (the radius; take the "positive square root" of EACH side of the equation:
__________________________________________________
→ +√(r²) = +√(15.2866242038216561)
__________________________________________________
→ r = 3.9098112747064475286 ; round to 3.91 inches .
___________________________________________________
Answer: the speed of the boat on the lake is 9 mph
Step-by-step explanation:
Let x represent the speed of the boat on the lake or in still water.
The speed of the current in a river is 6 mph. This means that if the boat goes upstream against the speed of the current, its total speed would be (x - 6)mph. If the boat goes downstream against the speed of the current, its total speed would be (x + 6)mph.
Time = distance/ speed
Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. This means that the time taken to travel upstream is
22.5/(x - 6). The time taken to travel downstream is
22.5/(x + 6)
Since the total time is 9 hours, it means that
22.5/(x - 6) = 22.5/(x + 6)
Cross multiplying, it becomes
22.5(x + 6) + 22.5(x - 6) = 9
Multiplying through by (x + 6)(x - 6), it becomes
22.5(x - 6) + 22.5(x + 6) = 9[(x + 6)(x - 6)]
22.5x - 135 + 22.5x + 135 = 9(x² - 6x + 6x - 36)
22.5x + 22.5x = 9x² - 324
9x² - 45x - 324 = 0
Dividing through by 9, it becomes
x² - 5x - 36 = 0
x² + 4x - 9x - 36 = 0
x(x + 4) - 9(x + 4) = 0
x - 9 = 0 or x + 4 = 0
x = 9 or x = - 4
Since the speed cannot be negative, then x = 9
Answer: 9 essay questions
Step-by-step explanation:
The test has 26 questions
The test is worth 123 points
The test has two types of questions:
Multiple choice worth 3 points each
Essays worth 8 points each
Let the number of multiple choice questions be, m, and the number of essay questions be , e.
This forms a simultaneous equation below:
m + e = 26 ... (i)
3m + 8e = 123 ... (ii)
Multiplying (i) by 3 and (ii) by 1 we get:
3m + 3e = 78 ... (i)
3m + 8e = 123 ... (ii)
Subtracting (ii) - (i) we get;
0m + 5e = 45
5e = 45
e = 45 ÷ 5 = 9
So there are 9 essay questions.
and;
m + 9 = 26
m = 26 - 9 = 17
There are also 17 multiple choice questions.
