Answer: There are 198 different combinations.
Step-by-step explanation:
To solve this type of problem, first, we need to identify the selections.
We have 3 selections.
Baby doll, Jigsaw puzzle, and a stuffed dog.
Now, we need to count the numbers of options for each case:
Baby doll: 11 options.
Jigsaw Puzzle: 6 options.
Stuffed dog: 3 options.
To find the total number of different combinations, we need to multiply all the numbers of options together, this is:
Combinations = 11*6*3 = 198
There are 198 different combinations.
Area of triangle = base x height /2
48 = (a+14)a/2
a^2 +14a = 96
a^2 + 14a - 96 = 0
Solving for a = 5.04
Answer:
y = 4
Step-by-step explanation:
The maximum value occurs at the vertex
vertex = (2, 4 )
when x = 2 the maximum value is y = 4
Answer:
x = 500 yd
y = 250 yd
A(max) = 125000 yd²
Step-by-step explanation:
Let´s call x the side parallel to the stream ( only one side to be fenced )
y the other side of the rectangular area
Then the perimeter of the rectangle is p = 2*x + 2* y ( but only 1 x will be fenced)
p = x + 2*y
1000 = x + 2 * y ⇒ y = (1000 - x )/ 2
And A(r) = x * y
Are as fuction of x
A(x) = x * ( 1000 - x ) / 2
A(x) = 1000*x / 2 - x² / 2
A´(x) = 500 - 2*x/2
A´(x) = 0 500 - x = 0
x = 500 yd
To find out if this value will bring function A to a maximum value we get the second derivative
C´´(x) = -1 C´´(x) < 0 then efectevly we got a maximum at x = 500
The side y = ( 1000 - x ) / 2
y = 500/ 2
y = 250 yd
A(max) = 250 * 500
A(max) = 125000 yd²
Speed = distance / time
speed = 135/3 = 45 miles per hr <==
