Answer:
The width of the prism is 2 cm
Step-by-step explanation:
The given parameters are;
The volume of the prism = 170 cm³
The length of the prism = 5 cm
The height of the prism = 17 cm
The volume of the prism is given by the relationship v = Length, l × Height, h × Width, w
Therefore;
The volume of the prism = 5 cm × 17 cm × w = 170 cm³
Which gives;
w = 170 cm³/(5 cm × 17 cm) = 170 cm³/(85 cm) = 2 cm
∴ The width of the prism = 2 cm.
Answer:
808
Step-by-step explanation:
The volume of the initial cylindrical metal must be equal to the total volume of the cubes.
Let the number of cubes made be x. Therefore:
where 
volume of the cylinder
volume of each cube
Each of the cubes have sides of length 3 cm.
The volume of a cube is given as:
where L = length of side of cube
Therefore, the volume of each cube is:
The volume of a cylinder is given as:
where r = radius
h = height of the cylinder
The volume of the cylinder is:
Therefore:
21823.55 = 27 * x
=> x = 21823.55 / 27
x = 808.27
Since the number of cubes can only be a whole number, the number of cubes that will be made is 808.
With the sum of 99, we will get 50 pairs whole numbers. Why?
Let’s start with
0+ 99
1 + 98
2 + 97
3 + 96
4 + 95
5 + 94
6 + 93
7 + 92
8 + 91
9 + 90
10 + 89
………
……..
43 + 49
44 + 50
Therefore, if you’re going to count all pairs of whole number, you will get 50 pairs of whole number with the sum of 99.
Hope this helps!
Answer: player A = 11/16 and player B = 5/16
Step-by-step explanation:
If a coin was to be tossed to determine the winner possible outcomes using arithmetical triangle.
Player A needs 2 points = 11
Player B needs 3 points = 5
Total outcome of tossing a coin = 16
Player A = 11/16 = 0.6875
Player B = 5/16 = 0. 3125
Or
Using the fifth roll of the pascal triangle (2+3) outcome
( 1, 4, 6, 4, 1 )
Addition of the first 3 represent Player A chances of winning = ( 1+ 4 + 6 ) = 11
And the last two = ( 1 + 4 ) = 5 represents the chances of team B winning
Total number of outcome = ( 1 + 4 + 6 + 4 + 1 ) = 16
Answer:
Correct option: first one -> all real values of x where x < −1
Step-by-step explanation:
First we need to find the roots of the function f(x):
0 = (x - 3)(x + 1)
(x - 3) = 0 -> x = 3
(x + 1) = 0 -> x = -1
The roots of the function are x = 3 and x = -1.
The vertex is between the roots (x = 1) and has a negative value of y (y = -4), so the concavity of the parabola is upwards.
So the graph is decreasing until it reaches the vertex, then the graph is increasing.
Then, we can affirm that the graph is positive and decreasing for all real values of x where x < -1 (for x > -1 and x < 3 we have negative values)
Correct option: first one
