Answer:
Volume = ⅓n²(n-1) or ⅓(n³ - n²)
Step-by-step explanation:
Given
Solid Shape: Right pyramid
Edge= n units
Height= n - 1 units
Required
Volume of the pyramid
The volume of a right pyramid is
Volume = ⅓Ah
Where A represents the area of the base
h represent the height of the pyramid
Since it has a square base;
The area is calculated as follows
Area, A = edge * edge
A = n * n
A = n²
Recall that
Volume = ⅓Ah
Substitute n² for A and n - 1 for h
The expression becomes
Volume = ⅓ * n² * (n - 1)
Volume = ⅓n²(n-1)
The expression can be solved further by opening the bracket
Volume = ⅓(n³ - n²)
Answer:
p(win)=0.00094
Step-by-step explanation:
-This is a factorial/combination question.
-The probability is calculated using the formula:
Where:
is the number of successful picks
is the total number of picks
Therefore, we calculate the probability as follows;
Hence, the probability of winning is 0.00094
Answer:
Step-by-step explanation:
el
Answer:
12.7 feet
Step-by-step explanation:
To solve this question, we use the trigonometric function of Sine
sin θ = Opposite side/Hypotenuse
θ = 42°
Hypotenuse = 19 foot ladder
Opposite side = Distance of the cat from the ground(height of the tree)= unknown
sin 42° = Opposite/19 feet
Opposite = sin 42° × 19
Opposite = 12.713481521 feet
Approximately to the nearest tenth of a foot = 12.7 feet.
Therefore, the cat was 12.7 feet above the ground.
Answer:
0.5,0.25,0.125
Step-by-step explanation:
Given that a card is drawn from a regular deck of 52 cards and is then put back in the deck. A second card is drawn.
Since here we have the draws with replacement we can say each trial is independent of the other.
i.e. the first card does not affect the second card at all.
the probability that:
a) The first card is red.
=
(b) The second card is hearts given that the first is red.
=P(second is hearts)
= 0.25
(c) The first card is red and the second is hearts.
= 
(since independent)
