how did world war 2 influence colonies to seek independence in 1 to two sentences
World War 2 had a major impact on colonies seeking independence, as it weakened the power of the colonial powers and allowed for the rise of nationalist movements that sought to end colonial rule.
The volume of a rectangular prism is given by V = lwh, where l, w, and h are the length, width, and height of the prism. Here, V = 27 inches cubed.
If the base and height of the rectangular pyramid are congruent to the prism, then the volume of the pyramid is given by V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. Since the base of the pyramid is congruent to the prism, its area is also the same as the base of the prism, which is lw.
Thus, we can write:
B = lw
h = w (since the base and height of the pyramid are congruent)
Substituting these values into the formula for the volume of the pyramid, we get:
V = (1/3)Bh = (1/3)(lw)(w) = (1/3)l(w^2)
Since we know that V = 27 inches cubed, we can solve for l:
27 = lwh
27 = l(w^2)
l = 27/w^2
Substituting this value of l into the formula for the volume of the pyramid, we get:
V = (1/3)l(w^2) = (1/3)(27/w^2)(w^2) = 9 inches cubed
Therefore, the volume of the rectangular pyramid is 9 inches cubed.
A rectangular prism has a volume of 27 inches cubed. If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?
A rectangular pyramid has a volume of 480 inches cubed. If a rectangular prism has a base and height congruent to the pyramid, what is the volume of the prism?
Let's start with the formula for the volume of a rectangular pyramid: V = (1/3)Bh, where V is the volume, B is the area of the base, and h is the height of the pyramid. We know that the volume of the pyramid is 480 inches cubed. Additionally, if the base and height of the rectangular pyramid are congruent, then the base of the pyramid is a square. Let's call the side length of the square base "s".
The area of a square is given by A = s^2, so the volume of the pyramid can also be expressed as V = (1/3)(s^2)(h).
We need to find the volume of the rectangular prism with a base and height congruent to the pyramid. Since the base is a square with side length "s", the length, width, and height of the prism are all "s". We can express the volume of the prism as V = lwh = (s)(s)(s) = s^3.
We know the volume of the pyramid is 480 inches cubed, so we can set the two equations for volume equal to each other:
(1/3)(s^2)(h) = 480
We don't know the height of the pyramid, but we do know that the base and height are congruent, so h = s. Substituting this into the equation above:
(1/3)(s^2)(s) = 480
Multiplying both sides by 3:
s^3 = 1440
Taking the cube root of both sides:
s = 12
Now we know that the side length of the base of the prism is 12. The volume of the prism is V = s^3 = 12^3 = 1728 inches cubed.
Each letter of the word movers is written on an individual paper strip and placed in a box. Which set represents the favorable outcomes of the event of randomly choosing a consonant letter?(1 point)
Responses
{o, e}
{o, e}
{m, o, v, e, r, s}
{m, o, v, e, r, s}
{v, r, s}
{v, r, s}
{m, v, r, s}
{m, v, r, s} represents the favorable outcomes of the event of randomly choosing a consonant letter.
On a science quiz, David got 45 out of 70 items correct. What is the empirical probability of his incorrect responses? Write your answer in the simplest form of a fraction.
David got 45 items correct, so the number of incorrect responses is:
Total number of items - Number of correct items = 70 - 45 = 25
Therefore, the empirical probability of his incorrect responses is:
Number of incorrect responses / Total number of responses = 25 / 70
Simplifying this fraction by dividing both numerator and denominator by 5, we get:
25 / 70 = 5 / 14
So the empirical probability of his incorrect responses is 5/14.
A calculator manufacturing company checks 500 calculator units, and 25 of them have non-functioning keys. Approximate the relative frequency of a non-defective unit from this batch of items. Express your answer in the simplest form of a fraction.(1 point)
Responses
120
Start Fraction 1 over 20 End Fraction
25500
Start Fraction 25 over 500 End Fraction
1920
Start Fraction 19 over 20 End Fraction
475500