Answer:
"13 / 204 ; No, they are dependent events
"
Step-by-step explanation:
The probability of getting a club at first throw is simply total number of clubs divided by total number of cards in the deck.
Total clubs is 13
Total cards in deck is 52
Hence, P(clubs) =
<em>Since the first card IS NOT replaced, the deck has now 51 cards. We want probability of diamond. There are still 13 diamonds, so probability of diamond now would be 13/51</em>
<em />
Hence, Probability that first card is a club and the second card is a diamond should be 13/52 MULTIPLIED by 13/51
P(1st Club, 2nd Diamond) =
<u></u>
<u>Note: </u>They are dependent events since we are calculating probability without replacement. The first draw affected the total number of cards in the 2nd draw.
2nd answer choice is right.
It is not correct.
The student found the volume by multiplying the base area with the height. He forgot to divide it by 3.
Formula to find the volume of the pyramid = 1/3 base area x height
volume = 1/3 x 92 x 54 = 1656 square meters
The answer is h = 5 m, w = 2 m
The volume of a rectangle is: V = w * l * h (w - width, l - length, h - height)
A rectangle is square based, so: w = l
V = w * w * h = w² * h
<span>The width of a square-based storage tank is 3m less than its height: w = h - 3
V = 20 m</span>³
w² * h = 20
(h - 3)² * h = 20
(h² - 2 * h * 3 + 3²) * h = 20
(h² - 6h + 9) * h = 20
h² * h - 6h * h + 9 * h = 20
h³ - 6h² + 9h = 20
h³ - 6h² + 9h - 20 = 0
h * h² - 5h² - h² + 5h + 4h - 4*5 =0
(h * h² - 5 * h²) - (h * h - 5h) + (4*h - 4*5) =0
h²(h - 5) - h(h - 5) + 4(h - 5) = 0
(h - 5)(h² - h + 4) = 0
We have that one solution is:
h - 5 = 0
h1 = 5
Other two solutions are:
h² - h + 4 = 0
Quadratic equation is: ax² + bx + c = 0
The only integer value is h1 = 5 m
h = 5 m
w = h - 3 = 5 - 3 = 2 m
A = r^2 * 3.14
A = 18^2 * 3.14
A = 324 * 3.14
A = 1017.36 squarefeet
A = 1017 Square feet