4 cards are drawn from a well-shuffled deck of 52 cards. What is the probability of obtaining 3 diamonds and one spade?
Answers
The probability is 286 20825.
Final answer:
The probability of drawing three diamonds and one spade from a well-shuffled deck of 52 cards is about 0.0137 or 1.37%.
Explanation:
The subject of this question is the probability in a deck of 52 cards. In a deck, there are 13 cards for each suit: diamonds, spades, clubs, and hearts. In drawing 4 cards, we want to find out the likelihood of picking 3 diamonds and one spade. This type of question deals with combinatorics and probability rules.
First, let's compute the number of ways we can draw 3 diamonds from 13. This is done through a combination, denoted as C(13,3), which equals 286. Next, the number of ways to draw one spade from the 13 available is C(13,1), which equals 13. Therefore, the total favourable outcomes are 286 x 13 = 3718.
Second, let's compute the total number of outcomes which is C(52,4) = 270,725. Therefore, the probability of obtaining 3 diamonds and one spade is 3718/270725, which simplifies to approximately 0.0137 or 1.37% when expressed as a percentage.
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Answers
Answer:
The general formula for nth term of given sequence is:
Step-by-step explanation:
Given sequence is:
54,18,6.....
In order to write the general formula of a sequence, first of all the common ratio has to be found. Common ratio is the ratio between consecutive terms of a geometric sequence.
The general formula is:
Putting the values of a1 and r
Hence,
The general formula for nth term of given sequence is:
Answers
First, let's make sure you know what Pythagoras said.
It's very important, mainly because it's so useful:
In any RIGHT triangle, the square of the longest side
is the sum of the squares of the other two sides.
Now let's look at #30:
This is two right triangles back-to-back.
'x' is the longest side of the one on the left, but we can't
solve for 'x' yet because we only know one of the other sides.
But look at the right triangle on the right side. We know the
longest side, and the vertical one, so we can find the base of it.
(longest side)² = (one short side)² + (the other short side)²
(15)² = (9)² + (the base)²
Subtract (9)² from each side:
(The base)² = (15)² - (9)²
(The base)² = 225 - 81 = 144
The base = √144 = 12 .
Do you see where we are now ?
The base of the right half is 12,
so the base of the left half is (25 - 12) = 13 .
Pythagoras again, on the left half:
x² = (13)² + (9)²
x² = 169 + 81 = 250
x = √250 = (√25)·(√10) = 5 √10 .
________________________________
#31:
Again, two right triangles back to back.
You know two sides in each one.
So you can find the base of each one, then add the bases to get 'x'.
Left half: (Base)² = (10)² - (6)²
(Base)² = 100 - 36 = 64
Base = √64 <== you know what that is
Right half: (Base)² = (7)² - (6)²
(Base)² = 49 - 36 = 13
Base = √13
x = sum of the two bases = √64 + √13 .
_________________________________
#32:
Two right triangles again.
Not back to back.
Right half: (Missing leg)² = (7)² - (2)²
(Missing leg)² = 49 - 4 = 45
Missing leg = √45 = (√9)·(√5) = 3 √5 .
Left half: The longest side is 3√5 .
x² + (5)² = (3√5)²
I'm sure you got the idea by now.
Answers
to get 3..
Answer:
3
Step-by-step explanation:
Since D=8, you input it in
5(8)-25/5=
5(8)=40
40-25= 15
15 divided by 5 is 3
Answers
Answer:
9.12 + 9.12 = 18.24 inches
Step-by-step explanation:
Diameter = 23 inches (given)
Radius = 11.5 inches
2 Chords of length = 14 inches ( You didn't specify if the 14 inches is for both chords or for a single cord. I'll assume it's for two cords 14 and 14inches apart.
To clearly solve this, we'll make some mild assumptions.
Let the perpendicular distance of the chords from the center of the circle to represented as " x and y"
Therefore:
x^2 + 7^2 = 11.5 ^ 2
x^2 + 49 = 132.25
x^2 = 132.25 - 49
x^2 = 83.25
x = √ 83.25
x = 9.12 inches
Since the cords have thesame length (Assumed from the way the question was structured, the distance would still be thesame)
y^2 + 7^2 = 11.5 ^ 2
y^2 + 49 = 132.25
y^2 = 132.25 - 49
y^2 = 83.25
y = √ 83.25
y = 9.12 inches
Therefore, the distance will be :
9.12 + 9.12 = 18.24 inches
Have fun!
Final answer:
To find the distance from each chord to the center of the circle, use the Pythagorean theorem to calculate the height of the isosceles triangle formed by the chord and two radii.
Explanation:
To find the distance from each chord to the center of the circle, we first need to find the radius of the circle. Since the diameter is given as 23 inches, the radius would be half of that, which is 11.5 inches. Now, let's consider one of the chords. When a chord is drawn in a circle, it forms an isosceles triangle with the center and two radii. The distance from the chord to the center of the circle is the height of this isosceles triangle. Using the Pythagorean theorem, we can find the height:
d² = r² - (c/2)²
where d is the distance from the chord to the center, r is the radius, and c is the length of the chord.
Plugging in the values, we get:
d² = (11.5)² - (14/2)²
Simplifying this equation gives:
d² = 132.25 - 49
d² = 83.25
Taking the square root of both sides gives:
d ≈ √83.25 ≈ 9.12 inches
Learn more about Finding distances in a circle here:
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Answers
what we do is we know that when height is 10, V=something, so solve for the diameter is at that point and compare it to 24, the full height
sorry if confusing
V=(1/3)hpir^2
when h=10
160pi/3=1/3(10)pir^2
ties 3 both sides
160pi=10pir^2
divide by 10pi
16=r^2
sqrt both sides
r=4
at that point, the radius is 4
the real radius of the ful is 24/2=12
4/12=1/3
it is 1/3 full
if 1/3=160pi/3cm
2/3=320pi/3cm^3
needs 320pi/3 cm^3
Answers
Answer:
The movie was 1 hour and 35 minutes long. (Or 95 minutes long)
Step-by-step explanation:
Well let's see:
It will take 15 minutes from the start to reach 5:00 PM
4:45+0:15=5:00
Now it will be 1 hour and 20 minutes from 5:00 PM to reach the end time of the movie.
Adding the minutes and hours together:
1 hour + 20 minutes + 15 minutes = 1 hour and 35 minutes
Answer:
1:35
Step-by-step explanation:
4:45 is where you start. If you go an hour at would be 5:45. Then count to 6:20. if it's tough go to a silent place and try not to think of anything else just of what your counting to. Hope this helps!