If you take all the possible 5 card draws, and multiply that by the probability all 5 cards are hearts, the result is all the possible 5 heart draws.
The number of ways to draw 5 cards from 52 is a combination...52C5. Remember the formula for combinations:
nCk = n! / (k! * (n-k)!. In this case n=52 and k=5:
52!/(5!*(52-5)!)= 52!/(5!*47!) = (52*51*50*49*48)/(5*4*3*2*1) = 2,598,960.
That's the total number of five-card combinations. But what is the probability that all five cards are hearts? There are 13 hearts in the deck of 52 cards.
P card 1 being a heart is 13/52.
<span>P card 2 being a heart (there are one less card and one less heart) is 12/51
</span>
<span>P card 3: 11/50
P card 4: 10/49
P card 5: 9/48
</span>
The probability of all five events is the product of their probabilities:
13/52 * 12/51 * 11/50 * 10/49 * 9/48 = 0.000495198079231693.
The number of combinations of five cards, times the probability of all five hearts, gives us the answer we want.
0.000495198079231693*2,598,960=1,287.
Answer: The answer would be the first choice.
Step-by-step explanation:
Remember that a function is where every INPUT has exactly ONE OUTPUT. That means for the coordinates (x, y), no pair could have an x value repeat. So, the first ordered row pair does not have any repeating x values, so it's the first answer.
Answer:
a) 3/4
b) 3/4
c) 3/4
d) all are 3/4
Step-by-step explanation:
The slope of a line is defined as the change in y divided by the change in x. This is often referred to as "rise over run":
slope = Δy/Δx = "rise"/"run"
The triangles are drawn against the line so that you can use them to identify values of "rise" (vertical change) and "run" (horizontal change) between two points on the line.
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<h3>a)</h3>
The slope of the segment AC is found by dividing the "rise" (BC = 3) by the "run"(AB = 4)
slope of AC = BC/AB = 3/4
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<h3>b) </h3>
The slope of FH is similarly computed. Here, it is made a little more difficult, because you must estimate the value of GH.
slope of FH = GH/FG = 1.5/2 = 0.75 = 3/4
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<h3>c) </h3>
The slope of CE is ...
slope of CE = DE/CD = 6/8 = 3/4
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<h3>d)</h3>
The slopes in a), b), c) are all 3/4.
You can reasonably draw the conclusion that the slope of a line is the same everywhere. A line has constant slope.
Answer:
C, D, B, A
Step-by-step explanation:
The greater the angle the tangent line makes with the positive x-axis, the greater the slope. Angles increase in the counterclockwise direction, so the question here is equivalent to asking for the tangent lines to be put in clockwise (decreasing slope) order.
That order is C, D, B, A.
