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o-na [289]
3 years ago
6

Christy draws 3 cards from the deck one at a time without replacement. What is the probability of selecting the cards in the ord

er: diamond, spade and diamond?
Mathematics
1 answer:
Inga [223]3 years ago
5 0
Start with a deck of 52 cards. Draw 1 card. Probability of drawing a diamond first:

\dfrac{\binom{13}1}{\binom{52}1}

Now draw another single card from the deck, which now contains 51 cards. Probability of drawing a spade:

\dfrac{\binom{13}1}{\binom{51}1}

Draw 1 last card. The deck has 50 cards left, and 12 of these are diamonds. Probability of drawing a diamond:

\dfrac{\binom{12}1}{\binom{50}1}

So the probability of drawing a diamond, then a spade, then another diamond is

\dfrac{\binom{13}1}{\binom{52}1}\cdot\dfrac{\binom{13}1}{\binom{51}1}\cdot\dfrac{\binom{12}1}{\binom{50}1}=\dfrac{13}{850}
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Which composition of transformations below will map figure K onto figure S and then onto figure U?
Elina [12.6K]
"Rotation and reflection" are the composition of transformations among the following choices given in the question that <span>will map figure K onto figure S and then onto figure U. The correct option among all the options that are given in the question is the second option or option "B". I hope that the answer has helped you. </span>
5 0
4 years ago
Read 2 more answers
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4,
zheka24 [161]
Answer: C ) y + 3 = 1/4 ( x + 4 )

Explanation:

Given that you did not include the "given line", I can help you by explaning how to solve this kind of problems, step by step.

The procedure is based of the property of perpendicular lines: the product of the slopes of perpedicular lines is negative 1.

If you call m1, the slope of a line and m2 the slope of a perpendicular line, then:

m1 * m2 = - 1, and you can solve for either m1 or m2:

m1 = - (1 / m2)

m2 = - (1 / m1).

With that this is the procedure:

1) find the slope of the "given line". Name it m1.

2) find the slope of the perpendicular line:

    m2 = - (1 / m1).

3) Use the equation of the line with the point (x1,y1) and slope m2

y - y1
-------- = m2
x - x1

4) In this case the point is (-4, - 3)=> x1 = - 4, y1 = - 3

=>

y - (-3)
---------= m2
x - (-4)

=> y + 3 = m2 * (x + 4)

=> y = m2*x + m2 * 4 - 3

Which is the point-slope form. You only have to replace m2 with the slope value of the perpendicular line, which I already explained that you find as m2 = (-1/m1).

Taking that the other line has m1 = - 4 so m2 = 1/4

      y = (1/4)x + (1/4) * 4 - 3

      y = (1/4) (x +4) - 3

      y + 3 = (1/4) (x + 4) and answer is: C ) y + 3 = 1/4 ( x + 4 )



7 0
3 years ago
Read 2 more answers
The measure of Angle 2 is twelve less than five
hoa [83]

Answer: The measure of Angle 2 = 148°

Step-by-step explanation:

Given: The measure of Angle 2 is twelve less than five  times the measure of Angle 1.

Let the measure of Angle 1 = x

Then, measure of Angle 2 = 5x-12

Since both the angles form linear pair, so their sum = 180°  [linear pair of angles must add up to 180°.]

Then, x+ (5x-12) = 180

⇒ x+ 5x-12= 180

⇒ 6x-12= 180

⇒ 6x= 180+12

⇒ 6x= 192

⇒ x= 32  [divide both sides by 6 ]

So,  measure of Angle 2 = 5(32)-12 = 160-12 = 148°

Hence, the measure of Angle 2 = 148°

7 0
3 years ago
Let Ir = 17 at an angle of 40° and s = 14 at an angle of 160°. Which expression represents r + s|?
vladimir1956 [14]

Answer:

B. I got it right on the quiz

Step-by-step explanation:

6 0
3 years ago
One serving of a certain brand of yogurt contains 8 g of fat the local fat version control is 45.25% less fat per serving how ma
cluponka [151]

Answer:

3.62 grams

Step-by-step explanation:

Multiply  by .4525 to get the answer.

(For percentages you want to move the decimal to the very front. Ex. 2% = 0.02 and multiply by the number you have, in this case 8 grams.)

This should look like this: 0.4525*8=3.62

4 0
3 years ago
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