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Reil [10]
2 years ago
14

A standard deck of has 52 cards, and contains 13 cards of each of the four suits: diamonds, spades, hearts, and clubs. What is t

he probability that you choose a spade, given that you have already chosen a diamond (and have not replaced it)?
Mathematics
1 answer:
Verizon [17]2 years ago
7 0

Answer: \frac{13}{51}

Step-by-step explanation:

Given: Number of cards in a standard deck = 52

If we already chosen a diamond card, then the number of cards left in the deck =52-1=51

The number of spades remains same = 13

Now, the probability that you choose a spade, given that you have already chosen a diamond is given by :-

P(Spade|diamond)=\frac{13}{51}

Hence, the the probability that you choose a spade, given that you have already chosen a diamond =\frac{13}{51}

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3 years ago
PLEASE HELP 50 COINS!!!!
tankabanditka [31]

Answer:

Therefore,

AB=16.25\ units

The Measurement of AB is 16.25 units.

Step-by-step explanation:

In Right Angle Triangle ABC

m∠C=90°

AC = 10.01    .....(Adjacent Side to angle A)

m∠A=52°

cos 52 ≈ 0.616

To Find:

AB = ? (Hypotenuse)

Solution:

In Right Angle Triangle ABC, Cosine Identity,

\cos A= \dfrac{\textrm{side adjacent to angle A}}{Hypotenuse}\\

Substituting the values we get

\cos 52= \dfrac{AC}{AB}=\dfrac{10.01}{AB}

But cos 52 ≈ 0.616 ....Given

AB=\dfrac{10.01}{0.616}=16.25\ units

Therefore,

AB=16.25\ units

The Measurement of AB is 16.25 units.

5 0
3 years ago
Consider the following equations. f(x) = − 4/ x3, y = 0, x = −2, x = −1. Sketch the region bounded by the graphs of the equation
Sindrei [870]

Answer:

1.5 unit^2

Step-by-step explanation:

Solution:-

- A graphing utility was used to plot the following equations:

                         f ( x ) = - \frac{4}{x^3}\\\\y = 0 , x = -1 , x = -2

- The plot is given in the document attached.

- We are to determine the area bounded by the above function f ( x ) subjected boundary equations ( y = 0 , x = -1 , x = - 2 ).

- We will utilize the double integral formulations to determine the area bounded by f ( x ) and boundary equations.

We will first perform integration in the y-direction ( dy ) which has a lower bounded of ( a = y = 0 ) and an upper bound of the function ( b = f ( x ) ) itself. Next we will proceed by integrating with respect to ( dx ) with lower limit defined by the boundary equation ( c = x = -2 ) and upper bound ( d = x = - 1 ).

The double integration formulation can be written as:

                           A= \int\limits_c^d \int\limits_a^b {} \, dy.dx \\\\A = \int\limits_c^d { - \frac{4}{x^3} } . dx\\\\A = \frac{2}{x^2} |\limits_-_2^-^1\\\\A = \frac{2}{1} - \frac{2}{4} \\\\A = \frac{3}{2} unit^2

Answer: 1.5 unit^2 is the amount of area bounded by the given curve f ( x ) and the boundary equations.

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