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3 years ago

Use the theoretical probability formula to solve the problem. Express the probability as a fraction

Mathematics

1 answer:

serg [7]3 years ago

4 0

Answer:

c. 3 / 13

d. 2 / 13

Step-by-step explanation:

A deck of cards has 52 cards. There are cards of 4 suits- Spades, Hearts, Diamonds and Clubs.

So, there are 52/4= 13 cards of each suit.

Among these 13 cards, there are 3 picture cards or face cards as they are called. These are the Jack, Queen and King cards.

So, the number of total picture cards = 4*3 = 12

the number of cards are 52

theoretical probability formula: P = favorable events/ possible events

P = 12 / 52

P = 3 / 13

there are four aces and four sevens in the deck

so favorable events = 4 + 4 = 8

possible eventas = 52

P = 8 / 52

P = 2 / 13

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3 years ago

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Option A: $(x+3)^2+(y+2)^2=4$ is the equation of the circle

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Let us subtract 10 from both sides of the equation.

Thus, we have,

$x^{2} +y^2+6x+4y=-9$

Grouping the terms,we have,

$(x^{2} +6x)+(y^2+4y)=-9$

Now, we shall complete the square, let us add and subtract the equation by 9 to write the term $\left(x^{2}+6 x\right)$ in the form of $(a+b)^2$

Thus, we have,

$(x^{2} +6x+9-9)+(y^2+4y)=-9$

Simplifying, we get,

$(x^{2} +6x+9)+(y^2+4y)=-9+9$

$(x+3)^2+(y^2+4y)=0$

Similarly, we shall complete the square for the term $\left(y^{2}+4 y\right)$ in the form of $(a+b)^2$

Thus, we have,

$(x+3)^2+(y^2+4y+4-4)=0$

Simplifying, we get,

$(x+3)^2+(y^2+4y+4)=4$

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Thus, the equation of the circle in standard form is $(x+3)^2+(y+2)^2=4$

Hence, Option A is the correct answer.

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