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4 months ago

If you select one card at random from a standard deck of 52 cards, what is the probability that the card is a king AND a spade?

Mathematics

1 answer:

ExtremeBDS [4]4 months ago

7 0

Given:

There are 52 cards.

So, n(s)=52

To find the probability that the card is a king and a spade:

Let A be an event of choosing a card that is king and a spade.

So, n(A)=1

Hence, the probability that the card is a king and a spade is,

$\frac{1}{52}$

You might be interested in

Which expression is equivalent to 4+2(1+3x)

Leviafan [203]

Answer:

I'm glad you asked!

Step-by-step explanation:

OK,let's simplify the number for a equivalent expression.

$4+2(1+3x)$

Distribute:

$=4+(2)(1)+(2)(3x)$

$= 4+2+6x$

Combine Like Terms:

$=4+2+6x$

$=(6x)+(4+2)$

$=6x+6$

The Final Answer is : $6x+6$

8 0

2 years ago

Which equation represents a line that passes through 4 6) and is parallel to the line whose equation is 3x - 4y= 6

Pachacha [2.7K]

Parallel means their slopes should equal to each other.

Thus we need to find the slope of the given line ,

Let's do it.....

$3x - 4y = 6$

Subtract sides -3x

$- 3x + 3x - 4y = - 3x + 6$

$- 4y = - 3x + 6$

Divided sides by -4

$\frac{ - 4}{ - 4}y = \frac{ - 3}{ - 4}x + \frac{6}{ - 4} \\$

$y = \frac{3}{4}x - \frac{3}{2} \\$

This is the slope-intercept of the line.

We know that the coefficient of the x in slope-intercept form , is the slope of the line.

Thus the slope of the equation which we want is :

$slope = \frac{3}{4} \\$

_________________________________

We have following equation to find the point-slope form of the linear functions.

$y - y(given \: point) = slope \times (x - x(g \: p) \: ) \\$

Now just need to put the slope and the given point in the above equation.

$y - 6 = \frac{3}{4} \times (x - 4) \\$

Multiply sides by 4

$4(y - 6) = 3(x - 4)$

$4y - 24 = 3x - 12$

Plus sides 24

$4y - 24 + 24 = 3x - 12 + 24$

$4y = 3x + 12$

Subtract sides -3x

$4y - 3x = 3x - 3x + 12$

$4y - 3x = 12$

And we're done....♥️♥️♥️♥️♥️

4 0

2 years ago

11 The wild tiger population in India increased from 1706 in the year 2010 to

IrinaK [193]

The percentage change is 20%

3 0

3 years ago

Monica sells lemonade over the summer and uses conical paper cups to serve

Alina [70]

Answer: She would need 206 paper cups.

Step-by-step explanation: First of all, Monica has a 10-gallon container full of lemonade and this translates into 37850 cubic centimetres volume of lemonade. The conversion rate has been provided as one gallon equals 3785 cubic centimetres, therefore ten gallons would be 3785 times ten which gives you 37,850 cubic centimetres of lemonade.

Each cone shaped paper cup has a diameter measuring 8 centimetres and 11 centimetres in height. The radius of the cone shaped cup therefore is 4 centimetres (radius equals diameter divided by two). The volume of each cup therefore is given as;

Volume of a cone = (πr²h)/3

Volume of a cone = (3.14 * 4² * 11)/3

Volume of a cone = 552.64/3

Volume of a cone = 184.2

If each cone could hold 184 cubic centimetres of lemonade, then the entire ten gallons would require the following number of cone shaped cups;

Number of cups = Total volume/Volume of a cup

Number of cups = 37850/184.2

Number of cups = 205.48

Rounded to the nearest whole number, this becomes

Number of cups ≈ 206

Therefore Monica would need 206 cone shaped paper cups to empty the entire 10 gallons of lemonade.

4 0

3 years ago

Suppose a triangle has two sides of length 3and 4 and that the angle between these two sides is 60. What is the length of the th

tangare [24]

9514 1404 393

Answer:

A. √13

Step-by-step explanation:

You can make an educated guess and come to the right conclusion.

The triangle is nearly an equilateral triangle. A triangle with two sides 3 and an angle of 60° would have a third side of 3. A triangle with two sides of 4 and an angle of 60° would have a third side of 4.

So, the third side must be between 3 and 4. Here is an evaluation of the answer choices:

A -- between 3 and 4, the correct choice

B -- 3, too short

C -- 1.73, too short

D -- more than 4, too long

The question can be answered using your triangle solver app on your calculator, or using the Law of Cosines.

c = √(a^2 +b^2 -2ab·cos(C))

c = √(3^2 +4^2 -2·3·4·(1/2)) = √(9 +16 -12)

c = √13 . . . . . length of the side opposite the 60° angle

5 0

2 years ago