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If you are dealt 5 cards at random from a standard deck of playing cards, what is the probability that at most 4 of them are spa

alexira [117]

Answer:

Step-by-step explanation:

No of ways in which 5 cards are chosen is $N=^{52}C_5$

No of ways in which at most 4 cards are spades $N_0=$ Total ways-5 spades

$=^{52}C_5-^{13}C_5$

Probability that at most 4 cards are spade $P=\frac{N_0}{N}$

$P=\frac{^{52}C_5-^{13}C_5}{^{52}C_5}$

$P=\frac{2598960-1287}{2598960}$

$P=\frac{2597673}{2598960}=0.9995$

3 0

3 years ago

The area is 144 square feet the width is 1\4 of the length of the banner so what are the dimensions ?

mina [271]

Answer:

width is 6 ft, length is 24 ft

Step-by-step explanation:

We can set up 2 equations to help us solve this.

Equation 1: "The area is 144 square feet" gives us

LW = 144 (area of a rectangle)

Equation 2: "the width is 1\4 of the length" give us

W = L/4

We can plug the second equation into the first equation...

Since W = L/4, we get

L(L/4) = 144 (W becomes L/4)

Now solve for L

L²/4 = 144

L² = 624 (multiply both sides by 4)

L = 24 ft (take the square root of each side)

Since L = 24, and W = L/4,

W = 24/6, so W = 6 ft

5 0

3 years ago

Sylvia buys a case of water that contains 24 bottles and sells x number of bottles to her co-workers. Sam buys a case of water t

Brrunno [24]

It is given that Sylvia sells x number of bottles and Sam sells three times as many bottles as Sylvia sold to his co-workers.

So, number of bottles Sam sold is 3x.

It is also given that, number of remaining bottle Sylvia and Sam have same.

So,

24 - x = 36 - 3x

3x - x = 36 - 24

2x = 12

x = 6

Therefore, Sylvia sells 6 bottles.

Hence, this is the required solution.

5 0

3 years ago

Write a slope-intercept form of the equation if it passed the

inna [77]

Answer:

$\sf\longrightarrow \boxed{\pink{\sf 3x + 4y -8=0}}$

Step-by-step explanation:

We need to write the slope intercept form of the equation which passes through (4,-1) and parallel to the line y = -3/4x .

We know that the line parallel to a given line has the same slope . Therefore the slope of the line will be , ( on comparing to Slope Intercept Form ) .

$\sf\longrightarrow Slope =\dfrac{-3}{4}$

On using point slope form ,

$\sf\longrightarrow y-y_1= m ( x - x_1)$

Substitute the respective values ,

$\sf\longrightarrow y - (-1) = \dfrac{-3}{4}( x - 4 )$

Simplify ,

$\sf\longrightarrow y +1 = \dfrac{-3}{4}x + 3$

Multiply both sides by 4 ,

$\sf\longrightarrow 4y + 4 = -3x + 12$

Put all terms on same side , i.e. on LHS ,

$\sf\longrightarrow \boxed{\pink{\sf 3x + 4y -8=0}}$

Hence the equation of the line is 3x + 4y - 8 = 0. 

6 0

3 years ago

The two hexagonal pyramids are similar.

spayn [35]

Answer: The approximate surface area of the larger pyramid is 159.31 ft².

Step-by-step explanation:

A pyramid is a solid,

And, When two solids are similar then the ratio of their surface area is the square of the scale factor of similarity.

Here, the scale factor of similarity

$=\frac{\text{Height of larger pyramid}}{\text{Height of smaller pyramid}}$

$=\frac{15}{6}$

Thus, by the above property,

$\frac{\text{ The surface area of larger pyramid}}{\text{The surface area of the smaller pyramid}}=(\frac{15}{6})^2$

It is given that, the smaller pyramid has a surface area of 25.49 ft²,

$\implies \frac{\text{ The surface area of larger pyramid}}{25.49}=\frac{225}{36}$

$\text{ The surface area of larger pyramid} = \frac{25.49\times 225}{36}$

$=\frac{5735.25}{36}$

$=159.3125\approx 159.31\text{ square ft}$

8 0

3 years ago

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