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3 years ago

Find the number of possible 5 card hands that contain the cards specified the cards are taken from a standard 52 card deck

Mathematics

1 answer:

Zarrin [17]3 years ago

5 0

Answer:

Step-by-step explanation:

Find the number of possible 5-card hands that contain the cards specified. The cards are taken from a standard 52-card deck.

5 red cards.

Ans: 26C5 = 26!/[21!*5!] = 65780

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4 spades and 1 card that is not a spade.

Ans: [13C4*39C1] = 27885

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3 face cards (kings, queens, or jacks) and 2 cards that are not face cards.

Ans: 12C3*40C2 = 171,600

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Two functions are shown in the table below.

SVETLANKA909090 [29]

Answer:

$(d)\ x = 4$

Step-by-step explanation:

Given

$f(x) = -x^2 + 4x + 12$

$g(x) = x + 8$

Required

Find x such that: $f(x) = g(x)$

This gives:

$-x^2 + 4x + 12 = x+8$

Collect like terms

$-x^2 + 4x -x + 12 -8=0$

$-x^2 + 3x +4 =0$

Expand

$-x^2 + 4x - x+4 =0$

Factorize

$x(x - 4) - 1(x-4) = 0$

Factor out x - 1

$(x- 1)(x - 4)=0$

Solve:

$x =1\ or\ x = 4$

8 0

3 years ago

A plane flying horizontally at an altitude of 3 miles and a speed of 500 mi/h passes directly over a radar station. Find the rat

konstantin123 [22]

Answer:

The rate at which the distance from the plane to the station is increasing is 331 miles per hour.

Step-by-step explanation:

We can find the rate at which the distance from the plane to the station is increasing by imaging the formation of a right triangle with the following dimensions:

a: is one side of the triangle = altitude of the plane = 3 miles

b: is the other side of the triangle = the distance traveled by the plane when it is 4 miles away from the station and an altitude of 3 miles

h: is the hypotenuse of the triangle = distance between the plane and the station = 4 miles

First, we need to find b:

$a^{2} + b^{2} = h^{2}$ (1)

$b = \sqrt{h^{2} - a^{2}} = \sqrt{(4 mi)^{2} - (3 mi)^{2}} = \sqrt{7} miles$

Now, to find the rate we need to find the derivative of equation (1) with respect to time:

$\frac{d}{dt}(a^{2}) + \frac{d}{dt}(b^{2}) = \frac{d}{dt}(h^{2})$

$2a\frac{da}{dt} + 2b\frac{db}{dt} = 2h\frac{dh}{dt}$

Since "da/dt" is constant (the altitude of the plane does not change with time), we have:

$0 + 2b\frac{db}{dt} = 2h\frac{dh}{dt}$

And knowing that the plane is moving at a speed of 500 mi/h (db/dt):

$\sqrt{7} mi*500 mi/h = 4 mi*\frac{dh}{dt}$

$\frac{dh}{dt} = \frac{\sqrt{7} mi*500 mi/h}{4 mi} = 331 mi/h$

Therefore, the rate at which the distance from the plane to the station is increasing is 331 miles per hour.

I hope it helps you!

4 0

2 years ago

How do u write these numbers from greatest to least

ycow [4]

I don't know what numbers you want me to order from great to least, but a example is 1,510, 964, 478, 219, 96, 57, 35, 10, 9, 4, 3,

8 0

3 years ago

Read 2 more answers

A company produces 7,200 gallons of bottled water a day. The company puts 81 gallon bottles in each carton. How many cartons are

Gre4nikov [31]

I think you probably divide 7,200 gallons by 81 gallons since it's asking how many in one.

3 0

3 years ago

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A triangle has height 4ft and an area 64ft square What is the length of its base?

kramer

Answer:the answer is 60

Step-by-step explanation:

The question is “what is the length” so what I think we are supposed to do is to add since the height is 4 and the area is 64 so the length has to be 6

Hope I helped

6 0

3 years ago