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3 years ago

How many 5 Card hands have exactly 2 aces and 3 kings?

1 answer:

3 0

It should be 24 because <span>Pick 3 aces: 4C3 = 4 ways
Pick 2 kings: 4C2 = 6 ways
# of full-house hands: 4*6 = 24</span>

You might be interested in

Which of the numbers below is less than zero? Select all that apply.

SSSSS [86.1K]

Answer:

-13 is less than zero in the options

7 0

2 years ago

7b divided by 12 = 4.2 what does b equal

iogann1982 [59]

It is 0.35 That is the answer.

7 0

3 years ago

Juli2301 [7.4K]

<h3>Answer: 6 ounces</h3>

========================================================

Work Shown:

(6 servings)/(4 oz of sauce) = (8 servings)/(x oz of sauce)

6/4 = 8/x

6*x = 4*8

6x = 32

x = 32/6

x = 5.333 approximately

x = 6 we round up despite 5.333 being closer to 5, than it is to 6.

If we went with 5 ounces, then we wouldn't clear the hurdle needed to serve 8 people.

The section below goes over why this is the case in more detail.

---------

6 servings : 4 ounces

6/4 servings : 4/4 ounces

1.5 servings : 1 ounce

So one ounce of sauce gets us 1.5 servings.

If we multiply both sides by 5, then,

1.5 servings : 1 ounce

5*1.5 servings : 5*1 ounce

7.5 servings : 5 ounces

This shows that 5 ounces of sauce will only produce 7.5 servings, which comes up short compared to 8 servings.

If we multiplied both sides by 6, then

1.5 servings : 1 ounce

6*1.5 servings : 6*1 ounce

9 servings : 6 ounces

This shows that 6 ounces of sauce yields 9 servings. We've gone overboard, but it's better to do that than come up short.

3 0

3 years ago

Which statement could be used to conclude that this parallelogram is a rhombus?

tatuchka [14]

A parallelogram is a four-sided shape where the opposite sides are parallel to each other.
A rhombus is a parallelogram with the four sides equal.
Some of the properties of a rhombus are:
<span>1.) All sides are parallel and equal.
2.) Opposite angles are equal
3.) Consecutive angles add up to 180 degrees.
4.) <span>The diagonals bisect the angles.</span></span>

6 0

3 years ago

The coordinates of a particle in the metric xy-plane are differentiable functions of time t with:

frez [133]

Answer:

The rate of change of the distance $\frac{ds}{dt}$ when x = 9 and y = 12 is $-7.6\:\frac{m}{s}$ .

Step-by-step explanation:

This is an example of a related rate problem. A related rate problem is a problem in which we know one of the rates of change at a given instant $\frac{dx}{dt}$ and we want to find the other rate $\frac{dy}{dt}$ at that instant.

We know the rate of change of x-coordinate and y-coordinate:

$\frac{dx}{dt}=-2\:\frac{m}{s} \\\\\frac{dy}{dt}=-8\:\frac{m}{s}$

We want to find the rate of change of the distance $\frac{ds}{dt}$ when x = 9 and y = 12.

The distance of a point (x, y) and the origin is calculated by:

$s=\sqrt{x^2+y^2}$

We need to use the concept of implicit differentiation, we differentiate each side of an equation with two variables by treating one of the variables as a function of the other.

If we apply implicit differentiation in the formula of the distance we get

$s=\sqrt{x^2+y^2}\\\\s^2=x^2+y^2\\\\2s\frac{ds}{dt}= 2x\frac{dx}{dt}+2y\frac{dy}{dt}\\\\\frac{ds}{dt}=\frac{1}{s}(x\frac{dx}{dt}+y\frac{dy}{dt})$

Substituting the values we know into the above formula

$s=\sqrt{9^2+12^2}=15$

$\frac{ds}{dt}=\frac{1}{15}(9(-2)+12(-8))\\\\\frac{ds}{dt}=\frac{1}{15}\left(-18-96\right)\\\\\frac{ds}{dt}=\frac{1}{15}(-114)=-\frac{38}{5}=-7.6\:\frac{m}{s}$

The rate of change of the distance $\frac{ds}{dt}$ when x = 9 and y = 12 is $-7.6\:\frac{m}{s}$

7 0

3 years ago