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2 years ago

State if each scenario involves a permutation or a combination. Then find the number of possibilities.

Mathematics

1 answer:

Drupady [299]2 years ago

8 0

The order can be in a few different ways like 213, 321, 132, 312. You get the idea

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2. In the diagram below, set I represents rational numbers, set II represents integers, and set III represents whole numbers. Sh

MrRa [10]

The information about the rational numbers and integers shows that the correct option is C.

<h3>How to explain the information?</h3>

It should be noted that rational numbers are numbers where we can write as a fraction of two integers. Any rational number is in the form a/b where a,b are integers and b is nonzero.

Terminating decimals can be written as a rational number. Something like 3.1 is equivalent to 31/10.

Of the four answer choices, only choice C is correct.

Choice A has the value '3' as a rational number, but it doesn't have it in the set of integers as well. So that's why choice A is incorrect.

Choice B has -3.4 in the set of integers, which is not correct. Integers do not have any decimal portion. The same applies to choice D also. We can rule choices B and D out.

Therefore, the correct option is C.

Learn more about integers on:

brainly.com/question/17695139

#SPJ1

5 0

1 year ago

What is the first whole number greater than √43?

eduard

Answer:

I believe the answer would be 7

Step-by-step explanation:

if you square root 43 you would get 6.557... and the next whole number would be 7.

3 0

2 years ago

Read 2 more answers

Find the absolute extrema for f(x,y)=4-x^2-y^4+1/2y^2 over the closed disk D:x^2+y^2 is less than or equal to 1

algol [13]

Find the critical points of $f(x,y)$ :

$\dfrac{\partial f}{\partial x}=-2x=0\implies x=0$

$\dfrac{\partial f}{\partial y}=y-4y^3=y(1-4y^2)=0\implies y=0\text{ or }y=\pm\dfrac12$

All three points lie within $D$ , and $f$ takes on values of

$\begin{cases}f(0,0)=4\\f\left(0,-\frac12\right)=\frac{65}{16}\\f\left(0,\frac12\right)=\frac{65}{16}\end{cases}$

Now check for extrema on the boundary of $D$ . Convert to polar coordinates:

$f(x,y)=f(\cos t,\sin t)=g(t)=4-\cos^2-\sin^4t+\dfrac12\sin^2t=3+\dfrac32\sin^2t-\sin^4t$

Find the critical points of $g(t)$ :

$\dfrac{\mathrm dg}{\mathrm dt}=3\sin t\cos t-4\sin^3t\cos t=\sin t\cos t(3-4\sin^2t)=0$

$\implies\sin t=0\text{ or }\cos t=0\text{ or }\sin t=\pm\dfrac{\sqrt3}2$

$\implies t=n\pi\text{ or }t=\dfrac{(2n+1)\pi}2\text{ or }\pm\dfrac\pi3+2n\pi$

where $n$ is any integer. There are some redundant critical points, so we'll just consider $0\le t< 2\pi$ , which gives

$t=0\text{ or }t=\dfrac\pi3\text{ or }t=\dfrac\pi2\text{ or }t=\pi\text{ or }t=\dfrac{3\pi}2\text{ or }t=\dfrac{5\pi}3$

which gives values of

$\begin{cases}g(0)=3\\g\left(\frac\pi3\right)=\frac{57}{16}\\g\left(\frac\pi2\right)=\frac72\\g(\pi)=3\\g\left(\frac{3\pi}2\right)=\frac72\\g\left(\frac{5\pi}3\right)=\frac{57}{16}\end{cases}$

So altogether, $f(x,y)$ has an absolute maximum of 65/16 at the points (0, -1/2) and (0, 1/2), and an absolute minimum of 3 at (-1, 0).

5 0

2 years ago

Fill in the blank. If 9/24 = 3/x , then x is _____. PLS HELP!!

lina2011 [118]

Answer:

Step-by-step explanation:

9 /3 3

-- --

24 /3 8

3 0

2 years ago

13.

brilliants [131]

Answer:

The answer to your question is: midsegment = 35 units

Step-by-step explanation:

Use the Thales' theorem

$\frac{3x + 55}{6x + 5} = \frac{86}{43} \\$

43( 3x + 55) = 86( 6x + 5)

129x + 2365 = 516x + 430

129x - 516x = 430 - 2365

-387x = -1935

x = -1935 / -387

x = 5

Midpoint length = 6(5) + 5

= 30 + 5

= 35 units

8 0

2 years ago