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1 year ago

8

A lock has a three number code made up of 17 numbers if none of the numbers are allowed to repeat how many different ways can yo

u choose three different numbers in order for unit code?

1 answer:

Marrrta [24]1 year ago

8 0

Answer:

680

Step-by-step explanation:

Use the binomial coefficient where you choose $k=3$ numbers out of $n=17$ possible numbers and find the total amount of combinations since order does not matter:

$\displaystyle \binom{n}{k}=\frac{n!}{k!(n-k)!}\\ \\\binom{17}{3}=\frac{17!}{3!(17-3)!}\\\\\binom{17}{3}=\frac{17!}{3!(14)!}\\\\\binom{17}{3}=\frac{17*16*15}{3*2*1}\\\\\binom{17}{3}=680$

Thus, you can make 680 three-non-repeating-number codes

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A sector with a radius of 8 cm has an area of 56pi cm2. What is the central angle measure of the sector in radians?

Maurinko [17]

Answer:

$\frac{7\pi}{4}$ .

Step-by-step explanation:

Given information:

Radius of circle = 8 cm

Area of sector = $56\pi\text{ cm}^2$

Formula for area of sector is

$A=\dfrac{1}{2}\theta r^2$

where, r is radius and $\theta$ is central angle in radian.

Substitute $A=56\pi$ and r=8 in the above formula.

$56\pi=\dfrac{1}{2}\theta (8)^2$

$56\pi=\dfrac{64}{2}\theta$

$56\pi=32\theta$

$\dfrac{56\pi}{32}=\theta$

$\dfrac{7\pi}{4}=\theta$

Therefore, the measure of the sector in radians is $\frac{7\pi}{4}$ .

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2 years ago

In the expression below, a is an integer. 12^3+ax-20 if 3x+4 is a factor of the expession above, what is the value of a

SVEN [57.7K]

Our function is:

$f(x)=12^3+ax-20$

Now, if $3x+4$ is a factor of $f(x)$ then $x=\frac{-4}{3}$ must satisfy the equation:

So, $f(\frac{-4}{3} )=0$

Putting $x=\frac{-4}{3}$

We get,

$f(\frac{-4}{3} )=12^3+a(\frac{-4}{3} )-20=0$

$12^3+\frac{-4}{3} a-20=0$

$\frac{-4}{3} a=20-12^3=20-1708$

$a=-1708 \times \frac{-3}{4} =1281$

So, the value of 'a' for the given expression is 1281.

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2 years ago

F divided by 28 equal 24

BabaBlast [244]

You can translate to:

F ÷ 28 = 24

F/28 = 24 Cross Multiply

F = 28 * 24

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3 years ago

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Hello there.

What is the reference angle in radians for 1380°?

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Arada [10]

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2 years ago

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