All categories

3 years ago

Express in the form 2^n

Mathematics

1 answer:

Paraphin [41]3 years ago

4 0

$\frac{1}{16} = \frac{1}{2^4} = 2^{-4}$

You might be interested in

There are 7 acts in a talent show.

lara31 [8.8K]

Answer:

Event A: 1/35

Event B: 1/840

Explanation:

Event A

For the event A, the order of the first 4 acts does not matter.

The number of different four acts taken from a set of seven acts, when the order does not matter, is calculated using the concept of combinations.

Thus, the number of ways that the first four acts can be scheduled is:

$C(m,n)=\dfrac{m!}{n!(m-n)!}$

$C(7,4)=\dfrac{7!}{4!(7-4)!}=\dfrac{7!}{4!(3)!}=35$

And the number of ways that four acts is the singer, the juggler, the guitarist, and the violinist, in any order, is 1: C(4,4).

Therefore the probability of Event A is:

$P(A)=1/35$

Event B

Now the order matters. The difference between combinations and permutations is ordering. When the order matters you need to use permutations.

The number of ways in which four acts can be scheculed when the order matters is:

$P(m,n)=\dfrac{m!}{(m-n)!}$

$P(m,n)=\dfrac{7!}{(7-4)!}=P(m,n)=\dfrac{7!}{4!}=840$

The number of ways the comedian is first, the guitarist is second, the dancer is third, and the juggler is fourth is 1: P(4,4)

Therefore, the probability of Event B is:

$P(B)=1/840$

7 0

3 years ago

Lines k and l are parallel. Lines m and n intersect lines k and l to form 2 triangles. The top triangle has angles 1, 2, 3. The

GaryK [48]

Answer:

It is C, line KL has a slope of 0 and line MN is undefined and they're perpendicular

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

shusha [124]

Step-by-step explanation:

-4x + 3 < 23

-4x < 20

x > -5

hmm,I don't think we need to put equal sign instead of (<) , for when we started calculating.

we can just keep the question as it is and calculate.

3 0

2 years ago

Read 2 more answers

ASAP!!! A proportional relationship is shown in the table below. X: 0 0.3 0.6 0.9 1.2 Y: 0 1 2 3 4 What is the slope of the line

Lera25 [3.4K]

The slope is 3/10, and just graph 2 points ( so like .3,1 and .9,2) and just use Desmos to figure out the line using the y=3/10x+3.64 and just type it in

7 0

3 years ago

A cylindrical container has a volume of 36 cm³. Another container made out of the same material is similar to the first containe

USPshnik [31]

I hope this helps you

Volume = pi.r^2.h

36= pi.r^2.h

Volume =pi.r^2.3/4h

Volume =pi.r^2.h.3/4

Volume =36.3/4

Volume =9.3

Volume =27

3 0

3 years ago

Read 2 more answers