All categories

3 years ago

What is the period of the function f(x) shown in the graph?

Mathematics

1 answer:

mixas84 [53]3 years ago

7 0

Answer:

8pi

Step-by-step explanation:

You might be interested in

How do i simplify this

leonid [27]

I no learn yet. buttttttt what ever I don't care

6 0

3 years ago

A store sells 8 colors of balloons with at least 28 of each color. How many different combinations of 28 balloons can be chosen?

Len [333]

Answer:

(a) $Selection = 6724520$

(b) $At\ most\ 12 = 6553976$

(c) $At\ most\ 8 = 6066720$

(d) $At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638$

Step-by-step explanation:

Given

$Colors = 8$

$Balloons = 28$ --- at least

Solving (a): 28 combinations

From the question, we understand that; a combination of 28 is to be selected. Because the order is not important, we make use of combination.

Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.

So:

$n => 28 + 8-1$ $= 35$

$r = 28$

$Selection = ^{35}^C_{28$

$Selection = \frac{35!}{(35 - 28)!28!}$

$Selection = \frac{35!}{7!28!}$

$Selection = \frac{35*34*33*32*31*30*29*28!}{7!28!}$

$Selection = \frac{35*34*33*32*31*30*29}{7!}$

$Selection = \frac{35*34*33*32*31*30*29}{7*6*5*4*3*2*1}$

$Selection = \frac{33891580800}{5040}$

$Selection = 6724520$

Solving (b): At most 12 red balloons

First, we calculate the ways of selecting at least 13 balloons

Out of the 28 balloons, there are 15 balloons remaining (i.e. 28 - 13)

So:

$n => 15 + 8 -1 = 22$

$r = 15$

Selection of at least 13 =

$At\ least\ 13 = ^{22}C_{15}$

$At\ least\ 13 = \frac{22!}{(22-15)!15!}$

$At\ least\ 13 = \frac{22!}{7!15!}$

$At\ least\ 13 = 170544$

Ways of selecting at most 12 =

$At\ most\ 12 = Total - At\ least\ 13$ --- Complement rule

$At\ most\ 12 = 6724520- 170544$

$At\ most\ 12 = 6553976$

Solving (c): At most 8 blue balloons

First, we calculate the ways of selecting at least 9 balloons

Out of the 28 balloons, there are 19 balloons remaining (i.e. 28 - 9)

So:

$n => 19+ 8 -1 = 26$

$r = 19$

Selection of at least 9 =

$At\ least\ 9 = ^{26}C_{19}$

$At\ least\ 9 = \frac{26!}{(26-19)!19!}$

$At\ least\ 9 = \frac{26!}{7!19!}$

$At\ least\ 9 = 657800$

Ways of selecting at most 8 =

$At\ most\ 8 = Total - At\ least\ 9$ --- Complement rule

$At\ most\ 8 = 6724520- 657800$

$At\ most\ 8 = 6066720$

Solving (d): 12 red and 8 blue balloons

First, we calculate the ways for selecting 13 red balloons and 9 blue balloons

Out of the 28 balloons, there are 6 balloons remaining (i.e. 28 - 13 - 9)

So:

$n =6+6-1 = 11$

$r = 6$

Selection =

$^{11}C_6 = \frac{11!}{(11-6)!6!}$

$^{11}C_6 = \frac{11!}{5!6!}$

$^{11}C_6 = 462$

Using inclusion/exclusion rule of two sets:

$Selection = At\ most\ 12 + At\ most\ 8 - (12\ red\ and\ 8\ blue)$

$Only\ 12\ red\ and\ only\ 8\ blue\ = 170544+ 657800- 462$

$Only\ 12\ red\ and\ only\ 8\ blue\ = 827882$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = Total - Only\ 12\ red\ and\ only\ 8\ blue$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 6724520 - 827882$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638$

3 0

3 years ago

Question:

Minchanka [31]

Answer:

18 feet

Step-by-step explanation:

9/12 = 0.75

24 x 0.75 = 18

8 0

4 years ago

Read 2 more answers

What is true of the type of angle in this lesson? It measures half the sum of the arc it intercepts. It measures twice the sum o

Karolina [17]

Answer:

Step-by-step explanation:

Answer: it is C because it is true of the type of angle in this lessonc. It measures half the difference of the arcs it intercepts.

7 0

3 years ago

Which domain restrictions apply to this rational expression? x2 4x 4x2−4 select each correct answer.

rosijanka [135]

Because domain restrictions apply to this rational expression, x cannot be equal to {-2, 2}.

<h3>What is domain?</h3>

Domain restrictions are any points in the domain where the function will not have a value. This basically means that there is a point in the function where x will not work.

For the numerator, any value of x will suffice. We can have a value of 0 in the numerator, or a positive, negative, or decimal number.

However, the denominator cannot be equal to zero. This is due to the fact that a fraction bar represents division, and we cannot divide by zero.

Here,

x²-4=0

Add 4 to both sides:

x²-4+4 = 0+4

x² = 4

Take the square root of both sides:

√x² = √4

x = 2 or x = -2

The x cannot be equal to {-2, 2} as domain restrictions apply to this rational expression.

To know more about domain,

brainly.com/question/10238709

#SPJ4

7 0

1 year ago