Is 1.888... an irrational number? (i have a 1 in math :C)

josephine has three chemistry books, three history books, and nine statistics books. she wants to choose one book of each type t

larisa86 [58]

She can choose three books in 54 ways

What is permutation?

Permutation is a technique involving in which a set or number of things can be ordered or arranged. We use permutation to solve and compute answers

We are given that, Josephine has three chemistry books, three history books, and nine statistics books

She has to choose one from each subject

Firstly She has 3 chemistry books

This can be selected in 3 ways

Then She has 3 history books

This can be selected in 3 ways

Ans finally she has 9 statistics books

This can be selected in 9 ways

Hence total ways in which she can select 3 books is 3*3*9= 54 ways

Hence in 54 ways she can choose three books

To learn more about permutation please refer

brainly.com/question/1216161

#SPJ4

7 0

1 year ago

SOLUTION We observe that f '(x) = -1 / (1 + x2) and find the required series by integrating the power series for -1 / (1 + x2).

Ann [662]

Answer:

Required series is:

$\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

Step-by-step explanation:

Given that

$f'(x) = -\frac{1}{1 + x^{2}}$ ---(1)

We know that:

$\frac{d}{dx}(tan^{-1}x)=\frac{1}{1+x^{2}}$ ---(2)

Comparing (1) and (2)

$f'(x)=-(tan^{-1}x)$ ---- (3)

Using power series expansion for $tan^{-1}x$

$f'(x)=-tan^{-1}x=-\int {\frac{1}{1+x^{2}} \, dx$

$= -\int{ \sum\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx$

$= -\sum{ \int\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx$

$=-[c+\sum\limits^{ \infty}_{n=0} (-1)^{n}\frac{x^{2n+1}}{2n+1}]$

$=C+\sum\limits^{ \infty}_{n=0} (-1)^{n+1}\frac{x^{2n+1}}{2n+1}$

$=C-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

as

$tan^{-1}(0)=0 \implies C=0$

Hence,

$\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

7 0

3 years ago

12x - 16 = 68 Solve for x

cricket20 [7]

Answer:

x = 7

Step-by-step explanation:

12x - 16 = 68

Add 16 to each side

12x - 16+16 = 68+16

12x =84

Divide by 12

12x/12 = 84/12

x = 7

6 0

3 years ago

Read 2 more answers

two supplementary angles consist of one acute angle and one obtuse angle. a)always b)sometimes c) never

mel-nik [20]

the sum of supplementary angles equals 180°

you can have an acute angle (less than 90°) + an obtuse angle (greater than 90°) equal to 180°

But you can also have a right angle (equal to 90°) + another right angle equal to 180°

Answer: (b) sometimes

4 0

3 years ago

4. If you spin the spinner twice, what is the probability that the spinner will land on 5 on the first spin and 2 on the second

uysha [10]

Answer:

1/16

Step-by-step explanation:

Given in comment:

5,4,3,2 = Spinner

Thus, there are 4 possible answer

Given:

If you spin the spinner twice, what is the probability that the spinner will land on 5 on the first spin and 2 on the second spin?

1/16

3/16

1/8

1/4

Solve:

Knowing that there only One 5 and One 2 on the spinner.

Thus, in fraction form - 1/4 and 1/4

Probability land on 5 = 1/4

Probability land on 2 = 1/4

Because there are 4 possible solution and one of each is 5,4,3,2

Now, multiply then together:

1/4 × 1/4 = {1 ×1 = 1 and 4 × 4 = 16}

Put Together:

1/16

Hence, the answer is " The Probability that the spinner will land on 5 on the first spin and 2 on the second spin is 1/16

~Lenvy~

5 0

2 years ago

Read 2 more answers