Twelve notebooks cost $15.48 in all. What is the price of one notebook?

A number cube with faces labeled from 1 to 6 was rolled 20 times. Each time the number

kari74 [83]

Answer:

0.4

Step-by-step explanation:

These are the relative frequencies of each face (data are missing in the text of the problem):

Number Showing on Top Face Frequency

1 0

2 3

3 3

4 6

5 3

6 5

The probability to obtain a certain number when throwing the dice is given by

$p(x_i)=\frac{f_i}{\sum f}$

where

$f_i$ is the relative frequency of the number $x_i$ to occur

$\sum f$ is the sum of the relative frequencies

Here the sum of the frequencies is:

$\sum f=0+3+3+6+3+5=20$

For number 5 here, we have:

$f_5 = 3$ (from the table)

So the probability of getting a 5 is

$p(5)=\frac{3}{20}$

For number 6 here, we have

$f_6=5$

So the probability of getting a 6 is

$p(6)=\frac{5}{20}$

So the probability to obtain either a 5 or a 6 in the next rolling is:

$p(5\cup 6)=p(5)+p(6)=\frac{3}{20}+\frac{5}{20}=\frac{8}{20}=0.4$

6 0

3 years ago

What is an algebraic expression that has no like terms and no parentheses is in this form

vaieri [72.5K]

"Simplest form is the one <span>algebraic expression that has no like terms and no parentheses is in this form. This is actually the simplest way of describing an algebraic expression. I hope that this is the answer that you were looking for and it has actually come to your desired help.</span>

8 0

3 years ago

Read 2 more answers

At one farmer’s market, bananas cost $0.80 per pound. At another farmer’s market, bananas are sold in 5-pound bags for $4.50 per

kow [346]

Answer:

if your looking for which is more cost effective it is the 0.80 per pound as 5 pounds of it would add up to $4.00

7 0

3 years ago

Please, I need help in this ??

nignag [31]

Answer:

$\int\frac{x^{4}}{x^{4} -1}dx = x + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1)-\frac{1}{2} arctanx + c$

Step-by-step explanation:

$\int\frac{x^{4}}{x^{4} -1}dx$

Adding and Subtracting 1 to the Numerator

$\int\frac{x^{4} - 1 + 1}{x^{4} -1}dx$

Dividing Numerator seperately by $x^{4} - 1$

$\int 1 + \frac{1}{x^{4}-1 }\, dx$

Here integral of 1 is x +c1 (where c1 is constant of integration

$x + c1 + \int\frac{1}{(x-1)(x+1)(x^{2}+1)}\, dx$ ----------------------------------(1)

We apply method of partial fractions to perform the integral

$\frac{1}{(x-1)(x+1)(x^{2}+1)}$ = $\frac{A}{x-1} + \frac{B}{x+1} + \frac{C}{x^{2} + 1}$ ------------------------------------------(2)

$\frac{1}{(x-1)(x+1)(x^{2}+1)} = \frac{A(x+1)(x^{2} +1) + B(x-1)(x^{2} +1) + C(x-1)(x+1)}{(x-1)(x+1)(x^{2} +1)}$

1 = $A(x+1)(x^{2} +1) + B(x-1)(x^{2} +1) + C(x-1)(x+1)$ -------------------------(3)

Substitute x= 1 , -1 , i in equation (3)

1 = A(1+1)(1+1)

A = $\frac{1}{4}$

1 = B(-1-1)(1+1)

B = $-\frac{1}{4}$

1 = C(i-1)(i+1)

C = $-\frac{1}{2}$

Substituting A, B, C in equation (2)

$\int\frac{x^{4}}{x^{4} -1}dx$ = $\int\frac{1}{4(x-1)} - \frac{1}{4(x+1)} -\frac{1}{2(x^{2}+1) }$

On integration

Here $\int \frac{1}{x}dx = lnx and \int\frac{1}{x^{2}+1 } dx = arctanx$

$\int\frac{x^{4}}{x^{4} -1}dx$ = $\frac{1}{4} ln(x-1)$ - $\frac{1}{4} ln(x+1)$ - $\frac{1}{2} arctanx$ + c2---------------------------------------(4)

Substitute equation (4) back in equation (1) we get

$x + c1 + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1) - \frac{1}{2} arctanx + c2$

Here c1 + c2 can be added to another and written as c

Therefore,

$\int\frac{x^{4}}{x^{4} -1}dx = x + \frac{1}{4} ln(x-1) - \frac{1}{4} ln(x+1)-\frac{1}{2} arctanx + c$

4 0

4 years ago

The length of a rectangle is four times the width. The perimeter of the rectangle is 45 inches. Write a system of

Yakvenalex [24]

Answer:

81 square inches.

Step-by-step explanation:

Draw a diagram to represent what you know.

You don't know the values of the lengths so represent them algebraically.

You know the perimeter is 45 inches and that the perimeter is calculated by the sum of all of the sides of a shape.

You can rearrange to find the value of a side you've denoted as some unknown variable.

The area is given by the product of the sides. Express this algebraically and then input the value you found.

4 0

3 years ago