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3 years ago

The total weight of 25 books is 125 pounds. How many pounds would 70 books weigh?

Mathematics

1 answer:

julia-pushkina [17]3 years ago

7 0

70 / 25 = 2.8

125 * 2.8 = 350

therefore 70 books would be 350 pounds

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How many different digits are needed for the base 6 system?

lorasvet [3.4K]

Answer:

0, 1, 2, 3, 4 and 5

Step-by-step explanation:

In a nutshell, base six is a number system that employs the numbers 0 through 5 instead of 0 through 9 in each digit. As a result, a number that would be stated as 6 in base ten is written as 10. We count one, two, three, four, five, ten, eleven, twelve, thirteen, fourteen, fifteen, twenty, and so on.

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3 years ago

Translate this verbal expression into an algebraic equation and solve: thirteen less than twice the sum of a number and six is 4

Vesna [10]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the verbal expression

''Thirteen less than twice the sum of a number and six is 47''.

Let us break down the verbal expression into an algebraic equation

Let the number be = n

Twice the number n = 2n

Sum of twice the number and six = 2n+6

Thirteen less than twice the sum of a number and six = 2n+6-13

And finally

Thirteen less than twice the sum of a number and six is 47:

2n+6-13 = 47

Therefore, the equation is: $2n+6-13 = 47$

Solving the algebraic expression

solving the equation for 'n'

$2n+6-13 = 47$

$2n-7=47$

Add 7 to both sides

$2n-7+7=47+7$

Simplify

$2n=54$

Divide both sides by 2

$\frac{2n}{2}=\frac{54}{2}$

Simplify

$n=27$

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3 years ago

In how many ways can 6 different kinds of pizza be listed on the menu?

vredina [299]

Answer: 720

Step-by-step explanation:

Since we are to list 6 different kinds of Pizza and no condition is attached , this arrangement could be done in 6! ways.

That is

6! = 720

This means that the different kind of pizza could be listed in 720 ways

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3 years ago

Question 5

anzhelika [568]

Answer:anwser would be c

Step-by-step explanation:

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3 years ago

Read 2 more answers

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

Leni [432]

Answer: $\dfrac{2x^2-1}{x(x^2-1)}$

Step-by-step explanation:

The given function : $y=\ln(x(x^2 - 1)^{\frac{1}{2}})$

$\Rightarrow\ y=\ln x+\ln (x^2-1)^{\frac{1}{2}}$ [ $\because \ln(ab)=\ln a +\ln b$ ]

$\Rightarrow y=\ln x+\dfrac{1}{2}\ln (x^2-1)}$ [ $\because \ln(a)^n=n\ln a$ ]

Now , Differentiate both sides with respect to x , we will get

$\dfrac{dy}{dx}=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})\dfrac{d}{dx}(x^2-1)$ (By Chain rule)

[Note : $\dfrac{d}{dx}(\ln x)=\dfrac{1}{x}$ ]

$\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x-0)$

[ $\because \dfrac{d}{dx}(x^n)=nx^{n-1}$ ]

$=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x) = \dfrac{1}{x}+\dfrac{x}{x^2-1}\\\\\\=\dfrac{(x^2-1)+(x^2)}{x(x^2-1)}\\\\\\=\dfrac{2x^2-1}{x(x^2-1)}$

Hence, the derivative of the given function is $\dfrac{2x^2-1}{x(x^2-1)}$ .

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4 years ago