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3 years ago

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The area of the continent of North America is about 9,540,000square miles. Write 9,540,000 in expanded form using exponents to s

how powers of 10

1 answer:

Kobotan [32]3 years ago

8 0

9,000,000+500,000+40,000

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How many ways can a person select 3 coins from a box consisting of a penny, a nickel, a dime, a quarter, a half dollar, and a on

tekilochka [14]

Answer:

A person can select 3 coins from a box containing 6 different coins in 120 different ways.

Step-by-step explanation:

Total choices = n = 6

no. of selections to be made = r = 3

The order of selection of coins matter so we will use permutation here.

Using the formula of Permutation:

nPr = $\frac{n!}{(n-r)!}$

We can find all possible ways arranging 'r' number of objects from a given 'n' number of choices.

Order of coin is important means that if we select 3 coins in these two orders:

--> nickel - dime - quarter

--> dime - quarter - nickel

They will count as two different cases.

Calculating the no. of ways 3 coins can be selected from 6 coins.

nPr = $\frac{n!}{(n-r)!}$ = $\frac{6!}{(6-3)!}$

nPr = 120

6 0

3 years ago

What is the percentage of cacao in hot chocolate which is made of 480 grams of milk and 20 grams of cacao?

galina1969 [7]

Given that the hot chocolate is made of 480 grams of milk and 20 grams of cacao.

We need to determine the percentage of cacao in hot chocolate.

<u>The percentage of cacao:</u>

The total grams of hot chocolate can be determined by adding the total grams of milk and the total grams of cacao.

Total grams of hot chocolate = Grams of Milk + Grams of cacao

Total grams of hot chocolate = 480 + 20 = 500 grams.

Thus, the total grams of hot chocolate is 500 grams.

Now, we shall find the percentage of cacao.

The percentage of cacao is given by

$\frac{100}{500}\times 20$

Simplifying, the values, we get,

$\frac{2000}{500}=4\%$

Thus, the percentage of cacao is 4%

6 0

3 years ago

The 70th term of the arithmetic sequence the 70th term of the arithmetic sequence 18,34,50,...

Sedbober [7]

Answer:1122

Step-by-step explanation:

Hve to work out the general equation first by calculating the common difference-16.

3 0

3 years ago

I need all three answer for an assignment

AfilCa [17]

This is false... you can get an easy example: (-2) + (10) = 10 - 2 = 8

7 0

3 years ago

Read 2 more answers

Find the tangent line approximation for 10+x−−−−−√ near x=0. Do not approximate any of the values in your formula when entering

Svetllana [295]

Answer:

$L(x)=\sqrt{10}+\frac{\sqrt{10}}{20}x$

Step-by-step explanation:

We are asked to find the tangent line approximation for $f(x)=\sqrt{10+x}$ near $x=0$ .

We will use linear approximation formula for a tangent line $L(x)$ of a function $f(x)$ at $x=a$ to solve our given problem.

$L(x)=f(a)+f'(a)(x-a)$

Let us find value of function at $x=0$ as:

$f(0)=\sqrt{10+x}=\sqrt{10+0}=\sqrt{10}$

Now, we will find derivative of given function as:

$f(x)=\sqrt{10+x}=(10+x)^{\frac{1}{2}}$

$f'(x)=\frac{d}{dx}((10+x)^{\frac{1}{2}})\cdot \frac{d}{dx}(10+x)$

$f'(x)=\frac{1}{2}(10+x)^{-\frac{1}{2}}\cdot 1$

$f'(x)=\frac{1}{2\sqrt{10+x}}$

Let us find derivative at $x=0$

$f'(0)=\frac{1}{2\sqrt{10+0}}=\frac{1}{2\sqrt{10}}$

Upon substituting our given values in linear approximation formula, we will get:

$L(x)=\sqrt{10}+\frac{1}{2\sqrt{10}}(x-0)$

$L(x)=\sqrt{10}+\frac{1}{2\sqrt{10}}x-0$

$L(x)=\sqrt{10}+\frac{\sqrt{10}}{20}x$

Therefore, our required tangent line for approximation would be $L(x)=\sqrt{10}+\frac{\sqrt{10}}{20}x$ .

8 0

3 years ago