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Alekssandra [29.7K]

3 years ago

8

There are 17 appetizers available at a restaurant. From these, Frank is to choose 13 for his party. How many groups of 13 appeti

zers are possible

1 answer:

Andrej [43]3 years ago

8 0

Answer:

2,380

Step-by-step explanation:

This is a selection problem, hence it is combination. It is simply telling us in how many ways can we select a group of 13 from 17.

This is straightforward, we only need to apply the combination formulae. Hence this goes thus:

17C13 = 2,380

There are 2,380 ways to do this task

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Which of the following statements are true?

Eduardwww [97]

Answer:

B, C

Step-by-step explanation:

Consider all options:

A. The graph of the function $f(x)=\dfrac{1}{2}\sqrt[3]{x}$ is vertically shrunk by a factor $\frac{1}{2}$ the graph of the function $f(x)=\sqrt[3]{x},$ so the domain and the range of both functions are the same. This option is false.

B. The graph of the function $f(x)=\dfrac{1}{2}\sqrt[3]{x}$ is vertically shrunk by a factor $\frac{1}{2}$ the graph of the function $f(x)=\sqrt[3]{x},$ so the domain and the range of both functions are the same. This option is true.

C. The graph of the function $f(x)=\dfrac{1}{2}\sqrt[3]{(x-2)}$ is translated 2 units to the right and vertically shrunk by a factor $\frac{1}{2}$ the graph of the function $f(x)=\sqrt[3]{x},$ so their graphs are similar except the first graph is shifted right and shrunk vertically by a factor of $\frac{1}{2}.$ . This option is true.

D. The function $f(x)=\dfrac{1}{2}\sqrt{x}$ has the domain and the range all non-negative real values. The function $f(x)=\sqrt[3]{x}$ has the domain and the range all real values. So this option is false.

3 0

3 years ago

A pipe is 24 feet long. It needs to be cut into pieces that are each 3/4 feet long. How many pieces can be made from the pipe?

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5 0

3 years ago

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Caleb bought groceries and paid

lutik1710 [3]

Answer:

Price of Caleb's groceries before tax= $6.4

Step-by-step explanation:

Let price of groceries before tax be = $ $x$

Sales tax % = 2.5%

Sales tax applied = $2.5\% \ of\ x = \frac{25}{100}\times x = \frac{25}{100} x$

Actual sales tax paid = $1.60

∴ $\frac{25}{100}x=1.60$

Multiplying both sides by 100.

$100\times \frac{25}{100}x=1.60\times 100$

$25x=160$

Dividing both sides by 25.

$\frac{25x}{25}=\frac{160}{25}$

$x=6.4$

∴ Price of groceries before tax= $6.4

8 0

3 years ago

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Please help!!!<br> Which expression is equivalent to (3m^-1n^2)^4/(2m^-2n)^3

Elza [17]

$\text{Use:}\\\\(a\cdot b)^n=a^nb^n\\\\(a^n)^m=a^{n\cdot m}\\\\\dfrac{a^n}{a^m}=a^{n-m}$

$\dfrac{(3m^{-1}n^2)^4}{(2m^{-2}n)^3}=\dfrac{3^4(m^{-1})^4(n^2)^4}{2^3(m^{-2})^3n^3}=\dfrac{81m^{-4}n^8}{8m^{-6}n^3}\\\\=10.125m^{-4-(-6)}n^{8-3}=10.125m^2n^5$

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2 years ago

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Show that cos(3x) = cos3(x) − 3 sin2(x)cos(x). (Hint: Use cos(2x) = cos2(x) − sin2(x) and the cosine sum

otez555 [7]

<u>Step-by-step explanation:</u>

To prove:

$\cos 3x=\cos^3x-3\sin^2 x\cos x$

Identities used:

$\cos(A+B)=\cos A\cos B+\sin A\sin B$ ......(1)

$\sin 2A=2\sin A\cos A$ ........(2)

$\cos 2A=\cos^2A-\sin^2 A$ .......(3)

Taking the LHS:

$\Rightarrow \cos 3x=\cos (x+2x)$

Using identity 1:

$\Rightarrow \cos (x+2x)=\cos x\cos 2x-\sin x\sin 2x$

Using identities 2 and 3:

$\Rightarrow \cos x(\cos ^2x-\sin^2 x)-\sin x(2\sin x\cos x)\\\\\Rightarrow \cos^3x-\sin^2x\cos x-2\sin^2 x\cos x\\\\\Rightarrow \cos^3x-3\sin^2x\cos x$

As, LHS = RHS

Hence proved

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2 years ago