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3 years ago

A pizza parlor offers 4 different pizza toppings. How many different kinds of 2-topping pizzas are available?

2 answers:

6 0

Order does not matter so use "n choose k" formula is used to find number of unique combinations.

c=n!/(k!(n-k)!) where n is total possible choices and k is number of selections.

c=4!/(2!(4-2)!)

c=4!/(2!2!)

c=24/(2*2)

c=24/4

c=6

So there are 6 different two topping options when there are four different toppings to choose from.

Murrr4er [49]3 years ago

3 0

There are six different options

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Find sin 2a and cot 2a:

geniusboy [140]

Answer:

$sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cot(2\alpha ) = \frac{16511}{18720}$

Step-by-step explanation:

$\text{if } cos(\alpha)=\frac{12}{13}\\\text{That must mean we have a triangle with base 12, and hypotenuse 13.}\\\text{Using Pythagoras, we can determine the base of the triangle must be 5.}\\a^2+b^2=c^2 \text{, where c is the hypotenuse and a, b are the two other sides.}\\c^2-b^2=a^2\\\sqrt{c^2-b^2}=a\\\sqrt{13^2-12^2}=\sqrt{169-144}=\sqrt{25}=5\\\text{Therefore, }sin(\alpha) = \frac{5}{12}\\sin(2\alpha)=2sin(\alpha )cos(\alpha)\\\text{(From double angle formulae identities)}\\$

$sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cos(2\alpha )=cos^2(\alpha)-sin^2(\alpha)\\cos(2\alpha )=(\frac{12}{13})^2-(\frac{5}{12})^2=\frac{16511}{24336}\\cot(2\alpha)=\frac{cos(2\alpha)}{sin(2\alpha)}=\frac{\frac{16511}{24336}}{\frac{10}{13}}=\frac{16511}{18720}$

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2 years ago

HCF(320, x) = 20, LCM(320, x) = 2240, then x =

HACTEHA [7]

Answer:

140

Step-by-step explanation:

When working HCF and LCM problems, I like to think in terms of this little diagram:

(a [ b ) c]

It shows me one of the numbers is ab, the other is bc, the HCF is b and the LCM is abc. "a" and "c" must be relatively prime for "b" to be the HCF.

Here, we're given ...

b = 20

ab = 320

abc = 2240

Then ...

c = abc/(ab) = 2240/320 = 7

x = bc = 20(7) . . . . . . equivalently, x = (abc·b)/(ab) = (2240·20)/320

x = 140

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3 years ago

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Ilia_Sergeevich [38]

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Solve for area 1:
Area rec = L * W = 5units * 4 units = 20 squared units

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Area cir = pi *r² = 3.14 * (2 units)² = 12.56 squared units

Total area = 20 + 12.56 = 32.56 foot²
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