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2 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]2 years ago

3 0

There are six different options

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Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant.

BlackZzzverrR [31]

This part of the plane is a triangle. Call it $\mathcal S$ . We can find the intercepts by setting two variables to 0 simultaneously; we'd find, for instance, that $y=z=0$ means $5x=20\implies x=4$ , so that (4, 0, 0) is one vertex of the triangle. Similarly, we'd find that (0, 5, 0) and (0, 0, 20) are the other two vertices.

Next, we can parameterize the surface by

$\mathbf s(u,v)=\langle4(1-u)(1-v),5u(1-v),20v\rangle$

so that the surface element is

$\mathrm dS=\|\mathbf s_u\times\mathbf s_v\|=20\sqrt{42}(1-v)\,\mathrm du\,\mathrm dv$

Then the area of $\mathcal S$ is given by the surface integral

$\displaystyle\iint_{\mathcal S}\mathrm dS=20\sqrt{42}\int_{u=0}^{u=1}\int_{v=0}^{v=1}(1-v)\,\mathrm dv\,\mathrm du$
$\displaystyle=20\sqrt{42}\int_{v=0}^{v=1}(1-v)\,\mathrm dv=10\sqrt{42}\approx64.8074$

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2 years ago

baker has 5\dfrac145 4 1 5, start fraction, 1, divided by, 4, end fraction pies in her shop. She cut the pies in pieces that a

kupik [55]

Answer:

The answer is "She cut a total of 42 pieces of pie".

Step-by-step explanation:

Given :

Total pie= $5 \frac{1}{4}$

cut pie = $\frac{1}{8}$

The number of pieces of the pie she has=?

Solve the mixed fraction value:

$\to 5 \frac{1}{4}= \frac{21}{4}$

If she cuts the pieces into the entire pie, that is = $\frac{1}{8}$

So, the equation is:

$\to \frac{21}{4} = \frac{1}{8} \times x$

$\to x= \frac{21 \times 8}{4}\\\\ \to x= 21 \times 2\\\\ \to x=42$

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1 year ago

Simplify the expression to a form in which 2 is raised to a single integer power. fraction numerator open parentheses 2 to the p

anzhelika [568]

Answer:

2^27

Step-by-step explanation:

Given the following expression:

[(2^10)^3 x (2^-10)] ÷ 2^-7

This can be easily simplified. Let us simplify the numerator first. To do that, we have

(2^10)^3 making use of the power rule of indices that says:

(A^a)^b = A^ab where a and b are powers, we have:

2^(10x3) = 2^30

Therefore the numerator becomes:

2^30 x 2^-10. Also making use of the multiplication rule that says:

A^a x A^b = A^(a + b), we have

2^30 x 2^-10 = 2^(30 – 10) = 2^20.

Now we have:

(2^20) ÷ (2^-7)

To simplify this, we need the division rule of indices which says:

A^a ÷ A^b = A^(a – b)

Therefore we have:

(2^20) ÷ (2^-7) = 2^[20 – (–7)] = 2^(20+7) = 2^27

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1 year ago

Joseph received a $20 gift card for downloading music. Each downloaded song costs $1.29. Explain how to write and solve an inequ

OleMash [197]

X= the amount of songs
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2 years ago

Carlos and Maria drove a total of 233 miles in 4.4 hours. Carlos drove the first part of the trip and averaged 55 miles per hour

Mandarinka [93]

Let x - hours Carlos drove ; Let y - hours Maria drove

Equation 1: x + y = 4.4
x = 4.4 - y

Equation 2: 55x + 50y = 233
55(4.4 - y) + 50y = 233
242 - 55y + 50y = 233
-5y = 233-242
-5y = -9
y=9/5 or 1.8 hours Maria drove

To find time Carlos drove:
x=4.4 - 1.8
x = 2.6 hours

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2 years ago

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