Find the number of ways to purchase 5 different kinds of juices from a selection of 10 juices

1 answer:

8 0

Formula for combinations:
(n!)/(r!(n-r)!)

For you, this is:
10!/(5!(10-5)!) = 10!/5!5! = (10•9•8•7•6•5•4•3•2)/(5•4•3•2)(5•4•3•2) = (10•9•8•7•6)/(5•4•3•2) = 30240/120=252 different ways.

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Which expression is equivalent to (x Superscript one-fourth Baseline y Superscript 16 Baseline) Superscript one-half?

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The expression that is equal to (x Superscript one-fourth Baseline y Superscript 16 Baseline) is x Superscript one-eighth Baseline y Superscript 8.

<h3>What is an Expression?</h3>

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that is equal to (x Superscript one-fourth Baseline y Superscript 16 Baseline) can be found by simplifying the given algebraic equation,

$(x^{\frac14}y^{16})^{\frac12}\\\\=x^{(\frac14 \times \frac12)} \times y^{(16 \times \frac12)}\\\\= x^{\frac18}y^{8}$

Hence, the expression that is equal to (x Superscript one-fourth Baseline y Superscript 16 Baseline) is x Superscript one-eighth Baseline y Superscript 8.

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Step-by-step explanation:

1. The solution is the set of x-values for which the graph is above the x-axis, where y = 0. Those x-values are in the interval (0, 4).

2. The solution is the set of x-values for which the graph is below the x-axis. Those x-values are in either of the two intervals (-∞, 0) or (4, ∞).

3. The x-intercepts of the graph are x=0 or x=4.

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