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2 years ago

Winnie has 7 trophies she wants to display in an array.How many different arrays are possible? Explain.

Mathematics

2 answers:

Lady_Fox [76]2 years ago

8 0

Answer:

Winnie can arrange 7 trophies in 7! = 5040 ways to display trophies.

Step-by-step explanation:

Consider an array of 7 places where trophies can be arranged.

Since trophy 1 has 7 places choices, we can place it in any of 7 places.

Similarly trophy 2 has 6 options left to be placed as we have placed trophy 1 already at one of the place.

Continuing similarly, trophy 3 has 5 options, trophy 4 has 4 options, trophy 3 has 3 options, trophy 2 has 2 options and trophy 1 has only 1 option left in which it can be placed in the array.

Thus, total number of ways to display = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 7!

So, Winnie can arrange 7 trophies in 7! = 5040 ways to display trophies.

Rama09 [41]2 years ago

6 0

5,040 I think because 7•6•5•4•3•2•1=5040

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3 years ago

In the figure below, points M, P, H, J, and K lie in plane Z.

marishachu [46]

Answers:

(a) LN
(b) PHJ
(c) K
(d) HK

===================================================

Explanation:

Part (a)

Lines LN and PN have the point N in common. This is the intersection point.

-----------------

Part (b)

To name a plane, pick any three non-collinear points that are inside it. We cannot pick points H, J, K together because infinitely many planes pass through it. Imagine the piece of flat paper able to rotate around this axis (like a propeller). Having the points not all on the same line guarantees we form exactly one unique plane.

I'll pick the non-collinear points P, H and J to get the name Plane PHJ. Other answers are possible.

------------------

Part (c)

Points H, J and K are collinear as they are on the same line. Pick either H or K to fill out the answer box. I'll go with point K

------------------

Part (d)

Point P and line HK are coplanar. They exist in the same flat plane, or on the same sheet of flat paper together.

We can think of that flat plane as the ground level while something like point N is underground somewhere. So point N and anything on that ground plane wouldn't be coplanar.

Note: there are other possible names for line HK such as line JH or line JK. The order doesn't matter when it comes to naming lines.

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2 years ago

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3 years ago

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Answer:

Step-by-step explanation:

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3 years ago

How many solutions exist for the given equation? 0.75(x 40) = 0.35(x 20) 0.35(x 20) zero one two infinitely many

zimovet [89]

Answer:

One solution

Step-by-step explanation:

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0.75x + 30 = 0.7x + 14

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Hope this helps!

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2 years ago