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netineya
7 days ago
8

The mean age of a dance troupe is 14.2 years. A 7-year-old sibling is invited to join the troupe. How does the sibling’s age aff

ect the mean?
A. The new mean age will be 10.6 years.
B. The new mean age will be greater than 14.2 years.
C. The new mean age will be less than 14.2 years.
D. The new mean age will still be 14.2 years.
Mathematics
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The side length, s, of a cube is x – 2y. If V = s3, what is the volume of the cube? x3 – 6x2y + 12xy2 – 8y3 x3 + 6x2y + 12xy2 +
Leona [12618]

V = x³ - 6x²y + 12xy² - 8y³

V = (x - 2y)³

   = (x - 2y)(x - 2y)(x - 2y) ( start by expanding the first pair of factors )

   = (x² - 4xy + 4y²)(x - 2y) ( multiply the terms from the first group with those in the second )

   = x³ - 4x²y + 4xy² - 2x²y + 8xy² - 8y³ ( combine similar terms )

  = x³ - 6x²y + 12xy² - 8y³




8 0
2 months ago
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Suppose we are given 4 sets A, B, C, D such that A ⊆ B and C ⊆ D such that A and C have no elements in common. Prove or give a c
babunello [11817]

Here’s a counterexample: consider

B = \{1, 2, 3, 4, 5\},\quad D = \{A, B, C, D, 5\}

Select the subsets in the following manner:

A = \{1, 5\},\quad C = \{A, B, C\}

It's accurate that A\subseteq B and C\subseteq D and that A\cap C=\emptyset, but A\cap D = \{5\}

8 0
3 months ago
How many numbers are 10 units from zero on number line
PIT_PIT [12445]

Answer:

I believe it's 2.

Step-by-step explanation:

10, and -10

4 0
3 months ago
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The expression 17n+11 represents the perimeter of a triangle. The other two sides measure 4n+5 and 5n+6. A simplified expression
Zina [12379]

Response: 8n

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

Clarification:

The two sides, 4n+5 and 5n+6, comprise terms 4n and 5n which total to 9n. We require 8n to add to this to achieve 17n. In simpler terms, 4n + 5n + 8n = 9n + 8n = 17n

That is the reason why the outcome is 8n. There are no additional terms because the "+5" and "+6" in the two given expressions (4n+5 and 5n+6) sum to 5+6 = 11, matching what we aim for in the perimeter expression 17n + 11

Side 1 = 4n + 5

Side 2 = 5n + 6

Side 3 = 8n

Perimeter = (side1) + (side2) + (side3)

Perimeter = (4n + 5) + (5n + 6) + (8n)

Perimeter = 4n + 5 + 5n + 6 + 8n

Perimeter = (4n + 5n + 8n) + (5 + 6)

Perimeter = 17n + 11

So this confirms we possess the correct expression for the third side that is missing.

3 0
2 months ago
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