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3 years ago

5

Nine stuffed animals, all different, are placed along a babies toy shelf. How many possible arrangements are there if: a) th

ere are no restrictions. b) Cookie Monster must be in the middle. c) BERT and ERNIE must be together. d) BERT, ERNIE, and OSCAR must be together. e) BERT, ERNIE, and OSCAR must not be together. f) they must not be in alphabetical order.

2 answers:

BartSMP [9]3 years ago

5 0

<span>BERT, ERNIE, and OSCAR must be together. e) </span>

zzz [600]3 years ago

4 0

A) there are no restrictions = 9^9 = 81
b) Cookie Monster must be in the middle = 8^8 = 64
c) <span>BERT and ERNIE must be together = Out of 9, 7 can be rearranged
d) </span><span>BERT, ERNIE, and OSCAR must be together = Out of 9, 6 can be rearranged
e) UNSURE OF ANSWER E AND F
</span>

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First of all, remember what the equation of a line is:

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3 years ago

What other points are on the line of direct variation through (5, 12)? Check all that apply. (0, 0) (2.5, 6) (3, 10) (7.5, 18) (

aalyn [17]

we know that

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the equation is

$y=\frac{12}{5}x$

Remember that

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$0=\frac{12}{5}*0$

$0=0$ -------> is true

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<u>case B)</u> point $(2.5,6)$

$x=2.5\ y=6$

Substitute the value of x and y in the direct variation equation

$6=\frac{12}{5}*2.5$

$6=6$ -------> is true

therefore

the point $(2.5,6)$ is on the line of direct variation

<u>case C)</u> point $(3,10)$

$x=3\ y=10$

Substitute the value of x and y in the direct variation equation

$10=\frac{12}{5}*3$

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<u>case D)</u> point $(7.5,18)$

$x=7.5\ y=18$

Substitute the value of x and y in the direct variation equation

$18=\frac{12}{5}*7.5$

$18=18$ -------> is true

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the point $(7.5,18)$ is on the line of direct variation

<u>case E)</u> point $(12.5,24)$

$x=12.5\ y=24$

Substitute the value of x and y in the direct variation equation

$24=\frac{12}{5}*12.5$

$18=30$ -------> is not true

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<u>case F)</u> point $(15,36)$

$x=15\ y=36$

Substitute the value of x and y in the direct variation equation

$36=\frac{12}{5}*15$

$36=36$ -------> is true

therefore

the point $(15,36)$ is on the line of direct variation

therefore

<u>the answer is</u>

$(0,0)$

$(2.5,6)$

$(7.5,18)$

$(15,36)$

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JulsSmile [24]

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1 year ago

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