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Radda [10]
3 years ago
6

Given six distinct pairs of gloves, 12 distinct gloves in all, how many ways are there to distribute two gloves to each of six s

isters
Mathematics
1 answer:
noname [10]3 years ago
7 0

a) if the two gloves someone receives might both be for the left hand or right hand.

b) if each sister gets one left and one right.

Soln:

a) So i thought about dissectng the problem first into finding the number of ways in which I could make pairs of gloves:

C(12, 2)

then I asked how many ways could the sets of gloves be assigned amongst the 6 sisters:

<span><span>6!</span><span>6!</span></span>

and taking the product of this would give me the amount of ways this could occur:

= C(12,2) * 6!

then for part b)

using this same idea except:

C(6,1) C(6,1) for the left and right glove each .

the C(6,1)*C(6,1)*6!

Right way to think them through?

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The rate of sales for a corporation t weeks from now is given by S(t)=59t+5 millions of dollars per week. Find the average sales
8090 [49]

Answer:

The average sales per week for the first 16 weeks is $477 million dollars per week.

Step-by-step explanation:

Here, you have to find the average value of a continuous function over an interval.

Suppose you have a function f(x) over an interval from a to b. The average of the function in this interval is given by:

\frac{1}{b-a}\int\limits^b_a {f(x)} \, dx

Solution:

In this problem, the function is given by:

S(t) = 59t + 5

The problem asks the average value for the first 16 weeks. It means that our interval goes from 0 to 16. So a = 0, b = 16.

The average value is given by the following integral:

A = \frac{1}{16}\int\limits^{16}_{0} {(59t + 5)} \, dt

A = \frac{59t^{2}}{32} + \frac{5t}{16}, 0 \leq t \leq 16

A =\frac{59*(16)^{2}}{32} + \frac{5*16}{16}

A = $477

The average sales per week for the first 16 weeks is $477 million dollars per week.

5 0
2 years ago
<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20-%2048%20%2B%206%7D%7B%20-%207%7D%20%20%2B%20%28%20-%203%29%28%20-%204%29%28%2
emmainna [20.7K]

Step-by-step explanation:

\frac{ - 48 + 6}{ - 7}   + ( - 3)( - 4)( - 2) \\  =  \frac{ - 42}{ - 7}  + 12( - 2) \\  = 6 + ( - 24) \\  = 6 - 24 \\  =  - 18

6 0
2 years ago
What kind of triangle is 6, 8, and 9
Vika [28.1K]

Answer:

equiangular -right -obtuse -acute.

5 0
2 years ago
If 3x - 1 = 11, what is the value of x2 + x?
Alex
3x -1 = 11
3x = 11 + 1
3x = 12
x = 4
I take it by, x2 + x, you mean 2x + x, since x = 4, then 
2x + x = 2(4) + (4) = 8 + 4 =12 
6 0
3 years ago
WILL MARK BRAINILESTWhich statements are true about the solution of 15 greater-than-or-equal-to 22 + x? Select three options.
shutvik [7]

Answer:

Statements 2, 4, and 5

Step-by-step explanation:

15≥22+x

okay so that's

22+x≤15

and that is

x≤-7

the graph would not be a closed circle, it is a vertical line.

this means your 3 correct statements would be:

x less-than-or-equal-to negative 7,

–6 is part of the solution.

–7 is part of the solution.

the last two are true based on the inequality.

7 0
3 years ago
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