A statistician for a chain of department stores created the following stem-and-leaf plot showing the number of pairs of glasses at each of the stores: \left| \quad \begin{matrix} 0 \vphantom{\Large{0}} \\ 1 \vphantom{\Large{0}} \\ 2 \vphantom{\Large{0}} \\ 3 \vphantom{\Large{0}} \\ 4 \vphantom{\Large{0}} \\ \end{matrix} \quad \right| \quad \begin{matrix} 9& \vphantom{\Large{0}} \\ 3&6&6&8& \vphantom{\Large{0}} \\ 1&2&3&5&6&9& ; \vphantom{\Large{0}} \\ 0& \vphantom{\Large{0}} \\ 1&2&3&3&5&7& ; \vphantom{\Large{0}} \\ \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ​ 00 10 20 30 40 ​ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ​ 9 3 1 0 1 ​ 0 6 2 0 2 ​ 6 3 3 ​ 8 5 3 ​ 0 6 5 ​ 9 7 ​ 0 0 ​ Key: 4\,|\,1=414∣1=414, vertical bar, 1, equals, 41 pairs of glasses What was the largest number of pairs of glasses at any one department store?

step-by-step explanation:

the first 5 right here the next 5 i will upload as separate question

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

cheater

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answer: r there any options?

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