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serious [3.7K]
2 years ago
8

A company has 31 salespeople. A board member at the company asks for a list of the top 4 salespeople, ranked in order of effecti

veness. How many such rankings are possible?
Mathematics
1 answer:
kvv77 [185]2 years ago
8 0

Answer:

31465 ways

Step-by-step explanation:

Given data

Let us apply the combination formula

nCr = n! / r! * (n - r)!

n= 31

r= 4

substitute

= 31!/4!(31-4)!

= 31!/4!(27)!

= 31*30*29*28*27!/ 4!(27)!

= 31*30*29*28/4!

=31*30*29*28/4*3*2*1

=755160/24

=31465 ways

Hence there are 31465 possible ways to rank it

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Let W be the subspace of R5 spanned by the vectors w1, w2, w3, w4, w5, where
Gwar [14]
To find W⊥, you can use the Gram-Schmidt process using the usual inner-product and the given 5 independent set of vectors. 

<span>Define projection of v on u as </span>
<span>p(u,v)=u*(u.v)/(u.u) </span>
<span>we need to proceed and determine u1...u5 as: </span>
<span>u1=w1 </span>
<span>u2=w2-p(u1,w2) </span>
<span>u3=w3-p(u1,w3)-p(u2,w3) </span>
<span>u4=w4-p(u1,w4)-p(u2,w4)-p(u3,w4) </span>
<span>u5=w5-p(u4,w5)-p(u2,w5)-p(u3,w5)-p(u4,w5) </span>

<span>so that u1...u5 will be the new basis of an orthogonal set of inner space. </span>

<span>However, the given set of vectors is not independent, since </span>
<span>w1+w2=w3, </span>
<span>therefore an orthogonal basis cannot be found. </span>
7 0
3 years ago
The temperature was 8°C then the temperature feel 9°C what was the temperature after it fell?
Vladimir79 [104]

Answer:

-1°C

Step-by-step explanation:

8°C - 9°C = -1°C

Hope it helps

4 0
3 years ago
(Find the HCF of):<br>p^2+4pq+4q^2, p^4 + 8pq^3 and 3p^4 - 10p^2q^2+ p^3q​
kow [346]

Answer:

12pq

Step-by-step explanation:

i dont know tbh but i try my best to help out now anyways

5 0
3 years ago
The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The d
kozerog [31]

Answer: 49.85%

Step-by-step explanation:

Given : The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped ( normal distribution ) and has a mean of 61 and a standard deviation of 9.

i.e.  \mu=61 and \sigma=9

To find :  The approximate percentage of lightbulb replacement requests numbering between 34 and 61.

i.e. The approximate percentage of lightbulb replacement requests numbering between 34 and 34+3(9).

i.e. i.e. The approximate percentage of lightbulb replacement requests numbering between \mu and \mu+3(\sigma). (1)

According to the 68-95-99.7 rule, about 99.7% of the population lies within 3 standard deviations from the mean.

i.e. about 49.85% of the population lies below 3 standard deviations from mean and 49.85% of the population lies above 3 standard deviations from mean.

i.e.,The approximate percentage of lightbulb replacement requests numbering between \mu and \mu+3(\sigma) = 49.85%

⇒ The approximate percentage of lightbulb replacement requests numbering between 34 and 61.= 49.85%

4 0
3 years ago
A company tests the life of its rechargeable batteries over six months of use. They test how long a battery will last after a fu
jonny [76]

Answer:

18.6 months

Step-by-step explanation:

Given that :

Best fit line from scatterplot :

y=-12.05x +224.26

x = Number of month

y = charge on battery

Number of months a typical battery uses before being dead completely :

When battery is dead completely ; charge =0, y = 0

y = -12.05x + 224.26

0 = - 12.05x + 224.26

12.05x = 224.26

x = 224.26 / 12.05

x = 18.610788

Hence, 18.6 months before battery is completely dead.

4 0
3 years ago
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