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3 years ago

The table shows the time 50 students spent on their homework.

Mathematics

1 answer:

seraphim [82]3 years ago

8 0

Answer: Mean = 52.8 mins

Step-by-step explanation:

We have lapses of 30 minutes, so we can write the average for each, this means that:

0 < t < 30 can be averaged to the middle of the range: 15 min.

Doing this, we have that:

7 students 15 min

27 students 45 min

12 students 75 min

4 students 105 min.

Now we can calculate the mean:

mean = (x1*n1 + x2*n2 + ...)/N

where x1 is the amount of time 1, and n1 is the number of students associated to that time and so on. N is the total number of students

Mean = (7*15min + 27*45min + 12*75min + 4*105min)/(7 + 27 + 12 + 4)

Mean = 52.8 mins

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What is each power of i with its multiplicative inverse.

pentagon [3]

Answer:

1) multiplicative inverse of i = -i

2) Multiplicative inverse of i^2 = -1

3) Multiplicative inverse of i^3 = i

4) Multiplicative inverse of i^4 = 1

Step-by-step explanation:

We have to find multiplicative inverse of each of the following.

1) i

The multiplicative inverse is 1/i

if i is in the denominator we find their conjugate

$=1/i * i/i\\=i/i^2\\=We\,\, know\,\, that\,\, i^2 = -1\\=i/(-1)\\= -i$

So, multiplicative inverse of i = -i

2) i^2

The multiplicative inverse is 1/i^2

We know that i^2 = -1

1/-1 = -1

so, Multiplicative inverse of i^2 = -1

3) i^3

The multiplicative inverse is 1/i^3

We know that i^2 = -1

and i^3 = i.i^2

$1/i^3\\=1/i.i^2 \\=1/i(-1)\\=-1/i * i/i\\=-i/i^2\\= -i/-1\\= i$

so, Multiplicative inverse of i^3 = i

4) i^4

The multiplicative inverse is 1/i^4

We know that i^2 = -1

and i^4 = i^2.i^2

$=1/i^2.i^2\\=1/(-1)(-1)\\=1/1\\=1$

so, Multiplicative inverse of i^4 = 1

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3 years ago