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LiRa [457]
3 years ago
11

If p and q are distinct primes. Find the number of positive divisors of p^2 * q^2

Mathematics
2 answers:
Dennis_Churaev [7]3 years ago
8 0

Answer:

The number of positive divisors are 7.

Step-by-step explanation:

Since it is given that p and q are prime numbers thus they will not have any divisors other that itself and 1

The number p^{2}\times q^{2} can be represented as

p^{2}\times q^{2}=p\times (p\times q^{2})\\p^{2}\times q^{2}=(p\times q)\times (p\times q)\\p^{2}\times q^{2}=(p^{2}\times q)\times q\\

Thus the number (pq)^{2} can be divided by:

1) 1

2) p

3) q

4) pq

5)p\times q^{2}

6)p^{2}\times q

7)(pq)^{2}

Thus the number of positive divisors are 7.

kkurt [141]3 years ago
3 0

Answer:

9

Step-by-step explanation:

We know that for p^mq^n  where p and q are different prime numbers the number of positive divisors are (m+1) (n+!)

We have given p^2q^2

So here m=2 and n=2

So number of positive divisors =(2+1)\times (2+1) =9

So the number of positive divisors of  p^2q^2 is 9

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Step-by-step explanation:

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Solve the equation:3x+6=51

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x=15

Since x=15 then the second number is 17 and then 19

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Answer:

Step-by-step explanation:

n = sample size = 5

a) Let us determine the sum

\sum x_i= 100+200+300+400+490=1490

\sum x_i^2= 100^2+200^2+300^2+400^2+490^2=540100

\sum y_i = 237+350+419+465+507=1978

\sum y_i^2= 237^2+350^2+419^2+465^2+507^2=827504

\sum x_i y_i=100  \times 237 + 200\times350+300 \times 419 + 400 \times 465 +  490 \times 507=653830

Now we can determine S_x_x, S_x_y, S_y_y

S_x_x = \sum x_i^2-\frac{(\sum x_1)^2}{n} \\= 540100 - \frac{1490^2}{5} \\= 96080

S_x_y = \sum x_i y_i -\frac{(\sum x_i)(\sum y_i) }{n} \\\\

653830 - \frac{1490 \times 1978 }{5}  = 64386

S_y_y = \sum y_i^2-\frac{(\sum y_i)^2 }{n} = 82750-\frac{1978^2}{5} \\\\= 45007.2

The estimate b of the slope β is the ratio of S_x_y and S_x_x

b = \frac{S_x_y}{S_x_x}

\frac{64386}{96080}  = 0.67

The mean is the sum of all value divide by number of values

\bar x= \frac{\sum x_i}{n} \\\\= \frac{100+200+300+400+490}{5} \\\\= \frac{1490}{5} = 298

\bar y= \frac{\sum y_i}{n} \\\\= \frac{237+350+419+465+507}{5} \\\\= \frac{1978}{5} = 395.6

The estimate a of the intercept is

a = \bar y - b \bar x

= 395.6 - 0.69 \times 298\\= 195.9

General least square equation;

\bar y = \alpha + \beta x

replace alpha by a = 3 and beta by b = 0.67 in general least equation

y = a + bx

195.9 + 0.67x

b)

<em>Scatter plot is shown in the attached file</em>

x is on the horizontal axis

y is n the vertical axis

The degree of freedom of regression is 1

because we use one variable s predictor variable

d_f_R = 1

The degree of freedom of error is the sample size n decrease by 2

d_f_E =n-2= 5 - 2=3

Total df is equal to the sum  of seperate degree of freedom dfR  and dfE

total df = 1 +3  4

SSR = \frac{(S_x_y)^2}{S_x_x} = \frac{64386^2}{96080} \\\\= 43146.9296

Total SS =Syy= 45007.2

SSE + Total SS = SSR

= 45007.2 - 43146.9296

= 1860.2705

7 0
3 years ago
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