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Furkat [3]
3 years ago
7

If s and t are integers greater than 1 and each is a factor of the integer n, which of the following must be a factor of n^{st}

?
1) s^t
2) (st)²
3) s+t
A) None
B) 1 only
C) 2 only
D) 3 only
E) 1 and 2
Mathematics
2 answers:
krek1111 [17]3 years ago
7 0

Answer:

E ( 1 and 2) only

Step-by-step explanation:

s is an integer  and a factor of n and is greater than 1 and t is also an integer  and a factor  of and equally greater than 1

s^t is a factor n^(st)

let s = 3 and t = 4  and n = 12

then n^(3×4) = 12 ^12= (3 × 4) ^(3×4) = 3³ × 4⁴ or 3⁴ × 4³

(st)² = (3×4)² = (12)² which is a factor of 12¹²

3^4

s + t = 3+4 = 7 and 7 is not a factor 12¹²

let say s = 2, and t = 3

2 + 3 = 5 and 5 is not a factor of 6⁶

andrey2020 [161]3 years ago
6 0

Answer:

E) 1 and 2

Step-by-step explanation:

We are given that there are two integers (s and t) and they are factors of another integer (n). For example if s = 3 and t = 2, we can have n = 6.

Thus:

n^(st) = 6^(2*3) = 6^6 = (2^6)(3^6)

For the first condition: s^t = 3^2 is a factor of (2^6)(3^6)

For the second condition: (st)^2 = (3*2)^2 = 6^2 is a factor of 6^6

For the third condition: s+t = 3+2 = 5 is not a factor of 6^6 or (2^6)(3^6)

Therefore, only 1 and 2 are factors of n^(st)

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Reptile [31]

Answer and Explanation:

Given : The random variable x has the following probability distribution.

To find :

a. Is this probability distribution valid? Explain and list the requirements for a valid probability distribution.

b. Calculate the expected value of x.

c. Calculate the variance of x.

d. Calculate the standard deviation of x.

Solution :

First we create the table as per requirements,

x      P(x)         xP(x)           x²            x²P(x)

0    0.25           0               0                0

1     0.20        0.20             1              0.20

2    0.15          0.3               4             0.6

3    0.30         0.9               9             2.7

4    0.10          0.4               16             1.6

   ∑P(x)=1     ∑xP(x)=1.8               ∑x²P(x)=5.1

a) To determine that table shows a probability distribution we add up all five probabilities if the sum is 1 then it is a valid distribution.

\sum P(X)=0.25+0.20+0.15+0.30+0.10

\sum P(X)=1

Yes it is a probability distribution.

b) The expected value of x is defined as

E(x)=\sum xP(x)=1.8

c) The variance of x is defined as

V=\sum x^2P(x)-(\sum xP(x))^2\\V=5.1-(1.8)^2\\V=5.1-3.24\\V=1.86

d) The standard deviation of x is  defined as

\sigma=\sqrt{V}

\sigma=\sqrt{1.86}

\sigma=1.136

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Answer:

Down below

Step-by-step explanation:

a. The range of y = sinθ is [-1,1]

b. The period of y = cosθ is 2π

c. The asymptotes of y = tanθ are -π2, π2, πn

d. The amplitude of y = sinθ is 1

e. The period of y = tanθ is π

f. The max value of y = cosθ is 1

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2 years ago
What is the solution of the system? Use the elimination method. 2x+y=20 6x?5y=12
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Answer:

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Step-by-step explanation:

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-5(2x + y = 20)

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<u> 6x + 5y = 12  </u>

-4x = -88  

x = 22

Plug 22 in for x in either equation

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Answer:

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Step-by-step explanation:

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And the second equation as:

f(x) = 3.05x + 4.05

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3.35x = 3.05x + 4.05

0.30x = 4.05

x = 13.5

This means once you buy 13.5 gallons, the prices will be the same. Any amount over that and the car wash will be cheaper

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Answer:

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Step-by-step explanation:

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