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labwork [276]
3 years ago
13

1. Given that (27 ^ (n + 3))/(81 ^ (p - 1)) = 3 , express p in terms of h.​

Mathematics
1 answer:
Troyanec [42]3 years ago
6 0

9514 1404 393

Answer:

  p = 3/4n +3

Step-by-step explanation:

Expressing the given equation in terms of powers of 3, we have ...

  (27^(n+3))/(81^(p-1)) = 3

  (3^3)^(n+3)/(3^4)^(p-1) = 3^1 . . . . as powers of 3

  3(n +3) -4(p -1) = 1 . . . . . . . . . . . . log base 3 (or, equate exponents)

  3n +9 -4p +4 = 1 . . . . . . . . . . . . . eliminate parentheses

  3n +12 = 4p . . . . . . . . . . . . . . . . add 4p -1

  p = 3/4n +3 . . . . . . . . . . divide by 4

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Factor this expression completely mr + ns - nr - ms
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(m - n)(r - s) Hope this helps and heve a nice day!

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From its founding through 2012, the Rock and Roll Hall of Fame has inducted 303 groups or individuals. Forty-seven of the induct
motikmotik

The probability of inductees who are female will be 0.155.

<h3>How to illustrate the probability?</h3>

Question: What proportion of inductees have been female or have included female members?

From the information, 303 groups or individuals and forty-seven of the inductees have been female or have included female members.

Therefore, the proportion will be:

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8 0
2 years ago
4 times a number is decreased by 9, the result is the same as when 15 is added to twice the number. find the number
igor_vitrenko [27]

Answer:

12

Step-by-step explanation:

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5 0
3 years ago
What is an equation for a sine curve with amplitude 2, and period 4pi radians ?
Nezavi [6.7K]
<span>1. a sine curve with amplitude 2, and period 4pi radians
</span>
the general equation of the sine curve ⇒⇒ y = a sin (nθ)
where: a is the amplitude  and  n = 2π/perid
∵ <span>amplitude 2, and period 4pi radians
</span>
∴ y = 2 sin (θ/2)

The correct answer is option D. y = 2 sin (θ/2)
===========================================

<span>2.The period and amplitude of the function ⇒⇒ y = 5 cos 2θ
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</span>
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</span>

The correct answer is option B. Period: pi radians: Amplitude:5

============================================================
3. tan (2π/3) = tan 120° = -√3 
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tan function in the second quadrant is negative
∴ tan 120° = - tan 60 = -√3

The correct answer is C. -sqrt3

=====================================================
4. <span>Tan 5π/6 = tan 150° = -(√3)/3
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The correct answer is <span>B.-sqrt3/3</span>
8 0
3 years ago
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