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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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Combine like terms.<br><br> -2x4+16+2x4+9-3x5
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Answer:

25 - 3x^5

Step-by-step explanation:

-2x^4+16+2x^4+9-3x^5

Combine like terms

-2x^4+2x^4+9+16-3x^5

0                 + 25 -3x^5

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In a crayon box there are 5 dark colors for every 8 light colors. If there are 20 dark colors, hoW many light colors are there.
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32

Step-by-step explanation:

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The 2000 population of a city was 710​,000 and was increasing at the rate of 1.49 % each year. At that​ rate, when will the popu
AlekseyPX

Answer:

23.1567

Step-by-step explanation:

710000(1+1.49/100)ⁿ=1000000

710000×1.0149ⁿ=1000000

1000000÷710000=1.0149ⁿ

1.4084507=1.049ⁿ

log1.4084507=ⁿlog1.0149

log1.4084507/log1.0149=ⁿ

7 0
3 years ago
A high school band asked a number of students whether they would like blue, gold, or both for the uniforms for the band. The res
Anna35 [415]
Given a Venn diagram showing the number of students that like blue uniform only as 32, the number of students that like gold uniform only as 25, the number of students that like blue and gold uniforms as 12 and the number of students that like neither blue nor gold uniform as 6.

Thus, the total number of students interviewed is 75.

Recall that relative frequency of an event is the outcome of the event divided by the total possible outcome of the experiment.

From the relative frequency table, a represent the relative frequency of the students that like gold but not blue.
From the Venn, diagram, the number of students that like gold uniform only as 25, thus the relative frequency of the students that like gold but not blue is given by
\frac{25}{75} = \frac{1}{3}=0.33=33\%

Therefore, a = 33% to the nearest percent.

Similarly, from the relative frequency table, b represent the relative frequency of the students that like blue but not gold.
From the Venn, diagram, the number of students that like blue uniform only as 32, thus the relative frequency of the students that like gold but not blue is given by
\frac{32}{75} = 0.427=42.7\%

Therefore, b = 43% to the nearest percent.
7 0
3 years ago
you are running a fuel economy study. One of the cars you find is blue. It can travel 31 1/2 miles on 1 1/4 gallons of gasoline.
SIZIF [17.4K]

Answer:

Step-by-step explanation:

<u><em>Blue Car:</em></u>  (31 1/2 miles)/(1 1/4 gallons)

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(63/2)*(4/5) = <u>25.2 miles/gallon.</u>

<u><em>Red Car:</em></u>  (27 1/5 miles)/(4/5 gallon)

= <u>34 miles/gallon.</u>

The Red Car will travel the furthest.

7 0
3 years ago
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