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Olegator [25]
3 years ago
12

Which of the following is the rational exponent expression of third root of 4 n? A) (4n)3

Mathematics
2 answers:
zhuklara [117]3 years ago
3 0

You have to check which of the following expressions is the rational exponent expression of third root of 4n, or mathematically, \sqrt[3]{4n} . Consider all cases:

A. (4n)^3=4^3\cdot n^3=64n^3\neq\sqrt[3]{4n} .

B. 3n^4\neq \sqrt[3]{4n} .

C. quantity of 4n to the one third power is (4n)^{\frac{1}{3} }=\sqrt[3]{4n} (by the definition of rational power).

D. 4 times n to the one third power is 4\cdot n^{\frac{1}{3} }=4\sqrt[3]{n}\neq \sqrt[3]{4n} .

Answer: correct choice is C.

BigorU [14]3 years ago
3 0
The answer to the question above should be letter "C. quantity of 4 n to the one-third power". This means that the radicand is the product of 4 and n. This product is raised to the power 1/3. Mathematically,
                                   (4n)^1/3
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The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 3 . If there were
cestrela7 [59]
First you divide 4955 by 5 to get 991, then you multiply that by 3 to get 2973, the amount of no votes, then you add those together to get 7928 total votes
7 0
3 years ago
Which choice is the explicit formula for the following geometric sequence? 0.2, -0.06, 0.018, -0.0054, 0.00162
Crazy boy [7]

Answer:

aₙ = 0.2(-0.3)⁽ⁿ⁻¹⁾

Step-by-step explanation:

The geometric sequence with the first term a, a common ratio r has the nth term given as

Tₙ = arⁿ⁻¹

where Tₙ is the nth term

From the given sequence

a = 0.2

r = -0.06/0.2

= -0.3

Hence the nth term

= 0.2 * -0.3ⁿ⁻¹

The right option is E

8 0
3 years ago
The rate of change of the number of mountain lions N(t) in a population is directly proportional to 725 - N(t), where t is the t
wolverine [178]

Answer:

a) The implied differential equation is \frac{dN}{725 - N} = kdt

b) The general equation is N = 725 - C e^{-kt}

c) The particular equation is N = 725 - 325 e^{-0.49t}

d) The population when t = 5, N(5) = 697 = 700( to the nearest 50)

Step-by-step explanation:

The rate of change of N(t) can be written as dN/dt

According to the question, \frac{dN}{dt} \alpha (725 - N(t))

\frac{dN}{dt} = k (725 - N)\\\frac{dN}{725 - N} = kdt

Integrating both sides of the equation

\int {\frac{1 }{725 - N}} \, dN  = \int {k} \, dt\\- ln (725 - N) = kt + C\\ ln (725 - N) = -(kt + C)\\725 - N = e^{-(kt + C)} \\725 - N = e^{-kt} * e^{-C} \\725 - N = C e^{-kt}\\N = 725 - C e^{-kt}

When t = 0, N = 400

400 = 725 - C e^{-k*0}\\400 = 725 - C\\C = 725 - 400\\C = 325

When t = 3,  N = 650

650 = 725 - (325 * e^{-3k})\\325 * e^{-3k} = 75\\e^{-3k} = 75/325\\e^{-3k} = 0.23\\-3k = ln 0.23\\-3k = -1.47\\k = 1.47/3\\k = 0.49

The equation for the population becomes:

N = 725 - 325 e^{-0.49t}

At t = 5, the population becomes:

N = 725 - 325 e^{-0.49*5}\\N = 725 - 325 e^{-2.45}\\N = 696.95\\N(5) = 697

N(5) = 700 ( to the nearest 50)

6 0
3 years ago
For which values of a, b, and c will Ax+ By=C be a horizontal line through the point (-4,2)
RUDIKE [14]

Answer:

A = 0, B = 1 and C = 2

Step-by-step explanation:

The slope of a horizonal line is zero.

y = mx + b              Use the slope intercept form with m = 0  and point (-4, 2).

2 = 0(-4) + b           Solve for "b"

2 = 0 + b

2 = b

The equation in slope intercept form is y = 0x + 2 ; y = 2.

The equation in standard form: Ax + By = C   has the value 0x + y = 2

3 0
2 years ago
Please help answer these
BabaBlast [244]
You should use the ratio so 

2/ 4  = 6.5 / n  

n= 6.5 x 4  / 2 =  13 inches 


2- for two hours ------> four inches of snow 
for x hours -----> y inches of snow 
the equation is 
2/4 = x/ y 

x= 2y / 4 
 for x is the hours and y is the inches 

exercice 2
5 gr granula ----------------------> 1750 calories 
2 gr granula ----------------------> n ?? calories 

by cross multiplication 
n = 2 x1750 / 5 =  700 calories .

2-
she wants to eat 175 calories so 
u put granula under granula  and calories under calories to make this cross 

<span>5 gr granula ----------------------> 1750 calories 
</span>??? m granula ---------------------> 175 calories 
<span>by cross multiplication </span>
m = 175 x 5 / 1750 =  0.5 gr of granula 
8 0
3 years ago
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