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2 years ago

Which logarithmic equation has the same solution as x minus 4 = 2 cubed

Mathematics

1 answer:

ziro4ka [17]2 years ago

7 0

Answer:

$\log_{2} (x-4) = 3$

Step-by-step explanation:

The initial expression is $x-4 = 2^{3}$ . Let apply the definition of logarithms to the expression:

$\log_{2} (x-4) = \log_{2} 2^{3}$

$\log_{2} (x-4) = 3$

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Carbon-141414 is an element which loses exactly half of its mass every 573057305730 years. The mass of a sample of carbon-141414

UkoKoshka [18]

Answer:

The function that models the mass of the carbon-14 sample remaining t years since the initial measurement is

M(t) = 741 e⁻⁰•⁰⁰⁰¹²¹ᵗ

with M(t) in grams and t in years.

Step-by-step explanation:

Radioactive reactions always follow a first order reaction dynamic

Let the initial concentration of Carbon-14 be M₀ and the concentration at any time be M

(dM/dt) = -kM (Minus sign because it's a rate of reduction)

(dM/dt) = -kM

(dM/M) = -kdt

∫ (dM/M) = -k ∫ dt

Solving the two sides as definite integrals by integrating the left hand side from M₀ to M and the Right hand side from 0 to t.

We obtain

In (M/M₀) = -kt

(M/M₀) = e⁻ᵏᵗ

M(t) = M₀ e⁻ᵏᵗ

Although, we can obtain k from the information on half life.

For a first order reaction, the rate constant (k) and the half life (T) are related thus

T = (In2)/k

The half life is the time taken for the radioactive substance to decay to hAlf of its original amount, and according to the question, T = 5730 years

k = (In 2)/5730 = 0.000120968 /year. = 0.000121 /year

M(t) = M₀ e⁻ᵏᵗ

k = 0.000121 /year, M₀ = 741 grams

The equation then becomes

M(t) = 741 e⁻⁰•⁰⁰⁰¹²¹ᵗ

with M(t) in grams and t in years.

Hope this Helps!!!

4 0

2 years ago

Scott wishes to make a line plot of the heights in inches for a basketball team. The heights are listed below. Use the drop-down

yaroslaw [1]

Answer:

a) Least (V):69 Greatest (V):84

b) 74 78 79 82 84 are equally the higher frequency so we go with the lower value (V): 74 which is also the mode and modal.

Step-by-step explanation:

5 0

2 years ago

: The You Move It Company (YMI) advertises that the cost to rent a moving truck for one day is $40 plus $1.99 for each mile the

mars1129 [50]

Part A: For 100 miles, the cost will be same for both companies.

Part B: Alex should use Drive and Move company as it will cost him less money.

Step-by-step explanation:

Given,

Starting amount of YMI= $40

Per mile charges = $1.99

Let,

x be the number of miles.

y be the total charges.

y = 1.99x+40 Eqn 1

Starting amount of DM = $60

Per mile charges = $1.79

y=1.79x+60 Eqn 2

Part A:

For same charges;

Eqn 1 = Eqn 2

$1.99x+40=1.79x+60\\1.99x-1.79x=60-40\\0.20x=20$

Dividing both sides by 0.20

$\frac{0.20x}{0.20}=\frac{20}{0.20}\\x=100$

For 100 miles, the cost will be same for both companies.

Part B:

Total miles = x = 150

Putting x=150 in Eqn 1

y=1.99(150)+40

y=298.5+40

y=$338.50

Putting x=150 in Eqn 2

y=1.79(150)+60

y=268.5+60

y=$328.50

Alex should use Drive and Move company as it will cost him less money.

4 0

2 years ago

The weight of a USB flash drive is 30 grams and is normally distributed. Periodically, quality control inspectors at Dallas Flas

Minchanka [31]

I have to think this again. be back later. X=2.22

3 0

2 years ago

Based on a study from the Chronicles of Flippin'' Awesomeness, the probability that Napoleon and Pedro make it to their first pe

muminat

Answer:

15.25% probability that Napoleon and Pedro catch the bus and make it to their first period class on time

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this problem, we have that:

Event A: Both Napoleon and Pedro catch the bus, so P(A) = 0.25.

Event B: Making to their first period class on time.

However, the probability that they make it to their first period class on time, given that they catch the bus is 0.61.

This means that $P(B|A) = 0.61$

What is the probability that Napoleon and Pedro catch the bus and make it to their first period class on time

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$0.61 = \frac{P(A \cap B)}{0.25}$

$P(A \cap B) = 0.61*0.25$

$P(A \cap B) = 0.1525$

15.25% probability that Napoleon and Pedro catch the bus and make it to their first period class on time

8 0

2 years ago