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2 years ago

Which exponential equation is equivalent to the logarithmic equation below? c = ln 2

Mathematics

2 answers:

krok68 [10]2 years ago

6 0

e^c=2

Step-by-step explanation:

ololo11 [35]2 years ago

5 0

1. To solve this problem, you need to remember that an exponential function has the following form:

f(x)=a^x

"a" is the base and "x" is the exponent.

2. It is important to know that the logarithmic functions and the exponential functions are inverse. Then, you have:

c=ln2
e^c=e^(ln2)
e^c=2

3. Therefore, the answer is:

e^c=2

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Un equipo de fútbol se conforma de cuatro líneas de jugadores: portero (9%), defensas (37%), medios (27%) y delanteros (27%), do

Tpy6a [65]

Answer:

According to the proble, the total number of goals are 1+11+15+23 = 50: 1 by the goalkeeper, 11 by defense, 15 by midfielders and 23 by strikers.

So, each probability can be found by using standard probabilities

$P=\frac{events}{total outcomes}$

<h3>(a) Defense</h3>

$P=\frac{11}{50} \approx 0.22$

Therefore, the defense has a probability of 22% of score that goal.

<h3>(b) Midfielders</h3>

$P=\frac{15}{50} \approx 0.30$

Therefore, midfielders have a probability of 30% of scoring that goal.

<h3>(c) Strikers.</h3>

$P=\frac{23}{50} \approx 0.46$

Therefore, strikers have a probability of 46% of scoring that goal.

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2 years ago

The average blood alcohol concentration (bac) of eight male subjects was measured after consumption of 15 ml of ethanol (corresp

Neporo4naja [7]

Answer:

After 5 minutes, the BAC was increasing at the rate of 0.0137 mg/mL a minute.

Step-by-step explanation:

The average blood alcohol concentration (bac) is modeled by the following function.

$c(t) = 0.0225te^{-0.0467t}$

In which t is measured in minuted.

How rapidly was the BAC increasing after 5 minutes?

This is c'(t) when t = 5.

Using the derivative of the product.

Derivative of the product:

$c(t) = f(t)*g(t)$

$c'(t) = f'(t)*g(t) + f(t)*g'(t)$

In which problem:

$f(t) = 0.0225t$

$g(t) = e^{-0.0467t}$

$c'(t) = 0.0225e^{-0.0467t} - 0.0225*0.0467*te^{-0.0467t}$

$c'(5) = 0.0225e^{-0.0467*5} - 0.0225*0.0467*5e^{-0.0467*5} = 0.0137$

After 5 minutes, the BAC was increasing at the rate of 0.0137 mg/mL a minute.

3 0

2 years ago

A frog catches insects for his lunch. The frog likes to eat flies and mosquitoes in a certain ratio, which is shown in the diagr

avanturin [10]

Answer:

ON MONDAY: 35 mosquitos.

ON TUESDAY: 6 flies.

Step-by-step explanation:

As you can see in the diagram, the frog eats 3 flies for every 7 mosquitoes (for lunch). Then you can expresed this ratio as following:

3:7 or $\frac{3}{7}$

Based on the table:

-If the frog eats 15 flies on monday, then the number of mosquitos that it eats can be calculated as following:

$\frac{3}{7}=\frac{15}{mosquitoes}\\\\mosquitoes=\frac{15*7}{3}\\\\mosquitoes=35$

-If the frog eats 14 mosquitoes on tuesday, then the number of flies that it eats can be calculated as following:

$\frac{3}{7}=\frac{flies}{14}\\\\flies=\frac{14*3}{7}\\\\flies=6$

8 0

2 years ago

the graph of g(x) is a translation of the function f(x) = x2. the vertex of g(x) is located 5 units above and 7 units to the rig

bulgar [2K]

Translation of 7 units to the right ⇒ subtract 7 units to the argument ⇒ f(x-7)

Translation of 5 units up ⇒ add 5 units to the function ⇒ f(x) + 5

g(x) = f (x-7) + 5 = (x-7)^2 + 5

The subtraction of 7 units to the argument of the function (this is x) translates the function 7 units to the right.

Adding 5 units to the function f, translates the graph 5 units up.

6 0

2 years ago

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Alana is writing a coordinate proof to show that the diagonals of a rectangle are congruent. She starts by assigning coordinates

tamaranim1 [39]

D(S,P) = √(0-0)^2 + √(b-0)^2
d(S,P) = √b^2
d(S,P) = b
so
SP = b

d(P, Q) = √(a-0)^2 + √(b-b)^2
d(P, Q) = √a^2
d(P, Q) = a
so
PQ = a

SQ = c^2 = a^2 + b^2
SQ = √(a^2 + b^2)

answer
the length of one of the diagonals of the rectangle is √(a^2 + b^2)

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2 years ago

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