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3 years ago

11

Use the graph shown to determine the TRUE statements.

1 answer:

Oliga [24]3 years ago

3 0

Answer:

The x-intercept tells the number of fish in the tank before any are sold.

Coordinates (20, 80) tell how many fish must be sold to have 80 fish remaining in the tank.

Step-by-step explanation:

You should know here that, the graph models a decreasing function. Also, the average rate of the change of the function, and which is the slope is -1 as it has a negative slope. And hence the correct option for this question are not these two. The correct options are the ones mentioned above. As the x-intercept tells the number of fish in the tank before any of them are sold. And the coordinates (20, 80) tells the number of fish that must be sold for having the 80 fish remaining in the tank.

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Write the equation of the trigonometric graph.

prisoha [69]

Answer:

$f(x)= \sin(6x)+3$

Step-by-step explanation:

The parent function of this graph is: y = sin(x)

The sine function is periodic, meaning it repeats forever.

Standard form of a sine function:

$f(x) = \sf A \sin (B(x + C)) + D$

A = amplitude (height from the mid-line to the peak)
2π/B = period (horizontal distance between consecutive peaks)
C = phase shift (horizontal shift - positive is to the left)
D = vertical shift

The parent function y = sin(x) has the following:

Amplitude (A) = 1
Period = 2π
Phase shift (C) = 0
Vertical shift (D) = 0
Mid-line: y = 0

From inspection of the given graph:

Amplitude (A) = 1
$\sf Period=\dfrac{\pi}{12}-\dfrac{-\pi}{4}=\dfrac{\pi}{3}$
Phase shift (C) = 0
Vertical shift (D) = +3 (as mid-line is y = 3)

$\sf If\:Period=\dfrac{\pi}{3} \implies \dfrac{2 \pi}{B}=\dfrac{\pi}{3}\implies B=6$

Substituting the values into the standard form:

$\implies f(x) =1 \sin (6(x + 0)) + 3$

$\implies f(x) = \sin (6x) + 3$

Therefore, the equation of the given trigonometric graph is:

$f(x)= \sin(6x)+3$

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2 years ago

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Answer:

a) 0.1535

b) 0.4866

c) 0.8111

Step-by-step explanation:

The probability that the next call come within the next t minutes is:

$p(t) = 1 -e ^{- t/3}$

According to this model,

a) the probability that a call in comes within 1/2 minutes is $p(t) = 1 -e ^{- (1/2)/3}$ =0.1535

b) the probability that a call in comes within 2 minutes is $p(t) = 1 -e ^{-2/3}$ =0.4866

c) the probability that a call in comes within 5 minutes is $p(t) = 1 -e ^{-5/3}$ =0.8111

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3 years ago

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laila [671]

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