Answer:
The number zero (0) is a rational number.
Step-by-step explanation:
The number zero can be written as a ratio of two integers, thus it is indeed a rational number. This statement is TRUE.
The <em>trigonometric</em> function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.
<h3>How to derive a sinusoidal expression</h3>
In this problem we need to find a <em>sinusoidal</em> expression that models the curve seen in the picture. The most typical <em>sinusoidal</em> model is described below:
f(x) = a · sin (b · x + c) + d (1)
Where:
- a - Amplitude
- b - Angular frequency
- c - Angular phase
- d - Vertical midpoint
Now we proceed to find the value of each variable:
Amplitude
a = - 2 - (-6.5)
a = 4.5
Angular frequency
b = 2π / T, where T is the period.
0.25 · T = 4 - 3
T = 4
b = 2π / 4
b = π / 2
Midpoint
d = - 6.5
Angular phase
- 2 = 4.5 · sin (π · 4/2 + c) - 6.5
4.5 = 4.5 · sin (π · 4/2 + c)
1 = sin (2π + c)
π = 2π + c
c = - π
The <em>trigonometric</em> function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.
To learn more on trigonometric functions: brainly.com/question/15706158
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Answer:
20 lawyers
Step-by-step explanation:
48 ÷ 12 = 4
which means every year 4 lawyers are hired
5 × 4 = 20
so this means the law firm has hired 20 lawyers in the last 5 years
Since there are a 100 cents in a dollar. the 100 is the denominator.
46/100, reduce; 23/50, can't be reduced any further. so 23/50 is the fraction.
If I'm understanding the question correctly, you're saying that <em>X</em> is a random variable following a normal distribution with mean 5 and standard deviation 4.2, and you want to find the proportion of the distribution that lies in the interval (-3, 8). In other words, the probability
P(-3 < <em>X</em> < 8)
Transform <em>X</em> to <em>Z</em>, which follows the standard normal distribution with mean 0 and standard deviation 1, using the rule
<em>X</em> = <em>µ</em> + <em>σZ</em> ==> <em>Z</em> = (<em>X</em> - <em>µ</em>)/<em>σ</em>
where <em>µ</em> and <em>σ</em> are the mean and standard devation of <em>X</em>, respectively.
We have
P(-3 < <em>X</em> < 8) = P((-3 - 5)/4.2 < (<em>X</em> - 5)/4.2 < (8 - 5)/4.2)
… ≈ P(-1.904 < <em>Z</em> < 0.714)
… ≈ P(<em>Z</em> < 0.714) - P(<em>Z</em> < -1.904)
… ≈ 0.762 - 0.028 ≈ 0.734