The rate of change of the linear function represented by the table is 3
<h3>Rate of change of a function</h3>
The rate of change of a function is also known as the slope of a function. The equation for calculating the slope is expressed as:
Slope = y2-y1/x2-x1
using the coordinates from the table (-2, -13) and (-1, -10)
Substitute
Slope = -10-(-13)/-1-(-2)
Slope = -10+13/-1+2
Slope =3
Hence the rate of change of the linear function represented by the table is 3
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The probability that a randomly selected student is in music/drama is 25%
<h3>How to determine the probability?</h3>
From the table, we have the following values
Music/Drama = 7 + 13 + 5 = 25
Total = (20 + 20 + 25 + 7 + 13 + 5 + 3 + 2 + 5) = 100
The probability is then calculated as:
P = Music/Drama / Total
So, we have:
P = 25/100
Express as percentage
P = 25%
Hence, the probability that a randomly selected student is in music/drama is 25%
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El volumen <em>remanente</em> entre la esfera y el cubo es igual a 30.4897 centímetros cúbicos.
<h3>¿Cuál es el volumen remanente entre una caja cúbica vacía y una pelota?</h3>
En esta pregunta debemos encontrar el volumen <em>remanente</em> entre el espacio de una caja <em>cúbica</em> y una esfera introducida en el elemento anterior. El volumen <em>remanente</em> es igual a sustraer el volumen de la pelota del volumen de la caja.
Primero, se calcula los volúmenes del cubo y la esfera mediante las ecuaciones geométricas correspondientes:
Cubo
V = l³
V = (4 cm)³
V = 64 cm³
Esfera
V' = (4π / 3) · R³
V' = (4π / 3) · (2 cm)³
V' ≈ 33.5103 cm³
Segundo, determinamos la diferencia de volumen entre los dos elementos:
V'' = V - V'
V'' = 64 cm³ - 33.5103 cm³
V'' = 30.4897 cm³
El volumen <em>remanente</em> entre la esfera y el cubo es igual a 30.4897 centímetros cúbicos.
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