Answer: The required system of equations are
y = 30x
13x + y = 258
Step-by-step explanation:
Let x represent the number of hours
that the driver worked.
Let y represent the number of miles that the truck drove.
For every truck that goes out, Mason must pay the driver $13 per hour of driving and also has an expense of $1 per mile driven for gas and maintenance. If on a particular day, his total expenses for the driver, gas and truck maintenance were $258, it means that
13x + y = 258
On that particular day, the driver drove an average of 30 miles per hour.
Speed = distance/time
It means that
y/x = 30
y = 30x
If the equation is in y = k*x form, then we have a direct proportional relationship between x and y. In this case, y = (1/5)*x is in the form y = k*x where k = 1/5. So this equation is proportional. The constant of proportionality is k = 1/5
In terms of a graph, you can tell if it has the following properties:
1) The graph goes through the origin (0,0) which is where the x and y axis cross
2) The graph is a straight line
You should find that graphing y = (1/5)x will satisfy both properties above, so that will visually confirm you have the right answer. The graph is shown in the attached image. The red line represents the graph of the equation. The red line goes through (0,0) and (5,1), which are point A and point B respectively.
Part 1:
Given a number line with the point

and the point

The sampling error is given by:

Part 2:
Given a number line with the point

and the point

The sampling error is given by:
Complete question:
Para ingresar a la Universidad del Chocó se aplica una prueba de razonamiento que consta de 30 preguntas. Por cada respuesta correcta se asignan 5 puntos y por cada incorrecta (o no contestada) se restan 2 puntos. Si un participante obtuvo un puntaje de 94 puntos, ¿cuantas preguntas respondió bien?
Responder:
número de respuestas correctas = 22
Explicación paso a paso:
Dado lo siguiente:
Número total de preguntas = 30
Deje respuestas correctas = y; Respuestas incorrectas = n
Marca otorgada por y = 5
Marca deducida por n = 2
Si el total de preguntas = 30; luego
y + n = 30 - - - - (1)
Puntuación total obtenida = 94; luego
5y - 2n = 94 - - - (2)
De 1),
y + n = 30
y = 30 - n
Sustituya y = 30 - n en equ (2)
5 (30 - n) - 2n = 94
150 - 5n - 2n = 94
150 - 7n = 94
-7n = 94-150
-7n = - 56
n = 56/7
n = 8
Sustituir n = 8 en (1)
y + n = 30
y + 8 = 30
y = 30 - 8
y = 22
y = número de respuestas correctas = 22
n = número de respuestas incorrectas = 8