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shtirl [24]
3 years ago
11

If f(x) = 5x - 2 and g(x) = 2x + 1, find (f + g)(x)

Mathematics
2 answers:
V125BC [204]3 years ago
7 0

Answer:

Thus, (f + g)(x) = 7x - 1

Step-by-step explanation:

(f + g)(x) = 7x - 1

Step-by-step explanation:

Given :  f(x) = 5x – 2 and g(x) = 2x + 1

We have to find  (f + g)(x)

Consider  (f + g)(x) = f(x) + g(x)

Also, given  f(x) = 5x – 2 and g(x) = 2x + 1

Substitute, we have,

f(x) + g(x) = 5x - 2 + 2x + 1

LIKE TERMS are terms having same variable with same degree.

Simplify by adding like terms,  we have,

f(x) + g(x) = 5x + 2x - 2  + 1

f(x) + g(x) = 7x  - 1

Thus, (f + g)(x) = 7x - 1

SVEN [57.7K]3 years ago
5 0

Answer:

(f + g)(x) = 7x - 1

Step-by-step explanation:

Given :  f(x) = 5x – 2 and g(x) = 2x + 1

We have to find  (f + g)(x)

Consider  (f + g)(x) = f(x) + g(x)

Also, given  f(x) = 5x – 2 and g(x) = 2x + 1

Substitute, we have,

f(x) + g(x) = 5x - 2 + 2x + 1

Like Terms are terms having same variable with same degree.

Simplify by adding like terms,  we have,

f(x) + g(x) = 5x + 2x - 2  + 1

f(x) + g(x) = 7x  - 1

Thus, (f + g)(x) = 7x - 1

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Ayuda porfa, es urgente
storchak [24]

Answer:

Media: 167.88 cm

Mediana:  167.6 cm

Modo: 166.67 cm

Step-by-step explanation:

Hola!

La variable de interés es:

X: estatura de un alumno de noveno año de educación básica.

<u>1)</u>

Primero debes ordenar los datos de menor a mayor y contar cuantos de ellos corresponden dentro de cada intervalo determinado, por ejemplo, el primer intervalo es:

[160;164)

Los intervalos están definidos con el límite inferior cerrado, es decir que incluye el valor de dicho límite, y el límite inferior abierto, es decir, que ese valor no está incluido en el intervalo.

160,160,160,161,162,163,164,165,165,165,165,166,167,167,167,167,168,168,168,169,170, 170, 170,171,173,173,173,175,175,176.

f(1)= 6 (seis valores de estatura corresponden a este intervalo)

La sumatoria de todas las frecuencias absolutas debe dar por resultado el total de observaciones n= 30

Para el segundo intervalo [164;168)

f(2)= 10

<u>2)</u>

hi representa la frecuencia relativa simple y esta se calcula como fi/n

Por ejemplo para el primer intervalo:

h(1)= f(1)/n= 6/30= 0.20

Esta indica la proporción de que las alturas estén entre 160 y 164 cm.

En porcentaje se expresa como hi*100, para el primer intervalo: 0.20*100)= 20%

Para el segundo intervalo h(2)= f(2)/n= 10/30= 0.33 y su porcentaje es 33%

Como indican la proporción de cada categoría de la distribución, la sumatoria de las frecuencias relativas simples de todas las categorías debe ser 1.

<u>3)</u>

Como lo dice su nombre, esta frecuencia es acumulada y se calcula como la sumatoria de las frecuencias absolutas simples, para el primer intervalo, dado que previo a él no hay "nada" es igual a la frecuencia absoluta simple:

F(1)= f(1)

Para el segundo intervalo, es la frecuencia absoluta simple del primer intervalo más la frecuencia relativa simple del segundo intervalo:

F(2)= f(1) + f(2)= 6 + 10= 16

<u>4)</u>

Esta frecuencia también representa la sumatoria de las frecuencias relativas simples.

H(1)= h(1)= 0.20 como previo al primer intervalo no existe distribución definida, la frecuencia relativa acumulada es igual a la frecuencia relativa simple.

Para el segundo intervalo la frecuencia relativa acumulada es:

H(2)= h(1)+h(2)?= 0.20+0.33= 0.57

Adjunta a la respuesta encontrarás la tabla completa.

5)

Como no específica medidas de tendencia central requeridas, voy a calcular la media, mediana y modo utilizando la tabla.

<u>Media</u>

X[barra]= (∑x'fi)/n= ∑x'*hi

Dónde x' representa la marca de clase de cada intervalo. Para calcular la marca de clase de los intervalos debes realizar un promedio entre sus límites y su valor siempre debe encontrarse dentro de los límites del intervalo. Si no es así, has cometido un error de cálculos:

(Limite inferior + Limite superior)/2

1. [160;164)  x₁'= (160+164)/2= 162

2. [164;168)  x₂'= 166

3. [168;172)  x₃'= 170

4. [172;176)  x₄'= 174

Una vez que calculaste las marcas de clase, puedes calcular la media:

X[barra]= ∑x'*hi= (162*0.20)+(166*0.33)+(170*0.27)+(174*0.20)= 167.88 cm

<u>Mediana:</u>

La mediana es el valor de la variable que divide a la muestra en dos (50%-50%).

Para poder calcularla primero debes identificar su posición, en este tipo de presentación, debes identificar el intervalo en el que se encuentra incluida la mediana.

Para muestras pares, la posición de la mediana se calcula como:

PosMe= n/2= 30/2= 15

Esto significa que la mediana corresponde a la 15va observación de la muestra, observando la columna de las frecuencias absolutas (simples o acumuladas) debes identificar cual es el intervalo de la mediana:

Al segundo intervalo se corresponde una frecuencia acumulada de 16, lo que significa que la posición de la mediana está incluida en este intervalo:

[164;168)

Entonces puedes calcular la mediana como:

Me= Li + c [\frac{PosMe-F_{(i-1)}}{f_i} ]

Dónde

Li: es el límite inferior del intervalo de mediana.

c: es la amplitud del intervalo

F₍i₋₁₎: frecuencia absoluta acumulada del intervalo anterior al intervalo mediana

fi: frecuencia absoluta del intervalo mediana

Me= 164 + 4 [\frac{15-6}{10} ]= 167.6

Me= 167.6 cm, como puedes notar, el valor de la mediana se encuentra entre los límites del intervalo.

<u>Modo o Moda:</u>

El modo o la moda de una distribución corresponde al valor más observado, es decir, al valor con mayor frecuencia absoluta simple. Al igual que la media, para calcular el modo primero debes identificar el intervalo que lo contiene. En este caso, el intervalo modal será aquel con la mayor frecuencia absoluta simple.

[164;168)

La fórmula para calcular el modo es:

Md= Li + c[\frac{(f_{max}-f_{ant})}{(f_{max}-f_{ant})+(f_{max}-f_{post})} ]

Li: es el límite inferior del intervalo modal

c: es la amplitud del intervalo

f_{max}: es la frecuencia absoluta simple del intervalo modal.

f_{ant}: es la frecuencia absoluta simple del intervalo anterior al intervalo modal.

f_{post}: es la frecuencia absoluta simple del intervalo posterior al intervalo modal.

Md= 164 + 4[\frac{10-6)}{(10-6)+(10-8)} ]= 164+4[\frac{4}{4+2} ]= 166.67

Md= 166.67 cm

¡Espero que tengas un buen día!

4 0
3 years ago
You and your friend are selling magazine subscriptions. You sell 8 fewer magazine subscriptions than your friend. Together you s
Xelga [282]

Answer:

b. you sold 17

c. your friend sold 25

Step-by-step explanation:

you=y your friend=x

y=x-8

42=x +y

42=x+(x-8)

42=x+x-8

42=2x-8

50=2x

25=x

Use x to solve for y...

y=25-8

y=17

3 0
3 years ago
PLEASE HELP IM ON A TEST RIGHT NOW: Twelve boxes of golf balls cost $30 and two boxes of hockey pucks cost $45. The cost per box
vlada-n [284]

Answer:362.5

Step-by-step explanation: thank me later

5 0
2 years ago
Read 2 more answers
What is -5.8+ (2.5) Evaluate expression
sweet [91]

-5.8 + (-2.5)

is just 5.8 - 2.5

Which is -8.3

8 0
3 years ago
How do you find the surface area square pyramid if you know thank you i am in 6th grade please help
Andreyy89

Answer:

Simple

Step-by-step explanation:

find the area of the square and all the other triangles ex:

Surface Area Formulas

In general, the surface area is the sum of all the areas of all the shapes that cover the surface of the object.

Cube | Rectangular Prism | Prism | Sphere | Cylinder | Units

Note: "ab" means "a" multiplied by "b". "a2" means "a squared", which is the same as "a" times "a".

Be careful!! Units count. Use the same units for all measurements. Examples

Surface Area of a Cube = 6 a 2

(a is the length of the side of each edge of the cube)

In words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a, or a 2 . Since these are all the same, you can multiply one of them by six, so the surface area of a cube is 6 times one of the sides squared.

Surface Area of a Rectangular Prism = 2ab + 2bc + 2ac

(a, b, and c are the lengths of the 3 sides)

In words, the surface area of a rectangular prism is the area of the six rectangles that cover it. But we don't have to figure out all six because we know that the top and bottom are the same, the front and back are the same, and the left and right sides are the same.

The area of the top and bottom (side lengths a and c) = a*c. Since there are two of them, you get 2ac. The front and back have side lengths of b and c. The area of one of them is b*c, and there are two of them, so the surface area of those two is 2bc. The left and right side have side lengths of a and b, so the surface area of one of them is a*b. Again, there are two of them, so their combined surface area is 2ab.

Surface Area of Any Prism

(b is the shape of the ends)

Surface Area = Lateral area + Area of two ends

(Lateral area) = (perimeter of shape b) * L

Surface Area = (perimeter of shape b) * L+ 2*(Area of shape b)

Surface Area of a Sphere = 4 pi r 2

(r is radius of circle)

Surface Area of a Cylinder = 2 pi r 2 + 2 pi r h

(h is the height of the cylinder, r is the radius of the top)

Surface Area = Areas of top and bottom +Area of the side

Surface Area = 2(Area of top) + (perimeter of top)* height

Surface Area = 2(pi r 2) + (2 pi r)* h

In words, the easiest way is to think of a can. The surface area is the areas of all the parts needed to cover the can. That's the top, the bottom, and the paper label that wraps around the middle.

You can find the area of the top (or the bottom). That's the formula for area of a circle (pi r2). Since there is both a top and a bottom, that gets multiplied by two.

The side is like the label of the can. If you peel it off and lay it flat it will be a rectangle. The area of a rectangle is the product of the two sides. One side is the height of the can, the other side is the perimeter of the circle, since the label wraps once around the can. So the area of the rectangle is (2 pi r)* h.

Add those two parts together and you have the formula for the surface area of a cylinder.

Surface Area = 2(pi r 2) + (2 pi r)* h

Tip! Don't forget the units.

These equations will give you correct answers if you keep the units straight. For example - to find the surface area of a cube with sides of 5 inches, the equation is:

Surface Area = 6*(5 inches)2

= 6*(25 square inches)

= 150 sq. inches

6 0
3 years ago
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