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Make an input-output table for the function g(x) =2x + 4. Use x-values of 1,2,3,4 and 5.

Masteriza [31]

ana is...

X g(x)

1 2(1)+4=6

2 2(2)+4=8

3 2(3)+4=10

4 2(4)+4=12

5 2(5)+4=14

7 0

3 years ago

After the data was recorded, Leah realized that she left out a student who handed out 42 flyers. How would the mean number of fl

Yuliya22 [10]

Answer:

Outlier An extreme value in a set of data which is much higher or lower than the other numbers. ... Outliers affect the mean value of the data but have little effect on the median or mode of a given set of data. Your question asks how number 42 would affect the mean, that depends on two things, is the 42 higher or lower than the mean before 42 is added to the data? If the 42 is higher, the mean would increase, if the 42 is lower, the mean would decrease. Hope that helps.

Step-by-step explanation:

8 0

3 years ago

A local pizzeria offers 15 toppings for their pizzas and you can choose any 3 of them for one fixed price. How many different ty

Shtirlitz [24]

Answer:

455 or 680, depending

Step-by-step explanation:

If we assume the three choices are different, then there are ...

15C3 = 15·14·13/(3·2·1) = 35·13 = 455

ways to make the pizza.

___

If two or three of the topping choices can be the same, then there are an additional ...

2(15C2) +15C1 = 2·105 +15 = 225

ways to make the pizza, for a total of ...

455 + 225 = 680

different types of pizza.

__

There is a factor of 2 attached to the number of choices of 2 toppings, because you can have double anchovies and tomato, or double tomato and anchovies, for example, when your choice of two toppings is anchovies and tomato.

_____

nCk = n!/(k!(n-k)!)

6 0

4 years ago

Solving Rational Functions Hello I'm posting again because I really need help on this any help is appreciated!!

Greeley [361]

Answer:

x = √17 and x = -√17

Step-by-step explanation:

We have the equation:

$\frac{3}{x + 4} - \frac{1}{x + 3} = \frac{x + 9}{(x^2 + 7x + 12)}$

To solve this we need to remove the denominators.

Then we can first multiply both sides by (x + 4) to get:

$\frac{3*(x + 4)}{x + 4} - \frac{(x + 4)}{x + 3} = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}$

$3 - \frac{(x + 4)}{x + 3} = \frac{(x + 9)*(x + 4)}{(x^2 + 7x + 12)}$

Now we can multiply both sides by (x + 3)

$3*(x + 3) - \frac{(x + 4)*(x+3)}{x + 3} = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}$

$3*(x + 3) - (x + 4) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}$

$(2*x + 5) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}$

Now we can multiply both sides by (x^2 + 7*x + 12)

$(2*x + 5)*(x^2 + 7x + 12) = \frac{(x + 9)*(x + 4)*(x+3)}{(x^2 + 7x + 12)}*(x^2 + 7x + 12)$

$(2*x + 5)*(x^2 + 7x + 12) = (x + 9)*(x + 4)*(x+3)$

Now we need to solve this:

we will get

$2*x^3 + 19*x^2 + 59*x + 60 = (x^2 + 13*x + 3)*(x + 3)$

$2*x^3 + 19*x^2 + 59*x + 60 = x^3 + 16*x^2 + 42*x + 9$

Then we get:

$2*x^3 + 19*x^2 + 59*x + 60 - ( x^3 + 16*x^2 + 42*x + 9) = 0$

$x^3 + 3x^2 + 17*x + 51 = 0$

So now we only need to solve this.

We can see that the constant is 51.

Then one root will be a factor of 51.

The factors of -51 are:

-3 and -17

Let's try -3

p( -3) = (-3)^3 + 3*(-3)^2 + +17*(-3) + 51 = 0

Then x = -3 is one solution of the equation.

But if we look at the original equation, x = -3 will lead to a zero in one denominator, then this solution can be ignored.

This means that we can take a factor (x + 3) out, so we can rewrite our equation as:

$x^3 + 3x^2 + 17*x + 51 = (x + 3)*(x^2 + 17) = 0$

The other two solutions are when the other term is equal to zero.

Then the other two solutions are given by:

x = ±√17

And neither of these have problems in the denominators, so we can conclude that the solutions are:

x = √17 and x = -√17

6 0

3 years ago

Problema de capacidades Una empresa aceitera ha envasado 3000 litros de aceite en 1200 botellas de dos y de cinco litros. ¿Cuánt

mariarad [96]

Answer:

Hay 200 botellas de 5 litros y 1000 botellas de 2 litros.

Step-by-step explanation:

Un sistema de ecuaciones lineales es un conjunto de dos o más ecuaciones de primer grado, en el cual se relacionan dos o más incógnitas.

Resolver un sistema de ecuaciones consiste en encontrar el valor de cada incógnita para que se cumplan todas las ecuaciones del sistema.

En este caso, las variables a calcular son:

x= cantidad de botellas de 2 litros.
y= cantidad de botellas de 5 litros.

Una empresa aceitera ha envasado 3000 litros de aceite en 1200 botellas de dos y de cinco litros. Entonces es posible plantear el siguiente sistema de ecuaciones:

$\left \{ {{2*x+5*y=3000} \atop {x+y=1200}} \right.$

Existen varios métodos para resolver un sistema de ecuaciones. Resolviendo por el método de sustitución, que consiste en despejar o aislar una de las incógnitas y sustituir su expresión en la otra ecuación, despejas x de la segunda ecuación:

x= 1200 - y

Sustituyendo la expresión en la primer ecuación:

2*(1200 - y) + 5*y=3000

Resolviendo se obtiene:

2*1200 - 2*y + 5*y= 3000

2400 +3*y= 3000

3*y= 3000 - 2400

3*y= 600

y= 600÷3

y= 200

Reemplazando en la expresión x= 1200 - y:

x= 1200 - y

x=1200 -200

x= 1000

<u><em>Hay 200 botellas de 5 litros y 1000 botellas de 2 litros.</em></u>

7 0

3 years ago