Find the value of f(x) = -3x^3 + 2x^2 for f(-1)

Answer:

The best measure of center is median = 37.50.

Step-by-step explanation:

The complete question is:

The data set gives the number of bottles filled by each of the workers in a bottling plant in one day.

{36, 18, 16, 28, 68, 35, 37, 66, 38, 40, 41, 44, 72, 29}

The best measure of center for this data set is the , and its value expressed up to one decimal place is?

Solution:

The three measures of center are:

1. Mean
2. Median
3. Mode

The mean is the average value of the data set and uses all the values of the data set.

The median is the middle value of the data set.

Mode is the value of the data st with the highest frequency or number of occurrence.

Compute the mean, median and mode of the data set provided as follows:

So, the mean is 40.57.

The data set in ascending order is:

{16, 18, 28, 29, 35, 36, 37, 38, 40, 41, 44, 66, 68, 72}

There are 14 values in the data set. That is an even data set.

The median for an even data set is the average of the middle two values.

The middle two values are: 37, 38

Average of {37, 38} =

So, the median is 37.50.

None of the values are repeating itself. Thus, the data does not have a mode.

For the provided data:

Mean > Median

Implying that the data set is right-skewed.

For a skewed distribution or data set the median is the measure of center.

Thus, the best measure of center is median = 37.50.

Answer: (1,2)

Step-by-step explanation:

You must:

- Multiply the first equation by 3.

- Add both equations.

- Solve for the variable left. In this case will be x.

Then:

Substitute x=1 into any of the original equtions and solve for y:

The solution is: (1,2)

Answer:

The solution of the system of equation is (1 , 2)

Step-by-step explanation:

The system of equation is:

* 13x + y = 15 ⇒ (1)

* -9x - 3y = -15 ⇒ (2)

- By using elimination ⇒ we must make on of the

 two variables in the two equations has the same value

 with different sign

- So we will multiply equation (1) by 3 to eliminate y

∴ 3(13x) + 3(y) = 3(15)

∴ 39x + 3y = 45 ⇒ (3)

- Now add (2) and (3)

∴ 39x + -9x = 45 + -15

∴ 30x = 30 ⇒ ÷ 30 both sides

∴ x = 1

- Substitute the value of x in equation (1) or (2)

- Lets use (1)

∴ 13(1) + y = 15

∴ 13 + y = 15 ⇒ subtract 13 from both sides

∴ y = 15 - 13  

∴ y = 2

∴ The solution of the system of equation is (1 , 2)

Answer:

x = -4      x=-1

Step-by-step explanation:

10x + 6 = -2x^2 -2

Add 2x^2 to each side

+2x^2 +10x + 6 =2x^2 -2x^2 -2

2x^2 +10x + 6 =  -2

Add 2 to each side

2x^2 +10x + 6+2 =  -2+2

2x^2 +10x + 8 = 0

Divide each side by 2

2/2x^2 +10/2x + 8/2 = 0/2

x^2 +5x+4 = 0

What 2 numbers multiply to 4 and add to 5

4*1 = 4

4+1 =5

(x+4) (x+1) = 0

Using the zero product property

x+4 = 0     x+1 =0

x+4-4 = 0-4       x+1-1 =0-1

x = -4      x=-1

Answer:

x = -4 or x = -1

Step-by-step explanation:

Given equation is :

10x+6 = -2x²-2

Adding 2x² and 2 to both sides of above equation , we get

2x²+2 +10x+6 = -2x²-2 +2x²+2

Adding like terms , we get

2x²+10x+8 = 0

As we have noticed that there are multiples of 2.

Taking 2 as common,we get

2(x²+5x+4) = 0

Multiplying by 1/2 to both sides of above equation , we get

1/2.2(x²+5x+4) = 1/2.0

x²+5x+4 = 0

Split the middle term of above equation so that the sum of two term should be 5 and their product be 4.

x²+4x+x+4 = 0

Making two groups ,we get

x(x+4)+1(x+4)

Taking (x+4) common,we get

(x+4)(x+1) = 0

Applying Zero-Product Property to above equation, we get

x+4 = 0 or x+1 = 0

Firstly, solve x+4 = 0

Adding -4 to both sides of above equation,we get

x+4-4 = 0-4

x +0 = -4

x = -4  

Secondly, solve x+1 = 0

Adding -1 to both sides of above equation,we get

x+1-1 = 0-1

x = -1

Hence, the solution of 10x+6 = -2x²-2 is {-4,-1}.