What is S7 for 6 – 24 + 96 – 384 + ... ?

Answers

Answer 1

Answer: 6 - 34 + 96 - 384 +...
a 1 = 6 , a 2 = a 1 * ( - 4 ) , a 3 = a 2 * ( - 4 ), a 4 = a 3 * ( - 4)...
a 5 = - 384 * ( - 4 ) = 1,536
a 6 = 1536 * ( - 4 ) = - 6,144
a 7 = - 6,144 * ( - 4 ) = 24,576
This is a sum of a geometric sequence:
S 7 = 6 - 24 + 96 - 384 + 1,536 - 6,144 + 24,576 = 19,662
Another way to solve this:
S 7 = a 1 * ( r^n - 1) / ( r - 1 ) = 6 * (( - 4) ^7 - 1 )/ (- 4 - 1)=
= 6 * (-16,385) / (-5 ) = 19,662

Answer 2

Answer:

The answer is 19,662

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Find the slope of the line passing through the points (2, 7) and (-1, 4). 3 1 -1

Answers

Answer:

Step-by-step explanation:

To find the slope of a line passing through two points, we can use the formula:

slope = (change in y) / (change in x)

Let's apply this formula to the given points (2, 7) and (-1, 4):

1. Determine the change in y:

change in y = 4 - 7 = -3

2. Determine the change in x:

change in x = -1 - 2 = -3

3. Calculate the slope using the formula:

slope = (-3) / (-3) = 1

Therefore, the slope of the line passing through the points (2, 7) and (-1, 4) is 1.

In summary, the slope of the line passing through the given points is 1.

If three times a number minus 2 equals 13, what is the number?

Answers

Change the messy words into numerals
3 times a number minus 2    equals    13
3 × n - 2 = 13

3n - 2 = 13
take 2 to the other side
3n - 2 + (2) = 13 + (2)
3n = 15

Divide by 3 on either sides to isolate n
$(3n)/(3)$ = $(15)/(3)$
3 and 3 cancels out

n = 5

check:
3 times 5 minus 2 equals 13
3   × 5 - 2 = 13
15 - 2 = 13
13 =    13

The number is 5

What is the median of the data set?

{16, 15, 17, 19, 12, 11, 14, 14, 13, 11, 18, 15}

Answers

The median is the numeric value separating the higher half of a sample data set from the lower half. The median of a data set can be found by arranging all the values from lowest to highest value and picking the one in the middle. If there is an odd number of data values then the median will be the value in the middle. If there is an even number of data values the median is the mean of the two data values in the middle. For the data set 16, 15, 17, 19, 12, 11, 14, 14, 13, 11, 18, 15 the median is 14.5. It is the mean of 14 and 15 or, (14+15)/2 = 14.5.

The shoe size for all the pairs of shoes in a person’s close are recorded. 7,7,7,7,7,7,7,7,7,7A. What is the mean?
B. What is the standard deviation?

Answers

Answer:

To find the mean (average) and standard deviation of the given shoe sizes, you can follow these steps:

A. Mean (Average):

The mean is calculated by adding up all the values and then dividing by the number of values.

Mean = (Sum of all values) / (Number of values)

In this case, the sum of all the shoe sizes is:

7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 70

And there are 10 values.

Mean = 70 / 10 = 7

So, the mean (average) shoe size is 7.

B. Standard Deviation:

The formula for the standard deviation of a set of values can be quite complex, but for this small dataset with all values being the same, the standard deviation is essentially zero because there is no variability between the values.

In mathematical terms:

Standard Deviation = 0

So, the standard deviation for the given shoe sizes is 0.

Pls help....................

Answers

$b^2+6b=0\nb(b+6)=0\nb=0 \vee b=-6\n\n5x^2-5x=0\n5x(x-1)=0\nx=0 \vee x=1\n\n-10x+35x=0\n25x=0\nx=0\n\n2x+15x=0\n17x=0\nx=0\n\n18x^2+6x=0\n6x(3x+1)=0\nx=0 \vee x=-(1)/(3)\n\n-32x^2-24x=0\n-8x(4x+3)=0\nx=0 \vee x=-(3)/(4)$

Write an equation that requires at least three steps to solve and whose solution is x=3.5

Answers

The expression can be written as (2x)² + 1 = 50

What is an expression?

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the solution for the value of x is 3.5. The expression will be solved as below:-

2x = 7 (1 step)

(2x)² = 49 (2 steps)

(2x)² + 1 = 50 ( 3 steps)

Therefore, the expression can be written as (2x)² + 1 = 50.

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Answer:

(2x)^2 + 1 = 50

Step-by-step explanation:

x = 3.5