geno3141

What do you mean by "the normal"?

This is inductive because you are using the knowledge of the past to predict the future.

Induction allows for the possibility that your prediction can be wrong; what happened in the past doesn't always predict the future.

To have deduction, you must already have a rule that always works.

Because you are guessing the rule, you are using induction.

An example:

Induction:  Guess the next number in this sequence:  1, 2, 4, ___.

Deduction: The rule is double the last number to get the next number in this sequence:  1, 2, 4, ___

<For the induction example, you might guess the next number is 7 because going from 1 to 2, you add 1, going from 2 to 4, you add 2, going from 4 to the next number, you add 3, etc. For the deduction example, the only possible correct anser is 8.

So, for induction, you might have more than one 'right' answer because you might be able to create more than one rule, while, for deduction, there is only one right answer, because there is only one rule.>

sec(x) = sqrt(2)

Since sec(x) = 1/cos(x)   --->   1/cos(x) = sqrt(2)

Multiply both sides by cos(x)   --->   1  =  sqrt(2) x cos(x)

Divide both sides by cos(x)   --->   1/sqrt(2)  =  cos(x)

Since cos(x)  =  1/sqrt(2)   --->  multiply both the numerator and denominator of 1/sqrt(2) by sqrt(2)

--->   1/sqrt(2) x sqrt(2)/sqrt(2)  =  sqrt(2) / 2

Therefore,  cos(x)  =  1/sqrt(2)  =  sqrt(2)/2.

To find the mean, add all the numbers together and divide by the number of numbers.

To find the median, rearrange the numbers so they are listed from smallest to largest, and take the middle number as the median.

The mode is the number that is used the most often.

If x and y are in the ratio a:b, then x:y  =  a:b  or  x/y  =  a/b.

Since  x + y  =  c,  then  y  =  c - x..

Since  x/y  =  a/b  and  y  =  c - x, then, by substituting:  x/(c - x)  =  a/b.

Cross multiplying:  x(b)  =  a(c - x)   --->   bx  =  ac - ax   --->   ax + bx  =  ac   --->   x(a + b)  =  ac

Dividing both sides by  (a + b)   --->   x  =  ac / (a + b)

If you need to do it "by hand", follow the instructions in your text book.

If you need help with those instructions, post back and we will help you.

If you can use an on-line calculator, I suggest:  https://www.easycalculation.com/statistics/standard-deviation.php

Good luck!

2 / [ 5 sqrt(5) - 3 ]

Multiply the numerator and the denominator by the conjugate of the denominator:

the conjugate of [ 5 sqrt(5) - 3 ] is [ 5 sqrt(5) + 3 ].

The numerator of the answer:  2 x [ 5 sqrt(5) + 3 ]  is  10 sqrt(5) + 6.

The denominator of the answer:  [ 5 sqrt(5) - 3 ] x [ 5 sqrt(5) + 3 ]  = 125 - 9  =  116.

Press (2nd)

arrow down and press (atan)

atan(      will appear in the window       enter .6114

atan(.6114)     will become 31.4    (approximately)

This will be the answer in degrees.

If you want the answer in radians, arrow down to the lowre left corner and highlight rad.

6 - 2(x - y)  =  -3x + 5

First, get rid of the parentheses by using the distributive property:

6 - 2x + 2y  =  -3x + 5

Get rid of the 6 from the left side by subtracting 6 from both sides:

-2x + 2y  =  -3x - 1

Get rid of the -3x from the right side by adding 3x to both sides:

x + 2y  =  -1

First, solve the problem with x to the left side:

2x - 5 < 3

2x < 8

x < 4

If your answer is less than (<), shade to the left.

If your answer is greater than (>), shade to the right.

The symbol, < or >, points to the direction that you should shade.

If the answer contains either < or >, graph with an open circle.

If the answer contains <= or >=, graph with a filled-in circle.