Given that cos (x) = k
what does cos (2x) = ?

Thanks in advance :)

Step-by-step explanation:

there are 36 (6×6) possible results and number combinations for 2 dice.

a)

to create a sum of 4 we need one of the following combinations :

1 3

2 2

3 1

so, 3 out of the overall possible 36 possibilities.

and that means the probability is 3/36 = 1/12

b)

to create a sum of 7 we need one of the following combinations :

1 6

2 5

3 4

4 3

5 2

6 1

so, 6 out of the overall possible 36 possibilities.

and that means a probability of 6/36 = 1/6

c)

since the possible outcomes in that regard are only 2 (even and uneven), with equal balance the probability is 1/2.

make it more formal ?

to get an even sum, every possible number on one die can be combined with 3 possibilities on the other.

1 can be combined with 1, 3, 5

2 with 2, 4, 6

3 with 1, 3, 5

4 with 2, 4, 6

5 with 1, 3, 5

6 with 2, 4, 6

these are 6×3 = 18 combinations of of the possible 36.

so, the probability is 18/36 = 1/2

d)

not a 6 ?

so, what does that mean ?

we are looking only at 5 possible outcomes per die.

that is 5×5 = 25 combinations out of the possible 36.

that means that probabilty is 25/36.

e)

not a perfect square ?

we have in the range of the possible sums with 2 dice (2 .. 12) only two perfect squares : 4 and 9

so, the sum must NOT be 4 AND NOT be 9.

so, here it might be easier to count the unwanted cases and then deduct the probability from 1 to express the opposite.

the combinations to get 4 we have already under a)

3 combinations with 3/36=1/12 probability.

the combinations to get 9

1 none

2 none

3 6

4 5

5 4

6 3

so, 4 combinations with a probability of 4/36 = 1/9

therefore, we have (3+4) = 7 cases out of the possible 36 we actually want to avoid.

so, the probability to get any one of the other (desired) combinations is therefore (36-7)/36 = 29/36

The probabilities are:

The probability for a given outcome is given by the quotient between the number of combinations that give that outcome and the total number of combinations.

Here each dice has 6 possible outcomes, so the total number of combinations for the two dice is:

6*6 = 36 combinations.

a) Here we need to count how many combinations add to 4, the notation I will use is:

dice 1   dice 2

1              3

3               1

2               2

There are 3 combinations that add to 4, then the probability of getting a sum equal to 4 is:

P = 3/36 = 0.083

b) Same thing as before, this time we count the combinations that add to 7.

dice 1   dice 2

1               6

6               1

5               2

2               5

4                3

3                4

There are 6 combinations that add to 7, so the probability is:

P = 6/36 = 0.167

c) The possible even numbers are: {2, 4, 6, 8, 10, 12}

A way of doing this, is:

If the first dice is even/odd, then the second also must be even/odd.

Then the probability is just 1/2  = 0.5 (because there are the same number of odd and even numbers in a dice).

d) The sum must not be equal to 6, the combinations that add up to 6 are:

dice 1   dice 2

2            4

4             2

3             3

1              5

 5            1

So 5 combinations add up to 6, then there are 31 combinations that do not add up to 6, this means that the probability of not getting a sum equal to 6 is:

P = 31/36 = 0.861

e) The perfect squares are 4 and 9, we already know that 3 combinations add up to 4, now let's find the combinations that add up to 9.

dice 1   dice 2

6             3

3              6

5              4

4               5

So 4 combinations add up to 9, then there is a total of 7 combinations that give a perfect square, then there are 29 combinations that do not add to a perfect square.

The probability is:

P = 29/36 = 0.806

If you want to learn more about probability, you can read:

https://brainly.com/question/251701

Answer:

the box volume is 34

Step-by-step explanation:

so you add then multiply 24 by 1/8 and that make 34 and sorry if it's not correct I'm bad at matg

Answer:

yes

Step-by-step explanation:

The perimeter of the rectangle ABCD and WXYZ are 14 units and 28 units respectively. The perimeter of the rectangle ABCD and WXYZ are 12 units² and 48 units² respectively.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The perimeter of a rectangle = 2(L+W)

The vertices of two rectangles are A(−5,−1),B(−1,−1),C(−1,−4),D(−5,−4) and W(1,6),X(7,6),Y(7,−2),Z(1,−2).

As per the given data, the figure of two rectangles has been attached below.

According to the graph,

The perimeter of the rectangle ABCD = 2(3 + 4) = 2(7) = 14 units

The perimeter of the rectangle WXYZ = 2(6 + 8) = 2(14) = 28 units

The area of the rectangle ABCD = (3 × 4) = 12 units²

The area of the rectangle WXYZ = (6 × 8) = 48 units²

The rectangles are similar because the ratio of length to width is equivalent.

The perimeter of the rectangle ABCD and WXYZ are 14 units and 28 units respectively. The perimeter of the rectangle ABCD and WXYZ are 12 units² and 48 units² respectively.

Learn more about the Perimeter of the rectangle here:

brainly.com/question/15287805

#SPJ5

Answer:

35

Step-by-step explanation:

49*5/7

=35

Answer:

a=-3

b=-63

c= 2

d=8

e=9

f=128

h=-21

i=24

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)^c = a^(bc)

__

The left-side expressions (all the same) can be simplified to ...

  (7^(1/5))·(49^(7/5)) = (7^(1/5))·((7^2)^(7/5))

  = (7^(1/5))·(7^(14/5)) . . . . . . matches 3rd right-side expression

  = 7^(1/5 +14/5) = 7^(15/5) = 7^3

  = 343 . . . . . . . . . . . . . . . . . . matches 1st right-side expression

__

49 is obviously not equivalent to 343.

49^(2/10) is obviously not equivalent to 49^(7/5).

Answer:

-1;undefined;1;0

Step-by-step explanation:

The first one (-9/9), can also be written as - 9/9 = - 1.

The second one (9/0), is undefined because every single term even 0 itself, if you divide it by 0, it'll be undefined!

The third one, we see we have division, and whenever we have division or multiplication and also 2 negative signs, they cancel each other, as you're left with 9/9=1.

The fourth one, whenever you have 0 at the numerator, no matter the denominator(only matters when it's =0, but that's undefined), the result will always be 0 !

Answer:

4(2+g)

Step-by-step explanation:

8+4g

Rewriting

4*2 + 4*g

Factor out the 4

4(2+g)

Answer:

-72=-72

Step-by-step explanation:

5n-42=12n

n=-6

5*(-6)-42 = 12*(-6)

-30-42=-72

-72=-72

So, n= -6 is the right number for this equation

Answer:

25.317977802344

Step-by-step explanation:

25x25= 625

4x4= 16

625+16= 641

The square root of 641 is 25.317977802344

n this case we are going to use the 'Babylonian Method' to get the square root of any positive number.

We must set an error for the final result. Say, smaller than 0.01. In other words, we will try to find the square root value with at least 1 correct decimal place.

Step 1:

Divide the number (641) by 2 to get the first guess for the square root.

First guess = 641/2 = 320.5.

Step 2:

Divide 641 by the previous result. d = 641/320.5 = 2.

Average this value (d) with that of step 1: (2 + 320.5)/2 = 161.25 (new guess).

Error = new guess - previous value = 320.5 - 161.25 = 159.25.

159.25 > 0.01. As error > accuracy, we repeat this step again.

Step 3:

Divide 641 by the previous result. d = 641/161.25 = 3.9751937984.

Average this value (d) with that of step 2: (3.9751937984 + 161.25)/2 = 82.6125968992 (new guess).

Error = new guess - previous value = 161.25 - 82.6125968992 = 78.6374031008.

78.6374031008 > 0.01. As error > accuracy, we repeat this step again.

Step 4:

Divide 641 by the previous result. d = 641/82.6125968992 = 7.7591072555.

Average this value (d) with that of step 3: (7.7591072555 + 82.6125968992)/2 = 45.1858520774 (new guess).

Error = new guess - previous value = 82.6125968992 - 45.1858520774 = 37.4267448218.

37.4267448218 > 0.01. As error > accuracy, we repeat this step again.

Step 5:

Divide 641 by the previous result. d = 641/45.1858520774 = 14.1858562034.

Average this value (d) with that of step 4: (14.1858562034 + 45.1858520774)/2 = 29.6858541404 (new guess).

Error = new guess - previous value = 45.1858520774 - 29.6858541404 = 15.499997937.

15.499997937 > 0.01. As error > accuracy, we repeat this step again.

Step 6:

Divide 641 by the previous result. d = 641/29.6858541404 = 21.5927760397.

Average this value (d) with that of step 5: (21.5927760397 + 29.6858541404)/2 = 25.63931509 (new guess).

Error = new guess - previous value = 29.6858541404 - 25.63931509 = 4.0465390504.

4.0465390504 > 0.01. As error > accuracy, we repeat this step again.

Step 7:

Divide 641 by the previous result. d = 641/25.63931509 = 25.0006678318.

Average this value (d) with that of step 6: (25.0006678318 + 25.63931509)/2 = 25.3199914609 (new guess).

Error = new guess - previous value = 25.63931509 - 25.3199914609 = 0.3193236291.

0.3193236291 > 0.01. As error > accuracy, we repeat this step again.

Step 8:

Divide 641 by the previous result. d = 641/25.3199914609 = 25.3159643039.

Average this value (d) with that of step 7: (25.3159643039 + 25.3199914609)/2 = 25.3179778824 (new guess).

Error = new guess - previous value = 25.3199914609 - 25.3179778824 = 0.0020135785.

0.0020135785 <= 0.01. As error <= accuracy, we stop the iterations and use 25.3179778824 as the square root.

So, we can say that the square root of 641 is 25.31 with an error smaller than 0.01 (in fact the error is 0.0020135785). this means that the first 2 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math. sqrt(641)' is 25.317977802344327.

Answer:

2

Step-by-step explanation:

two plus four equals six

Answer:

Step-by-step explanation:

The perimeter is:

Total:

Correct choice is A

Answer:

A is correct

Step-by-step explanation:

Answer:

10x - 1

Step-by-step explanation:

(x + 8) - (-9x + 9) = x + 8 + 9x - 9 = (x+9x) + (8-9) = 10x -1

The equivalent Expression is (10x- 1).

An expression in math is a sentence with a minimum of two numbers/variables and at least one math operation in it.

For example,  A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression.

Given:

We have to find the difference when (-9x +9) is subtracted from (x + 8)

so, (x + 8) - (-9x + 9)

= x + 8 + 9x - 9

= (x+9x) + (8-9)

= 10x -1

Hence, the equivalent Expression is (10x- 1).

Learn more about Expression here:

https://brainly.com/question/14083225

#SPJ2

Answer:

4^(-14)

Step-by-step explanation:

When multiplying or dividing powers of the same number, you can just add or subtract the powers.

Answer:

6

Step-by-step explanation:

=15+21+17+26+18+29/

/ 21

=126/21

=6

Answer:

$154.52

Step-by-step explanation:

First, you need to know the formula for this type of question.

The formula is I = Prt. These variables are: I = Interest, P = Principle investment, r = Rate, and t = Time.

So, your equation is I = 572.30(0.045)(6), where you have to find "I".

If you multiply 0.045 and 6, you get 0.27. Then, you multiply 0.27 and 572.30, which is 154.521.

The interest you earn will be $154.521. You can round the thousandths digit based on how you have been taught to do, but I will round the answer to 154.52.

Good luck!

Answer:

35

Step-by-step explanation:

Given k=-5

Substitute into the equation given

-7(-5) = 35

Answer:

The distance between A and B is 8.5 after rounded to the nearest tenth

Step-by-step explanation:

The formula you always use for distance between points is as pictured.

Point A is (-6, 4), this is x1 and y1

Point B is (2, 1), this is x2 and y2

(2-[-6])^2 + (1-4)^2

since 2 negatives make a positive, 2 - -6 = 8

1 - 4 = -3

This makes 8 squared and -3 squared

8x8 = 64

-3x-3 = 9

64 + 9 = 73

the square root of 73 = 8.544003745

After rounding to the nearest tenth, it is 8.5

I hope this helps you! Good luck :)

9514 1404 393

Answer:

  (a) f(g(x)) = g(f(x)) = x; functions are inverses

  (b) f(g(x)) = g(f(x)) = x +4; functions are not inverses

Step-by-step explanation:

f(g(x)) = f(1/(6x)) = 1/(6(1/(6x))) = 1/(6/(6x)) = 1/(1/x)

f(g(x)) = x

__

g(f(x)) is the same, because f(x) = g(x).

g(f(x)) = x

__

f(g(x)) = f(x +2) = (x +2) +2

f(g(x)) = x +4

__

g(f(x)) is the same, because f(x) = g(x).

g(f(x)) = x+4

__

Answer:

X = -20

Step-by-step explanation:

X = -2(6+4)

            ^ add 6 and 4 together first because they are in parentheses

-2(10)

   ^ this parenthesis means you want to multiply -2 and 10

because 2 x 10 = 20

that must mean -2 x 10 = -20

therefore, the value of X is -20

X= -20

5/0.25 = 20km/h

or

5000/1500 = 3.33m/s

Answer:

help with this https://brainly.com/question/25211060

Step-by-step explanation:

Step-by-step explanation:

$864 of 4%

864/100 x 4

=8.64 x 4

=34.56

Therefore, the total income tax deduction is 34.56.

Answer:

where is the n in the equation?

Step-by-step explanation:

If a polygon has 20 sides, then the sum of all of its interior angles is 3240°.

Answer:

B

Step-by-step explanation:

the converse of alternate interior angles theorem states that if two lines are intersected by a transversal forming congruent alternate interior angles then the lines are parallel.

Answer:

Step-by-step explanation:

Similar triangles given:

The ratio of corresponding sides:

Answer:

15/8 or 1 7/8

Step-by-step explanation:

Multiply the numerator by the number of workbooks (5)

You get 15/8.

Simplify

The length of 5 workbooks is 7 1/8 inch.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Thickness of workbook = 3/8 inch

Total workbooks = 5

So, the thickness of 5 workbooks

=5* 3/8

=15/8

=7 1/8 inch

Hence, the thickness of 5 workbooks is 7 1/8 inch.

Learn more about unitary method here:

https://brainly.com/question/22056199

#SPJ5

Answer:

$1.4

Step-by-step explanation:

$5.25 + $1.75 = $7

20/100 × $7

= 20× 7 /100

= 140/100

= $1.4

Answer:

Step-by-step explanation: