NEED HELP ! 20 POINTS
Use Demoivres Theorem to find ( 1 - i )^10
a. 32 - 32i
b. -32i
c. -32 + 32i
d. 32

Answer:

108°

Step-by-step explanation:

Suppose that circle with center A is a circular arena. Points B, C, D, E and F are 5 lights. These 5 points form regular pentagon (because these 5 lights are equally spaced around the perimeter of the arena).

The sum of all interior angles of pentagon can be calculated using following formula

[tex](n-2)\cdot 180^{\circ},\\ \\(5-2)\cdot 180^{\circ}=3\cdot 180^{\circ}=540^{\circ}[/tex]

All interior angles in regular pentagon are of equal measure, so

[tex]\dfrac{540^{\circ}}{5}=108^{\circ}[/tex]

Thus, the measure of each angle formed by the lights on the perimeter is 108°.

Answer:

D. 108

Step-by-step explanation:

I just did the test yourself

the answer in decimal form is .25 but in fraction form is 1/4

The value of cos(75°)cos(15°) is 0.25.

To solve the expression cos(75°)cos(15°), we use the identity cos(a)cos(b) = 0.5[cos(a+b) + cos(a-b)]. Applying this identity, we have:

cos(75°)cos(15°) = 0.5[cos(75°+15°) + cos(75°-15°)].

Using the values of cos(90°) = 0 and cos(60°) = 0.5, we can simplify the expression:

cos(75°)cos(15°) = 0.5[cos(90°) + cos(60°)] = 0.5[0 + 0.5] = 0.25.

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Answer:

Step-by-step explanation:

Let's call the ages D for daughter and S for son.

We know that the son is twice as old as the daughter, so:

S = 2D

We also know that in 15 years, their ages add up to 100, so:

(40+15) + (S+15) + (D+15) = 100

55 + S + 15 + D + 15 = 100

85 + S + D = 100

S + D = 15

Substituting the first equation:

2D + D = 15

3D = 15

D = 5

Therefore:

S = 2D = 10

The son is 10 and the daughter is 5.

Answer:

son = 10

daughter  = 5

Step-by-step explanation:

Let the daughter = d

Let the son =          s

s = 2*d

there ages in 15 years

Mother = 40 + 15 = 55

Son = s + 15

daughter = d + 15

Total: s + 15 + d+15 + 55 = 100    Combine the like terms.

s + d + 85 = 100                            Subtract 85 from both sides.

s + d = 100 - 85

s + d = 15

s = 2*d                                            Substitute for son

2d + d = 15

3d = 15

d = 15/3

d = 5

son = 2*5

son = 10

Check

son = 15 =           25

daughter + 15 =  20

Mother + 15    =   55

Total                   100 just as it should be.

Answer:

either of ...

• quadrant 1 only

• quadrant 1 and 4 only

Step-by-step explanation:

Time since the storm started is always positive. The values of x are positive in quadrants 1 and 4.

Temperatures in a blizzard are not always terribly cold. Some of the coldest snowstorms on record have temperatures in the range of +5 °F to +18 °F. These values are negative temperatures on the Celsius scale, so the quadrant used for plotting them will depend on the temperature scale you choose.

While temperatures in Alaska can be well below zero (on either the F or C temperature scales), the air usually has to warm up to the range indicated above before it can snow. US temperatures are generally reported using the Fahrenheit scale, but weather records are often kept using the Celsius scale.

I would be inclined to choose "Quadrant 1 and 4 only", but arguments can be made for "1 only" and "4 only" as suggested above.

Answer:Answer:

either of ...

• quadrant 1 only

• quadrant 1 and 4 only

Step-by-step explanation:

Time since the storm started is always positive. The values of x are positive in quadrants 1 and 4.

Temperatures in a blizzard are not always terribly cold. Some of the coldest snowstorms on record have temperatures in the range of +5 °F to +18 °F. These values are negative temperatures on the Celsius scale, so the quadrant used for plotting them will depend on the temperature scale you choose.

While temperatures in Alaska can be well below zero (on either the F or C temperature scales), the air usually has to warm up to the range indicated above before it can snow. US temperatures are generally reported using the Fahrenheit scale, but weather records are often kept using the Celsius scale.

I would be inclined to choose "Quadrant 1 and 4 only", but arguments can be made for "1 only" and "4 only" as suggested above.

Step-by-step explanation:

Answer:

C 1/2

Step-by-step explanation:

There are 4 suits, 2 suits are  red (hearts and diamonds) while 2 are black (clubs and spades)

Since 13 cards are in each suit, 26 cards are red ( 2 * 13)  

There are 52 total cards

P (red) = red cards/ total cards

           = 26 / 52

           = 1/2

Answer:

  42.5 ft by 21.3 ft

Step-by-step explanation:

The largest area is obtained when half the available fence is used parallel to the existing fence, and the other half is used to fence the two ends of the rectangle. Here, that means the dimension parallel to the existing fence is ...

  (85 ft)/2 = 42.5 ft

and the ends of the rectangular garden are ...

  (42.5 ft)/2 = 21.25 ft ≈ 21.3 ft

_____

You can figure this as follows:

Let x represent the length of fence parallel to the existing fence. Then the other dimension of the fenced area is (85 -x)/2 and the fenced area is the product of these dimensions.

  area = x(85-x)/2

This expression describes a downward-opening parabola with zeros at x=0 and at x=85. The vertex (maximum) will be found where x is halfway between these values, at x = (0 +85)/2 = 42.5.

Area is maximized when 42.5 ft of fencing is used parallel to the existing fence, and the other half of the fencing is used for the other two sides of the enclosure.

Answer:

T= 200+45m

Step-by-step explanation:

m= months

T=total money

Answer:

400,000,000

Step-by-step explanation:

4000000000000×.0001 is the answer above

Answer:

[tex]4 \times {10}^{8 }m \: or \: 400,000,000m[/tex]

Step-by-step explanation:

Put them both into standard form.

[tex]0.0001 = 1 \times {10}^{ - 4} \: and \: 4 \: trillion \: is \: 4 \times {10}^{12} [/tex]

Multiply them together.

[tex](1 \times {10}^{ - 4} ) \times (4 \times {10}^{12}) = 4 \times 10^{8} [/tex]

Answer:

  n = -2

Step-by-step explanation:

Eliminating parentheses, you have ...

  2n +6 -6n = 14

Combining terms and subtracting 6, you get ...

  -4n = 8

Dividing by the coefficient of n gives ...

  n = -2

_____

Check

  2(-2) +3(2 -2(-2)) = 14

  -4 +3(2+4) = 14

  -4 +3(6) = 14

  -4 +18 = 14 . . . . answer checks OK

n+5=2n-1

5=n-1

6=n <— Answer

Answer:

  C(n, 2)a^(n-2)b^2

Step-by-step explanation:

Generally, the expansion is written in decreasing powers of "a", so the first few terms would have variable constellations that look like ...

  a^n, a^(n-1)b, a^(n-2)b^2, ...

The coefficients would be (in order), C(n, k) for k increasing from 0, so the coefficient of the 3rd term would be C(n, 2).

Answer:

see below for explanation

3x +2y = 15

Step-by-step explanation:

The x-coordinate and the y-coordinate are both linear functions of t, so their relationship to each other is linear. A graph of those (x, y) points must be a line.

___

You can find an equation by solving one of the expressions for t, then substituting that into the other.

x = 2t +3

t = (x -3)/2

Substituting into the y expression, we get ...

y = 3 -3(x -3)/2

y = (-3/2)x + 15/2

3x +2y = 15 . . . . . . . add 3/2x and multiply by 2 to put into standard form

_____

The attached graph shows a portion of the line defined parametrically (0 ≤ t ≤ 1). It is dotted so you can see it overlays the line defined by the linear equation in x and y.

E and F

The standard form for a quadratic function is f(x) = ax^2 + bx + c.

E follows this pattern. a = -2; b = -8; c = 3

F also follows this pattern. a = 1/2; b = -2; c = 0

Answer:

  Factor pairs of 36 are ...

     1×36, 2×18, 3×12, 4×9, 6×6 . . . and the reverse of these

There is nothing in the problem statement limiting the dimensions to integer numbers of feet, so any dimensions x and 36/x will do. (x in feet)

Step-by-step explanation:

Area is the product of length and width. The desired dimensions are the length and width of the floor, so any pair of numbers resulting in a product of 36 will be a possible set of dimensions.

If the dimensions are supposed to be integer numbers of feet, then the possibilities for length×width are ...

  1×36, 2×18, 3×12, 4×9, 6×6, 9×4, 12×3, 18×2, 36×1

_____

As a practical matter, the tree house probably needs to be wider than 2 feet, leaving 3×12, 4×9, and 6×6 as possible dimensions (length×width or width×length). Depending on the flooring material and the difficulty of cutting it, there may be other limitations on the dimensions.

The possible dimensions for the floor of the tree house that Matt and his dad are building are 1 ft x 36 ft, 2 ft x 18 ft, 3 ft x 12 ft, 4 ft x 9 ft, and 6 ft x 6 ft. These pairs are derived by identifying the factors of 36 square feet.

To determine all possible dimensions of the floor that Matt and his dad need to cover, we need to find pairs of whole numbers that multiply to 36 square feet. This is a classic problem in mathematics involving factors.

Here are the pairs of whole numbers that multiply to 36:

Each of these pairs represents a possible dimension for the tree house floor.

Answer:

So first, we need to find the area of the whole circle since we already had the radius:

A = πr² = 3.14 . 7.53² = 178.040826 (cm²)

Now our next job is to find the area of the square inside the circle.

Looking at the picture, we can see that the radius of the circle is also half of the diagonal of the square, so the whole diagonal of the square should be: 7.53 . 2 = 15.06 (cm)

*Now this is where things get a little bit more complicated:

Imagine that x is the length of the side of the square.

Using Pythagorean theorem, knowing that d is the diagonal of the square and also the hypotenuse of the right triangle inside the square, we have the equation:

a² + a² = d²

2a²      = d²

a²        = d²/2

a²        = 226.8036/2 = 113.4018

So a², which is also the area of the square, is 113.4018 (cm²)

So the are of the yellow region is: 178.040826 - 113.4018 ≈ 64.6 (cm²)

*I could be wrong though

Answer:

9936 inch.

Step-by-step explanation:

Note the measurements:

1 Yard = 3 Feet

1 Feet = 12 Inch

1 Yard = 3 Feet = (12)(3) Inches = 36 Inches; 1 Yard = 36 Inches

Multiply 276 with 36

276 x 36 = 9936

9936 inches is your answer.

~

Answer:

1. P(A) = 0.6826

2. P(B) = 0.13591

Step-by-step explanation:

the first graph is given just as an example to show the percentage distribution values for bell shaped curve

Answer:

68.3%, 33.3%

Step-by-step explanation:

PLATO answer!! pls mark brainliest :)))

The answer is B. It is the most reasonable answer that I see.

Answer:

[tex]704 in^2[/tex]

Step-by-step explanation:

The figure is a parallelogram.

The area of a parallelogram is

[tex]=base\:\:\times\:\:height[/tex]

The base is 22 inches and the height is 32 inches.

We multiply to obtain:

[tex]22\times 32=704in^2[/tex]

the correct answer is B

Answer:

x = ab/c

Step-by-step explanation:

The product of the distances from the point of intersection of the chords (secants) to the circle is the same for both chords (secants). (This is true whether the point of intersection is inside or outside the circle.)

ab = cx

x = ab/c

Answer:

0.335

Step-by-step explanation:

1. There is a 30 percent chance of a flight being delayed because of icy weather ,then the probability of being delayed is 0.3 and of being not delayed is 0.7.

2. If a flight is delayed because of icy weather, there is a 10 percent chance the flight will also be delayed because of a mechanical problem, then the probability of being delayed is 0.1 and the probabilty of not being delayed is 0.9.

3. If a flight is not delayed because of icy weather, there is a 5 percent chance that it will be delayed because of a mechanical problem (MP), then the probability of being delayed is 0.05 and the probabilty of not being delayed is 0.95. (See attached probability tree)

Delayed of icy weather - 0.3

Delayed of MP when weather is not icy - 0.7·0.05=0.035

Now, if one flight is selected at random from the airport in January, the probability that the flight selected will have at least one of the two types of delays is

0.3+0.035=0.335

The probability that the flight selected will have at least one of the two types of delays is  [tex]0.335[/tex].

1. There is a [tex]30[/tex]% chance of a flight being delayed because of icy weather, [tex]\therefore[/tex] probability of being delayed is  [tex]P(a)=0.3[/tex]  

probability of not being delayed is [tex]P(a')=1-0.3=0.7[/tex].

2. If a flight is delayed because of icy weather, there is [tex]10[/tex]% chance the flight will also be delayed because of a mechanical problem,

[tex]\therefore[/tex] probability of being delayed is [tex]P(b)=0.1[/tex]

probability of not being delayed is [tex]P(b')=1-0.1=0.9[/tex].

3. If a flight is not delayed because of icy weather, there is [tex]5[/tex]% chance that it will be delayed because of a mechanical problem ,

[tex]\therefore[/tex]probability of being delayed is [tex]P(c)=0.05[/tex]

probability of not being delayed is [tex]P(c')=1-0.05=0.95[/tex].

Delayed of mechanical problem when weather is not icy is:

[tex]P(a'\cap c)=P(a').P(c)=0.7\times 0.05=0.035[/tex]

Now, if one flight is selected at random from the airport in January, the probability that the flight selected will have at least one of the two types of delays is

[tex]P(a'\cap c)+P(a)=0.035+0.3=0.335[/tex]

Learn more about Probability.

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Answer:

• The function is a linear function

• The function changes at a constant rate

Step-by-step explanation:

A graph of the function shows it to be a straight line (linear function). Such a function always changes at a constant rate. The line goes downward to the right, so the function is a decreasing function.

___

"changes at a constant rate" and "linear function" are two different ways of saying the same thing: the graph of the function is a straight line.

Answer:

  D.  37.22%

Step-by-step explanation:

One of my favorite probability z-table websites calculates the fraction as 0.3722 = 37.22%.

___

Your graphing calculator or spreadsheet can probably do the same for you.

Using the concepts of the normal distribution and z-scores, you calculate the z-scores for $25,000 and $40,000. Then, looking up these z-scores in a standard normal distribution table, and subtracting these, you get the percentage 37.17%, making the closest answer option D: 37.22%.

This question requires understanding of both normal distribution and z-scores. A Z-score measures how many standard deviations an element is from the mean. To solve this, we calculate the z-scores for $25,000 and $40,000, respectively, using the formula: z = (X - μ) / σ where X is the value, μ is the mean, and σ is the standard deviation.

Then, look up these z-scores in a standard normal distribution table (also known as a Z table). The values corresponding to -1.35 and -0.10 are 0.0885 and 0.4602, respectively. Substract these to find the percentage of homeowners with incomes between $25,000 and $40,000. That is, (0.4602 - 0.0885) * 100 = 37.17%. The closest answer is then option D: 37.22%

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Answer:

4 to 13

4:13

Step-by-step explanation:

I finished my test and these were the answers

The ratio of the number of fish to the total number of pets Dalia has is 4 to 13 or 4:13.

The subject of this question is the calculation of a ratio. In this case, the asked ratio is the number of fish to the total number of pets that Dalia has. Dalia has 4 fish and a total of 9 hamsters + 4 fish = 13 pets. Therefore, the correct answer is the ratio of 4 (fish) to 13 (total pets). This ratio can be represented in two ways: B) 4 to 13 or E) 4:13. The other options represent different ratios and do not correctly answer the question.

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Answer:

The measure of angle JKP is 61°

Step-by-step explanation:

we know that

If the measure of angle m<LOI=38°

then

m arc IL=38° -----> by central angle

and

If the measure of angle m<JOP=84°

then

m arc JP=84° -----> by central angle

Remember that

The measure of the interior angle is the semi-sum of the arcs that comprise it and its opposite.

so

m<JKP=(1/2)[arc IL+arc JP]

substitute the values

m<JKP=(1/2)[38°+84°]=61°

The answer is x=17. Since it says that the plot point is the answer to square root 4.1^2 = 16.81 which is closest to 17.

Hope this helps and hope you have a great day and brainiest is always appreciated

ANSWER

[tex]f(0) = g(0)[/tex]

EXPLANATION

From the graph we

[tex]g(0) = - 2[/tex]

because this is where the line x= 0 meets the graph of g(x).

Also

[tex]f(0) = - 2[/tex]

because this is where the line x= 0 meets the graph of f(x).

This implies that,

[tex]f(0) = g(0)[/tex]

The correct choice is A.

Answer:

Step-by-step explanation:

Givens

Cyclist A

r = r_a - 3

t = 5 hours.

d = ?

Cyclist B

r = r _a

t = 5 hours - 1/2 hour = 4.5 hours.

d = d - 31.5

Formula

(r - 3)*5 + 5*r = d

r*4.5 = d - 31.5

Explanation

The rate of A is 3 less than the rate of B. Together, they bicycle the entire distance (d). That's the first equation

The second equation is a lot harder. That equation has to do with the one starting off from B. His useful cycling time is 4 1/2 hours because he starts off 1/2 hour later.

He travels d - 31.5 which A travels 31.5

Solution

The total distance is the same. We will use that fact to solve for r first.

(r - 3)*5 + 5r = d

4.5r + 31.5 = d

Remove the brackets in the top equation.

5r - 15 + 5r = d

10r - 15 = 4.5r + 31.5             Add 15 to both sides

10r -15+15 = 4.5r + 31.5+15

10r = 4.5r + 46.5                   Subtract 4.5 r from both sides.

10r-4.5r = 46.5

5.5r = 46.5

r = 8.45 mph

====================

4.5r + 31.5 = d

4.5*8.45 + 31.5 = d

d = 69.53 miles

====================

If this proves to be incorrect, and you have choices, please list them.

Answer:

  D. [tex]f^{-1}(x)=\log_2{(x-6)}[/tex]

Step-by-step explanation:

Solve x = f(y) for y:

  x = 2^y +6

  x -6 = 2^y . . . . subtract 6

  log2(x -6) = y . . . . take the log base 2 . . . . matches choice D

Answer:

The answer is D

Step-by-step explanation:

In order to find out the inverse of the function, you have to express a new function where the independent variable must be "y" instead of "x".

So, you have to reorganize the base function and then free the variable "x".

[tex]f(x)=2^x+6\\f(x)=y\\y=2^x+6\\2^x=y-6\\log_2(2^x)=log_2(y-6)\\x*log_2(2)=log_2(y-6)\\log_2(2)=1\\x=log_2(y-6)\\[/tex]

Then, we recall "y" as "x" and [tex]x=f^-^1(x)[/tex]

Finally, the answer is:

[tex]f^-^1(x)=log_2(x-6)[/tex]

For this case we have that by definition, the slope-intersection equation of a line is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

[tex]m = \frac {y2-y1} {x2-x1} = \frac {-1 - (- 7)} {2-0} = \frac {-1 + 7} {2} = \frac {6} { 2} = 3[/tex]

Thus, the equation is:

[tex]y = 3x + b[/tex]

Substituting a point we find b:[tex]-7 = 0 + b\\b = -7[/tex]

Finally the equation is:

[tex]y = 3x-7[/tex]

ANswer:

The missing value is 3

Answer:

The value of missing is 3

Step-by-step explanation:

* To form an equation of a line from two points on the line, you

  must find the slope of the line at first

- The form of the equation is y = mx + c, where m is the slope of the

 line and c is the y-intercept

- The rule of the slope of a line passes through point (x1 , y1) and (x2 , y2)

  is m = (y2 - y1)/(x2 - x1)

* Lets solve the problem

∵ (0 , -7) and (2 , -1) are tow points on the line

- Let (0 , -7) is the point (x1 , y1) and (2 , -1) is the point (x2 , y2)

∴ m = (-1 - -7)/(2 - 0) = (-1 + 7)/2 = 6/2 = 3

- Lets write the equation

∴ y = 3x + c

- c is the y-intercept means the line intersect the y-axis at point (0 , c)

∵ Point (0 , -7) on the line

∴ The line intersect the y-axis at point (0 , -7)

∴ The y-intercept is -7

∴ The equation of the line is y = 3x - 7

* The value of missing is 3

Answer:

  745.5 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the trig function relating the hypotenuse and the side opposite an angle. It tells you ...

  Sin = Opposite/Hypotenuse

The line marked x (the hypotenuse of the triangle) is a transversal crossing the two parallel horizontal lines. That means the interior angle of the triangle at lower right (the angle of elevation) has the measure 28°. That angle is opposite the side marked 350 ft. So, you have ...

  sin(28°) = (350 ft)/x

Multiplying by x/sin(28°), this equation becomes ...

  x = 350 ft/sin(28°)

  x ≈ 745.5 ft