Use DeMoivre's theorem to find the two square roots of the following number in polar form
38( cos 150° + sin 150°)
The square root with the smaller angle is (cos+)sin
The square root with the larger angle is (cos + sin
)
(Simplify your answers. Type integers or decimals. Type any angle measures in degrees. Use angle measures greater than or equal to 0 and less than 360.)

The given function shows imply that the graph g(x) is shifted two units right and three units up.

Option B is correct.

The transformation of a function occurs in a fancy way such that a function maps itself. f: x → x.

From the given information:

Let's take a look at the function f(x) that goes through 0 just when x = 0. Now we want to move it to the right by 2. It implies that it has to go through 0 when x = +2.

Now, we have to add 2 to x, then the function becomes f'(x) = f(x-2) will be shifted by 2 units to the right.

Similarly, the same scenario occurs when shifting up. Again imagine your function passes 0 when x = 0.  We have to add 3. Now, the function f’’(x) = f(x) + 3 will be shifted by 3 units up.

Combining the two transformations, we have:

Therefore, we can conclude that the function implies that the graph g(x) is shifted two units right and three units up.

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we conclude that the distance to the other side is 467 feet.

We know that the width of the river is 602ft. This means that the distance from shore to shore is 602 feet.

If the boy is at a distance of 135 from the shore, then the distance to the other side is given by the difference:

d = 602ft - 135ft = 467ft

Then, we conclude that the distance to the other side is 467 feet.

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Answer:

Step-by-step explanation:

Kcbsakhucvdwaiucvaewiugcvawdiugvcdwakugcwvjugvcdwauhbcwjuagvcejygavcjywetvfsjygeavcsaegycygaecyjgasa c

Step-by-step explanation:

Area of circle =   pi r^2

10 inch = pi (5)^2 = 25 pi

12 inch = pi (6)^2 = 36 pi

12 inch is 11pi bigger

    percentage:  11 pi is what percentage of 25 pi ?

        11 pi / 25 pi x 100%  = 44 % bigger

The area of a pizza increases with the square of the diameter. Therefore, a 10-inch pizza has an area of \(π*(10/2)^2= 78.54\)  square inches, and a 12-inch pizza has an area of \(π*(12/2)^2 = 113.10\) square inches. This is an increase of 113.10 - 78.54 = 34.56 square inches, or an increase of 44.2%.

To explain further, the diameter of a pizza is measured from one side to the other through the center of the pizza. As the diameter of the pizza increases, the area of the pizza increases. This is because the area of a pizza is calculated as \(π*(d/2)^2\), where d is the diameter. So, if the diameter increases, the area increases as well.

For example, if a 10-inch pizza has an area of 78.54 square inches, a 12-inch pizza would have an area of 113.10 square inches. This is an increase of 113.10 - 78.54 = 34.56 square inches, or an increase of 44.2%. This is because the diameter of the pizza has increased by 2 inches (10 inches to 12 inches), and the area has increased by 44.2%.

It is important to note that increasing the diameter of the pizza does not just increase the circumference of the pizza, but also the area. The increase in area is directly related to the increase in diameter, and can be calculated by taking the difference between the areas of the two pizzas.

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

Work Shown:

1 km = 1000 m

3.5 km = 3500 m  ............. multiplying both sides by 3.5

(70 paces)/(50 m) = (x paces)/(3500 m)

70/50 = x/3500

7/5 = x/3500

7*3500 = 5x .............. cross multiply

5x = 7*3500

x = (7*3500)/5

x = (7*5*700)/5

x = 7*700

x = 4900

Ann takes 4900 paces to walk 3.5 km

Answer:

12

Step-by-step explanation:

4/5 x -6 = -2

4 x -30 = -10

-120 = -10

12

Answer:

yz

Step-by-step explanation:

........

........

answer is YZ

The expression 7∛7 - ∛128 is: 49∛7 - 8∛2.

We can simplify this expression using the fact that ∛(a * b) = ∛a * ∛b and ∛(a^3) = a.

First, let's factor ∛128 into prime factors: ∛128 = ∛(2^7) = 2 * ∛(2^5) = 2 * ∛(32).

Next, we can simplify 7∛7 as much as possible:

7∛7 = ∛(7^3) * ∛7 = 7∛(7^2) * ∛7 = 7 * 7∛7.

Now we can substitute these simplifications into the original expression:

7∛7 - ∛128 = 7 * 7∛7 - 2 * ∛32

We can simplify ∛32 as follows:

∛32 = ∛(2^5) = 2 * ∛(2^2) = 4∛2

Now, we can substitute this back into the expression:

7 * 7∛7 - 2 * ∛32 = 7 * 7∛7 - 2 * 4∛2

= 49∛7 - 8∛2

So the simplified expression is 49∛7 - 8∛2.

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The paint cans and the spaces serve as examples of equivalent ratios. 5.5 cans of paint will be required to cover 2200 sq. unit.

Two ratios that have the same values are said to be equivalent. The same number can be used to multiply or divide both sums to get an equivalent ratio. The method is the same as determining equivalent fractions. When two or more ratios are reduced to their most basic form, they have the same value. Examples of equivalent ratios are 1:2, 2:4, and 4:8. In their most basic form, all three ratios have the same value, which is 1:2. They are in proportion if two ratios are equal. Equations in algebra are said to be equivalent if their solutions or roots are equal. When the same amount or expression is added to or removed from both sides of an equation, the result is the same.

To paint a 2200 square unit space, 5.5 cans are required.

The given parameter is:

Cans: Area\(=1:400\)

Express as fraction

Cans/Area\(=1/400\)

Multiply both sides by Area

Cans\(=\frac{1}{400}*Area\)

When the area is 2200, we have:

Cans\(=\frac{1}{400}*2200\)

Cans\(=5.5\)

5.5 cans are therefore required to paint a 2200 units square space.

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Step-by-step explanation:

5y-6py

y(5-6p)

Answer

hope it helps

Answer:

5y - 6py

y(5-6p)

is the answer

Max pays less for the jacket because he receives a discount through his father's employment at the store.

Let's compare the amounts paid by Max and Evan for the jacket.

Max pays 70% of the original price because his father works at the store. So Max pays 0.7 * $40 = $28.

Evan, on the other hand, has a coupon for $10 off. This means he can subtract $10 from the original price. Therefore, Evan pays $40 - $10 = $30.

Comparing the amounts, we see that Evan pays $30 for the jacket, while Max pays $28. Since $28 is less than $30, Max pays less for the jacket.

In summary, Max pays less for the jacket because he receives a discount through his father's employment at the store. Even though Evan has a coupon, Max's discounted price is lower than the price Evan pays after applying the coupon.

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The function g(x) is not one-to-one. However, a restricted domain where g(x) is one-to-one and non-decreasing is x ≤ -4.

To determine if g(x) is one-to-one, we need to check if different inputs (x-values) produce different outputs (y-values). In the case of g(x) = -(x+4)^2 - 7, we can see that different x-values can result in the same y-value. For example, if we substitute x = -5 and x = -3 into g(x), we get the same output of -7. This violates the one-to-one property. To find a restricted domain where g(x) is one-to-one and non-decreasing, we can analyze the graph of the function. The graph of g(x) is a downward-opening parabola with its vertex at (-4, -7). It is symmetric with respect to the vertical line x = -4. This symmetry indicates that the function is not one-to-one across its entire domain. However, if we restrict the domain to x ≤ -4 (including -4), we can observe that the function is one-to-one within this range. As x values decrease, the corresponding y values also decrease, making g(x) non-decreasing. In other words, within this restricted domain, different x-values will always produce different y-values, satisfying the one-to-one property.

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Answer:

7 inches

Step-by-step explanation:

The area of a rectangle A is equal to its length times its width (or base times height if you want to put it that way.)

Since A = b*h, h = A/b. Plugging in values gives you 91.7/ 13.1 = 7 inches.

So the answer is 7 inches.

You can find the coefficient of variation for your data set using a TI-84 calculator by following the below steps.

To find the coefficient of variation (CV) using a TI-84 calculator, follow these steps:

1. Enter the data set values into a list on your calculator. For example, if your data is stored in the list L1, enter the values into L1.

2. Calculate the mean of the data set using the calculator's statistical functions. Press the [STAT] button and navigate to the "Calc" menu. Choose the appropriate mean function (e.g., "1-Var Stats" or "mean") and select the list that contains your data (e.g., L1).

3. Calculate the standard deviation of the data set using the calculator's statistical functions. Press the [STAT] button, navigate to the "Calc" menu, and choose the appropriate standard deviation function (e.g., "1-Var Stats" or "stdDev"). Select the list containing your data (e.g., L1).

4. Divide the standard deviation by the mean and multiply by 100 to calculate the coefficient of variation. Store the standard deviation and mean values in variables if necessary. Use the formula CV = (stdDev / mean) * 100 to calculate the coefficient of variation.

By following these steps, you can find the coefficient of variation for your data set using a TI-84 calculator.

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To find the coefficient of variation on a TI-84 Plus calculator, enter the dataset into a list, calculate the mean and standard deviation, and then divide the standard deviation by the mean and multiply by 100.

To find the coefficient of variation on a TI-84 Plus calculator, follow these steps:

By following these steps, you can find the coefficient of variation for a dataset using a TI-84 Plus calculator.

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   "

The solution to the system of equations is x = 8/3 and y = 41/43.

To find the solution for the given system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:

Given equations:

3x + 2y = 22 ---(1)

-x + 15y = 21 ---(2)

To eliminate one variable, we can multiply equation (2) by 3 and equation (1) by -1, then add the resulting equations:

-3x + 45y = 63 ---(3) (multiplying equation (2) by 3)

-3x - 2y = -22 ---(4) (multiplying equation (1) by -1)

Adding equations (3) and (4) eliminates the x variable:

43y = 41

Dividing both sides by 43 gives us:

y = 41/43

Now we can substitute this value of y into either equation (1) or (2). Let's use equation (1):

3x + 2(41/43) = 22

Multiplying both sides by 43 to eliminate the fraction:

129x + 82 = 946

Subtracting 82 from both sides:

129x = 864

Dividing both sides by 129:

x = 864/129

Simplifying:

x = 8/3

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Answer:

\(1,171,862\)

Step-by-step explanation:

Original equation: \(5^7 * 15-8-5\)

Remember the PEMDAS rule --> in this case the exponents are first.

\(5^7\)= 5*5*5*5*5*5*5 = 78,125

=  \(78,125*15-8-5\)

The next step to this problem is multiplication because you are starting from left to right and its after the exponents.

= \(1,171,875-8-5\)

The last 2 steps is to subtract (from left to right)

= \(1,171,867-5\)

= \(1,171,862\)

Hope this helps!!!

To find the probability distribution, mean, and variance of X, which represents the longest string of heads occurring when a fair coin is tossed four times, we can analyze the possible outcomes.

When tossing a fair coin four times, the possible values of X can range from 1 to 4. Let's calculate the probability of each value:

X = 1: This means that the longest string of heads is one, indicating that there are no consecutive heads. There is only one way this can happen: TTTT (T denotes tails). The probability of this outcome is (1/2)^4 = 1/16.

X = 2: This means that the longest string of heads is two. There are two ways this can happen: HTTT or TTHH. The probability of each outcome is (1/2)^4 = 1/16. Since there are two equally likely outcomes, the probability of X = 2 is 2/16 = 1/8.

X = 3: This means that the longest string of heads is three. There are three ways this can happen: HHTT, THHT, or TTTH. The probability of each outcome is (1/2)^4 = 1/16. Since there are three equally likely outcomes, the probability of X = 3 is 3/16.

X = 4: This means that the longest string of heads is four, indicating that all four coin tosses result in heads. There is only one way this can happen: HHHH. The probability of this outcome is (1/2)^4 = 1/16.

Now, let's calculate the mean and variance of X:

Mean (μ) = ∑(X * P(X))

  = (1 * 1/16) + (2 * 1/8) + (3 * 3/16) + (4 * 1/16)

  = 1/16 + 2/8 + 9/16 + 4/16

  = 16/16

  = 1

Variance (σ^2) = ∑((X - μ)^2 * P(X))

  = (0^2 * 1/16) + (1^2 * 1/8) + (2^2 * 3/16) + (3^2 * 1/16)

  = 1/16 + 1/8 + 3/8 + 9/16

  = 26/16

  = 13/8

Therefore, the probability distribution of X is:

P(X = 1) = 1/16

P(X = 2) = 1/8

P(X = 3) = 3/16

P(X = 4) = 1/16

The mean of X is 1 and the variance of X is 13/8.

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Answer:

1 1/3

Step-by-step explanation:

3 - 1 2/3

We need to borrow 1 in fraction form from the 3.

3 becomes 2 3/3

2 3/3 - 1 2/3

1 1/3

Answer:

1 1/3

Step-by-step explanation:

\(\sf 3\:-1\dfrac{2}{3}\)

First, write the fractions as improper fractions.

\(\sf 3\:-\dfrac{5}{3}\)

Now, make the denominators the same to subtract the fractions.

\(\sf \dfrac{3}{1}\:-\dfrac{5}{3}\\\\\sf \dfrac{3*3}{1*3}\:-\dfrac{5}{3}\\\\\sf \dfrac{9}{3}\:-\dfrac{5}{3}\\\\\dfrac{4}{3}\)

Now, write the answer as a mixed number.

To convert the improper fraction 4/3 into a mixed number, we divide the numerator (4) by the denominator (3):

4 ÷ 3 = 1 remainder 1

The quotient 1 becomes the whole number, and the remainder 1 becomes the numerator of the fractional part. The denominator remains the same.

Therefore, the mixed number representation of 4/3 is:

1 1/3

Answer:

Addition. “Also, I have to stop at the store on the way home.” ...

Comparison. “In the same way, the author foreshadows a conflict between two minor characters.” ...

Concession. “Granted, you did not ask ahead of time.” ...

Step-by-step explanation:

Answer:

x = 2

y = -3

Step-by-step explanation:

The given equation is,

22(x + yi) + (28 + 4i) = 72 - 62i

By solving this equation further,

22x + 22yi + 28 + 4i = 72 - 62i

(22x + 28) + (22y + 4)i = 72 - 62i

Now both the sides of the equation is in the form of complex number,

By comparing real and imaginary parts given on both the sides,

22x + 28 = 72

22x = 72 - 28

22x = 44

x = 2

22y + 4 = -62

22y = -62 - 4

22y = -66

y = -3

Therefore, x = 2 and y = -3 are the values for which the given equation is true.

The polynomial function with zeroes at -2, 0, and 3√2 is (x+2)(x-0)(x-3√2) = \((x+2)*(x-3\sqrt{2}) = x^3 - 3x\sqrt{2x} - 2x^2.\)

The polynomial function with zeroes at -1, 3, and 2i is (x+1)(x-3)(x-2i) = \((x+1)(x-3)(x^2+4) = x^3 +x^2 - 11x -12\)

A polynomial function is a function of the form f(x) = a_nx^n + a_{n-1}x^{n-1} + ... + a_1x + a_0, where n is the degree of the polynomial and the a_i are constants. To find a polynomial function with zeroes at -2, 0, and 3√2, we can use the fact that if a polynomial function has a zero at x=c, then (x-c) is a factor of the polynomial. Therefore, we can write the polynomial function as \((x+2)(x-0)(x-3\sqrt{2}) = (x+2)x(x-3√2) = x^3 - 3x\sqrt{2x} - 2x^2\).

In this case, we can see that x = -2, x = 0, x = 3√2 are the zeroes, so we know that (x+2), x and (x-3√2) are the factors of the polynomial.

Similarly, to find a polynomial function with zeroes at -1, 3, and 2i, we can use the fact that if a polynomial function has a zero at x=c, then (x-c) is a factor of the polynomial. Therefore, we can write the polynomial function as \((x+1)(x-3)(x-2i) = (x+1)(x-3)(x^2+4) = x^3 +x^2 - 11x -12\)

In this case, we can see that x = -1, x = 3, x = 2i are the zeroes, so we know that \((x+1), (x-3), (x^2+4)\)are the factors of the polynomial.

It is worth noting that (x-2i) is a zero of the polynomial, so (x-2i)(x+2i) = \(x^2\)+4 is a factor of the polynomial and it is included in the polynomial..

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Answer:

\(m = \frac{ - 5 - 1}{2 - ( - 3)} = - \frac{6}{5} \)

Answer:

x=2/3

Step-by-step explanation:

25-(3x+5)=2(x+8)+x

25-3x-5=2x+16+x

20-3x=3x+16

20-3x-3x=16

20-6x=16

6x=20-16

6x=4x=4/6

simplify

x=2/3

Answer:

x=2/3

Step-by-step explanation:

Answer:

Daniel's is correct

Step-by-step explanation:

Daniel split the coin toss into Heads and Tails and has 3 sections for the spinner coming off of each coin toss branch.

Answer:

Figure D

Step-by-step explanation:

dilation by a factor of 1/2: (x,y) -> (1/2 x , 1/2 y)

rotation 180°: (1/2 x , 1/2 y) -> (-1/2 x , -1/2 y)

Answer:

Number 1 is a function. If you can draw a vertical line through the line graphed and it doesn't pass through it twice, it is considered a function.

Number 2 is B.

Number 3 is A. **I don't know this one for certain, but I graphed A and B for you.

I don't know number 4.

Number 5 is Beatz on Demand. This company charges $5.99 a month, while iTunez charges $8.99 a month.

Step-by-step explanation:

Below is the graph for number 3.

The coordinate matrix of x relative to the orthonormal basis b is then: [x]b = [19, -9, 10]

To get the coordinate matrix of x relative to the orthonormal basis b in Rn, we need to express x as a linear combination of the basis vectors in b. We can do this by using the formula: x = [x · b1]b1 + [x · b2]b2 + [x · b3]b3
where · denotes the dot product and b1, b2, and b3 are the orthonormal basis vectors in b.
First, we need to normalize the basis vectors:
|b1| = √(3^2 + 4^2) = 5
b1 = (3/5, 4/5, 0)
|b2| = √(4^2 + 3^2) = 5
b2 = (-4/5, 3/5, 0)
|b3| = 1
b3 = (0, 0, 1)
Next, we compute the dot products:
x · b1 = (5, 20, 10) · (3/5, 4/5, 0) = 19
x · b2 = (5, 20, 10) · (-4/5, 3/5, 0) = -9
x · b3 = (5, 20, 10) · (0, 0, 1) = 10
Using these values, we can express x as a linear combination of the basis vectors:
x = 19b1 - 9b2 + 10b3
The coordinate matrix of x relative to the orthonormal basis b is then:
[x]b = [19, -9, 10]
Note that this matrix is a column vector since x is a column vector.

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Answer: x=0

Step-by-step explanation: step 1: Simplify both sides of the equation.

4x-6/3=5x-14/7

4x+−2=5x+−2

4x−2=5x−2

Step 2: Subtract 5x from both sides.

4x−2−5x=5x−2−5x

−x−2=−2

Step 3: Add 2 to both sides.

−x−2+2=−2+2

−x=0

Step 4: Divide both sides by -1.

-x/1=0/-1

x=0