Recall that an angle making a full rotation measures 360 degrees or 2π radians. Write a formula that expresses the degree angle measure of an angle, d, in terms of the radian measure of that angle, θ. (Enter "theta" for θ.) d= ______ Hint: θ radians is what portion (or percent) of a full rotation? Use that percentage, and the fact that there are 360 degrees in one full rotatiaon, to determine the degree measure of the angle.

the function will be f(x) = x³ + 2 x² - 8x.

We are given that:

The degree of the polynomial function f(x) is = 3

Roots of the function for f(x) = 0 are:

-4, 0 and 2

That is

x = -4, x = 0 and x = 2

Which can also be written as:

x + 4 = 0, x = 0 and x - 2 = 0

So, the function will be:

f(x) = (x + 4) (x) (x - 2)

f(x) = x (x² - 2 x + 4 x - 8)

f(x) = x (x² + 2 x - 8)

f(x) = x³ + 2 x² - 8x

Graph of the function is shown in the image.

Therefore, the function will be f(x) = x³ + 2 x² - 8x.

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Latanya can use up to 5 gigabytes while staying within her budget.

To determine the number of gigabytes Latanya can use while staying within her budget, we need to write an inequality that represents her monthly cell phone bill.

Let x be the number of gigabytes she uses. Then, her monthly bill can be represented as:

35 + 4x < 55

This inequality represents her monthly bill, which is the flat cost plus the cost per gigabyte, being less than $55.

To calculate the value of x, we'll isolate x on one side of the inequality:

35 -35 + 4x < 55 -35

4x/4 < 20/4

x < 5

So, Latanya can use up to 5 gigabytes while staying within her budget.

Note that this solution is in terms of the number of gigabytes and not the total bill amount. The total bill amount would be 35 + 4x, which should be less than or equal to 55.

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The volume of the prism is

The volume of the prism is solved by the formula

= area of triangle * depth

Area of the triangle

= 1/2 base * height

base = p = cos 51.34 * √41 = 4

height = q = sin 51.34 * √41 = 5

= 1/2 * 4 * 5

= 10

volume of the prism

= area of triangle * depth

= 10 * 7

= 70 cm³

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Option d. dependent variable. In an experiment, the dependent variable is the factor that is being measured or observed.

It is the variable that is expected to change or be affected as a result of the manipulation of the independent variable. The independent variable is the factor that is being manipulated or controlled in the experiment, while the controlled variable is a factor that is kept constant or consistent throughout the experiment to prevent it from affecting the dependent variable. The dependent variable is often used to draw conclusions about the relationship between the independent variable and the outcome of the experiment.

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Answer:

86in²

Step-by-step explanation:

Find the complete question attached

Area of the circle = πr²

Area of the square = L²

Length of the side of the square

r is the radius of the circle

r = L/2 = 20/2 =10in

Given

Length of the side of the circle = 20in

Area of the square = 20²

Area of the square = 400in²

Area of the circle =π(10)²

Area of the circle = 3.14(100)

Area of the circle= 314in²

Amount of plywood left over = 400in²-314in² = 86in²

Step-by-step explanation:

.25 or 1/4 hope this helps

Answer:

1/4

Step-by-step explanation:

Any expression divided by itself equals 1

1/4÷1

Any expression divided by 1 remains the same

1/4

the solution is 1/4

Step-by-step explanation:

we don't need to actually do the detailed area calculation.

all we need to consider is that an area, ANY area (for triangles, rectangles,...) is always the product or the sum of products of 2 dimensions (like side lengths).

the scaling factor of similar objects (incl. triangles of course) applies to each individual line, length, height or side.

so, when calculating the area of a similar figure, the scaling factor has to be multiplied in twice (once for every multiplied dimension) - making it the square of the normal single-dimensional scaling factor.

so, in other words, the area scaling factor is the square of the side scaling factor.

coming from A1 to A2 the area scaling factor is

80/45 = 16/9

the side scaling factor is then

sqrt(16/9) = 4/3

we have to multiply a side of A1 by 4/3 to get the corresponding side of A2.

and so, the ratio of A1 side lengths to A2 side lengths is

3:4

(the inverse, upside-down form of the scaling factor as a consequence of the question "how do I convert the 3 length units of A1 into 4 length units of A2 ?" by multiplying the 3 units by the scaling factor 4/3).

Rope = 225 cm

Needed rope = 11/2m = (11/2) × 100 cm = 550cm

So, rope needed to be cut

= 550cm - 225cm

= 225cm

=225/100m

=2.25 m

The equation of the parallel line is: v y - 1 = -6(x - (-3))y - 1 = -6(x + 3)y - 1 = -6x - 18y + 6x = -17y = 6x - 17In general form, the equation of the parallel line is 6x - y + 17 = 0.

3. Find the equation of the perpendicular line to y = -5x + 2 that passes through (5, 4). In slope intercept form.The given equation is:y = -5x + 2The given point is (5,4)To find the slope of the line, we can write the equation of the given line in slope-intercept form:y = -5x + 2Comparing it with y = mx + c, we get:m = -5So, the slope of the given line is -5The slope of the perpendicular line is the negative reciprocal of the slope of the given line. Let's find it:-5 × m = -1m = 1/5Now, we have the slope of the perpendicular line (m = 1/5) and a point that passes through the line (5,4).

Let's substitute these values in the point-slope form of a line to find its equation: y - y₁ = m(x - x₁)where m = slope of the line, and (x₁, y₁) = given point

So, the equation of the perpendicular line is: y - 4 = (1/5)(x - 5)y - 4 = (1/5)x - 1y = (1/5)x + 3In slope-intercept form, the equation of the perpendicular line is y = (1/5)x + 3. 4. Find the equation of the parallel line to y = -6x +4 that passes through (-3, 1). In the general form.

The given equation is: y = -6x + 4The given point is (-3,1)To find the slope of the line, we can write the equation of the given line in slope-intercept form: y = -6x + 4Comparing it with y = mx + c, we get: m = -6So, the slope of the given line is -6

The slope of the parallel line is the same as the slope of the given line (-6). Now, we have the slope of the parallel line (m = -6) and a point that passes through the line (-3,1). Let's substitute these values in the point-slope form of a line to find its equation: y - y₁ = m(x - x₁)where m = slope of the line, and (x₁, y₁) = given point

So,

the equation of the parallel line is: v y - 1 = -6(x - (-3))y - 1 = -6(x + 3)y - 1 = -6x - 18y + 6x = -17y = 6x - 17In general form, the equation of the parallel line is 6x - y + 17 = 0.

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Answer:

Common ratio = r

r = \(\frac{a_2}{a_1} =\frac{3}{4}=0.75\)

With side lengths of 5 inches, 8 inches, and 20 inches, it is not possible to construct a triangle.

To construct a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In this case, let's check the conditions:

1. The sum of the lengths of the sides 5 inches and 8 inches is 13 inches, which is less than the length of the third side, 20 inches. So, a triangle cannot be formed using these side lengths.

2. The sum of the lengths of the sides 5 inches and 20 inches is 25 inches, which is greater than the length of the third side, 8 inches. However, the difference between these two sides is 15 inches, which is less than the length of the third side, 8 inches. So, a triangle cannot be formed using these side lengths.

3. The sum of the lengths of the sides 8 inches and 20 inches is 28 inches, which is greater than the length of the third side, 5 inches. However, the difference between these two sides is 12 inches, which is less than the length of the third side, 5 inches. So, a triangle cannot be formed using these side lengths.

Therefore, it is not possible to construct a triangle with side lengths of 5 inches, 8 inches, and 20 inches.

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There is no particular solution that satisfies the initial condition y(0) = 6 for the given differential equation.

To find the particular solution of the first-order linear differential equation that satisfies the initial condition, we'll solve the equation step by step. The given differential equation is: y' + 7y = ex. To solve this, we'll use an integrating factor. The integrating factor for the equation y' + 7y = ex is given by e^(∫7 dx) = e^(7x).

Multiplying both sides of the equation by the integrating factor, we get: e^(7x)y' + 7e^(7x)y = e^(7x)ex. Next, we'll simplify the left side of the equation using the product rule: (d/dx)(e^(7x)y) = e^(7x)ex. Integrating both sides, we have: e^(7x)y = ∫e^(7x)ex dx. Now, we need to evaluate the integral on the right side. We can use integration by parts: u = ex (differential: du = ex dx). dv = e^(7x) dx (differential: v = (1/7)e^(7x)). Using the formula for integration by parts: ∫u dv = uv - ∫v du. Applying the formula, we get: ∫e^(7x)ex dx = (1/7)e^(7x)ex - ∫(1/7)e^(7x)ex dx

Notice that the integral on the right side is the same as the original integral, so we can substitute it back in: ∫e^(7x)ex dx = (1/7)e^(7x)ex - (1/7)∫e^(7x)ex dx. Now, we can solve for the integral: ∫e^(7x)ex dx = (1/6)e^(7x)ex. Substituting this back into our previous equation, we have: e^(7x)y = (1/7)e^(7x)ex - (1/7)(1/6)e^(7x)ex. Simplifying, we get: e^(7x)y = (1/7 - 1/42)e^(7x)ex. Dividing both sides by e^(7x), we obtain: y = (1/7 - 1/42)ex. Simplifying further: y = (6/42 - 1/42)ex, y = (5/42)ex. Now, we can apply the initial condition y(0) = 6: 6 = (5/42)e^0, 6 = (5/42)

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The price of the call option should be approximately $7.03.

To calculate the price of the call option using the Black-Scholes model, we need the following inputs:

- Stock price (S): $95

- Exercise price (X): 11% below the stock price = $95 - (11% * $95) = $95 - $10.45 = $84.55

- Time to expiration (T): 6 months = 0.5 years

- Variance of the stock return (σ^2): 0.0144

- Annual interest rate (r): 10% = 0.10

- Dividend yield (q): 0 (no dividend involved)

Using these inputs, we can calculate the price of the call option as follows:

d1 = [ln(S/X) + (r + σ^2/2) * T] / (σ * sqrt(T))

d2 = d1 - σ * sqrt(T)

N(d1) and N(d2) represent the cumulative standard normal distribution function, which can be looked up from a standard normal distribution table or calculated using software.

Call option price (C) = S * N(d1) - X * exp(-r * T) * N(d2)

Let's calculate the price of the call option step by step:

First, calculate d1:

d1 = [ln(S/X) + (r + σ^2/2) * T] / (σ * sqrt(T))

  = [ln(95/84.55) + (0.10 + 0.0144/2) * 0.5] / (sqrt(0.0144) * sqrt(0.5))

  = [ln(1.1211) + (0.10 + 0.0072) * 0.5] / (0.12 * 0.7071)

  ≈ [0.113 + 0.0536] / 0.0848

  ≈ 1.51

Next, calculate d2:

d2 = d1 - σ * sqrt(T)

  = 1.51 - 0.12 * 0.7071

  ≈ 1.51 - 0.0848

  ≈ 1.43

Now, calculate N(d1) and N(d2) using a standard normal distribution table or software. Let's assume N(d1) = 0.9357 and N(d2) = 0.9251.

Finally, calculate the call option price:

C = S * N(d1) - X * exp(-r * T) * N(d2)

 = $95 * 0.9357 - $84.55 * exp(-0.10 * 0.5) * 0.9251

 ≈ $88.91 - $84.55 * 0.9512

 ≈ $88.91 - $80.42

 ≈ $8.49

Therefore, according to the Black-Scholes model, the price of the call option in this case would be approximately $8.49.

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Answer:

was,rang or had been , had rung

Step-by-step explanation:

He <was><had been> watching TV when the telephone <rang><had rung>.

Start at -7 then go up to -6 then just go right 1

Jody has created a systematic sampling error by forgetting to include a segment of the population that is relevant to the study.

Systematic sampling is a sampling method where every nth member of a population is selected to be part of the sample. In Jody's case, she forgot to include a specific segment of the population, which means that the sampling process was not systematic. This error can introduce bias and affect the representativeness of the sample.

No calculations are required for this type of error.

Jody's mistake in not including a relevant segment of the population has resulted in a systematic sampling error. To ensure the accuracy and validity of the study, it is important to rectify this error by including the missing segment or adjusting the sampling method accordingly.

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Answer:

\( \boxed{n = 6} \)

Step-by-step explanation:

\( = > 2 = \frac{n}{3} \\ \\ = > \frac{n}{3} = 2 \\ \\ = > n = 2 \times 3 \\ \\ = > n = 6\)

The cosine function of the form f(t) is f(t) = 12cos((π/360)(t - 270))

Let's denote the low tide as t = 0. Hence, the first low tide of a day will always be at t = 0. There is no vertical shift in the tide levels, so we can assume that the mean tide level is 0 inches.

Therefore, the high tide is 24 inches above the low tide.

The time period for the function is the time difference between two successive low tides which is equal to 12 hours or 720 minutes.

A cosine function can be written as f(t) = Acos(B(t-C)) + D where A is the amplitude, B is the period, C is the phase shift, and D is the vertical shift.

We can write a cosine function for the ocean tide as follows:f(t) = 24/2 cos((2π/720)(t - 270))

Here, the amplitude A is 24/2 = 12 since the high tide is 12 inches above the low tide.

The period B is 720 minutes since it takes 12 hours or 720 minutes for the tides to repeat themselves.The phase shift C is 270 since the high tide occurred halfway between the two low tides.

The vertical shift D is 0 because the mean tide level is 0 inches.

Hence, the required cosine function is f(t) = 12cos((π/360)(t - 270))

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34 students red is their favorite color

2 out of 7 of the pupils in year 9 say their favourite colour is red

Fraction of pupil that say red is their favorite colour is 7/9

There are 119 pupils in year 9

We need to calculate the number of students out of 119 that would say that their favourite colour is red

To find that,

we multiply the fraction of students that like red with the total number of students

2/7 * 119

= 34

Therefore, if 2 out of 7 of the pupils in year 9 say their favourite colour is red. Then 34 out of 119 pupil will say that their favourite colour is red.

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Answer:

1 in 30

Step-by-step explanation:

1 in 6 chance Mary picks the red marble in the first place. After this there is a 1 in 5 chance her sister picks the blue one. 5 multiplied by 6 is 30.

The probability that Mary picks the red marble and her sister picks the blue marble is \(\frac{1}{30}\) .

Thus, the probability that Mary picks the red marble and her sister picks the blue marble is \(\frac{1}{30}\) .

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Answer:

Step-by-step explanation:

since GCF(162,108,180)=18

and you have not mentionned it was the maximum of arrangements you want:

\(\begin{array}{c|c|c|c}\#arrangement&\#Roses&\#Dahlias&\#Tulips\\-------&-------&-------&-------\\1&162&108&180\\2&81&54&90\\3&54&36&60\\6&27&18&30\\9&18&12&30\\18&9&6&10\\-------&-------&-------&-------\\\end {array}\)

The addition inequality 37 + x ≥ 42 can be used to determine how much taller William must be to ride the coaster, where x represents the additional height he needs to meet the height requirement.

To write an addition inequality to determine how much taller William must be to ride the coaster, we first need to convert his height to inches. Since he is 3 feet 1 inch tall, his height is (3 x 12) + 1 = 37 inches.

Let x be the amount of additional height William needs to ride the roller coaster. The inequality can be written as:

37 + x ≥ 42

This inequality ensures that William's total height after adding x must be greater than or equal to the required height of 42 inches to ride the roller coaster.

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The union of two sets is to avoid counting the same elements twice.

The mathematical logic subfield of set theory investigates sets, which can be loosely defined as collections of objects. Although any object can be combined into a set, set theory, as a mathematical discipline, focuses primarily on those that are relevant to mathematics as a whole.

Given union of set

(A ∪ B),

The set of all objects that are members of either A or B, or both, is the union of the sets A ∪ B.

let us take example,

A = { 1, 2, 3, 4}

B = {3, 4, 5, 6, 7}

(A ∪ B) = { 1, 2, 3, 4} ∪  {3, 4, 5, 6, 7}

we can simply write all of A and B's elements in a single set to avoid duplicates to find A U B.

(A ∪ B) = {1, 2, 3, 4, 5, 6, 7}

Hence the  union of two sets is a set that contains all the elements of both set and avoid duplicates.

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The coordinate of the centroid of the given triangle will be at (-2.33,5).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The given triangle with vertices has been drawn.

The midpoint of H( – 6, 3) and F(1, 5) will be as,

x = (-6 + 1)/2 = -2.5

y = (3 + 5)/2 = 4 so D(-2.5,4)

The coordinate of the centroid will intersect 2:1 of the median from the vertex side.

Thus by intercept formula,

x = (2 × -2.5 + 1 × -2)/(2 + 1) and y = (2 × 4 + 1 × 7)/(2 + 1)

x = -2.33 and y = 5

So the coordinate of vertices will be (-2.33,5).

Hence "The specified triangle's centroid's coordinate will be at (-2.33,5)".

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Answer:

720 Should be the answer I think.

The flux of the vector-field F = 1i + 1j + 2k across the surface S is 2. We find out the flux of the vector-field using Green's Theorem.

Flux form of Green's Theorem for the given vector-field

φ = ∫ F.n ds

= ∫∫ F. divG.dA

Here G is equivalent to the part of the plane = 2x+4y+z = 2.

and given F = 1i + 1j + 2k

divG = div(2x+4y+z = 2) = 2i + 4j + k

Flux = ∫(1i + 1j + 2k) (2i + 4j + k) dA

φ = ∫ (2 + 4 + 2)dA

= 8∫dA

A = 1/2 XY (on the given x-y plane)

2x+4y =2

at x = 0, y = 1/2

y = 0, x = 1

1/2 (1*1/2) = 1/4

Therefore flux = 8*1/4 = 2

φ = 2.

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Answer:

c I think but I am not sure but I hope you have a good day

The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

x^2 - x + 3 = (2x - 3) + x^2

x^2 - x + 3 = x^2 + 2x - 3

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

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The required, expression -7 + 24i with the form a + bi, we can see that the value of b is 24.

To find the value of b in the expression (3 + 4i)^2, we can simply expand the expression and identify the coefficient of the imaginary part.

(3 + 4i)² = (3 + 4i)(3 + 4i)

Using the FOIL method, we can multiply the terms:

= 3 * 3 + 3 * 4i + 4i * 3 + 4i * 4i

= 9 + 12i + 12i + 16i²

Since i² is defined as -1, we can substitute it:

= 9 + 12i + 12i - 16

= -7 + 24i

Comparing the expression -7 + 24i with the form a + bi, we can see that the value of b is 24.

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Complete question:

(3+4i)²

if the expression above is written in the form a+ bi, where a and b are real numbers, what is the value of b?