h shows the cost of hosting a dance, c, as a function of the number of students attending, n.
What is a restriction on the domain?

Answer: To find two complex numbers that add up to c = -11 + 3i, we can set up the following system of equations:

a + b = -11

ai + bi = 3i

Solving for a and b, we can multiply the first equation by i and subtract it from the second equation multiplied by -1 to eliminate b:

ai + bi = 3i

-ai - bi = 11i

0 + 10bi = 14i

Simplifying, we get b = 1.4. Substituting this into the first equation gives:

a + 1.4 = -11

a = -12.4

So the two complex numbers that add up to c are -12.4 + 1.4i and 1.4i.

To find the value of iº, we need to evaluate i raised to the power of 90 degrees (or pi/2 radians) using Euler's formula:

e^(iθ) = cos(θ) + i sin(θ)

So we have:

iº = i^(90°) = e^(iπ/2) = cos(π/2) + i sin(π/2) = 0 + i(1) = i

Therefore, iº = i.

Step-by-step explanation:

Answer:

A= $116.05

Step-by-step explanation:

A=P(1+E)kt

A=100(1+0.03/2)^10

A= $116.05

The value of Tanθ is 20/21.

What is Pythagorean Theorem?

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here, we have

Given: sinθ = -20/29 and that angle terminates in quadrant III.

We have to find the value of tanθ.

Using the definition of sine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

Sinθ = Perpendicular/hypotenuse

Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.

Adjacent = - √Hypotenuse² - perpenducualr²

Replace the known values in the equation.

Adjacent = -√29² - (-20)²

Adjacent = -21

Find the value of tangent.

Tanθ = Perpendicular/base

Tanθ = -20/(-21)

Hence, the value of Tanθ is 20/21.

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Answer:

Step-by-step explanation:

36 26 so 36 +26 = 89

The expression that represents the area of the remaining rectangular portion is given as follows:

A = -4x² + 12x + 6.

To obtain the area of a rectangle, you need to multiply its length by its width. The formula for the area of a rectangle is:

Area = Length x Width

The dimensions for the rectangle are given as follows:

Hence the area is given as follows:

A = 3(4x + 2)

A = 12x + 6.

Four squares of side length x -> area = x² are cut, hence the remaining area is given as follows:

A = -4x² + 12x + 6.

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It follows that the translation direction is 8 units to the left and 0 units up or down.

A translation is a geometric change in Euclidean geometry where each point in a figure, shape, or space is moved uniformly in one direction. A translation can either be thought of as moving the origin of the coordinate system or as adding a constant vector to each point

The new vertices of a triangle with vertex locations of (0,0), (1,0), and (0,1), for instance, would be (2,3, (3,3), and (2,4) if the triangle were translated 2 units to the right and 3 units up.

We can use the following procedures to get the translation direction and number of units for R′(7, 4):

1. Determine the difference between R and R′'s x-coordinates:  −7 − 1 = 8

2. Determine the difference between R and R′'s y coordinates: 4 − 4 = 0

It follows that the translation direction is 8 units to the left and 0 units up or down.

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To the nearest inch, there are 4 inches in 10.16 centimetres.

The process of translating a measurement from one unit to another is known as a units conversion. This is frequently done when comparing measurements from various sources or when working with several unit systems. In order to communicate a measurement in a different unit of the same physical amount that is more suitable or useful for a specific context, units conversion is required.

If you are speaking with someone who uses the Imperial system of units, for instance, you may need to convert from metres to feet when estimating distance. If you are working with someone who utilises the American customary system, you may need to convert from kilogrammes to pounds when measuring weight.

In order to prevent mistakes in calculations and measurements, it is crucial to be precise and accurate while converting between units. Unit conversion is a crucial component of scientific and technological activity.

Since there are 2.54 centimetres in one inch, we may multiply 4 inches by 2.54 to convert them to centimetres:

4 inches * 2.54 centimeters per inch = 10.16 centimeters

We multiply by 2.54 to convert centimetres to inches:

10.16 centimeters / 2.54 centimeters per inch = 4 inches (rounded to the nearest inch)

Therefore, rounding to the closest inch, there are 4 inches in 10.16 centimetres.

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In the Unit conversion,to the nearest inch, there are 4 inches in 10.16 centimeters.

Describe Units Conversion?

The process of translating a measurement from one unit to another is known as a units conversion. This is frequently done when comparing measurements from various sources or when working with several unit systems. In order to communicate a measurement in a different unit of the same physical amount that is more suitable or useful for a specific context, units conversion is required.

If you are speaking with someone who uses the Imperial system of units, for instance, you may need to convert from meters to feet when estimating distance. If you are working with someone who utilises the American customary system, you may need to convert from kilograms to pounds when measuring weight.

In order to prevent mistakes in calculations and measurements, it is crucial to be precise and accurate while converting between units. Unit conversion is a crucial component of scientific and technological activity.

Since there are 2.54 centimeters in one inch, we may multiply 4 inches by 2.54 to convert them to centimeters:

=> 4 inches * 2.54 centimeters per inch = 10.16 centimeters

We multiply by 2.54 to convert centimeters to inches:

=> 10.16 centimeters / 2.54 centimeters per inch

=> 4 inches (rounded to the nearest inch)

Therefore, rounding to the closest inch, there are 4 inches in 10.16 centimeters.

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The answers below provides the elements of the sets L1 ∪ L2, L1 ∩ L2, L1 concatenation L2, L1*, and L2* where L1 and L2 are languages over Σ = {a, b}.

a) L1 ∪ L2:

The union of two sets is the set of all elements that are in either set. Therefore,

L1 ∪ L2 = {a, b, ab, λ, bb}

b) L1 ∩ L2:

The intersection of two sets is the set of all elements that are in both sets. Therefore,

L1 ∩ L2 = {ab}

c) L1 concatenation L2:

The concatenation of two languages is the set of all possible combinations of elements where the first element comes from the first language and the second element comes from the second language. Therefore,

L1 concatenation L2 = {aλ, a bb, aab, bλ, bbb, bab, abλ, abb, abab}

d) L1*:

L1* is the Kleene star of L1, which is the set of all possible combinations of elements from L1, including the empty string λ. Therefore,

L1* = {λ, a, b, ab, aa, bb, aaa, aab, abb, bbb, aaaa, aaab, aabb, abbb, ...}

e) L2*:

Similarly,

L2* = {λ, bb, ab, bbbb, abb, aabb, abbb, aabbb, ...}

Note that the Kleene star of L2 includes only elements made up of b's and λ.

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Answer:$26,141.13.

Step-by-step explanation:

Using the formula A = P * (1 + r/n)^(n*t), where A is the balance, P is the principal, r is the interest rate, n is the number of times per year that the interest is compounded, and t is the time in years, we can calculate the balance in the savings account after 10 years:

A = 8,063.00 * (1 + 0.1469/4)^(4*10)

A ≈ 26,141.13

Therefore, the balance in the savings account after 10 years, rounded to the nearest cent, is $26,141.13.

The radius of the cylinder is approximately 6.75 inches.

We can use the formula for the volume of a cylinder to solve this problem:

[tex]V = \pi r^2h[/tex]

We know that the volume V is 2,035.75 [tex]in^3[/tex], and the height h is 3 times the radius r. So we can write:

[tex]V = \pi r^2(3r)[/tex]

Simplifying this expression, we get:

V = 3π[tex]r^3[/tex]

To solve for r, we can divide both sides of the equation by 3π[tex]r^2[/tex]:

V/(3π[tex]r^2[/tex]) = r

Substituting the given value for V, we have:

2,035.75/(3π[tex]r^2[/tex]) = r

Multiplying both sides by 3πr^2, we get:

2,035.75 = 3π[tex]r^3[/tex]

Dividing both sides by 3π, we have:

[tex]r^3[/tex] = 2,035.75 / (3π)

Taking the cube root of both sides, we get:

r = [tex](2,035.75 / (3\pi ))^{1/3[/tex]

Using a calculator, we find that:

r ≈ 6.75 inches

Therefore, The cylinder has a radius of about 6.75 inches.

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Answer:

a. For the study of 40 children who had survived a brain tumor, the appropriate hypothesis test would be a single-sample t test. This is because the study involves comparing the ratings data from the parents with known means from published population norms. A single-sample t test is used to determine whether a sample mean is statistically different from a known population mean. In this case, the sample mean is the ratings data from the parents, and the population mean is the known means from published population norms.

b. For Talarico and Rubin's study of memories, the appropriate hypothesis test would be a paired-samples t test. This is because the study involves comparing the consistency of flashbulb memories and everyday memories over time, for the same group of individuals. A paired-samples t test is used to determine whether there is a statistically significant difference between two related samples, such as before and after measurements for the same group of individuals.

c. For the HOPE VI Panel Study, the appropriate hypothesis test would be an independent-samples t test. This is because the study involves comparing the means of residents in the five HOPE VI developments at the beginning of the study with known national data sources that had summary statistics, including means and standard deviations. An independent-samples t test is used to determine whether there is a statistically significant difference between the means of two independent groups. In this case, the two independent groups are the residents in the HOPE VI developments and the known national data sources.

Step-by-step explanation:

The two consecutive natural numbers whose sum of squares is 181 are 9 and 10

Let's assume that the two consecutive natural numbers are x and x+1. Then, we can write an equation based on the given information:

x² + (x+1)² = 181

Expanding the equation:

x² + x² + 2x + 1 = 181

Combining like terms:

2x² + 2x - 180 = 0

Dividing both sides by 2:

x² + x - 90 = 0

Now, we can use the quadratic formula to solve for x:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 1, and c = -90

x = (-1 ± √(1 + 360)) / 2

x = (-1 ± √(361)) / 2

x = (-1 ± 19) / 2

We discard the negative value, as it does not correspond to a natural number:

x = 9

Therefore, the two consecutive natural numbers are 9 and 10, and their sum of squares is 81 + 100 = 181.

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Answer:

Step-by-step explanation:

i believe it is nearly as hard as my usual amount of challenge

Answer:

data given

principal 300

rate12%

time 4 years

Step-by-step explanation:

from

A=P[1+r/100]^n

where

A is amount

p is principal

r is rate

n is interest period

now,

A= 300[1+12/(100×12)]^(12×4)

A=300×1.01^48

A=483.67

: .would be 483.67

3 Σ n=1 (17n-25) = 3(27) = 81.The notation "3 sigma n=1 (17n-25)" represents a mathematical series. The Greek letter sigma (Σ) indicates

what is  sigma  ?

Sigma (Σ) is a Greek letter used in mathematics to represent the sum of a sequence of terms. The lowercase sigma (σ) is often used to represent standard deviation in statistics.

In the given question,

The notation "3 sigma n=1 (17n-25)" represents a mathematical series. The Greek letter sigma (Σ) indicates that we are adding up a sequence of terms, with "n=1" indicating that we start the series with n=1, and "3" indicating that we add up three terms in total.

The expression inside the parentheses, "17n-25", represents the general term in the series. To find each term in the series, we plug in the values of n=1, n=2, and n=3 into the general term and add them up:

17(1)-25 + 17(2)-25 + 17(3)-25 = -8 + 9 + 26 = 27

Therefore, 3 sigma n=1 (17n-25) = 3(27) = 81.

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find  3 ∑ n=1 (17n-25)  and give the answer ?

verbal phrase can be represented by 7.16.

Part A:

The verbal phrase can be represented by the following expression:

[tex]2.19g + 0.59[/tex]

Here, "Two and nineteen hundredths times a number g" can be written as 2.19g, and "plus fifty-nine hundredths" can be written as [tex]0.59[/tex]  .

Part B:

To evaluate the expression when  [tex]g = 3[/tex], we substitute 3 for g in the expression and simplify:

[tex]2.19g + 0.59[/tex]

[tex]= 2.19(3) + 0.59 [\ Substitute g = 3][/tex]

[tex]= 6.57 + 0.59[/tex]

[tex]= 7.16[/tex]

Therefore, the correct answer is [tex]7.16.[/tex]

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The given question is incomplete. the complete question is given below:

Consider the verbal phrase.

Two and nineteen hundredths times a number g, plus fifty-nine hundredths

Part A

Enter an expression to represent the verbal phrase.

g +

Part B

Evaluate the expression when g = 3.

3.96

7.16

8.34

8.93

The length of arc FED is approximately 51.1 yards, rounded to the nearest tenth.

The length of a section of a circle's circumference is known as an arc length.

The radius of the circle and the angle the arc subtends at the centre of the circle are two variables that affect an arc's length.

To find the length of FED, we need to first find the measure of the arc EGD. Since a circle has 360 degrees, we can find the measure of arc EGD by subtracting the measures of arcs DGC, CGF, and FGE from 360:

m(EGD) = 360° - m(DGC) - m(CGF) - m(FGE)

m(EGD) = 360° - 80° - 47° - 90°

m(EGD) = 143°

The formula for arc length is:

Arc length = (central angle / 360) x (2πr)

We can use this information to find the radius of the circle:

FG = 2r

27 yd = 2r

r = 13.5 yd

Now we can use the formula for arc length to find the length of arc FED:

Arc length FED = ((∠FED) / 360) x (2πr)

We know that ∠(EGD) + ∠(FED) = 360, so we can solve for ∠(FED):

∠(FED) = 360° - ∠(EGD)

∠(FED) = 360° - 143°

∠(FED) = 217°

Plugging in the values, we get:

Arc length FED = (217° / 360) x (2π x 13.5 yd)

Arc length FED = (0.6028) x (84.78 yd)

Arc length FED = 51.11 yd

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1) the  expression in words can be written as "Nineteen times the difference between twenty-three thousand and seven hundred and eighty-nine."

1) The expression (23,000-789) × 19 can be written in words using the following steps:

The expression inside the parentheses is the difference between 23,000 and 789, which is 22,211.

The expression is then multiplied by 19, which means it is being increased by 19 times.

So the final expression in words can be written as "Nineteen times the difference between twenty-three thousand and seven hundred and eighty-nine."

2) The expression 2.6+(88×7) can be read in words using the following steps:

The expression inside the parentheses, 88×7, means 88 multiplied by 7.

The result of the multiplication is 616.

The expression then becomes 2.6 added to 616.

So the final expression in words can be read as "Two point six plus six hundred and sixteen."

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1. The initial mass of the sample was 32 mg. 2. The mass of the sample 7 weeks after the start is approximately 0.162 mg.

An unstable atomic nucleus releases particles or electromagnetic radiation as it undergoes radioactive decay, changing into a different nucleus. Since this process is unpredictable and spontaneous, the decay's timing cannot be anticipated. The radioactive substance's half-life, or the amount of time it takes for half of its radioactive atoms to decay, is used to calculate the rate of decay. Radiometric dating, nuclear energy production, and medical imaging all employ radioactive decay, which can cause the emission of alpha particles, beta particles, or gamma rays. Understanding the behaviour of matter at the atomic and subatomic level requires knowledge of radioactive decay.

1. The radioactive decay is given by the formula:

[tex]N(t) = N_0 * (1/2)^{(t/T)}[/tex]

Now, for half-life of Palladium-100 is 4 days and t = 16 and N(t) = 2 we have:

[tex]2 = N_0 * (1/2)^{(16/4)}\\2 = N_0 * (1/2)^4\\2 = N_0* 1/16\\N_0 = 2 * 16\\N_0 = 32 mg[/tex]

2. Foe 7 weeks:

7 weeks = 7 * 7 days = 49 days.

[tex]N(49) = N_0 * (1/2)^{(49/4)}\\N(49) = 32 * (1/2)^{(49/4)}\\N(49) = 0.162 mg[/tex]

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Answer:

The circumference of the circle is 119.32 ft.

Step-by-step explanation:

The circumference of a circle can be solved through the formula:

C = πd

where d is the diameter

Given: d = 38 ft

π = 3.14

Solve:

C = πd

C = 3.14 (38 ft)

C = 119.32 ft

The polynomial in factor form is y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3).

In this problem we find a representation of polynomial set on Cartesian plane, whose expression is described by the following formula in factor form:

y(x) = a · (x - r₁) · (x - r₂) · (x - r₃) · (x - r₄)

Where:

Then, by direct inspection we get the following information:

y(0) = - 3, r₁ = - 3, r₂ = - 1, r₃ = 2, r₄ = 3

First, determine the lead coefficient:

- 3 = a · (0 + 3) · (0 + 1) · (0 - 2) · (0 - 3)

- 3 = a · 3 · 1 · (- 2) · (- 3)

- 3 = 18 · a  

a = - 1 / 6

Second, write the complete expression:

y(x) = - (1 / 6) · (x + 3) · (x + 1) · (x - 2) · (x - 3)

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Answer: We can use the two given points to find the equation of the line and then plug in 39 for the calling time to find the corresponding monthly cost.

Let x be the calling time (in minutes) and y be the monthly cost (in dollars). Then we have the following two points:

(x1, y1) = (35, 16.83)

(x2, y2) = (52, 18.87)

The slope of the line passing through these two points is:

m = (y2 - y1) / (x2 - x1) = (18.87 - 16.83) / (52 - 35) = 0.27

Using point-slope form with the first point, we get:

y - y1 = m(x - x1)

y - 16.83 = 0.27(x - 35)

Simplifying, we get:

y = 0.27x + 7.74

Therefore, the monthly cost for 39 minutes of calls is:

y = 0.27(39) + 7.74 = $18.21

Step-by-step explanation:

The required graph of the function given; h (x) has been attached.

In mathematics, graph theory is the study of graphs, which are mathematical structures used to represent pairwise interactions between objects. In this definition, a network is made up of nodes or points called vertices that are connected by edges, also called links or lines. In contrast to directed graphs, which have edges that connect two vertices asymmetrically, undirected graphs have edges that connect two vertices symmetrically. Graphs are one of the primary areas of study in discrete mathematics.

Here as per the question the graph of the function, h (x) has been attached.

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The value of x is given as follows:

x = 16.2.

Similar triangles are triangles that share these two features listed as follows:

First we must obtain the bases, splitting the figure into two separate similar triangles, with equivalent dimensions given as follows:

Hence the proportional relationship used to obtain the value of y is given as follows:

16/y = 30/(34 - y)

Hence:

30y = 16(34 - y)

46y = 544

y = 544/46

y = 11.83.

Hence the bases are:

11.83 and 34 - 11.83 = 22.17.

Applying the geometric mean theorem, the value of x is given as follows:

x = sqrt(11.83 x 22.17)

x = 16.2.

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This problem involves integration and algebraic manipulation, and belongs to the subject of calculus. The solutions are:

[tex]A) $\int_{0}^{2} (f(x) + g(x)) dx = -3$[/tex]
[tex]B) $\int_{0}^{3} (f(x) - g(x)) dx = -4$[/tex]
[tex]C) $\int_{2}^{3} (3f(x) + g(x)) dx = -32$[/tex]

This is a problem that asks us to find the values of some definite integrals using given values of other definite integrals. We are given three definite integrals, and we are asked to compute three other integrals involving the same functions, using the given values.

The problem involves some algebraic manipulation and the use of the linearity of the integral.

It also involves finding the constant "a" that makes a definite integral equal to zero. The integral involves two functions, "f(x)" and "g(x)," whose definite integrals over certain intervals are also given.

See the attached for the full solution.

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