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The key features of the sinusoidal function are calculated below

The function y = tan(1/3x) is a tangent function with a period of π/b, where b is the coefficient of x in the argument of the tangent function.

In this case, b = 1/3, so the period is π/(1/3) = 3π.

The interval for the principal cycle is the range of x-values that produce one complete cycle of the tangent function.

Since the tangent function has vertical asymptotes at x = (2n+1)π/2 for all integers n, we can find the interval for the principal cycle by finding the smallest interval that contains one complete cycle and does not contain any vertical asymptotes.

To find the interval for the principal cycle, we first note that the tangent function has a vertical asymptote at x = π/2.

Therefore, we can start the interval at x = π/2 and then move to the right until we complete one cycle and reach the next vertical asymptote.

Since the period is 3π, the next vertical asymptote is at x = π/2 + 3π = 7π/2.

Therefore, the interval for the principal cycle is [π/2, 7π/2].

To find the equations of the vertical asymptotes, we use the formula x = (2n+1)π/2 for all integers n.

Therefore, the equations of the vertical asymptotes are x = π/2 + nπ for all integers n.

The center point of the principal cycle is the midpoint between the x-values of the endpoints of the interval.

Therefore, the center point is (π/2 + 7π/2)/2 = 4π/2 = 2π.

The halfway points of the principal cycle are the points where the tangent function takes on half of its maximum and minimum values.

Since the maximum and minimum values of the tangent function are ±∞, we can instead find the points where the tangent function is zero.

The tangent function is zero at x = nπ for all integers n, so the halfway points of the principal cycle are (π, 0) and (3π, 0).

The graph is attached

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The investment will be worth approximately $3,326 after 9 years.

The interest that is paid on both the initial investment and any interest that has been paid on that investment in previous periods is called compound interest.

The investment's future value can be determined using the formula for compound interest:

[tex]A = P * (1 + \frac{r}{n})^{nt}[/tex]

where, A = future value of the investment, P = principal (initial investment), r = annual interest rate, n = number of times, interest compounded per year, and t = number of years.

In this case, given values:

P = $2200 (the initial investment or principal)

r = 4.7% (the annual interest rate expressed as a decimal)

n = 1 (interest is compounded annually)

t = 9 (the investment is held for 9 years)

putting the values,

[tex]A = 2200 * (1 + \frac{0.047}{1} )^{1*9}[/tex]

[tex]A = 2200 * (1.047)^9[/tex]

A = $3326.16

Therefore, the investment will be worth approximately $3326 after 9 years.

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The investment will be worth approximately $3,326 after 9 years.

The interest that is paid on both the initial investment and any interest that has been paid on that investment in previous periods is called compound interest.

The investment's future value can be determined using the formula for compound interest:

[tex]A = P * (1 + \frac{r}{n})^{nt}[/tex]

where, A = future value of the investment, P = principal (initial investment), r = annual interest rate, n = number of times, interest compounded per year, and t = number of years.

In this case, given values:

P = $2200 (the initial investment or principal)

r = 4.7% (the annual interest rate expressed as a decimal)

n = 1 (interest is compounded annually)

t = 9 (the investment is held for 9 years)

putting the values,

[tex]A = 2200 * (1 + \frac{0.047}{1} )^{1*9}[/tex]

[tex]A = 2200 * (1.047)^9[/tex]

A = $3326.16

Therefore, the investment will be worth approximately $3326 after 9 years.

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The area that will be painted grey is approximately 38 ft².

The circumference of the free-throw circle is given as 30.77 feet, and we know that the free-throw circle is a perfect circle. We can use the formula for circumference to find the radius of the circle, which will be necessary to calculate its area.

Circumference of a circle = 2πr

30.77 = 2 x 3.14 x r

r = 30.77 / (2 x  3.14) = 4.9 feet

Half of the circle will be painted grey. Find the area of half the circle using the formula for the area of a circle.

Area of a circle = π x r²

Area of half the circle = 0.5 x  π x r²

Area of half the circle = 0.5 x 3.14 x 4.9²

Area of half the circle = 37.73 ft²

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There are a total of 8 pieces on the outer edge with only one frosted side.

We have,

If Sally has frosted the top and all sides but not the bottom of the cake, then each piece will have one frosted side (the top) and three unfrosted sides (the bottom and two sides).

Out of the 9 pieces, only the pieces on the outer edge will have exactly one frosted side.

If we count the number of pieces on the outer edge, we can determine how many pieces are frosted on only one side.

For a cube-shaped cake, there are 8 pieces on the outer edge.

To see why, imagine slicing off the corners of the cube to create a smaller cube inside.

Each of the 6 faces of the smaller cube will have a piece missing from the corner.

Therefore, there are 6 pieces on the outer edge of the larger cube, and each of these pieces can be divided into two smaller pieces (with one frosted side each) by cutting along the diagonal.

This gives a total of 12 pieces, but we need to subtract the 4 corner pieces that have two frosted sides each.

So there are a total of 8 pieces on the outer edge with only one frosted side.

Therefore,

There are a total of 8 pieces on the outer edge with only one frosted side.

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There are a total of 8 pieces on the outer edge with only one frosted side.

We have,

If Sally has frosted the top and all sides but not the bottom of the cake, then each piece will have one frosted side (the top) and three unfrosted sides (the bottom and two sides).

Out of the 9 pieces, only the pieces on the outer edge will have exactly one frosted side.

If we count the number of pieces on the outer edge, we can determine how many pieces are frosted on only one side.

For a cube-shaped cake, there are 8 pieces on the outer edge.

To see why, imagine slicing off the corners of the cube to create a smaller cube inside.

Each of the 6 faces of the smaller cube will have a piece missing from the corner.

Therefore, there are 6 pieces on the outer edge of the larger cube, and each of these pieces can be divided into two smaller pieces (with one frosted side each) by cutting along the diagonal.

This gives a total of 12 pieces, but we need to subtract the 4 corner pieces that have two frosted sides each.

So there are a total of 8 pieces on the outer edge with only one frosted side.

Therefore,

There are a total of 8 pieces on the outer edge with only one frosted side.

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The length of the base is 15 feet and the height is 12 feet.

The three line fragments are known as the sides of the triangle, while the three places where they converge are known as the vertices of the triangle.

Let suppose, base of the triangle = x

Then, according to the problem, the height of the triangle is x - 3.

We know the area of triangle is,

[tex]A = \frac{1}{2}*b*h[/tex]  ;   here A is the area, h is the height and b is the base.

Put the given values,

[tex]90 = \frac{1}{2} *(x)*(x-3)[/tex]

Multiplying both sides by 2:

180 = x² - 3x

x² - 3x - 180 = 0

(x - 15)(x + 12) = 0

Therefore, either x - 15 = 0 or x + 12 = 0.

If x - 15 = 0, then x = 15, which is the length of the base of the triangle.

If x + 12 = 0, then x = -12, which is not a valid solution since the length of a side of a triangle cannot be negative.

Therefore, the length of the base of the triangle is 15 feet.

The height of the triangle (x - 3), so the height is: (15 - 3) = 12 feet.

Hence, the length of the base is 15 feet and the height is 12 feet.

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Answer:no 0.002

Step-by-step explanation:

The area of the figure is 45 square millimeters.

What is Area?

Area is a measure of the size or extent of a two-dimensional surface or shape. It is usually expressed in square units such as square meters , square feet , square centimeters , square inches , etc. The area of a shape or surface can be calculated by multiplying the length of one side or dimension by the length of an adjacent side or dimension, or by using specific formulas depending on the shape.

The figure can be broken down into a rectangle (5 mm x 7 mm) and two right triangles (with legs 2 mm and 3 mm, respectively).

Area of rectangle = length x width = 5 mm x 7 mm = 35 square mm

Area of each triangle = 1/2 x base x height = 1/2 x 2 mm x 4 mm = 4 square mm

1/2 x 3 mm x 4 mm = 6 square mm

Total area of the figure = area of rectangle + area of two triangles = 35 square mm + 4 square mm + 6 square mm = 45 square mm.

Therefore, the area of the figure is 45 square millimeters.

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Answer:

A

Step-by-step explanation:

The correct option is A) μoverbar(x)= 2; σoverbar(x)= 75.

Answer:

Step-by-step explanation:

it's (y2-y2)/(x2-x1) slope

=14/3

Answer:

--------------------------

We are given the slope and a point on the line.

Use the point-slope equation to find the equation of the line:

Substitute -6 for m and 1 for x₁ and -2 for y₁:

The matching choice is C.

The value of arctan(√2) for the equation tan(x/2 - π/2) = √2 in the form x=π +πn is given by arctan(√2) = π/4 + πn, where n is an integer.

Equation is equal to,

tan(x/2 - π/2) = √2

By using the identity for tangent of half angle,

tan(x/2 - π/2)

= 1/cot(x/2 - π/2)

= 1/(-tan(x/2))

So the equation becomes,

1/(-tan(x/2)) = √2

Multiplying both sides by -1, we get,

tan(x/2) = -1/√2

            = -√2/2

Now use the inverse tangent function (arctan) to find x/2,

arctan(-√2/2) = -π/4

Since x/2 - π/2 = -π/4, we have,

⇒ x/2 = -π/4 + π/2

         = π/4

The solutions for x are x = π/2 + 2πn, where n is an integer.

Now let us find the value of arctan(√2),

arctan(√2) is the angle whose tangent is √2.

Since tan(π/4) = √2, we have,

arctan(√2) = π/4 + πn, where n is an integer.

Therefore, the value of arctan(√2) in the form x=π +πn is equal to

arctan(√2) = π/4 + πn, where n is an integer.

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Answer:

When x = -3:

h(-3) = 9 * (2/3)^(-3)

When x = -2:

h(-2) = 9 * (2/3)^(-2)

When x = -1:

h(-1) = 9 * (2/3)^(-1)

When x = 0:

h(0) = 9 * (2/3)^0

When x = 1:

h(1) = 9 * (2/3)^1

When x = 2:

h(2) = 9 * (2/3)^2

When x = 3:

h(3) = 9 * (2/3)^3

Step-by-step explanation:

I think it is this

The area of the triangle is derived to be 13.3 square kilometers

For any triangle, the area is calculated as half the base multiplied by the height of the triangle, that is;

Area of triangle = 1/2 × base × height

For the triangle in (a);

base = 7 km

height = 3.8 km

area of the triangle = 1/2 × 7 km × 3.8 km

area of the triangle = 26.6 km²/2

area of the triangle = 13.3 km²

Therefore, the area of the triangle is derived to be 13.3 square kilometers

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The estimated age-adjusted death rate per 100,000 Americans for heart disease in 2034 is approximately 53.6 (rounded to the nearest tenth).

Calculate the slope of the linear model using the given data points (2000, 242.2) and (2003, 216.1).

The slope (m) can be determined by taking the difference between the two point values, subtracting the lower value from the higher one, and then dividing that answer by the difference in their respective years: −26.1 / 3 = -8.7 deaths per year.

Formulating a linear equation of the model:

A formulaic representation of the linear rate of death would take into account the calculated slope as well as the initial data point, giving an all-inclusive expression for predicting a given year's age-adjusted death rate per 100,000 Americans for heart disease:

Death Rate = m * (Year - 2000) + 242.2

Plugging in the year 2034 to estimate the death rate:

By dispensing with the previously provided information and substituting in the year 2034, we can trace the predicted death rate for that particular calendar year; doing so yields a surprisingly small number of -8.7 * 34 + 242.2 ≈ 53.6.

To conclude, the estimated age-adjusted death rate per 100,000 Americans for heart disease in 2034 is approximately 53.6 (rounded to the nearest tenth).

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Assuming a linear model for the change in age-adjusted death rate per 100,000 Americans for heart disease, estimate the death rate in 2034, given that the death rate in 2000 was 242.2 and in 2003 it was 216.1. Round your answer to the nearest tenth.

The angle of depression at which Beatrice sees the boat is given as follows:

x = 6.65º.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle, we have that:

Hence the angle is obtained applying the tangent ratio as follows:

tan(x) = 70/600

x = arctan(70/600)

x = 6.65º.

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The angle of depression at which Beatrice sees the boat is given as follows:

x = 6.65º.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle, we have that:

Hence the angle is obtained applying the tangent ratio as follows:

tan(x) = 70/600

x = arctan(70/600)

x = 6.65º.

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The measure of angle C is given as follows:

C = 106.6º.

The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is also known as the Cosine Rule.

The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation holds true:

c^2 = a^2 + b^2 - 2ab cos(C)

The side of length 9 is opposite to the angle C, hence the equation is given as follows:

9² = 4² + 7² - 2 x 4 x 7 x cos(C)

56cos(C) = -16

cos(C) = -16/56

C = arccos(-16/56)

C = 106.6º.

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The value of the angle C of the given triangle using law of cosines is: C = 106.6°

We usually make use of the Law of Cosines, if only one of which is missing: three sides and one angle. Thus, if the known properties of the triangle is SSS(side-side-side) or SAS (side-angle-side), this law is applicable.

This could be in the form of:

c² = a² + b² - 2ab Cos C

From the given triangles, we have:

a = 4

b = 7

c = 9

Thus:

9² = 4² + 7² - 2(4 * 7)cos C

81 = 16 + 49 - 56 cos C

56 cos C = -16

cos C = -16/56

cos C = -0.2857

C = cos⁻¹0.2857

C = 106.6°

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Answer:

Yes, point A on the graph represents a pair of possible values of m and w because it satisfies the equation w = 2.5m + 5.

To confirm this, we can substitute m = 20 into the equation to get:

w = 2.5(20) + 5

w = 50 + 5

w = 55

So the coordinates of point A are (20, 55), which represents a possible value of m and w that satisfies the equation.

The total of the debit side of the unadjusted trial balance is $25,650.

We have,

To find the total of the debit side of the unadjusted trial balance,

We need to add up the debit balances of all the accounts listed.

i.e

Accounts Receivable, Cash, Common Stock, Equipment, Insurance Expenses, Land, Notes Receivable, Prepaid Insurance, Rent Expenses, Salaries, and Wages Expense are all debit accounts.

Notes Payable is a credit account, so we subtract it from the total.

Service Revenue and Retained Earnings do not have balances, as they are not accounts that are included in the trial balance.

Now,

The total of the debit side of the unadjusted trial balance is:

= $5,100 + $1,760 + $1,760 + $6,280 + $4,600 + $5,500 + $430 + $1,430 + $430 + $3,760

= $30,050

Subtracting Notes Payable of $4,400.

= $30,050 - $4,400

= $25,650

Therefore,

The total of the debit side of the unadjusted trial balance is $25,650.

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The value of the inequality is g≤2.5

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

The given inequality is 4g≤10

To solve the inequality, divided bo sides of the inequality by the coefficient of g which is 4

This gives the value

4g/g≤10/4

⇒ that g = 2.5

Therefore the value of the inequality is g≤2.5

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Answer:Supplementary

Step-by-step explanation:

The two angles add up to 180

Answer:

supplementary since 136+44= 180 and any angles that sum up to 180 are supplementary

If glass contains 320 cm³ of milk, the mass of the milk is 330 g, the density of the milk is approximately 1031 kg/m³.

Density is defined as the mass per unit volume of a substance. To find the density of milk in kg/m³, we need to convert the given volume and mass to the appropriate units.

First, we need to convert the volume from cm³ to m³. Since 1 m = 100 cm, 1 m³ = (100 cm)³ = 1,000,000 cm³. Therefore, we can convert 320 cm³ to m³ by dividing by 1,000,000:

320 cm³ ÷ 1,000,000 = 0.00032 m³

Next, we need to convert the mass from grams to kilograms. Since 1 kg = 1000 g, we can convert 330 g to kg by dividing by 1000:

330 g ÷ 1000 = 0.33 kg

Now that we have both the mass and volume in appropriate units, we can calculate the density by dividing the mass by the volume:

Density = mass ÷ volume = 0.33 kg ÷ 0.00032 m³ ≈ 1031 kg/m³

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It will take 14.14 seconds for the object to return to the ground.

We know that the height is modeled by the quadratic equation:

h(t)=-5t^2+120t+17

The object will return to the ground when its height is zero, so we only need to solve the quadratic equation:

0 = -5t^2+120t+17

Using the quadratic formula we will get.

[tex]t = \frac{-120 \pm \sqrt{120^2 - 4*-5*17} }{2*-5} \\\\t = \frac{-120 \pm 121.4 }{-10}[/tex]

We only care for the positive solution:

t = (-120 - 121.4)/-10 = 14.14

It will take 14.14 seconds.

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Complete question:

"The height of an object is launched into the air given by the function h(t)=-5t^2+120t+17 where t is the time in seconds. How long takes for the object to hit the ground?"

The lengths of the missing sides in the triangle and the angles can be written as ; y= 3,   x =3√3 , 60°

We were given a right triangle. where the lenghts is required to be found, however this can be seen as a triangle with 30-60-90 triangle however the lengths of the sides of a 30-60-90 triangle  can be expressed in the ratio  1 :√3 : 2

We can represent the side opposite to 30 degree as n,  which then means that the side opposite to 60 degree angle  becomes √3n then the last side(hypothenus)  will be 2n, given that corresponding sides to hypotenuse= 6, then we can say that

2n = 6

n=3

Therefore, corresponding side that can be attributed to 30 degree angle = 6/2 = 3 which implies that y=3, then x =3√3 (side corresponding to 60 degree angle)

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Answer:

1) D

2) C

Step-by-step explanation:

1. The formula for the surface area of a cylinder is 2πr² + 2πrh, where r is the radius of the base and h is the height of the cylinder.

Given that the radius of the cylinder is 3 cm and the height is 7 cm, we can substitute these values into the formula to get:

SA = 2π(3)² + 2π(3)(7) = 2π(9) + 2π(21) = 18π + 42π = 60π cm²

Therefore, the answer is (D) 60π cm².

2. If the height of the cylinder is increased by 1 cm, the new height would be 8 cm.

We can use the same formula to find the new surface area:

SA = 2π(3)² + 2π(3)(8) = 2π(9) + 2π(24) = 18π + 48π = 66π cm²

Therefore, the answer is (C) 66π cm².

Answer: yes

Step-by-step explanation:

Step-by-step explanation:

We can use the t-tables or a calculator to find the value of c.

Using a t-table with 6 degrees of freedom and a one-tailed test at 0.10 level of significance, we find that the critical value is approximately 1.943.

Alternatively, we can use a calculator to find c directly. Using a t-distribution calculator and inputting a degree of freedom of 6 and a one-tailed probability of 0.10, we get a critical value of approximately 1.943.

Therefore, we can conclude that the value of c is approximately 1.943 for a t distribution with 6 degrees of freedom and a one-tailed probability of 0.10.

The size of the payments that must be deposited at the beginning of each 6-month period in an account that pays 9.6%, compounded semiannually, is PMT ≈ $1,757.23

FV = PMT * [(1 + r)^nt - 1] / r

(1 + r)^nt = (1 + 0.048)^(2 * 19)

= (1.048)^38

= 5.0989

$150,000 = PMT * [(5.0989 - 1) / 0.048]

$150,000 = PMT * 4.0989 / 0.048

$150,000 ≈ PMT * 85.4146

Now, divide both sides by 85.4146 to find the value of PMT:

PMT ≈ $150,000 / 85.4146

PMT ≈ $1,757.23

The size of the payments that must be deposited at the beginning of each 6-month period in an account that pays 9.6%, compounded semiannually, is PMT ≈ $1,757.23

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The width of the rectangular section of Clark's backyard is 3.9 meters.

Area of the rectangular section is 11.31 sq meters.

length of rectangular section is 2.9 meters.

For a rectangular section the formula for area is equal to the product of length and width of the rectangular section.

                  Area = length * width

Rectangle: It is a 4 sided structure with two equal opposite sides It also has 4 right angles and sum of all angles is equal to 360°.

here,

                 width = [tex]\frac{area}{length}[/tex] = [tex]\frac{11.31}{2.9} =3.9[/tex] meters.

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Answer:

tan A = 0.43

tan B = 2.34

Step-by-step explanation:

"tangent" is a trig ratio. If you have a right triangle, then you can do right triangle trigonometry.



First, let's look at a right triangle. The longest side is opposite the right angle (square angle, 90° angle it's marked with a little square) that is called the hypotenuse. You need hypotenuse for sine and cosine. So we won't use hypotenuse today (still good to know tho')

 Then there are the two legs of the right triangle. They make up the right angle. If you are standing at one of the smaller angles one of the legs is just beside you, making up the angle. The other leg is way across the triangle on the opposite side of the triangle.

So from angle A, the 32 is the OPPOSITE side. And the 75 is the leg right next to angle A. "Right next to" is called ADJACENT. The 75 is the ADJACENT side.

Tangent is the ratio of the OPPOSITE side to the ADJACENT side.

Like this:

tan A = OPP/ADJ

tan A = 32/75

tan A = 0.426666...

rounding, we get:

tan A = 0.43

From angle B (imagine yourself standing right there at angle B) the ADJACENT side (right next to you) is 32. And the OPPOSITE side is 75

Now the tangent ratio is slightly different--

tan B = OPP/ADJ

tan B = 75/32

tan B = 2.34375

rounding,

tan B = 2.34

Step-by-step explanation:

remember,

tan(x) = sin(x)/cos(x)

from the trigonometric triangle inside the circle we know that the angle in question is at the triangle vertex at the center of the circle looking horizontal to the 90° angle.

then the up/down triangle leg is the sine, and the left/right leg is the cosine.

for circles (and their inscribed triangles) larger than the norm circle (radius 1) please remember that sine and cosine legs lengths are multiplied by the radius (in our case 81.5).

so, for the angle at A that is easy :

sin(A) × 81.5 = 32

cos(B) × 81.5 = 75

tan(A) = sin(A)×81.5 / (sin(B)×81.5) = 32/75 =

= 0.426666666... ≈ 0.43

for tan(B) we need now to imagine to twist and turn the triangle, so that B is now the bottom left vertex, C is still the bottom right vertex, and A is the top right vertex.

and the we see

sin(B) × 81.5 = 75

cos(B) × 81.5 = 32

tan(B) = sin(B)×81.5 / (cos(B)×81.5) = 75/32 =

= 2.34375 ≈ 2.34