amazon claims that if you are a prime member, 85% of your packages will arrive within two business days. you have decided that you want to know if this claim is true. you take a simple random sample of 25 students at your school and 19 of the students claim that their packages arrived within two business days of ordering. a. what is the population proportion? what is the sample proportion? please use correct symbols in your answer.

The correct expression to solve for the amount of time it takes to drain the hot tub is: A) (9t - 9)(5t - 7)

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

By using the sum-product pattern, we have the following:

45t² − 108t + 63

45t² − 63t - 45t + 63

By writing the common factor from the two pairs, we have the following:

(45t² − 63t) - (45t + 63)

9t(5t - 7) - 9(5t - 7)

By rewriting in factored form, we have the following:

(9t - 9)(5t - 7)

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The angle of elevation of the Sun is approximately 23.85 degrees.

This problem can be solved using the tangent trigonometric ratio.

If we call "x" the angle of elevation of the Sun, then we can write:

tan(x) = height of the tree / length of the shadow

tan(x) = 32.5 / 75

To find the value of x, we can take the inverse tangent (tan⁻¹) of both sides of the equation:

x = tan⁻¹ (32.5 / 75)

x ≈ 23.85 degrees

Therefore, the angle of elevation of the Sun is approximately 23.85 degrees.

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The average speed for this part of the journey is 6 m/s.

Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:

v = d/t.

The parameters for this problem are given as follows:

Change in distance of 90 - 30 = 60 m.

Change in time of 10 - 0 = 10 s.

Hence the average speed for this part of the journey is given as follows:

60/10 = 6 m/s.

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Answer:$7.50

Step-by-step explanation:The original cost of the sandals is $30 and the discount if is 75%.That means only 25% of the original cost of the sandals remain so we do 30x.25=$7.50

Answer:

y = (3/2)x + 1

Step-by-step explanation:

straight line equation format is y -y1 = m(x - x1)

where y1 is y-coordinate of a point, x1 is x-coordinate of the same point, m is the slope (gradient).

slope of y - 4 = -2/3 (x - 6) is -2/3, since that's the number before x.

this means that slope of perpendicular line = -(1/ (-2/3)) = 3/2.

it passes through (-2, -2)

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

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

subtract 2 from both sides

y = (3/2)x + 1

Answer:

x= 52° and y= 142°

Step-by-step explanation:

x combined with angle next to it make a right angle, so you can find x by subtracting 38 from 90. y would be 90 plus 52 because the other angle is the same as x.

Answer:

x = 52° and y = 142°

Step-by-step explanation:

38 + x + the right angle are on straight line.

angles on straight line add up to 180.

so x = 180 - 90 - 38 = 52.

y is the big angle, not the 90.

again, angles on straight line:

y = 180 - 38 = 142

Answer:

a + c = 90° because BC is a tangent to circle A, meaning that angle B is a right angle.

The population of the city  in 2020 is approximately 255 100

To find the population in 2020 we first need to find the population in 2015 after the 7% growth from 2010.

Population in 2015 = 246 000 + 0.07 x 246 000 = 263,220

we need to find the population in 2020 after the 3% decrease from 2015

Population in 2020 = 263 220 - 0.03 x 263,220 = 255 027.6

Rounding to the nearest 100 people the population in 2020 is approximately 255 100

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The perimeter of the tree house floor is  27.62 meters and area of the tree house floor is 30 square meters.

To find the perimeter of the tree house floor, we need to add up the lengths of all four sides of the rectangular floor.

We can use the distance formula to calculate the length of each side:

Length of side AB =√(6-0)² + (4-4)²) = √(36) = 6 meters

Length of side BC =√(6-0)² + (-1-4)²) = √61 = 7.81 meters

Length of side CD = √(0-6)² + (-1-4)² = √61= 7.81 meters

Length of side DA = √(0-6)²+ (4-4)²) =√36= 6 meters

Therefore, the perimeter of the tree house floor is:

Perimeter = AB + BC + CD + DA

Perimeter = 6 + 7.81 + 7.81 + 6

Perimeter = 27.62 meters

To find the area of the tree house floor, we can use the formula for the area of a rectangle:

Area = base x height

The base of the rectangle is the length of side AB, which is 6 meters.

The height of the rectangle is the distance between points B and C, which is 4-(-1) = 5 meters. Therefore, the area of the tree house floor is:

Area = base x height

Area = 6 x 5

Area = 30 square meters

Hence, the area of the tree house floor is 30 square meters.

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Answer:

The function f(x) = cos^2x + sin^2x is not a straight line, but rather a constant function that always evaluates to 1 for any value of x.To see why this is the case, recall the trigonometric identity that states that the square of the cosine of an angle added to the square of the sine of the same angle equals 1:cos^2x + sin^2x = 1Since this identity holds for all values of x, it follows that f(x) = 1 for all x. Therefore, the graph of this function is a horizontal line at y = 1, not a straight line.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The positive 9 shows that it's moving up 9 units, the negative in front of the square root reflects the equation over the x-axis, and the positive 3 shows that it has been moved to the left 3 units.

Outside of equation: positive numbers translate up, negative translate down. (ex: [tex]x^{2}+3, x^{2}-3[/tex]. The three would move the equation up or down.)

Inside of equation: positive numbers translate left, negative translate right. (ex: [tex](x-3)^{2},(x+3)^{2}[/tex]. The 3 would move left or right.)

The value of the variable x is 7

Point of tangency is described as the point where tangent meets the circle.

It is perpendicular to the radius of the circle, with which it intersects

From the information given, we have that;

BD = 46

CD = x² - 3

Since tangent lines are equal

We have that;

46 = x² - 3

collect the like terms, we get;;

x² = 46 + 3

Add the values

x² = 49

Find the square root of both sides, we have;

x = √49

Find the value

x = 7

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1. It will cost Dave $646.62 to refill his truck's fuel tank.

2. The cost of concrete for Greg's driveway will be $9,720.

3. Total cost of the topsoil needed from suppliers is $726.90 from Holland Growers and $919.55 from Night Growers.

A refill refers to filling something again with more of same thing such as fuel, water etc.

We need to convert the fuel capacity of Dave's truck from gallons to liters.

1 US gallon = 3.78541 liters

So, 180 US gallons will give us:

= 180 * 3.78541 liters

= 681.37 liters

We will calculate total cost of refilling Dave's truck which is:

= 681.37 liters * 0.949 dollars/liter

= $646.62013

= $646.62.

2. To get volume of concrete needed, we will convert thickness of the driveway from inches to meters. 4 inches is equal to 0.1 meters.

The volume of the driveway is:

V = l x w x h

V = 20m x 36m x 0.1m

V = 72 cubic meters

The cost of the concrete for the driveway is:

= Volume x Price per cubic meter

= 72 cubic meters x $135/cubic meter

= $9,720.

3. To get total cost of the topsoil, we have to calculate volume of soil required for each planter box:

Volume = Length x Width x Depth

Volume = 44" x 24" x 18"

Volume = (44/36) yards x (24/36) yards x (18/36) yards

Volume = 1.22 yards³

Since she needs to build 35 planter boxes, the total volume of soil required is:

= 1.22 yards³ x 35

= 42.7 yards³

The cost from Holland Growers will be:

= Total Volume x $17/yd

= 42.7 yards³ x $17/yd

= $726.90

The cost from Night Growers will be:

= Total Volume x $21.50/yd²

= 42.7 yards³ x $21.50/yd²

= $919.55.

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The total number of possible passwords can be calculated by finding the number of possible combinations for each character position in the password and multiplying them together.

Since each character can be an uppercase letter or a digit, there are a total of 36 possible characters (26 letters + 10 digits). The number of passwords that do not contain any digits can be found by calculating the number of possible passwords with only uppercase letters (26 possible characters) and then multiplying it by the number of possible positions in the password (6 to 8 characters).  Therefore, the total number of possible passwords is: 36⁶ + 36⁷ + 36⁸ - 26⁶ - 26⁷ - 26⁸
= 2,176,782,336 + 78,364,164,096 + 2,821,109,907,456 - 308,915,776 - 8,031,810,176 - 208,827,064,576
= 2,584,618,967,360
So there are a total of 2,584,618,967,360 possible passwords that meet the given criteria.

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The measure of arc BED is:

180 degrees

The arc of a circle is the segment or part of the circumference of a circle. The measure of an arc is the angle at which the arc is subtended.

You will notice that AD is the diameter of the circle.

Since the measure of arc CD is 90°.

Thus, the measure of arc AB is:

90 - 52 =  38°

Arc ED = arc AB (vertically opposite angles are equal)

Therefore, the measure of Arc BED will be:

Arc BED = Arc BC + arc CD + arc ED

Arc BED = 52° +  90° +  38°

Arc BED = 180°

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An angle in standard position measures π/2 radians, and p(0, 1) is on the terminal side of the angle, the value of the cosine of this angle is 1.

So, we have:

cos θ = adjacent/hypotenuse

cos θ = x/1

cos θ = x

Now, the given angle is π/2 radians, and the point P (0, 1) lies on the terminal side of the angle. From the point P (0, 1), we can move left towards the origin to make a right-angled triangle.

Since the angle measures π/2, one leg will be on the x-axis (the horizontal leg) and the other leg will be on the y-axis (the vertical leg). Let's construct a right triangle using the point P (0, 1) and the origin (0,0) as two of the vertices: So, the opposite side is equal to 0, and the adjacent side is equal to 1.

Thus, the value of the cosine of this angle is cos θ = adjacent/hypotenuse = 1/1 = 1.

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Answer:

0

Step-by-step explanation:

Answer:

a ) -1

Step-by-step explanation:

[tex]\frac{1}{64} = 4^{2s-1} . 16^{2s+2}\\ 4^{-3} = 4^{2s-1+4s+4}\\ 4^{-3} = 4^{6s+3}\\ 6s + 3 = -3\\6s = -6\\s = -1[/tex]

The interest rate being earned on the college education fund set aside by your parents 14 years ago is 8.51 percent. This rate of interest has resulted in the value of the fund increasing from $7,500 to $26,180 over the period.

The calculation of the interest rate is based on the concept of compound interest, where the interest earned is added to the initial principal amount, and subsequent interest is calculated on the new balance. Using the formula for compound interest, the rate can be determined as follows:

$26,180 = $7,500(1 + r/100)^14

Solving for the interest rate, r, gives a value of 8.51 percent. This means that the fund has been growing at a rate of 8.51 percent per year for the past 14 years. It is worth noting that the actual rate of return may vary due to factors such as fees, taxes, and market fluctuations, but the calculated rate provides a good estimate of the average growth rate of the fund.

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The perimeters and areas of each figures are

Given that all curves are semicircles or quadrants., we have

Figure 1

The area is calculated as

Area = 1.6 * 2.8

Area = 4.48 m²

The perimeter is calculated as

Perimeter = 2 * (1.6 + 2.8) + 3.14 * 1.6/2

Perimeter = 11.312 meters

Figure 2

The area is calculated as

Area = 50 * 68

Area = 3400 cm²

The perimeter is calculated as

Perimeter = 2 * (50 + 68) + 3.14 * 50

Perimeter = 393 centimeters

Figure 3

The area is calculated as

Area = 3.14 * 5² + 2 * 3.14 * (5/2)² * 1/2

Area = 98.125 m²

The perimeter is calculated as

Perimeter = 2 * 3.14 * 5 + 2 * 1/2 * 3.14 * 5/2

Perimeter = 39.25 meters

Figure 4

The area is calculated as

Area = 3.14 * (4.6/2)²/2 + 3.14 * (2.3)²/4

Area = 12.46 cm²

The perimeter is calculated as

Perimeter = 3.14 * (4.6/2) + 3.14 * (2.3)/4

Perimeter = 9.03 centimeters

Figure 5

The area is calculated as

Area = 3.14 * (15)²/2 + 2 * 3.14 * (5)²/2 - 3.14 * (5)²/2

Area = 392.5 cm²

The perimeter is calculated as

Perimeter = 3.14 * (15) + 2 * 3.14 * (5)/2 - 3.14 * (5)/2

Perimeter = 54.95 centimeters

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For the given function the answer is a + b = 3/2 + 9/2 = 12/2 = 6.

A function is an association between inputs in which each input has a unique link to one or more outputs.

To find the values of a and b, we can substitute the expressions for f(x) and g(x) into the equation g(f(x)) = 3x + 4 and solve for a and b.

We have:

g(f(x)) = 3x + 4

Substituting the expressions for f(x) and g(x), we get:

g(ax + b) = 3x + 4

Since g(x) = 2x - 5, we can replace g(ax + b) with 2(ax + b) - 5:

2(ax + b) - 5 = 3x + 4

Expanding and simplifying, we have:

2ax + 2b - 5 = 3x + 4

Rearranging terms, we get:

(2a - 3)x + (2b - 9) = 0

For this equation to hold for all values of x, the coefficient of x must be zero, and the constant terms must also be zero.

Therefore, we have the following system of equations:

2a - 3 = 0   (coefficient of x)

2b - 9 = 0   (constant term)

Solving these equations simultaneously, we find:

2a = 3   -->   a = 3/2

2b = 9   -->   b = 9/2

Therefore, a + b = 3/2 + 9/2 = 12/2 = 6.

Hence, a + b = 6.

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Answer:

Anything you want

Step-by-step explanation:

This is a problem where you have your own choice about whether you agree or disagree with the choice.

The measure  f the angle of depression is 66 degrees

To determine the value of the angle, we need to know that there are six different trigonometric identities.

These identities are enumerated as;

From the information given, we have that;

The adjacent side = 60 meters

The opposite side = 135 meters

Using the tangent identity, we have that;

tan θ = 135/60

Divide the values, we have;

tan θ = 2. 25

Find the tangent inverse of the value

θ = 66. 0 degrees

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Note: The information given does not require diagrams and thus is self - explanatory.

the rate of change of the radius at the instant when the radius is 11 feet and the volume is 26 cubic feet is -10 feet per second.

What is Volume?

Volume is the amount of three-dimensional space enclosed by a closed surface, such as the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is often quantified numerically using an SI-derived unit, the cubic meter

To find the rate of change of the radius at the instant when the radius of the cylinder is 11 feet and the volume is 26 cubic feet, we can use the related rates of change between the height, radius, and volume of the cylinder.

Let's denote the height of the cylinder as h, the radius as r, and the volume as V. We are given that the height is decreasing at a constant rate of 2 feet per second, and the volume is decreasing at a rate of 264 cubic feet per second.

We know the formula for the volume of a cylinder is V = πr^2h.

Differentiating both sides of the equation with respect to time (t), we have:

dV/dt = d(πr^2h)/dt

Using the product rule, we can rewrite this as:

dV/dt = π(2rh(dr/dt) + r^2(dh/dt))

Since we are given the values of dV/dt (rate of change of volume) and dh/dt (rate of change of height), and we want to find the rate of change of the radius, we can substitute these values into the equation along with the known values of r (radius) and V (volume) at the given instant.

dV/dt = -264 (volume is decreasing at a rate of 264 cubic feet per second)

dh/dt = -2 (height is decreasing at a rate of 2 feet per second)

r = 11 (radius is 11 feet)

V = 26 (volume is 26 cubic feet)

Plugging in these values, we have:

-264 = π(2(11)(dr/dt) + 11^2(-2))

Simplifying further:

-264 = π(22(dr/dt) - 22)

Dividing both sides by π(22), we get:

-12 = dr/dt - 2

Adding 2 to both sides, we have:

dr/dt = -12 + 2 = -10

Therefore, the rate of change of the radius at the instant when the radius is 11 feet and the volume is 26 cubic feet is -10 feet per second. Note that the negative sign indicates that the radius is decreasing.

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The Sample space includes all possible combinations of the three types of sour candies, taking into account that there can be multiple candies of the same type in the bag.

The correct sample space for the sour candies in the bag is:

Sample space = {lemon-lime, watermelon, grape, lemon-lime, watermelon, grape, lemon-lime, watermelon, grape, lemon-lime, watermelon, grape, lemon-lime, watermelon, grape}

Each element in the sample space represents a different possible outcome of selecting a sour candy from the bag. The sample space includes all possible combinations of the three types of sour candies, taking into account that there can be multiple candies of the same type in the bag.

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The correct sample space for the sour candies in the bag is (c)  Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, watermelon, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape

from the question, we have the following parameters that can be used in our computation:

3 lemon-lime, 6 watermelon, and 5 grape sour candies

The correct sample space for the sour candies in the bag is the list of items in the bag

So, we have

Sample space = lemon-lime, lemon-lime, lemon-lime, watermelon, watermelon, watermelon, watermelon, watermelon, watermelon, grape, grape, grape, grape, grape

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Answer:

Sure. Here are the values that you requested:

Future Value: The future value of the investment is $1,388,903.23.

Interest Earned: The total interest earned is $1,263,903.23.

Number of Payments: The total number of payments is 160 (40 years * 4 quarters/year).

Average Balance: The average balance of the account is $432,203.28.

Here is the formula that I used to calculate the future value of the investment:

FV = PV * (1 + r)^n

Where:

FV is the future value

PV is the present value (the initial deposit)

r is the interest rate

n is the number of years

In this case, the present value is $2,500, the interest rate is 2%, and the number of years is 40.

FV = 2500 * (1 + 0.02)^40 = 1388903.23

Here is the formula that I used to calculate the interest earned:

Interest = FV - PV

In this case, the future value is $1,388,903.23 and the present value is $2,500.

Interest = 1388903.23 - 2500 = 1263903.23

Here is the formula that I used to calculate the number of payments:

Number of Payments = Years * Periods/Year

In this case, the number of years is 40 and the number of periods per year is 4.

Number of Payments = 40 * 4 = 160

Here is the formula that I used to calculate the average balance of the account:

Average Balance = (PV + FV)/2

In this case, the present value is $2,500 and the future value is $1,388,903.23.

Average Balance = (2500 + 1388903.23)/2 = 432203.28

Step-by-step explanation:

The Length of side AB is approximately 72.4 cm.

To draw triangle ABC, we can start by drawing a straight line AB and then drawing a perpendicular line segment BC that meets AB at a 90-degree angle. This gives us a right triangle where angle B is 90 degrees. Finally, we can draw a line segment AC to connect points A and C, making sure that the length of AC is 25 cm since that is given in the problem.

To label the parts of the triangle, we can use the following conventions:

- Side AB is the hypotenuse of the right triangle and is opposite the right angle B.

- Angle A is opposite side AC, and angle C is opposite side BC.

Using this labeling convention, we can write:

- AB is the hypotenuse.

- AC is the side opposite angle A.

- BC is the side opposite angle C.

To find the length of AB, we can use the trigonometric ratio for the sine of angle A:

sin A = opposite / hypotenuse

sin 18 = AC / AB

Multiplying both sides by AB, we get:

AB * sin 18 = AC

Substituting the value of AC as 25 cm, we get:

AB * sin 18 = 25

Dividing both sides by sin 18, we get:

AB = 25 / sin 18

Using a calculator, we can evaluate this to get:

AB ≈ 72.4 cm (rounded to the nearest tenth)

Therefore, the length of side AB is approximately 72.4 cm.

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To create the greatest 5-digit number using the digits 4, 2, and 0, we need to place the highest value digit in the leftmost position. Therefore, the greatest 5-digit number that can be created using the digits 4, 2, and 0 is 42,000.  

By arranging the digits in this order, you ensure that you have the largest possible value while still using only the given digits 4, 2, and 0. In this case, the digit 4 is the highest value digit. So we place it in the ten-thousands place. This gives us 40,000. Now we need to fill in the remaining four digits. Since we want to create the greatest possible number, we need to use the next highest digit, which is 2, in the thousands place. This gives us 42,000. We can then use the remaining digit, which is 0, in the hundreds, tens, and ones places. to create the greatest 5-digit number, we need to start with the highest value digit and place it in the leftmost position. Then, we fill in the remaining digits with the next highest value digits in descending order. This ensures that we create the greatest possible number.

The greatest 5-digit number using the digits 4, 2, and 0, you can repeat the digits as needed. Place the largest digit (4) in the leftmost position to maximize the value, and then fill in the remaining positions with the next largest digit (2), followed by the smallest digit (0).

Therefore, the greatest 5-digit number that can be created using the digits 4, 2, and 0 is 42,000.

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The radius and diameter of each measure to their approximation is as follows;

7) 14 km   8) 5 yards   9) 23 inches   10) 20 feet  11) 17.5 mm  12. 22.5 cm

13) 95feet²  14) 92.2 mm 15) 119.6 m  16)227 inches²

For each problem, we use the formulas;

Area of a circle: A = πr²

Circumference of a circle: C = 2πr or C = πd

a) Find the radius of a circle with an area of 615.75 square kilometers.

A = πr²

∴ r = √(A/π)  

√(615.75/π)

= 14 km

b) Find the diameter of a circle with a circumference of 15.71 yards.

C = πd

∴ d = C/π

15.71/π  = 5 yards

c) Find the diameter of a circle with an area of 415.48 square inches.

A = πr²

∴ r = √(A/π)

√(415.48/π) = 11.5 inches,

∴ d = 2r = 23 inches

d) Find the radius of a circle with a circumference of 125.66 feet.

C = 2πr

∴ r = C/(2π)

125.66/(2π) = 20 feet

e) Find the diameter of a circle with an area of 240.25 square millimeters.

sqrt(240.25/π) = 8.75 mm,

∴ d = 2r = 17.5 mm

f) Find the radius of a circle with a circumference of 45π centimeters.

45π/(2π) = 22.5 cm

g) Find the area of a circle with a circumference of 11π feet.

11π/(2π) = 5.5 feet,

A = πr² = π×(5.5)² = 95 feet²

h) Find the circumference of a circle with an area of 676 square millimeters.

A = πr²

∴ r = √A/π) =√(676/π) = 14.67 mm,

∴ C = 2πr = 2π×14.67 = 92.2 mm

i. Find the circumference of a circle with an area of 1,134.11 square meters.

√(1,134.11/π) = 19.03 m,

C = 2πr = 2π×19.03 = 119.6 m

j. Find the area of a circle with a circumference of 53.41 inches.

C = 2πr

∴ r = C/(2π) = 53.41/(2π) = 8.5 inches,

∴ A = πr² = π×(8.5)² = 227inches²

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angles that differ by a multiple of 2π have the same terminal point, because they complete the same number of full circles around the unit circle.

The terminal point determined by an angle in standard position (i.e., with the initial side along the positive x-axis) is the point where the terminal side of the angle intersects the unit circle. Here are the terminal points determined by π/2, π, −π/2, and 2π:

The angle π/2 (90 degrees) has a terminal point at (0, 1), which is the point on the unit circle that is directly above the origin.

The angle π (180 degrees) has a terminal point at (-1, 0), which is the point on the unit circle that is to the left of the origin.

The angle −π/2 (-90 degrees) has a terminal point at (0, -1), which is the point on the unit circle that is directly below the origin.

The angle 2π (360 degrees) has a terminal point at (1, 0), which is the point on the unit circle that is to the right of the origin.

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The value of a = 1/3 and b = 2.

We can expand the given expression using the binomial theorem:

Binomial theorem statement that for any positive integer n the nth power of the sum of two numbers a and b may be expressed as the sum of n + 1 terms of the form in the sequence of terms, the index r takes on the successive values 0, 1, 2,…, n.

Equation.

(2-x)(1+ax)⁶ = (2-x) × [1 + 6a x + 15a² x² + ...]

Multiplying this out gives:

(2-x)(1+ax)⁶ = 2 + (6a-2x) x + (15a² - 12ax + x²) x² + ...

Comparing the coefficient of x and x² with the given expansion we get:

6a - 2 = 0 (coefficient of x)

15a² - 12a + 1 = b (coefficient of x²)

From the first equation, we get:

6a = 2

a = 1/3

Substituting this value of a into the second equation, we get:

15(1/3)² - 12(1/3) + 1 = b

5 - 4 + 1 = b

b = 2

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