a bag contains 14 pieces of candy. in how many ways can six pieces be selected?

Answer:

[tex]\Huge \boxed{\boxed{\texttt{\bf{\$2346.09} } } }[/tex]

Step-by-step explanation:

We can use the compound interest formula to get the final value of a $2000 investment at an interest rate of 2% compounded quarterly for 8 years, using:

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

Substituting the values:

So, the final value of the investment after 8 years would be approximately $2346.09.

________________________________________________________

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Answer:

200cm3

Step-by-step explanation:

L=8cm

W=5 cm

H=10cm

=200cm

a. The length of the arc drawn across the fair landing area is approximately 6.777 meters.

b. The area of the sector bounded by the arc is approximately 162.042 square meters.

To find the length of the arc, we need to calculate the circumference of the circle formed by the landing area.

The central angle of the sector is given as 34.92°, which represents a fraction of the total circumference of the circle.

The formula to find the length of an arc is given by:

Arc Length = (Central Angle / 360°) × Circumference

In this case, the central angle is 34.92° and the circumference is the distance covered by the farthest throw, which is 21.89 meters.

Arc Length = (34.92° / 360°) × 2πr

We need to find the radius (r) of the circle. Since the farthest throw covers the radius, we have:

r = 21.89 meters

Now we can calculate the arc length:

Arc Length = (34.92° / 360°) × 2π × 21.89 meters

Arc Length ≈ (0.097 × 2π × 21.89) meters

Arc Length ≈ 6.777 meters

To calculate the area of the sector bounded by the arc, we need to use the formula:

Area of Sector = (Central Angle / 360°) × π × r²

Using the given central angle of 34.92° and the radius of 21.89 meters, we can calculate the area:

Area of Sector = (34.92° / 360°) × π × (21.89 meters)²

Area of Sector ≈ (0.097 × π × 21.89²) square meters

Area of Sector ≈ 162.042 square meters

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Answer:

9π m²

Step-by-step explanation:

area of circle = πr², where r is the radius.

area = π (3)²

= 9π m²

Answer:

45

Step-by-step explanation:

20/x=28/(x+18)

Solving for x, we get that x=45

Answer:

1260 is the answer

Step-by-step explanation:

you solve for the area of the rectangle and multiply it by 3 because there are three sides so 17x20=340x3=1020 then, you solve for the area of a triangle which is 1/2 x base x height so, 1/2 x 16 x 15 = 120 then you multiply that by 2 since there are 2 triangles so 120 x 120=240 finally, you add 1020+240 = 1260

The LCM of 24 and 64 is 192.

To find the distance between x and y, we need to know their coordinates. Let's assume x is located at point (x1, y1) and y is located at point (x2, y2). The distance between them can be calculated using the distance formula:

Distance = √[(x2 - x1)^2 + (y2 - y1)^2]

The distance formula is derived from the Pythagorean theorem and can be used to find the distance between any two points in a plane. The formula involves taking the square root of the sum of the squared differences in x and y coordinates between the two points.

In order to find the distance between x and y, we need to know their coordinates and then apply the distance formula. It is a useful formula to know when working with geometric figures and can be applied in various real-life situations such as calculating the distance between two cities on a map.

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The distance between x and y can be calculated using the distance formula, which is √((x2 - x1)^2 + (y2 - y1)^2).

In order to find the distance between x and y, we need to know the coordinates or positions of x and y. Without this information, we cannot calculate the distance between them. Therefore, we cannot provide a specific answer to this question.

To use this formula, you need the coordinates of the points x and y (x1, y1) and (x2, y2). Plug the coordinates into the formula, then calculate the differences between the x and y values, square them, add them together, and finally, find the square root of the sum. This will give you the distance between x and y.

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The ice cream shop could order a different size scoop with a diameter closer to 1.732 in for an even better fit.

Ice cream scoop will be the best fit for the waffle cones need to find out the diameter of the cones.

We can use the given height and volume of the cones to calculate the diameter using the formula for the volume of a cone:

V = (1/3) × π × r² × h

V is the volume r is the radius (which is half the diameter) and h is the height.

Rearranging the formula to solve for r we get:

r = √((3V) / (πh))

Substituting the given values of V = 3π in³ and h = 4 in we get:

r = √((3π) / (4π))

= √(3/4)

= 0.866 in

So, the diameter of the waffle cones is approximately 1.732 in (twice the radius).

Now we can compare this diameter to the diameters of the #12 and #6 scoops.

The #12 scoop has a diameter of 2.5 in is larger than the cone diameter of 1.732 in so it may not be the best fit.

The #6 scoop has a diameter of 3 in is larger than the cone diameter but closer in size so it may be a better fit than the #12 scoop.

The ice cream shop could order a different size scoop with a diameter closer to 1.732 in for an even better fit.

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After considering the given data we conclude that the given expression upon calculation is equivalent to cot(2β), under the condition that the given expression is cot2β(1−cos2β).

In order to elaborate this given expression we have to use trigonometric identities. Furthermore, the identity cot(2β)(1-cos(2β)) = cot(2β) can be derived applying the following steps:
cot(2β)(1-cos(2β)) = cot(2β) - cos(2β)cot(2β)
= cot(2β) - cos(2β)/sin(2β)
= (cos(2β)sin(2β)/sin(2β)) - cos(2β)/sin(2β)
= (cos(2β)-cos(2β)sin²(2β))/sin(2β)
= cos(2β)(1-sin²(2β))/sin(2β)
= cos(2β)cos²(2β)/sin(2β)
= cot(2β)
Trigonometric identities are considered equalities that have trigonometric functions and are proclaimed as true for each and every value taking place in variables for which both sides of the equality are defined.
These identities are really helpful  in the event expressions involving trigonometric functions need to be simplified.
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Answer:

you got them all correct! good job :)

Step-by-step explanation:

Without that information, I cannot interpret or evaluate the validity of the interval. However, I can provide general guidance on how to interpret a confidence interval.

A 95% confidence interval for a parameter (such as the mean age of the six presidents at their inaugurations) is an interval estimate calculated from sample data that has an associated probability of capturing the true population parameter. Specifically, it means that if we were to repeat the sampling process many times and construct 95% confidence intervals each time, approximately 95% of those intervals would contain the true population parameter.

Therefore, if the confidence interval you provided was calculated correctly and is valid, it means that we are 95% confident that the true mean age of the six presidents at their inaugurations falls within the given interval. However, if there are any issues with the data or the assumptions made in calculating the interval, it may not be appropriate to interpret it in this way.

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Answer:

'x' only has one solution

Step-by-step explanation:

First multiply both sides by 'x^2'

40x = -5x^2

(bring both values to one side and factorize to solve for 'x')

5x^2 +40x=0

5x(x+8)=0

5x= 0 ; x+8 = 0

x=0 ; x=-8

x cannot equal to '0' as zero cannot be a denominator.

Hence, x=-8 is the only correct solution.

So, 'x' only has one solution.

Cassandra will earn $65 in simple interest at the cease of the 4 years.

The formulation for simple interest is:

I = P * r * t

Wherein

In this case Cassandra's preliminary deposit is $500 so that' why the interest rate is some about 3.25% & the time period is four years.

Plugging these values into the formulation, we get:

I = $500 * 0.0325 * 4

I = $65

Therefore, Cassandra will earn $65 in simple interest at the cease of the 4 years.

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The car travels 45.84 meters in 3 seconds.

To solve this problem, we need to convert the speed of the car from kilometers per hour to meters per second since the time given is in seconds.
To do this, we can use the conversion factor that 1 kilometer is equal to 1000 meters and 1 hour is equal to 3600 seconds.
So, 55 kilometers per hour is equal to (55 x 1000) / 3600 = 15.28 meters per second.
Now, we can use the formula: distance = speed x time
Plugging in the values, we get distance = 15.28 meters per second x 3 seconds = 45.84 meters.
Therefore, the car travels 45.84 meters in 3 seconds.

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The distance from the Earth to the Sun is approximately 412 million km.

To find the distance from the Earth to the Sun and calculate the remaining information, we can utilize basic trigonometry principles and the given distances.

Let's denote the distance from the Earth to the Sun as "x" (unknown), the distance from the Sun to the Moon as "y" (150 million km), and the distance from the Moon to the Earth as "z" (384 million km).

To determine the missing side lengths and angle measures, we can use the concept of right-angled triangles.

First, let's consider the triangle formed by the Moon, Earth, and Sun. The side lengths and angle measures are as follows:

Side lengths:

Moon to Earth (z) = 384 million km

Earth to Sun (x) = unknown (to be determined)

Sun to Moon (y) = 150 million km

Angle measures:

Angle at Moon (θ1) = 90 degrees (perpendicular angle)

Angle at Earth (θ2) = unknown (to be determined)

Angle at Sun (θ3) = 90 degrees (perpendicular angle)

Next, let's examine the triangle formed by the Earth, Sun, and Moon. The side lengths and angle measures in this triangle are:

Side lengths:

Earth to Moon (z) = 384 million km

Moon to Sun (y) = 150 million km

Sun to Earth (x) = unknown (to be determined)

Angle measures:

Angle at Earth (θ4) = 90 degrees (perpendicular angle)

Angle at Sun (θ5) = unknown (to be determined)

Angle at Moon (θ6) = 90 degrees (perpendicular angle)

To find the distance from the Earth to the Sun (x), we can use the Pythagorean theorem on the triangle involving the Moon, Earth, and Sun:

[tex]x^2 = z^2 + y^2[/tex]

[tex]x^2[/tex] [tex]= (384 million km)^2 + (150 million km)^2[/tex]

[tex]x^2[/tex] [tex]= 147,456,000,000,000 km^2 + 22,500,000,000,000 km^2[/tex]

[tex]x^2[/tex] [tex]= 169,956,000,000,000 km^2[/tex]

Taking the square root of both sides:

x ≈  [tex]\sqrt(169,956,000,000,000 km^2)[/tex]

x ≈ 412 million km (approximately)

Therefore, the distance from the Earth to the Sun is approximately 412 million km.

For the trigonometric functions, we can calculate them for the angles θ2 and θ5.

Trig functions for the angle from Moon, Earth, Sun (θ2):

sin(θ2) = Opposite/Hypotenuse = z/y = 384 million km / 150 million km

cos(θ2) = Adjacent/Hypotenuse = x/y = 412 million km / 150 million km

tan(θ2) = Opposite/Adjacent = z/x = 384 million km / 412 million km

csc(θ2) = 1/sin(θ2)

sec(θ2) = 1/cos(θ2)

cot(θ2) = 1/tan(θ2)

Trig functions for the angle from Earth, Sun, Moon (θ5):

sin(θ5) = Opposite/Hypotenuse = y/x = 150 million km / 412 million km

cos(θ5) = Adjacent/Hypotenuse = z/x = 384 million km / 412 million km

tan(θ5) = Opposite/Adjacent = y/z = 150 million km / 384 million km

csc(θ5) = 1/sin(θ5)

sec(θ5) = 1/cos(θ5)

cot(θ5) = 1/tan(θ5)

Please note that the trigonometric functions can be calculated using a calculator or software capable of performing trigonometric calculations.

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To find the equation of the tangent line to the curve y = 7sin(x) at x = π, we first need to find the slope of the tangent line.

We can use the derivative of y with respect to x to find the slope:

dy/dx = 7cos(x)

At x = π, the value of the derivative is:

dy/dx = 7cos(π) = -7

So the slope of the tangent line at x = π is -7.

To find the equation of the tangent line, we also need to know the y-coordinate of the point on the curve where x = π.

y = 7sin(π) = 0

So the point on the curve where x = π is (π, 0).

Now we can use the point slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line.

Plugging in the values we found, we get:

y - 0 = -7(x - π)

Simplifying, we get:

y = -7x + 7π

So the equation of the tangent line to y = 7sin(x) at x = π is y = -7x + 7π.

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The equation of the line that passes through the point (6,8) and is perpendicular to a line is y = (-2/3)x + 12.

Given the equation, y= 3/2x + 5. Compare it with the general equation of the line,

y =  m₁   x + c₁

y= (3/2) x + 5

Therefore, the slope of the given line is m₁=(3/2).

Since it is needed to find the line that is perpendicular to y= 3/2x + 5, therefore, the slope of the two lines can be written as,

(Slope of line 1) × (Slope of line 2) = -1

m₁ × m₂ = -1

(3/2) × m₂ = -1

m₂ = -2/3

Now, the equation of the given line can be written as,

y = m₂x + c₂

y = (-2/3)x + c₂

Substitute the given coordinate in the above equation to get the value of y-intercept(c),

8 = (-2/3)6 + c₂

8 = -4 + c₂

c₂ = 8 + 4

c₂ = 12

Hence, the equation is y = (-2/3)x + 12.

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The complete question is:

What is an equation of the line that passes through the point (6, 8) and is perpendicular to a line with equation y=3/2x 5.

The calculated value of the number is -45

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

Represent the number with x

So, we have the following equation

2/3x + 5 = x - 10

Collect the like terms

This gives

2/3x - x = -10 - 5

When the like terms are evaluated, we have

1/3x = -15

So, we have

x = -45

Hence, the value of the number is -45

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The minimum sum of products (MSP) expression of the given function F(A, B, C, D) can be obtained by using the Quine-McCluskey method.  In this case, the MSP expression for the given function is F(A, B, C, D) = A'C'D' + A'BCD + AB'C'D + ABCD.

The MSP expression is a simplified Boolean expression that represents the function in terms of its essential prime implicants.

The Quine-McCluskey method is an algorithm that uses the concepts of prime implicants, essential prime implicants, and petrick's method to simplify Boolean functions. The method starts with finding all the prime implicants of the function and then grouping them to form essential prime implicants. The essential prime implicants are then used to form the MSP expression of the function. The MSP expression obtained using this method is minimal, which means that it has the least number of terms and literals compared to other simplified expressions.

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Answer: To solve this problem, we will use the formula d = a2 - a1, where d is the common difference and a1 and a2 are two consecutive terms in the sequence.

Step 1: Identify two consecutive terms in the sequence.

In this case, the two consecutive terms are 13 and 18.

Step 2: Substitute the two consecutive terms into the formula d = a2 - a1.

d = 18 - 13

Step 3: Simplify the equation to calculate the common difference.

d = 5

Therefore, the common difference of the arithmetic sequence 13, 18, 23, 28,... is 5.

Step-by-step explanation:

The area of the cone that gets sprayed, from using the radius obtained from the formula for the lateral surface area is about 186.22 in²

The lateral surface area of a cone is the area covered by the curved surface of the cone.

The lateral surface area of the cone = 65·π square inches

The distance of the can from the canvas = 12 inches

The distance of the can from the canvas is the height, h, of the cone

The formula for finding the lateral surface area of a cone, A, can be presented as follows;

A = π·r·√(h² + r²)

Therefore, we get;

A = π·r·√(12² + r²) = 65·π

r·√(12² + r²) = 65

r²·(12² + r²) = 65²

12·r² + (r²)² = 65²

(r²)² + 12·r² - 65² = 0

r² = -6 ± √(4261)

r = √(-6 ± √(4261))

r ≈ 7.699, and r ≈ √(-71.28) (An imaginary number)

The area of the part of the canvas that gets sprayed with paint therefore is; A = π × (7.699 in)² ≈ 186.22 in²

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The probability that the spinner lands on 4​ under the condition that he rolls a 1 is 2/27,

Given that the spinner with 9 equally spaced regions numbered 1 to 9​ and a standard number cube is rolled,

So, the probability of spinning a 4 is = 4/9

The probability of rolling a 1 is = 1/6

The probability of both happening is = 1/6 x 4/9 = 4 / 54 = 2/27

Hence the probability that the spinner lands on 4​ under the condition that he rolls a 1 is 2/27,

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After 3 years, Ana's account balance would be approximately $1221.96, assuming a constant withdrawal rate of $200 per year.

Ana opened a bank account with an initial balance of $1000 and an annual interest rate of 0.02, compounded continuously. The function P(t) models the balance of the account in dollars at time t.
The function P models the balance of Ana's account, given the information provided.

1. Ana opens a bank account with $1000. This is the initial amount in the account.
2. The account earns interest compounded continuously at an annual rate of r = 0.02.
3. Money can be withdrawn, but no additions can be made.

Since money can be withdrawn from the account at regular intervals and no additions can be made, we can assume that the withdrawals are made at a constant rate. Let's call this rate "w" (in dollars per year). Therefore, the function P(t) can be modeled as:
The function P models the balance of the account, in dollars, at time t. Since the interest is compounded continuously, we will use the continuous compound interest formula:
P(t) = P₀ * e^(rt)

Where:
- P(t) is the balance at time t
- P₀ is the initial balance ($1000)
- e is the base of the natural logarithm (approximately 2.71828)
- r is the annual interest rate (0.02)
- t is the time in years

We get: P(t) = 1000*e^(0.02t) - wt

where e is the mathematical constant, approximately equal to 2.71828. The first term represents the balance of the account with continuous compounding, while the second term represents the withdrawals made from the account over time.

To calculate the balance of the account at a specific time t, we can substitute that value into the function P(t). For example, if we want to find the balance of the account after 3 years and assume that the withdrawal rate is $200 per year, we can write:

P(3) = 1000*e^(0.02*3) - 200*3
P(3) = 1000*e^(0.06) - 600
P(3) ≈ $1221.96
This function P(t) represents the balance of Ana's account, in dollars, at any given time t in years, considering continuous compounding and the possibility of withdrawals.

Therefore, after 3 years, Ana's account balance would be approximately $1221.96, assuming a constant withdrawal rate of $200 per year.

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The required value of x for this polygon is - 90.

We know that,

Polygons are two-dimensional geometric figures with a fixed number of sides. A polygon's sides are made up of straight line segments that are joined end to end. As a result, the line segments of a polygon are referred to as sides or edges.

The place where two line segments meet is known as the vertex or corners, and an angle is generated as a result.

A triangle with three sides is an example of a polygon. A circle is a plane figure, however it is not regarded a polygon because it is curved and lacks sides and angles.

As a result, we can argue that all polygons are 2d shapes, but not all two-dimensional figures are polygons.

Since,

Sum of interior angles of polygons = 360 degree

Therefore,

130 + x + 20 + 120 + 140 + x - 20 + 150 + x = 360

                                                                2x = 360 - 540

                                                                   x = -180/2

                                                                   x = -90

Thus,

The value of x = - 90

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The statements about the bowl that are accurate include:

A. The area of the opening of the bowl is 63.6 square inches.

E. The volume of the bowl, rounded to the nearest tenth is 575.2 cubic inches.

In Mathematics and Geometry, the volume of a hemisphere can be calculated by using the following mathematical equation (formula):

Volume of a hemisphere = 2/3 × πr³

Where:

r represents the radius.

By substituting the given parameters into the formula for the volume of a hemisphere, we have the following;

Volume of a bowl = 2/3 × 3.142 × (6.5)³

Volume of a bowl = 575.2 in³

Area of circle = π × (radius)²

Area of bowl = 3.142 × (6.5)²

Area of bowl = 132.7 in².

Volume of a bowl = 575.2/3 = 191.7 in³

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

35 seventh-graders will watch at least one movie this weekend based on the survey.

We have,

If 70% of seventh-graders watch at least one movie during the weekend, then the number of seventh-graders who watch at least one movie is:

= 70% of 50

= 70/100 x 50

= 0.7 x 50

= 35

Therefore,

35 seventh-graders will watch at least one movie this weekend based on the survey.

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Answer:

14/3

Step-by-step explanation:

Answer:

58/3

Step-by-step explanation:

7 1/4 ÷ 3/8

= 29/4 x 8/3

= 29 x 2/3

= 58/3

The lower limit for the 95% confidence interval for the true graduation rate is 0.704.

The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level.

We can use the formula for the confidence interval for a proportion:

lower limit = sample proportion - z * √((sample proportion * (1 - sample proportion)) / sample size)

where z is the z-score corresponding to the desired level of confidence (95% in this case), and sample size is 500.

The sample proportion is 371/500 = 0.742.

The z-score for a 95% confidence level can be found using a standard normal distribution table or calculator, and is approximately 1.96.

Plugging in the values, we get:

lower limit = 0.742 - 1.96 * √((0.742 * 0.258) / 500)

lower limit = 0.704

Rounding to three decimal places, the lower limit for the 95% confidence interval for the true graduation rate is 0.704.

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