In a poll conducted by the Gallup organization 16% of adult, employed Americans were dissatisfied with the amount of vacation time. You conduct a survey of 500 adult, employed Americans.

(3 points) Using the binomial formula (or technology) – find the probability that less than 70 are dissatisfied with their vacation time.



(2 points) Show that this distribution can be approximated by the normal distribution.



(5 points) Use the normal curve to approximate the probability that less than 70 are dissatisfied with their vacation time.

The length of the side of the hexagon is 12 cm and option d is the correct answer.

A regular polygon is a closed shape made up of straight line segments with sides and angles that are all of the same length. For instance, a regular hexagon is a polygon having six equal-length sides and six equal-sized angles. Regular polygons have a variety of intriguing characteristics. For instance, their diagonals (lines connecting non-adjacent vertices) all intersect at a single point, and their centre of symmetry is located at the centre of the polygon's circumscribed circle (the circle that passes through all of the polygon's vertices).

Given that, regular hexagon is inscribed into a circle.

The radius of a circle enclosing a regular hexagon is the same as the length of the hexagon's sides.

Hence, the length of the side of the hexagon is 12 cm and option d is the correct answer.

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The probability of selecting a blue marble on the first draw and a green marble on the second draw is 0.09.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

There are 12 marbles in total in the bag, so the probability of selecting a blue marble on the first draw is 4/12.

After the first marble is drawn, there are 11 marbles left in the bag, so the probability of selecting a green marble on the second draw, given that the first marble was blue and has already been removed, is 3/11.

To determine the probability of both events occurring together, we multiply the probabilities. Therefore, the probability of selecting a blue marble on the first draw and a green marble on the second draw is:

(4/12) * (3/11) = 0.0909

Rounding to the hundredth place, the probability is approximately 0.09.

Therefore, the probability of selecting a blue marble on the first draw and a green marble on the second draw is 0.09.

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Answer:

To find the Taylor series of a function f(x) about a point a, we can use the following formula:

f(x) = f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...

where f'(a), f''(a), f'''(a), ... denote the first, second, third, ... derivatives of f evaluated at a.

In this case, we have:

f(x) = 1 + 3e^(x+1)

To find the Taylor series about x=0, we need to evaluate the function and its derivatives at x=0.

f(0) = 1 + 3e^(0+1) = 1 + 3e

f'(x) = 3e^(x+1)

f'(0) = 3e^(0+1) = 3e

f''(x) = 3e^(x+1)

f''(0) = 3e^(0+1) = 3e

f'''(x) = 3e^(x+1)

f'''(0) = 3e^(0+1) = 3e

and so on.

Substituting these values into the formula for the Taylor series, we get:

f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ...

= (1 + 3e) + 3ex + 3ex^2/2! + 3ex^3/3! + ...

= 1 + (3 + 3e)x + (3/2)e x^2 + (1/2)e x^3 + ...

Therefore, the Taylor series for 1+3e^x+1 about x=0 is:

1 + (3 + 3e)x + (3/2)e x^2 + (1/2)e x^3 + ...

Answer:

Step-by-step explanation:

Section 1

1: 2x + 20

2. 8x - 49
3: 7x + 21

4.8x - 4

5. 15x + 5

6. 12x + 15

7. 20x - 50

8. 21x + 14

9. 24x - 6

10. 45x - 18

11. 18x - 8

12. 30x + 9

13. 24x + 36

14. 25x - 20

15. 14x - 63

16. 32x + 20

17. 24x - 10

18. 42x - 18

19. 24x - 80

20. 48x - 32

Answer: -1/6

Step-by-step explanation:

Put the equation into y = mx + b (slope) form.

3x + 18y = -486

18y = -3x - 486

y = -1/6x - 27

If the line is parallel to this line, the slope must be the same.

Answer:

Step-by-step explanation:

[tex](3x+5)+(x-25)=180 \text{ \ (angles on a straight line are supplementary)}[/tex]

                 [tex]4x-20=180[/tex]

                         [tex]4x=200[/tex]         (+20 both sides)

                           [tex]x=50[/tex]           (÷4 both sides)

Answer: x = 2, y = 0

Step-by-step explanation:

Assuming you need help solving for x or y, and the capital Y is y, we have the system of equations:

3x + y = 6

y + 2 = x

Substituting x for y + 2 gives us

3(y + 2) + y = 6

3y + 6 + y = 6

4y = 0

y = 0

Plugging y = 0 in for the second equation gives us

x = 0 + 2, or x = 2

Therefore , the solution of the given problem of unitary method comes out to be  the attraction sold 943 child tickets and 736 adult tickets on that particular day.

It is possible to accomplish the objective by using previously recognized variables, this common convenience, or all essential components from a prior malleable study that adhered to a specific methodology. If the expression assertion result occurs, it will be able to get in touch with the entity again; if it does not, both crucial systems will undoubtedly miss the statement.

Here,

Assume the attraction sold x tickets for adults and y tickets for kids.

Based on the supplied data, we can construct the following two equations:

=>  x + y = 1679 (equation 1, representing the total number of tickets sold)

=>  35x + 20y = 44620 (equation 2, representing the total revenue generated)

Using the elimination technique, we can find the values of x and y.

When we divide equation 1 by 20, we obtain:

=>  20x + 20y = 33580 (equation 3)

Equation 3 is obtained by subtracting equation 2 to yield:

=>  15x = 11040

=>  x = 736

When we enter x = 736 into equation 1, we obtain:

=>  736 + y = 1679

=> y = 943

As a result, the attraction sold 943 child tickets and 736 adult tickets on that particular day.

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The perimeter of the garden in the drawing is 22 inches and the perimeter of the actual garden is 770 inches

The perimeter of the garden in the drawing is calculated as

Perimeter of garden in drawing = 2(length + width)

So, we have

Perimeter of garden in drawing = 2(7 inches + 4 inches)

Evaluate

Perimeter of garden in drawing = 22 inches

So the perimeter of the garden in the drawing is 22 inches.

For the perimeter of the actual garden, we have

Perimeter of actual garden = 22 inches * 35

Perimeter of actual garden = 770 inches

We can see that the perimeter of the actual garden is 35 times larger than the perimeter of the garden in the drawing.

This makes sense since the length and width of the actual garden are 35 times larger than the length and width in the drawing, so the perimeter (which is the sum of the lengths of all four sides) would also be 35 times larger.

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Answer:

D. 7/5

Step-by-step explanation:

In right triangle ABC with right angle C,

sinA = 4/5 = cosB

cosA = 3/5 = sinB

sinB + cosB = 3/5 + 4/5 = 7/5

Answer:

b the solution is (3,5)

Step-by-step explanation:

look at the points where the lines intersect

For the equations 2xy - y^2 = 1 and xy + x + y = x^2y^2 using implicit differentiation the value Dxy is given by Dxy = (1 - 2xy + 3y^2)/(x - y)^3 and Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3  respectively.

Equation 2xy - y^2 = 1,

Differentiate both sides of the equation with respect to x,

Treating y as function of x and then differentiate again with respect to x.

Using implicit differentiation,

First, differentiate both sides with respect to x,

2y + 2xy' - 2yy' = 0

Next, solve for y',

⇒2xy' - 2yy' = -2y

⇒y' (2x - 2y) = -2y

⇒y' = -y/(x - y)

Now, differentiate again with respect to x,

y''(x - y) - y'(2x - 2y) = y/(x - y)^2

Substitute the expression we obtained for y' in terms of y and x,

y''(x - y) - (-y/(x - y))(2x - 2y) = y/(x - y)^2

Simplify and solve for y'',

y''(x - y) + (2xy - 3y^2)/(x - y)^2 = 1/(x - y)^2

The expression for Dxy is,

Dxy = (1 - 2xy + 3y^2)/(x - y)^3

For the equation xy + x + y = x^2y^2,

Differentiate both sides of the equation with respect to x,

Using implicit differentiation,

First, differentiate both sides with respect to x,

⇒y + xy' + 1 + y' = 2xyy'

Solve for y',

⇒xy' - 2xyy' + y' = -y - 1

⇒y' (x - 2xy + 1) = -y - 1

⇒y' = -(y + 1)/(x - 2xy + 1)

Now, differentiate again with respect to x,

y''(x - 2xy + 1) - y'(2y - 2x y' + 1) = (y + 1)/(x - 2xy + 1)^2

Substitute the expression we obtained for y' in terms of y and x,

y''(x - 2xy + 1) - (-y - 1)/(x - 2xy + 1)^2 (2y - 2x y' + 1) = (y + 1)/(x - 2xy + 1)^2

Simplify and solve for y''

y''(x - 2xy + 1) - (2y^2 - 2xy - 2y)/(x - 2xy + 1)^2 = (y + 1)/(x - 2xy + 1)^2

The expression for Dxy is,

Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3

Therefore , the value of Dxy using implicit differentiation for two different functions is equal to

Dxy = (1 - 2xy + 3y^2)/(x - y)^3 and Dxy = (2y^2 - 2xy - 3y - 1)/(x - 2xy + 1)^3

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Answer: Area = 113.14 ft sq. Perimeter =

Step-by-step explanation:

break down the figure and solve area and perimeter for each

triangle = A = 1/2bh

A = 1/2 (8) (6)

A = 24 ft sq.

square = A = LW

A = (8) (8)

A = 64 ft sq

semi circle = A = 1/2 TT r^2

A = 1/2 (3.14) (4)^2

A = 1/2 (3.14) (16)

A = approximately 25.14 ft sq

rounded to hundredths

total AREA = 24 + 64 + 25.14 = 113.14

now we can find perimeter by breaking down the figures again

triangle

we know one leg is 6 ft and the other is 8 ft

we need to find the hypoteneuse using Pythagorean theorem.

a^2 + b^2 = c^2

6^2 = 8^2 = c^2

36 + 64 = c^2

100 = c^2

√100 = √c^2

10 ft = c

square

given two sides are 8ft and 8ft

semi circle - P is the same as circumference

P = ( 1/2 ) 2 π r

P = (1/2) (2) (3.14) (4)

P = 12.56

total PERIMETER = 12.56 + 8 + 8 + 6 + 10 = 44.56 ft

i attached a print screen showing my breakdowns

Answer:

[-1,inf) and [-2,inf)

Step-by-step explanation:

Domain is all the X coordinates that the function will pass through. it starts at -1 and goes to inf so [-1,inf) is the domain. The range is all the Y coordinates the function will pass through. It starts at -2 and goes up to inf so [-2,inf) and that is your answer

The elements in the set  (A∩B¹) = {2,11,12,} and (B∩A¹) ={5,7,8,9,13,15,16,18}

You should understand that Set theory is a branch of mathematical logic that studies sets, which can be informally described as collections of objects such as numbers, alphabets and variables.

The universal set

S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

A = {1,2,6,11,12,19,20}

B = {1,5,6,7,8,9,13,15,16,18,19,20}

S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

B¹ = {2.3.4.10.11.12.14.17)

A = {1,2,6,11,12,19,20}

(A∩B¹) = {2,11,12,}

The elements of (B∩A¹) is

S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}

A = {1,2,6,11,12,19,20}

A¹ = {3,4,5,7,8,9,10,13,14,15,16,17,18}

B = {1,5,6,7,8,9,13,15,16,18,19,20}

(B∩A¹)  = {5,7,8,9,13,15,16,18}

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Using compounding we know that the additional amount Jason has more than Kayden is $249.48.

Calculating interest on the principal borrowed as well as any prior interest.

In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one.

So, the amount of Jason after 8 years:

Amount: $5500

Interest: 1.875%

Compounded: Quarterly

Using a compounding calculator:

Amount after 8 years: $6,387.85

The amount of Kayden:

Amount: $5500

Interest: 1.375%

Compounded: Quarterly

Using a compounding calculator:

Amount after 8 years: $6,138.37

The additional amount Jason got: 6,387.85 - 6,138.37 = $249.48

Therefore, using compounding we know that the additional amount Jason has more than Kayden is $249.48.

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Answer:253

Step-by-step explanation:

The given statement 'to calculate the average of the numeric values in a list  the first step is to get the sum of all the given values ' is a true.

Average of the numeric values in a list,

First step is to get the sum of values in the list.

It is not the total number of values.

Once we have the sum, we can divide it by the number of values to get the average.

Here is an example,

Suppose we have a list of numeric values are as follow,

[2, 4, 6, 8, 10].

To calculate the average of these values, we first find their sum,

2 + 4 + 6 + 8 + 10 = 30

Next,

divide the sum by the number of values in the list

Number of values = 5

30 / 5 = 6

This implies,

The average of the values in the list is 6.

Therefore, to get the average first step is to get the total of all values is true statement.

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Answer:

60 - 10 = 50

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The value of R500 decrease to ratio 9:8 is x = 400.

By using the cross multiplication approach, the denominator of the first term is multiplied by the numerator of the second term, and vice versa. Using the mathematical rule of three, we may determine the answer based on proportions. The best illustration is cross multiplication, where we may write in a percentage to determine the values of unknown variables.

Given that, decrease R450 in the ratio 9:8.

Let 9 = 450

Then 8 will have the value = x.

That is,

9 = 450

8 = x

Using cross multiplication we have:

9x = 450(8)

x = 50(8)

x = 400

Hence, the value of R500 decrease to ratio 9:8 is x = 400.

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The volume of the globe is 905 cubic inches, for the given surface area.

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a form with a curved base and surface is equal to the sum of the two areas.

The volume of the globe is given as:

V = 4/3πr³

The surface area if given as:

SA = 4πr²

Substituting the values of the given SA we have:

452.39 = 4 * 3.14(r²)

r = 6.01

Now, substitute the value of r in the equation of volume we have:

V = 4/3(3.14)(6.01)³

V = 904.78.

Hence, the volume of the globe is 905 cubic inches, for the given surface area.

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Answer:

Step-by-step explanation:

We can factor out a common factor of -4x from the equation:

y = -4x(x² + 4x - 21)

To factor the quadratic expression in the parentheses, we need to find two numbers that multiply to -21 and add to 4. These numbers are 7 and -3:

y = -4x(x + 7)(x - 3)

To check our work, we can multiply the three factors:

y = -4x(x + 7)(x - 3) = -4x(x² + 4x - 21) = -4x³ - 16x² + 84x

So the factored form is y = -4x(x + 7)(x - 3), and the check shows that we have factored the equation correctly.

The displacement of the block at any time t is then x= 0.05cos5tm. (option b).

Now, when the block is released, it starts oscillating back and forth about its equilibrium position due to the force exerted by the spring. This motion is described by the equation of motion for a simple harmonic oscillator:

x = Acos(ωt + φ)

The angular frequency ω of the oscillation is given by:

ω = √(k/m)

where k is the spring constant and m is the mass of the block.

Substituting the given values of k and m, we get:

ω = √(50/2) = 5 rad/s

The phase angle φ depends on the initial conditions of the system, i.e., the initial displacement and velocity of the block. Since the block is initially at rest, its initial velocity is zero and the phase angle is zero as well.

Therefore, the equation of motion for the displacement of the block is:

x = 0.05cos(5t)

Hence, option B, x = 0.05cos(5t), is the correct answer.

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Answer:b

Step-by-step explanation:

Answer:

15.

The trick to working out 5 divided by 1/3 is similar to the method we use to work out dividing a fraction by a whole number.All we need to do here is multiply the whole number by the numerator and make that number the new numerator. The old numerator then becomes the new denominator.

So, the answer to the question "what is 5 divided by 1/3?" is
15!

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Answer: 6234 × 32 = 199488.

Step by step:

To calculate 6234 × 32 without using a calculator, you can use the traditional multiplication method as follows:

   6234

x    32

-------

  12468   (2 x 6234)

+ 62340   (3 x 6234 with a zero added)

--------

 199488

The cube has 8 vertices. Exercise 21 states that for a polyhedron with V vertices, E edges, and F faces, the following equation holds:

V - E + F = 2

To use this equation to find the number of vertices of a cube with 12 edges and 6 faces, we first need to identify the values of E and F.

A cube has 12 edges, as given in the problem statement, and it has 6 faces since a cube has 6 square faces.

Substituting these values into the equation, we get:

V - 12 + 6 = 2

Simplifying this equation, we have:

V - 6 = 2

Adding 6 to both sides, we get:

V = 8

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Consider the line segment AB shown the locations for point C makes ABC a right triangle with hypotenuse AB

In a coordinate pair the points are as represented as (x, y).

The point that forms the right triangle is located by tracing the point on the x axis of of the point A and the point on the y axis of the point B.  This is done below

therefore we can say that the point C that forms the right triangle is

C (2, 3)

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Since we can't find an ordered pair (x, y) that satisfies all the conditions, there is no solution to this problem.

An equation is a mathematical statement that asserts the equality of two expressions. It typically contains variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true. Equations can be used to model relationships between variables, solve real-world problems, and make predictions.

Here,

Let's start by defining the variables:

x: number of hot dogs

y: number of peanuts

We need to find an ordered pair (x, y) that satisfies the following conditions:

x and y are both integers

x is greater than or equal to 0

y is greater than or equal to 0

2x + y ≤ 7 (total cost of snacks can't exceed $7)

x ≥ 4 (at least 4 snacks)

We can use trial and error to find a suitable ordered pair. Let's start with x = 4 and see if we can find a corresponding y value that satisfies the conditions:

If x = 4, then the total cost of hot dogs is 4 * $2 = $8.

We need to spend no more than $7, so we have $7 - $8 = -$1 left for peanuts.

Since we can't spend a negative amount of money, there is no solution for x = 4.

Let's try x = 5:

If x = 5, then the total cost of hot dogs is 5 * $2 = $10.

We have $7 - $10 = -$3 left for peanuts, so there is no solution for x = 5 either.

Finally, let's try x = 6:

If x = 6, then the total cost of hot dogs is 6 * $2 = $12.

We have $7 - $12 = -$5 left for peanuts, so there is no solution for x = 6 either.

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Complete question:

Cody has $7 dollars. he wants to buy at least 4 snacks. Hot dogs (x) and $2 each. Peanuts (y) are $1 each. Find the solution for this question of equation?

Students were asked to simplify the expression using trigonometric identities:

 A.  student A is correct; student B was confused by the division

 B.  3: cos²(θ)/(sin(θ)csc(θ)); 4: cos²(θ)

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

The six trigonometric ratios serve as the foundation for all trigonometric identities. Sine, cosine, tangent, cosecant, secant, and cotangent are some of their names.

Each student correctly made use of the trigonometric identities

cosec(θ) = 1/sin(θ)

1 -sin²(θ) = cos²(θ)

A.

Student A's work is correct.

Student B apparently got confused by the two denominators in Step 2, and incorrectly replaced them with their quotient instead of their product.

The transition from Step 2 can look like:

[tex]\frac{(\frac{1-sin^2\theta}{sin\theta} )}{cosec\theta} =\frac{1-sin^2\theta}{sin\theta} .\frac{1}{cosec\theta} =\frac{cos^2\theta}{(sin\theta)(cosec\theta)}[/tex]

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Complete question:

Students were asked to simplify the expression the quantity cosecant theta minus sine theta end quantity over cosecant period Two students' work is given. (In image below)

Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)

Part B: Complete the student's solution correctly, beginning with the location of the error. (5 points)

Answer:

19782m

Step-by-step explanation:

1  revolution = circumference

circumference = π * diameter

π = 3.1416

Then

circumference = 3.1416 * 63

= 197.92m

1 revolution = 197.82m

100 revolutions = 100*197.82m

= 19782m

Answer:

19.8 km

Step-by-step explanation:

To find:-

Answer:-

We are here given that,

We can first find the circumference of the wheel using the formula,

[tex]:\implies \sf C = 2\pi r \\[/tex]

Here radius will be 63/2 as radius is half of diameter. So on substituting the respective values, we have;

[tex]:\implies \sf C = 2\times \dfrac{22}{7}\times \dfrac{63}{2} \ m \\[/tex]

[tex]:\implies \sf C = 198\ m \\[/tex]

Now in one revolution , the cycle will cover a distance of 198m . So in 100 revolutions it will cover,

[tex]:\implies \sf Distance= 198(100)m\\[/tex]

[tex]:\implies \sf Distance = 19800 m \\[/tex]

[tex]:\implies \sf Distance = 19.8 \ km\\[/tex]

Hence the bicycle would cover 19.8 km in 100 revolutions.