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The probability that at least six hamburgers are contaminated in a random sample of 10 hamburgers is approximately 0.2 or 20%

We can approach this problem using the binomial distribution, where:

n = 10 (the sample size)

p = 0.25 (the probability of a hamburger being contaminated)

q = 1 - p = 0.75 (the probability of a hamburger not being contaminated)

We want to find the probability that at least six hamburgers are contaminated, which can be expressed as:

P(X ≥ 6) = P(X = 6) + P(X = 7) + ... + P(X = 10)

where X is the number of contaminated hamburgers in the sample.

Using the binomial probability formula, we can calculate each individual probability:

P(X = b) = (n choose b) x pᵇ x q⁽ⁿ⁻ᵇ⁾

where (n choose k) represents the number of ways to choose k items from a set of n items, and is calculated as:

(n choose k) = n! / (k! x (n-k)!)

Using a calculator or software, we can find each individual probability and sum them up to get the total probability:

P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

= (10 choose 6) x 0.25⁶ x 0.75⁴ + (10 choose 7) x 0.25⁷ x 0.75³ + (10 choose 8) x 0.25⁸ x 0.75² + (10 choose 9) x 0.25⁹ x 0.75¹ + (10 choose 10) x 0.25¹⁰ x 0.75⁰

= 0.0197

= 0.02

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Answer:

  (c)  B'(3, -2); C'(7, 8); D'(-5, -1)

Step-by-step explanation:

Apparently, you want to know the coordinates of B', C', and D' after reflection of B(-2, 3), C(8, 7), and D(-1,-5) in the line y = x.

The reflection in the line y = x has the effect of swapping the x- and y-coordinates:

  (x, y) ⇒  (y, x)

No sign changes are involved.

The reflected coordinates are ...

  B'(3, -2); C'(7, 8); D'(-5, -1)

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The graph of the functions f(x) and g(x) is given below.

Given that:

Function, f(x) = x³

Translated function, g(x) = (x + 6)³

If the function is translated by 'h' units horizontally and 'k' units vertically, then x and y are replaced with (x - h) and (y - k), respectively.

The curve of the function g(x) is translated left side by 6 units.

The graph of the functions is given below.

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Step-by-step explanation:

it follows practically the same rules as a division between plain numbers.

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴

we take the first term (x⁵) and divide it by the x term(s) of the divisor (we ignore constants for the moment). the resulting x term : x⁴

as x⁵/x = x⁴

now we multiply the intermediate result with the full divisior and subtract that result from the left side of the dividend :

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴

- x⁵ - x⁴

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

0 0

now we "pull down" the next term of the dividend and we calculate

(0 + 0 + 9x³) / x = 9x²

so, we have now

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x²

and we do the same thing as before (multiply intermediate result with divisor and subtract the result)

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x²

0 0 9x³

- 9x³ - 9x²

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

0 0

and, again, we pull down the next term of the dividend abd divide by the x term(s) of the divisor

(0 + 0 + 0 + 0 + 9x) / x = 9

so, we have now

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x² + 9

and we do the same thing as above again

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) = x⁴ + 9x² + 9

- 0 0 0 0 9x - 9

-----------

0 - 1

since we ran out of additional terms, we are finished.

the quotient is

x⁴ + 9x² + 9

the remainder is

-1

which makes the full division result

(x⁵ - x⁴ + 9x³ - 9x² + 9x - 10)/(x - 1) =

= x⁴ + 9x² + 9 - 1/(x - 1)

let's check :

(x⁴ + 9x² + 9 - 1(x - 1)) × (x - 1) =

= x⁵ + 9x³ + 9x - x⁴ - 9x² - 9 - 1 =

= x⁵ - x⁴ + 9x³ - 9x² + 9x - 10

perfect.

The profit earned if 53 mowers are sold is $1104.50.

To find the profit polynomial, we need to subtract the cost polynomial from the revenue polynomial:

Profit = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = (-0.5x^2 + 91x) - (38x + 300)

P(x) = -0.5x^2 + 53x - 300

So the profit polynomial is P(x) = -0.5x^2 + 53x - 300.

To find the profit earned if 53 mowers are sold, we substitute x = 53 into the profit polynomial:

P(53) = -0.5(53)^2 + 53(53) - 300

P(53) = -0.5(2809) + 2809 - 300

P(53) = -1404.5 + 2509

P(53) = 1104.5

Therefore, the profit earned if 53 mowers are sold is $1104.50.

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Check the picture below.

so notice, the area of the pyramid is really just the area of the four triangles with an altitude of 3 and a base of "s", and a square that s² in area, and we happen to know that's 40 inches.

[tex]\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{four triangles} }{4\left[\cfrac{1}{2}(\underset{b}{s})(\underset{h}{3}) \right]}~~ + ~~\stackrel{ square }{(s)(s)}}~~ = ~~40\implies 6b+s^2=40\implies s^2+6b-40=0 \\\\\\ (s+10)(s-4)=0\implies s= \begin{cases} -10\\ ~~ ~~ 4 ~in~~ \textit{\LARGE \checkmark} \end{cases}[/tex]

now, let's notice, we can't use the negative value, because the sides are never negative.

There is a 48% chance of selecting a club or a face card from a standard 52-card deck.

To find the probability of picking a club or a face card from a standard 52-card deck, we need to determine the number of favorable outcomes (cards that are either clubs or face cards) and divide it by the total number of possible outcomes (all the cards in the deck).

There are 13 clubs in a deck, as there is one club for each rank (Ace, 2, 3, ..., 10, Jack, Queen, King). Additionally, there are 12 face cards (Jack, Queen, and King) in each suit, including clubs. So, the number of favorable outcomes is 13 (clubs) + 12 (face cards in clubs) = 25.

The total number of cards in a deck is 52.

Therefore, the probability of picking a club or a face card is 25/52 ≈ 0.48 (rounded to two decimal places).

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Answer:

60 and 40

Step-by-step explanation:

a) To find the number of people who like both tea and coffee, we can use the formula:

Number of people who like both = Number of people who like tea + Number of people who like coffee - Number of people who like only teaPlugging in the given values, we get:

Number of people who like both = 50 + 30 - 20 = 60Therefore, there are 60 people who like both tea and coffee.

b) To find the number of people who like either of the drinks, we can add the number of people who like tea only, the number of people who like coffee only, and the number of people who like both tea and coffee. Mathematically,

Number of people who like either drink = Number of people who like tea only + Number of people who like coffee only + Number of people who like both tea and coffeePlugging in the given values, we get:

Number of people who like either drink = 20 + (30-60) + 50 = 40Therefore, there are 40 people who like either tea or coffee (or both).

The surface area of the cylinder is 948m²

The area occupied by a three-dimensional object by its outer surface is called the surface area. The surface of a cylinder is expressed as ;

SA = 2πr(r+h)

Where r is the radius of the base and h is the height of the cylinder.

r =8m

h = 4m

SA = 2 × 3.14 × 8 (8+4)

SA = 78.96 × 12

SA = 947.52 m²

to the nearest whole number

SA = 948 m²

therefore the surface area of the cylinder is 948 m²

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The rectangle with points (0, 0), (0, 1), (2, 0), and (2, 1) could be the result of dilating the given rectangle with a scale factor between 0 and 1.

Option B is the correct answer.

We have,

Dilation is a transformation that changes the size of an object.

When a figure is dilated with a scale factor between 0 and 1, the resulting figure is smaller than the original.

The scale factor indicates how much smaller the image is compared to the original.

For example, a scale factor of 0.5 would mean that the image is half the size of the original.

Now,

The rectangle with points (0, 0), (0, 1), (2, 0), and (2, 1) could be the result of dilating the given rectangle with a scale factor between 0 and 1.

This is because the side lengths of the second rectangle are half of the side lengths of the first rectangle, which means that the second rectangle is a dilation of the first rectangle with a scale factor of 0.5.

Thus,

The rectangle with points (0, 0), (0, 1), (2, 0), and (2, 1) could be the result of dilating the given rectangle with a scale factor between 0 and 1.

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The minimum number of tickets the agent must sell to have a 95% chance of selling at least one prize-winning ticket is 368 tickets

To unravel this issue, we are able to utilize the concept of likelihood. Let's begin with discovering the likelihood of not offering any prize-winning tickets with one ticket:

- The likelihood of not winning with one ticket is 499/500 (since there's as it were one winning ticket out of 500).

- The likelihood of not winning with n tickets is (499/500)[tex]^n[/tex](since the probabilities are autonomous and we duplicate them together).

Presently, we need to discover the least number of tickets the specialist must offer to have a 95% chance of offering at the slightest one prize-winning ticket. In other words, we need to discover the least esteem of n such that:

- The likelihood of not winning with n tickets is less than or rises to 5% (or 0.05).

- This can be identical to (499/500)[tex]^n[/tex]≤ 0.05.

We will illuminate for n utilizing logarithms:

- Take the normal logarithm of both sides:

ln[(499/500)[tex]^n[/tex]] ≤ ln(0.05).

- Utilize the logarithmic property of types to bring down the example:

n ln(499/500) ≤ ln(0.05).

- Fathom for n by partitioning both sides by ln(499/500) and taking the ceiling work (since n must be an entire number):

n = ceil[tex][ln(0.05) / ln(499/500)].[/tex]

Employing a calculator, we get 

n = ceil[tex][ln(0.05) / ln(499/500)][/tex]≈ 368

In this manner, the specialist must offer at the slightest 368 tickets to have a 95% chance of offering at the slightest one prize-winning ticket. 

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a) Value of K is Option 3. 98.83%

b) It takes Option 2. 183 bounces for the ball to bounce back to a height of less than 3 inches (1/4 of a foot).

a) To determine k, we can use the formula for the nth term of a geometric sequence:

[tex]a_n[/tex] = [tex]a_1[/tex] * [tex]r^{(n-1)}[/tex]

where a_1 is the initial term, r is the common ratio, and n is the term number.

We know that [tex]a_1[/tex] = 10 feet and [tex]a_5[/tex] = 9.04 feet, so we can set up the equation:

[tex]a_5[/tex] = [tex]a_1[/tex] * [tex]r^{(5-1)}[/tex]

9.04 = 10 * [tex]k^4[/tex]

Solving for k, we get:

k = [tex](9.04/10)^{(1/4)}[/tex] = 0.9883 or 98.83%

Therefore, the answer is (Option 3) 98.83%.

b) We can use the formula for the nth term of a geometric sequence again to find the height of the ball after the nth bounce:

[tex]a_n[/tex] = 10 * [tex]k^{(n-1)}[/tex]

We want to find the smallest n such that a_n < 1/4 foot, or 0.25 feet. Substituting k = 0.9883, we get:

10 * [tex]0.9883^{(n-1)}[/tex] < 0.25

Solving for n, we get:

n > log(0.25/10) / log(0.9883) + 1

n > 183.3

Since n must be a whole number, the smallest n that satisfies this inequality is n = 184. Therefore, it takes 183 bounces for the ball to bounce back to a height of less than 3 inches (Option 2).

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After completing the square for the equation [tex]\(x^2 + 12x - 85\)[/tex], we find that the possible result is [tex]\((x + 6)^2 = 49\)[/tex].

To complete the square for the equation [tex]\(x^2 + 12x - 85\)[/tex], we follow these steps:

1. Take half of the coefficient of the [tex]x[/tex] term, which is [tex]\(12/2 = 6\)[/tex].

2. Square this result, [tex]\(6^2 = 36\)[/tex].

3. Add this value, 36, to both sides of the equation to maintain balance:

[tex]\[x^2 + 12x + 36 - 85 = 36 - 85.\][/tex]

4. Simplify both sides of the equation by combining like terms:

  [tex]\[(x + 6)^2 - 49 = 0.\][/tex]

5. Rearrange the equation to isolate the perfect square term:

 [tex]\[(x + 6)^2 = 49.\][/tex]

From this process, we can conclude that the equation [tex]\((x + 6)^2 = 49\)[/tex] could be the result of completing the square for the given equation [tex]\(x^2 + 12x - 85\)[/tex]. This equation represents a perfect square trinomial with a perfect square term, and it allows us to solve for the value of [tex]x[/tex] by taking the square root of both sides.

It's important to note that completing the square allows us to rewrite quadratic equations in a form that reveals key properties and facilitates solving for unknowns.

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Answer:

3/10

Step-by-step explanation:

7/10 – 2/5

=7/10 – 4/10

=(7–4)/10

=3/10

Answer:

0.3

Step-by-step explanation:

12/70 is the probability of getting a point in the triangle.

From the dimension given in the figure,

height of the triangle  = 6 cm

base of the triangle  = 4 cm

width of the rectangle = 7 cm

length of  the rectangle = 10 cm

From the general formula of the area of a triangle and a rectangle,

The area of the triangle = 1/2*base*height

in a given case,

Area of triangle = 1/2*4*6=12 cm²

The area of the rectangle = length * width

in the given case,

Area of the rectangle = 7*10=70 cm²

So the probability of randomly choosing a point in the triangle:

Probability =Area of triangle/area of the rectangle

probability = 12/70

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When not considering the order of choice, there are also 3 ways to choose 2 letters from a, b, and c.

When choosing 2 letters without replacement from the 3 letters a, b, and c, the number of ways can be calculated considering the order of choice and without considering the order of choice.

1. Considering the order of choice:

In this case, the order in which the letters are chosen matters. We can think of this as a permutation problem.

To calculate the number of ways when order matters, we use the formula for permutations:

[tex]nPr = n! / (n - r)![/tex]

where n is the total number of items and r is the number of items chosen.

In this case, we have 3 letters and we want to choose 2, so n = 3 and r = 2.

Using the formula, we get:

[tex]3P2 = 3! / (3 - 2)![/tex]

 [tex]= 3! / 1![/tex]

    = 3

Therefore, when considering the order of choice, there are 3 ways to choose 2 letters from a, b, and c.

2. Without considering the order of choice:

In this case, the order in which the letters are chosen does not matter. We can think of this as a combination problem.

To calculate the number of ways when order does not matter, we use the formula for combinations:

[tex]nCr = n! / (r!(n - r)!)[/tex]

Using the same values of n = 3 and r = 2, we get:

[tex]3C2 = 3! / (2!(3 - 2)!)[/tex]

    = [tex]3! / (2! * 1!)[/tex]

    = 3

Therefore, when not considering the order of choice, there are also 3 ways to choose 2 letters from a, b, and c.

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Answer: yes

Step-by-step explanation:

The area of the given kite is,

⇒ A = 26 units²

Now, In this case we have that the area of the kite is given by the area of two triangles,

And, the triangles share the same base with length,

2 + 2 = 4.

And, One of the triangles has height of 6 and the other has height of 7.

So, the total area of kite is,

A = 1/2 × 4 × 6 + 1/2 × 4 × 7

A = 12 + 14

A = 26 units²

Therefore, The area of the given kite is,

⇒ A = 26 units²

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The required scale factor for the dilation of segment AB to create segment A'B' is 2.

If the length of the original segment AB is 5 units and the length of the dilated segment A'B' is 10 units, the scale factor can be calculated as follows:

Scale factor = Length of A'B' / Length of AB

Scale factor = 10 / 5

Scale factor = 2

Therefore, the correct scale factor for the dilation of segment AB to create segment A'B' is 2.

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Step-by-step explanation:

If the lines are parallel then    3x + 9x = 180 degrees

                                                12 x = 180

                                                    x = 15

The least common denominator will be (x-1)(x²-1).

When two or more fractions have the same denominators, they are termed as the common denominators.

The least common denominator (LCD) refers to the smallest number that is a common denominator for a given set of fractions.

For addition and subtraction of fractions and for comparing two or more fractions, the given fractions need to have common denominators.

The least common denominator is defined as the smallest common multiple of all the common multiples of the denominators when 2 or more fractions are given.

Given is an expression, -2x/x-1 + x+3/x²-1, we need to find the least common denominator,

So,

-2x/x-1 + x+3/x²-1

Taking the LCM,

-2x(x²-1) + (x+3)(x-1) / (x-1)(x²-1).

Hence the least common denominator will be (x-1)(x²-1).

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The number of solutions the system of equations have is (a) more than one solutions

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

3y-3x = -9

4y-4x=-12

Simplify the equations

So, we have

y - x = -3

y - x = -3

Subtract the equations

0 = 0

The above equation is true for all values of x and y

This means that the number of solutions in the equation is many i.e. more than one solutions

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Answer:

The correct answer is (D) 4/5.

Step-by-step explanation:

First, we need to find the number of cars that are neither red nor have a backup camera.

Number of cars that are not red = 50 - 12 = 38

Number of cars that do not have a backup camera = 50 - 10 = 40

Number of cars that are neither red nor have a backup camera = 38 + 10 - 50 = 8

Therefore, the probability of selecting a car that is not red and does not have a backup camera is:

P(not red and no backup camera) = 8/50

Simplifying:

P(not red and no backup camera) = 4/25

So the correct answer is (D) 4/5.

Answer: there is one solution

Step-by-step explanation:

12x − 13y = 5

x = 23y + 10

lets substitute x into the first equation.

12(23y + 10) - 13y = 5

276y + 120 - 13y = 5

263y = -115

y = -115/263

substituting for x:

x = 23(-115/263) + 10

x = -2645/263 + 10

x = -15/263

As we can see, we get one value of x;

this means there is one solution

The surface area of the rectangular prism is 1476 square units

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

30 mm by 12 mm by 9 mm

The surface area of the rectangular prism is calculated as

Surface area = 2 * (Length * Width + Length * Height + Width * Height)

Substitute the known values in the above equation, so, we have the following representation

Area = 2 * (30 * 12 + 30 * 9 + 12 * 9)

Evaluate

Area = 1476

Hence, the area is 1476 square units

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The setting of a novel is important because it provides the reader with context on the time, place, and environment that the story takes place in.

It aids in setting the tone, showcasing personalities and tensions, and offering hints about the story's message.

One can establish an ambiance or emotional tone in a novel by means of its setting. One illustration can be seen in the book "The Great Gatsby" authored by F. Scott Fitzgerald uses the backdrop of the Jazz Age to generate a feeling of splendor and exhilaration.

The rapid tempo of the book mirrors the busy lives led by the characters, while the opulent festivities and luxurious habits of the affluent are employed to cultivate an air of indulgence and debauchery.

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The full question is:

On the importance of setting in the novel, comment on how it can be used to create a sense of realism, atmosphere, and meaning?