Find the twenty-seventh term of the arithmetic sequence 21, 18, 15, ...

Answer:

25.66

Step-by-step explanation:

Helping in the name of Jesus.

Answer:

that would be if you were to rounded you 9,302 it would = 10,300 cuz

Step-by-step explanation:

A 95% confidence interval for percent of american adults who believe in aliens:  (0.6578, 0.7822)

In this question we have been given that in a survey conducted on an srs of 200 american adults, 72% of them said they believed in aliens

We need to find the 95% confidence interval for percent of american adults who believe in aliens.

95% confidence interval = (p ± z√[p(1 - p)/n])

Here, n = 200

p = 72%

p = 0.72

And the z-score for 95% confidence interval is 1.960

The upper limit of interval would be,

(p + z√[p(1 - p)/n])

= 0.72 + 1.960 √[0.72(1 - 0.72)/200]

= 0.72 + 1.960 √[(0.72 * 0.28)/200]

= 0.72 + 1.960 √0.001008

= 0.72 + 0.0622

= 0.7822

The lower limit of interval would be,

(p - z√[p(1 - p)/n])

= 0.72 - 1.960 √[0.72(1 - 0.72)/200]

= 0.72 - 1.960 √[(0.72 * 0.28)/200]

= 0.72 - 1.960 √0.001008

= 0.72 - 0.0622

= 0.6578

Therefore, a 95% confidence interval = (0.6578, 0.7822)

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Answer:

y = 2/3x - 3

2/3x is the slope

-3 is the y-intercept

We know, point on a line segment which cut a line into the ratio m : n is given by :

\([(\dfrac{mx_1+nx_2}{m+n}),(\dfrac{my_1+ny_2}{m+n}) ]\)

Putting value of point A and B and m =2 and n = 5 .

We get :

\([(\dfrac{2(2)+5(18)}{2+5}),(\dfrac{2(6)+5(12)}{2+5}) ]\\\\(\dfrac{94}{7},\dfrac{72}{7})\)

Hence, this is the required solution.

The solution to the differential equation dx/dt = 3x(x - 8), with the initial condition x(0) = 1, involves finding the function x(t) that satisfies the equation.

To solve the given differential equation, we can separate variables and integrate. Rearranging the equation, we have dx/(x(x - 8)) = 3dt. Now, we can integrate both sides.

Integrating the left side requires partial fraction decomposition. We can express the integrand as A/x + B/(x - 8), where A and B are constants. By finding a common denominator and equating the numerators, we get A(x - 8) + Bx = 1. Expanding and equating coefficients, we find A = -1/8 and B = 1/8.

Substituting these values back into the integral, we have (-1/8)∫(1/x)dx + (1/8)∫(1/(x - 8))dx = 3∫dt. Simplifying, we obtain -(1/8)ln|x| + (1/8)ln|x - 8| = 3t + C, where C is the constant of integration.

To determine the value of the constant C, we use the initial condition x(0) = 1. Plugging in t = 0 and x = 1, we get -(1/8)ln|1| + (1/8)ln|1 - 8| = 3(0) + C. This simplifies to C = -(1/8)ln|7|.

Finally, we can write the solution as -(1/8)ln|x| + (1/8)ln|x - 8| = 3t - (1/8)ln|7|. This equation represents the solution x(t) to the given initial value problem.

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Answer:

y=0.5x-3.5

Step-by-step explanation:

(-4)-(-5)=1

3-1=2

1/2=0.5

y=0.5x-3.5

Answer:

\(y=-2y-7\)

Step-by-step explanation:

Coordinates plotted on the equation:

\((1,-4)\)

\((4,-5)\)

{check the image for your reference}

The transformation that maps the pre-image δSTV to the image δUTV is a translation.

A translation is a transformation that shifts each point in a figure by the same distance and in the same direction. In this case, the pre-image δSTV undergoes a transformation resulting in the image δUTV. This indicates that the figure has been moved or shifted.

Unlike other transformations like dilation, reflection, or rotation which involve changing the size, orientation, or mirroring of the figure, a translation specifically involves a shift in position. By applying a translation, each point in the pre-image is moved a certain distance and direction, resulting in the corresponding points of the image. Therefore, the given information suggests that the transformation from δSTV to δUTV is best described as a translation.

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The mass of the radioactive sample at the beginning of the 11th day of the experiment is approximately 286 grams.

Since the mass is decreasing by 14% per day, we can find the mass at the beginning of each day by multiplying the previous day's mass by 0.86 (which is 100% - 14%).

At the beginning of the first day, the mass was 1300 grams.

At the beginning of the second day, the mass is:

1300 grams x 0.86 = 1118 grams (rounded to the nearest gram)

At the beginning of the third day, the mass is:

1118 grams x 0.86 = 962 grams (rounded to the nearest gram)

We can continue this pattern to find the mass at the beginning of the 11th day:

Mass at the beginning of the fourth day: 962 grams x 0.86 = 828 grams

Mass at the beginning of the fifth day: 828 grams x 0.86 = 711 grams

Mass at the beginning of the sixth day: 711 grams x 0.86 = 612 grams

Mass at the beginning of the seventh day: 612 grams x 0.86 = 526 grams

Mass at the beginning of the eighth day: 526 grams x 0.86 = 452 grams

Mass at the beginning of the ninth day: 452 grams x 0.86 = 388 grams

Mass at the beginning of the tenth day: 388 grams x 0.86 = 333 grams

Mass at the beginning of the eleventh day: 333 grams x 0.86 = 286 grams (rounded to the nearest gram)

Therefore, the mass of the radioactive sample at the beginning of the 11th day of the experiment is approximately 286 grams.

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The Area of triangle with the given height 10 cm and base 6 cm is calculated to be  30 square centimeters.

To calculate the area of a triangle with height 10 cm and base 6 cm, we can use the formula:

Area = (1/2) x Base x Height

Substituting the given values, we get:

Area = (1/2) x 6 cm x 10 cm

Area = 30 square cm

Therefore, the area of the triangle is 30 square centimeters.

We can see that the area of the triangle is calculated by multiplying the base and height and then dividing the result by 2. In this case, the height of the triangle is 10 cm and the base is 6 cm, so the area is 30 square cm. This formula can be used to calculate the area of any triangle, regardless of its size or shape.

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The complete question is :

Calculate the Area of triangle with the height 10 cm and base 6 cm .

The probability that a German child recognized both Spongebob and Squidward is approximately 0.6786 or 67.86%.

First we can use the formula for conditional probability to solve this problem:

P(Spongebob and Squidward) = P(Squidward | Spongebob) * P(Spongebob)

We know that 87% of children recognized Spongebob, so P(Spongebob) = 0.87. We also know that among those who recognized Spongebob, 78% recognized Squidward, so P(Squidward | Spongebob) = 0.78.

Substituting these values into the formula, we get:

P(Spongebob and Squidward) = 0.78 * 0.87 = 0.6786

Rounding this to four decimal places, we get:

P(Spongebob and Squidward) ≈ 0.6786

Therefore, the probability that a German child recognized both Spongebob and Squidward is approximately 0.6786 or 67.86%.

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The most appropriate choice for linear equation will be given by -

By solving this equation, the value of n obtained is n = 2

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Linear equation is a very important tool in solving real life problem.

Here

The given equation is

-y+2+3y-6

Now,

-y + 2 + 3y - 6=ny - 4

2y - 4 = ny - 4

2y = ny

n = 2

Value of n = 2

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Answer:

tan ∅ = 15/8

Step-by-step explanation:

tan ∅ = 15/8

Answer:K= -4

Step-by-step explanation:

\(~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-9}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{4}) ~\hfill AB=\sqrt{(~~ 7- (-9)~~)^2 + (~~ 4- 4~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 16)^2 + ( 0)^2}\implies \boxed{AB=16} \\\\\\ B(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{7}~,~\stackrel{y_2}{-8}) ~\hfill BC=\sqrt{(~~ 7- 7~~)^2 + (~~ -8- 4~~)^2}\)

\(~\hfill BC=\sqrt{( 0)^2 + ( -12)^2}\implies \boxed{BC=12} \\\\\\ C(\stackrel{x_1}{7}~,~\stackrel{y_1}{-8})\qquad A(\stackrel{x_2}{-9}~,~\stackrel{y_2}{4}) ~\hfill CA=\sqrt{(~~ -9- 7~~)^2 + (~~ 4- (-8)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -16)^2 + (12)^2}\implies CA=\sqrt{400}\implies \boxed{CA=20} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Perimeter}{16~~ + ~~12~~ + ~~20\implies \text{\LARGE 48}}\)

Answer:18

Step-by-step explanation:

That's 18

Solution

or, x+x+x=54

or, 3x=54

x=18

The BNF rules for implementing variable names according to the given idea can be defined as follows:

```

<Identifier> → <Letter> <LetterOrDigit>*

<Letter> → 'a' | 'b' | ... | 'z' | 'A' | 'B' | ... | 'Z'

<LetterOrDigit> → <Letter> | <Digit>

<Digit> → '0' | '1' | ... | '9'

```

To implement the variable name rules specified by the new language designer, we use BNF (Backus-Naur Form) notation. The rule `<Identifier> → <Letter> <LetterOrDigit>*` defines the structure of a valid identifier. It states that an identifier starts with a single letter (`<Letter>`) followed by zero or more letters or digits (`<LetterOrDigit>`).

The rule `<Letter>` enumerates all possible letters, including lowercase and uppercase alphabets, while `<Digit>` represents all the digits.

By using the defined BNF rules, we can ensure that a variable name begins with a valid letter, followed by any combination of valid letters or digits. This enforces the requirement of starting with a letter, allowing subsequent characters to be either letters or digits, while excluding any other special characters.

For example, the variable names "ab2", "_a", and "_b4" are valid as they adhere to the specified rules. On the other hand, names like "Z" (too short), "a\%5" (contains a special character), "3w1" (starts with a digit), and "wla" (second character is not a letter) violate the defined rules.

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Answer:

69min

Step-by-step explanation:

sue: 24min 40km

.6 min per 1km

×115

115 km = 69 min

When two lines and a transversal form comparable angles that are congruent, the lines are parallel, which is the converse of the corresponding angles theorem's flow proof. Which means that line c ║ to line d.

The two different lines that meet at an angle of 90 degrees are called perpendicular lines. Do your walls' connecting corners—or the letter "L"—share any similarities? They are the straight lines, referred to as perpendicular lines, that intersect at the proper angle. An angle of 90 degrees between two straight lines is known as a perpendicular. The illustration depicts a little square in between two perpendicular lines to indicate the 90° angle, which is also known as a right angle. Here, a right angle between the two lines Two lines that cross each other at a 90° angle are referred to as perpendicular lines in mathematics. I

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Answer:

Step-by-step explanation:

12h + 15(4) = 444

12h + 60 = 444

12h = 444 - 60

12h = 384

h = 384/12

h = 32 <===== Hector worked 32 hrs

0.529 is the probability that a student does not have a college degree.

From the information given, we know that:

The formula for conditional probability:

P(A|B) = P(A and B) / P(B)

Let A be the event of not having a college degree, and B be the event of being married. We want to find P(A).

Using these values, we can calculate:

P(college degree and B) = (1/2) * (400/850) = 0.235

P(A and B) = 310/850 - 0.235 = 0.07

Finally, we can calculate P(A) using the formula for total probability:

P(A) = 1 - P(college degree)

= 1 - (400/850)

= 0.529

Therefore, the probability that a student does not have a college degree is 0.529.

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Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by using the formula

\(d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ \)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(5,14) and (-3,-9)

The distance is

\(d = \sqrt{ ({5 + 3})^{2} + ({14 + 9})^{2} } \\ = \sqrt{ {8}^{2} + {23}^{2} } \\ = \sqrt{64 + 529} \\ = \sqrt{593} \: \: \: \: \: \: \: \: \: \: \\ = 24.3515913\)

We have the final answer as

\( \sqrt{593} \: \: or \: \: 24.35 \: \: \: units\)

Hope this helps you

The function with the largest value at x = 5 is p(x) = 2x² + 4x +11, and the answer is not that all functions are equal at x = 5.

To find which function has the largest value when x = 5, we simply need to evaluate each function at x = 5 and compare the results.

For p(x) = 2x² + 4x +11, we have p(5) = 2(5)² + 4(5) + 11 = 61.

For h(x) = 4x, we have h(5) = 4(5) = 20.

For s(x) = 10x, we have s(5) = 10(5) = 50.

Therefore, the function with the largest value when x = 5 is p(x) = 2x² + 4x +11, with a value of 61.

It is important to note that the other answer choices, h(x) and s(x), are not equal to p(x) at x = 5. However, if we were asked which functions are equal at x = 5, we could find the answer by evaluating each function at x = 5 and comparing them. In this case, we can see that the functions are not equal at x = 5.

In summary, the function with the largest value at x = 5 is p(x) = 2x² + 4x +11, and the answer is not that all functions are equal at x = 5.

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Answer:

D.3

Step-by-step explanation:

We are going to use the Slope Formula --> (y2-y1)/(x2-x1)

(9-3)/(3-1)=6/2=3

No, the use of the binomial distribution may not be appropriate for calculating the probability that exactly six 18-20 year olds consumed alcoholic beverages in a random sample of ten.

The binomial distribution assumes that the trials are independent, there are only two possible outcomes (success or failure), and the probability of success remains constant throughout the trials. In the case of consuming alcoholic beverages, the assumption of independence may not hold, as one person's decision to consume alcohol may influence another person's decision. Additionally, the probability of consuming alcohol may not remain constant throughout the sample, as some people may have stronger tendencies or preferences for drinking than others.

A more appropriate distribution for this scenario may be the hypergeometric distribution, which takes into account the finite population size (i.e. the total number of 18-20 year olds from which the sample is drawn) and the varying probabilities of success (i.e. the varying number of individuals in the population who consume alcohol).

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value of variable x on the parallel line is 12.

In geometry, a co exterior angle is an angle that is formed outside of a geometric figure by extending one of its sides. More specifically, a co exterior angle is formed when a transversal intersects two parallel lines, and it is an angle that is located outside of the parallel lines and on the same side of the transversal as one of the angles formed by the intersection.

Given

m ║n

8x+6 and 9x-30 are co exterior angle

8x+6+9x-30=180°

17x-24=180°

x=12

hence, value of variable x on the parallel line is 12.

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