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Answer:

Step-by-step explanation:

simple 59

The distance between the middle school and the fire station is 4.5 miles

Pythagoras theorem states that, in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

The distance between the middle school and the fire station is is the hypotenuse

therefore;

c² = 2² + 4²

c² = 4 + 16

c² = 20

c = √20

c = 4.5 miles(nearest tenth)

therefore the distance between the middle school and fire station is 4.5 miles

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Answer: B

Step-by-step explanation:

(7x^3-10x^2- 5)-(2x^3+7x^2-9)

= 5x^3 -3x^2-14

The variable consists of five categories: excellent, good, average, poor, and terrible.

The variable of interest in this scenario is the rating of the service provided by the hotel during the guests' most recent visit.

This variable is a way of measuring guests' perceptions of the quality of the service provided by the hotel.

The variable is categorical because the guests were asked to provide their rating by choosing one of five distinct categories - excellent, good, average, poor, and terrible.

The categories stated in (a) above represent the different levels of quality the guests perceived in the hotel's service.

Each rating category is non-numerical and non-sequential, meaning they don't have a natural numerical order or a defined distance between each other.

So, the number of categorical variables is 5

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Complete question

A hotel chain sent​ 2,000 past guests an email asking them to rate the service in the hotel during their most recent visit. Of the 500 who​ replied, 450 rated the service as excellent.

(a) Give a name to the variable and indicate if the variable is​ categorical, ordinal, or numerical

(b) If you answered "Categorical" in the previous question, how many categories does the variable of interest consist of? If you answered "Numerical", what is the range of values the variable can take?

Answer: $634.99

Step-by-step explanation:
Regular price, R - Discount, D = S

subtract discount from regular price

Answer: $634.99

Step-by-step explanation:

$828.15 - 193.16 would equal 634.99

so the discounted price would be $634.99

The length of the shadow cast by a nearby elm tree that that is 16 feet tall is given as follows:

12 feet.

The length of the shadow is obtained applying the proportions in the context of the problem.

A shadow 9 feet long is cast by a plum tree that is 12 feet tall, and we want the shadow for a tree that is 16 feet tall, hence the rule of three is given as follows:

9 feet - 12 feet

x feet - 16 feet.

Applying cross multiplication, the shadow is obtained as follows:

12x = 9 x 16

12x = 144

x = 144/12

x = 12 feet.

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The first step would be to multiply both sides by 5 when solving the equation (3(x+4))/(5)=6.

This will allow us to eliminate the denominator on the left side of the equation and simplify the equation.After multiplying both sides by 5, the equation becomes: 3(x+4) = 30

Next, we can distribute the 3 on the left side of the equation: 3x + 12 = 30

Then, we can subtract 12 from both sides of the equation: 3x = 18

Finally, we can divide both sides by 3 to solve for x: x = 6

Therefore, the solution to the equation is x=6.

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Answer:

27

Step-by-step explanation:

factors are numbers that divide exactly into a number , leaving no remainder.

then the only factor of 27 from the list is 27

Answer:

7/10 - 2/5 = 7/10 - 4/10 = 3/10

Step-by-step explanation:

Equalize both denominators, as in 2/5 = 4/10.

The length of the missing side is 3 units

Using the Pythagorean theorem, we have that;

Square of the hypotenuse is equal to the sum of the squares of the other two sides.

This is written as;

a² = b² + c²

Now, for the larger triangle, substitute the values, we have;

9² = 6² + c²

find the squares

c²= 81 - 36

add the values

c² = 45

c = √45

c = 6, 7 units

For the smaller triangle

6.7² - 6² = x²

x² = 45 - 36

x² = 9

Find the square root

x = 3

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The value of the series 4 + 9 + 14 + ... + (5n-1) using the summation notation is (5n^2 + 3n)/2.

The value of the series 4 + 9 + 14 + ... + (5n-1) can be found using the summation notation as follows:

Identify the first term, common difference, and number of terms in the series. The first term is 4, the common difference is 5, and the number of terms is n.

Use the summation notation to write the series as ∑_{i=1}^{n} (5i-1).

Use the formula for the sum of an arithmetic series to find the value of the series. The formula is S_n = n/2 (a_1 + a_n), where S_n is the sum of the series, n is the number of terms, a_1 is the first term, and a_n is the last term.

Substitute the values of n, a_1, and a_n into the formula and simplify. S_n = n/2 (4 + (5n-1)) = n/2 (5n+3) = (5n^2 + 3n)/2.

The value of the series is (5n^2 + 3n)/2.

Therefore, the value of the series 4 + 9 + 14 + ... + (5n-1) using the summation notation is (5n^2 + 3n)/2.

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When copying segments and angles, drawing a ray with one endpoint step is the same.

A line segment is a part of a continuous line, having two fixed ends and a definite length.

When a common part in constructing a line segment and an angle is drawing a ray because a ray is a common part, when we see the figures of a segment and an angle we see a common a ray, so a ray is the common part in both.

Hence, when copying segments and angles, drawing a ray with one endpoint step is the same.

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Answer:

Let's start by using the formula for mixing two solutions to set up an equation. The formula is:

(concentration of solution 1) x (volume of solution 1) + (concentration of solution 2) x (volume of solution 2) = (concentration of resulting solution) x (total volume of resulting solution)

In this problem, solution 1 is the 25% sugar syrup, solution 2 is the 10% sugar syrup, and the resulting solution is 15% sugar syrup. We are also given that the total volume of the resulting solution is 120 grams. Let's use x to represent the volume of the 10% sugar syrup that is mixed with the 25% sugar syrup. Then we can write:

(0.25)(120-x) + (0.10)(x) = (0.15)(120)

Simplifying this equation, we get:

30 - 0.25x + 0.10x = 18

0.15x = 12

x = 80

Therefore, we need to mix 80 grams of the 10% sugar syrup with 40 grams of the 25% sugar syrup to get 120 grams of 15% sugar syrup.

To find the amount of pure sugar in the 120 grams of 15% syrup, we can use the fact that the concentration of pure sugar in the resulting solution is 15%. That means that 15% of the 120 grams is pure sugar. We can find this by multiplying 120 by 0.15:

120 x 0.15 = 18

So there are 18 grams of pure sugar in the 120 grams of 15% syrup.

For the airplane, we have v = -453.01, 79.88. Similarly, for the wind, we have w = -75.18, -27.36.

The actual speed would be 530.79 mph.

The actual ground speed and direction of the airplane are 530.79 mph and 174.32 deg, respectively.

The component form of the velocity of the airplane can be found by using the formula:

v = r < cos theta, sin theta >, where r is the speed and theta is the bearing. For the airplane, we have v = 460 < cos 170, sin 170 > = <-453.01, 79.88>. Similarly, for the wind, we have w = 80 < cos 200, sin 200 > = <-75.18, -27.36>.

To find the actual ground speed and direction of the airplane, we need to add the velocity vector of the airplane and the wind vector. This gives us the velocity vector = v + w = <-453.01, 79.88> + <-75.18, -27.36> = <-528.19, 52.52>.

The actual speed can be found by taking the magnitude of the velocity vector, which is given by |v+w| = sqrt((-528.19)^2 + (52.52)^2) = 530.79 mph.

The actual direction can be found by using the formula theta = arctan(y/x), where x and y are the x and y components of the velocity vector. In this case, we have theta = arctan(52.52/-528.19) = -5.68 deg. However, since the velocity vector is in the third quadrant, we need to add 180 deg to get the actual direction, which is 180 + (-5.68) = 174.32 deg.

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Answer:

[tex] \frac{2}{15} = 0.13[/tex]

Step-by-step explanation:

[tex]1. \: lcd = 15 \\ 2. \: \frac{4 \times 3}{5 \times 3} - \frac{2 \times 5}{3 \times 5} \\ 3. \: \frac{12}{15} - \frac{10}{15} \\ 4. \: \frac{12 - 10}{15} \\ 5. \: \frac{2}{15} = 0.13[/tex]

The inverse transform method allows us to generate a random variable having a specific distribution function by finding the inverse of the distribution function and plugging in a random value from the uniform distribution on the interval [0, 1].

To generate a random variable having the distribution function F(x) = x² + x / 2 using the inverse transform method, we need to follow the following steps:

Step 1: Find the inverse of the distribution function F(x). This can be done by solving the equation F(x) = u for x, where u is a uniform random variable on the interval [0, 1]. In this case, we have:

x² + x / 2 = u

Step 2: Use the quadratic formula to solve for x:

x = (-1 ± √(1 - 4(1/2)(-u))) / (2(1/2))

x = (-1 ± √(1 + 2u)) / 1

Step 3: Since we want the inverse function, we need to choose the positive solution:

x = (-1 + √(1 + 2u)) / 1

Step 4: Now we have the inverse function F^-1(u) = (-1 + √(1 + 2u)) / 1. To generate a random variable having the distribution function F(x), we simply need to plug in a random value of u from the uniform distribution on the interval [0, 1]:

x = F^-1(u) = (-1 + √(1 + 2u)) / 1

Step 5: This gives us a random variable x having the desired distribution function F(x) = x² + x / 2.

In conclusion, the inverse transform method allows us to generate a random variable having a specific distribution function by finding the inverse of the distribution function and plugging in a random value from the uniform distribution on the interval [0, 1].

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The final amount for the investment of $5,000 over 5 years at an annual interest rate of 6% compounded quarterly is $ 6,749.29.

To find the final amount for an investment P over t years at an annual interest rate of r compounded quarterly, we can use the formula for compound interest:  

[tex]{\displaystyle A=P\left(1+{\frac {r}{n}}\right)^{nt}}[/tex]

Where:

A = Final amount

P = Principal (initial investment)

r =  Annual interest rate (as a decimal)

n = Number of times the interest is compounded per year

t = Time period in years

Here we have

P = $5,000,

r = 6% = 0.06,

n = 4 (since the interest is compounded quarterly), and

t = 5 years.  

Using the above formula

[tex]A = 5000(1 + 0.06/4)^{(4*5)[/tex]

[tex]A = 5000(1.015)^{20}[/tex]

[tex]A = 5000(1.34985711)[/tex]

[tex]A = $6,749.29[/tex]

Therefore,

The final amount for the investment of $5,000 over 5 years at an annual interest rate of 6% compounded quarterly is $ 6,749.29.

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not intersect.

To determine if two lines intersect in R3, we need to solve for both parameters (t and s) in the two equations and then check if the values are equal.

For Line 1: x = 2 - t, y = -3 + 5t, z = t. We can solve for t by setting all three equations equal to each other, giving t = x - 2 = y + 3 = z.

For Line 2: P = (4,-1,16) + s (1,4,-7). We can solve for s by setting the three equations equal to each other, giving s = (x - 4) / 1 = (y + 1) / 4 = (z - 16) / -7.

If the two values of t and s are equal, then the lines intersect at the point (x, y, z). If they are not equal, then the lines do not intersect.

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Using algebraic expressions, the expression that is equivalent to 9(4w) is: 36w.

Mathematical statements having at least two terms that involve variables or numbers are called algebraic expressions.

Every combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is a recognised algebraic expression (or variable expression).

We just join like terms in an algebraic expression to make it simpler. Hence, related variables will be combined. Now, the identical powers will be merged from the similar variables.

Now in the given case,

9(4w)

= 9×4×w

=36w.

Therefore, the expression that is equivalent to 9(4w) is: 36w.

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Answer: 14/3 or 3/4 are in 7/2

Step-by-step explanation:

The sοlutiοn οf the given prοblem οf expressiοn cοmes οut tο be examples abοve are equal tο 16t - 0.25.

Mathematical prοcesses like multiplying, dividing, adding, and nοw even deleting are required. If they were merged, the fοllοwing claim wοuld be made: An equatiοn, sοme statistics, and a mathematical fοrmula Values, cοmpοnents, and mathematical prοcesses like additiοns, subtractiοns, reversals, algebraic fοrmulas, and divisiοns make up a statement οf truth. Wοrds and phrases can be rated and analyzed.

Here,

We pοssess 16t – 0.25.

A) The fοrmula 42t/40.5 equals (22t)² / (20.5) = 24t / (20.5) = 16t / (20.5)4 = 16t / 4 = 4(16t).

Expressiοn A is nοt equal because 4(16t) is nοt the same as 16t - 0.25.

B) [tex](16)^t/2^4 = (2^4)^t / 2^4[/tex]

=> [tex]2^{4t} / 2^4 = 2^{(4t-4)} = 16^{(t-1)} (t-1).[/tex]

Expressiοn B is not equivalent because 16(t-1) is nοt equal to 16(t - 0.25).

C) [tex]16^t/2 = (2^4)^t / 2[/tex]

[tex]= > 2^{4t} / 2 = 2^{(4t-1)} = 16^t \times 0.5.[/tex]

Expression C is nοt equivalent because 16t * 0.5 does not equal 16t - 0.25.

Hence, As a result, nοne of the examples above are equal to 16t - 0.25.

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Answer:

Step-by-step explanation:

Javier worked a total of 23 hours over the two weekends (True), Javier earned $184 over the two weekends(True)

A double bar chart, also known as a grouped bar chart, is a graphical representation of data that compares two or more categories or groups of data. It is similar to a standard bar chart, but with two or more bars grouped together for each category.

In a double bar chart, the horizontal axis represents the categories or groups being compared, while the vertical axis represents the values being measured. The height of each bar represents the value of the data for that category or group, and the bars are usually colored or patterned differently to differentiate between the groups being compared.

Double bar charts are useful for comparing data between two or more groups or categories, such as different time periods, geographic regions, or demographic groups. They can be used to highlight similarities and differences between the groups, and to identify trends and patterns in the data.

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The complete question is

Answer:

Step-by-step explanation:

5.  15 multiplied by 4/5 = 3 multiplied by 4 = 12.

6.  3/11 multiplied by 66 = 3 multiplied by 6 = 18.

The exact value οf cοs(2θ) is 27/25.

The exact value οf sin(θ/2) is -√[(5 + √13) / 10].

Trigοnοmetry is a branch οf mathematics that deals with the relatiοnships between the sides and angles οf triangles, and the trigοnοmetric functiοns that describe thοse relatiοnships.

Given: sin(θ) = (2√3) / 5, and π/2 < θ < π.

Part A:

cοs(2θ) = 2cοs²(θ) - 1

We can find cοs(θ) using the Pythagοrean identity:

cοs²(θ) + sin²(θ) = 1

cοs²(θ) = 1 - sin²(θ)

cοs(θ) = ±√(1 - sin²(θ))

Since π/2 < θ < π, sin(θ) is pοsitive and cοs(θ) is negative in the secοnd quadrant. Therefοre, we have:

cοs(θ) = -√(1 - (2√3/5)²) = -√(1 - 12/25) = -√13/5

Substituting intο the fοrmula fοr cοs(2θ), we get:

cοs(2θ) = 2cοs²(θ) - 1 = 2(-√13/5)² - 1 = 52/25 - 1 = 27/25

Therefοre, the exact value οf cοs(2θ) is 27/25.

Part B:

We can use the half-angle fοrmula fοr sine tο find sin(θ/2):

sin(θ/2) = ±√[(1 - cοs(θ)) / 2]

Since π/2 < θ < π, sin(θ/2) is negative in the secοnd quadrant. Therefοre, we have:

sin(θ/2) = -√[(1 - cοs(θ)) / 2] = -√[(1 - (-√13/5)) / 2] = -√[(5 + √13) / 10]

Therefοre, the exact value οf sin(θ/2) is -√[(5 + √13) / 10].

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The lunch period that has more students is the second lunch period.

In order to determine which lunch period that has more students, the number of students that eat in the second lunch period has to be determined. In order to determine this value, the mathematical operation that would be used is subtraction.

Subtraction is the process of determining the difference between two or more numbers. The sign that is used to represent subtraction is -.

Number of students that ear in the second lunch period = total number of students - students that eat in the first lunch period

758 - 371 = 387

387 > 371

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0 and variance 1.

For (a), L follows a Chi-squared distribution with 6 degrees of freedom. This is because L is a sum of squares of 6 random variables (the 5 Yi - Y plus Y^3).

For (b), J follows a Student's t-distribution with 6 degrees of freedom. This is because it is the ratio of two independent normally distributed random variables with mean 0 and variance 1.

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The value of Connor's card is 18, so Helen must choose the card with (22)⁻⁴, since it has a value of 1/262144, which is the same as 18.

Matching games are a type of game often used to help develop memory skills. In a matching game, players must match objects, pictures, or words to one another. This can involve matching a picture to a word, or a word to a definition. Matching games can be used to help children learn new vocabulary or to review already learned words.

The card with 2⁻³ has a base of 2 and an exponent of -3. This means that the value of the card is 1/8, which is the same as 2⁻³.

The card with (12)⁻² has a base of 12 and an exponent of -2. This means that the value of the card is 1/144, which is the same as 12⁻².

The card with (22)⁻⁴ has a base of 22 and an exponent of -4. This means that the value of the card is 1/262144, which is the same as 22⁻⁴.

In this matching game, Connor and Helen must find the card with the same value as it is written on Connor's card.

The value of Connor's card is 18, so Helen must choose the card with (22)⁻⁴, since it has a value of 1/262144, which is the same as 18.

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A^8 = [\begin{array}{ccc}252&-3&3\\3&252&-3\\-3&3&252\end{array}\right]

To find the eigenvalues and eigenvectors of matrix A, use the characteristic polynomial of A which is given by:
P(λ) = det(A-λI) = λ^3-6λ^2+11λ-6

The roots of the equation are λ1 = 2, λ2 = 3, and λ3 = 1.

The corresponding eigenvectors are:
v1 = [\begin{array}{ccc}-1\\1\\1\end{array}\right]
v2 = [\begin{array}{ccc}1\\-1\\1\end{array}\right]
v3 = [\begin{array}{ccc}1\\1\\1\end{array}\right]

The eigenvalues and eigenvectors of A can be put together in the following matrix:
T = [\begin{array}{ccc}-1&1&1\\1&-1&1\\1&1&1\end{array}\right]

The eigenvalues of A can be put together in the following matrix:
Λ = diag{λ1, λ2, λ3} = [\begin{array}{ccc}2&0&0\\0&3&0\\0&0&1\end{array}\right]

Now, to calculate A^8, you will need to use the eigenvalues and eigenvectors of A. A^8 can be calculated using the following equation: A^8 = T * Λ^8 *T^-1, where Λ= diag{λ1, λ2, λ3} is diagonal matrix composed of eigenvalues λi of matrix A and matrix T is matrix composed of corresponding eigenvectots of matrix A.

Thus, A^8 can be calculated as follows:
A^8 = [\begin{array}{ccc}-1&1&1\\1&-1&1\\1&1&1\end{array}\right] * [\begin{array}{ccc}256&0&0\\0&6561&0\\0&0&1\end{array}\right] * [\begin{array}{ccc}-1&1&1\\1&-1&1\\1&1&1\end{array}\right]^-1

= [\begin{array}{ccc}252&-3&3\\3&252&-3\\-3&3&252\end{array}\right]

Therefore, the result of A^8 is: A^8 = [\begin{array}{ccc}252&-3&3\\3&252&-3\\-3&3&252\end{array}\right]

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The number lines for the given inequalities are drawn as shown in the figures below.

A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point. On a number line, inequalities are represented by drawing a straight line and designating the endpoints with either an open or closed circle. An open circle indicates that the value is not included. A closed circle indicates that the value is included.

1) Number line A

 The closed circle at -2 means greater than or equal or less than or equal to -2.

Now the arrow is extending to the left.

So the inequality is numbers less than or equal to -2.

2) Number line B

 The open circle at -2 means greater than or less than  -2.

Now the arrow is extending to the left.

So the inequality is numbers less than  -2.

3) Number line C

  The closed circle at -2 means greater than or equal or less than or equal to -2.

Now the arrow is extending to the right.

So the inequality is all the numbers greater than or equal to -2.

4) Number line D

  The open circle at -2 means greater than or less than  -2.

Now the arrow is extending to the right.

So the inequality is all the numbers greater than  -2.

Therefore the number lines for the given inequalities are drawn as shown in the figures below.

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The slope of a line perpendicular to given line is 4.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The given equation of a line is x+4y=4.

Here, 4y=4-x

y=1-x/4

So, slope m is -1/4

The slope of a line perpendicular to given line is m1=-1/m2

Slope of perpendicular to line is -1/(-1/4)

= 4

Therefore, the slope of a line perpendicular to given line is 4.

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The slope of parallel line is,

m = - 1/4

And, Slope of perpendicular line are,

m = 4

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The equation of line is,

⇒ x + 4y = 4

Now, We can write as;

⇒ x + 4y = 4

⇒ 4y = - x + 4

⇒ y = - 1/4x + 4

Hence, The slope of the line is,

⇒ y = - 1/4x + 4

⇒ dy/dx = - 1/4

⇒ m = - 1/4

Now, We know that;

The slope of parallel line are equal.

Hence, The slope of parallel line is,

m = - 1/4

And, Product of Slopes of perpendicular lines are - 1.

Hence, Slope of perpendicular line are,

m = - 1/ (- 1/4)

m = 4

Thus, The slope of parallel line is,

m = - 1/4

And, Slope of perpendicular line are,

m = 4

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