Two communications companies offer calling plans. With Company​ X, it costs 35¢ to connect and then 5¢ for each minute. With Company​ Y, it costs 20¢ to connect and then 4¢ for each minute. Write and simplify an expression that represents how much more Company X​ charges, in​ cents, for n minutes.

Answer:

Yes, The pole will fit through the door because the diagonal width of the door is 10.8 feet, which is longer than the length of the pole.

Step-by-step explanation:

Using the Pythagorean Theorem, (\(a^2+b^2=c^2\) ) we can measure the hypotenuse of a right triangle. Since the doorway is a rectangle, and a rectangle cut diagonally is a right triangle, we can use Pythagorean Theorem to measure the diagonal width of the doorway.

Plug in the values of the length and width of the door for a and b. The c value will represent the diagonal width of the doorway:

\(6^2+9^2=c^2\)

\(36+81=c^2\)

\(117=c^2\)

Since 117 is equal to the value of c multiplied by c, we must find the square root of 117 to find the value of c.

\(\sqrt{117} =10.8\)

\(10.8=c\)

Yes, The pole will fit through the door because the diagonal width of the door is 10.8 feet, which is longer than the length of the pole, measuring 10 feet.

\(\begin{array}{| c | c |}\boxed{ \bf{Equations} }&\boxed{ \bf{YES \: OR \: NO}} \\ \\ \tt{1. \: \:y = {x}^{2} + 2} & \tt{YES} \\\tt{2. \: \:y = 2x - 10}& \tt{NO} \\ \tt{3. \: \:y = 9 - {2x}^{2}} & \tt{YES} \\ \tt{ 4. \: \:y = {2}^{x} + 2}& \tt{ NO} \\ \tt{5. \: \:y = {3x}^{2} + {x}^{3} + 2}& \tt{NO} \\ \tt{ 6. \: \:y = {2}^{x} + 3x + 2}& \tt{NO} \\ \tt{ 7. \: \:y = {2x}^{2}} & \tt{ YES} \\ \tt{ 8. \: \:y = (x - 2)(x + 4)}& \tt{YES} \\ \tt{9. \: \:0 = (x - 3)(x + 3) + {x}^{2} - y}& \tt{YES} \\ \tt{10. \: \:{3x}^{3} + y - 2x = 0}& \tt{NO}\end{array}\)

First of all we can solved the function

We using the identity,

(x + a)(x + b) = x² + (a + b)x + ab

(x - 2)(x + 4)

= x² + (-2 + 4)x + (-2)(4)

= x² + 2x - 8

First of all we can solved the function

We using the identity,

(a + b)(a - b) = a² - b²

(x - 3)(x + 3) + x² - y

= x² - 3² + x² - y

= x² - 9 + x² - y

= x² + x² - y - 9

= 2x² - y - 9

The radian measure of angle A is (16/9)π.

To convert degrees to radians, we use the conversion factor:

\(1\ degree = \pi /180\ radians\)

Given that angle A is 320 degrees, we can calculate its radian measure as follows:

Angle A in radians = (320 degrees) * (π/180 radians/degree)

                    = (320π)/180 radians

                    = (16/9)π radians

Therefore, the radian measure of angle A is (16/9)π.

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For the point (5, 4) to the directrix, the distance to the directrix is equal to the distance to the focus. For the other points on the list, the distance to the directrix is equal to the distance to the focus. The distance to the directrix is equal to the distance to the focus, we can conclude that (-1, 5) is on the parabola.

A perfect, U-shaped curve is referred to by the term parabola in mathematics. It is described as the collection of all plane points that are equidistant from a focus and a fixed broadband (the directrix). The point where the parabola's curve changes direction is known as its vertex, and the line that runs through it and is perpendicular toward the directrix is known as its axis of symmetry. The behavior of electromagnetic waves, projectile motion, reflector and antenna forms, and other real-world phenomena are frequently modelled using parabolas.

To determine whether a point is on a parabola with a given focus and directrix, we can use the definition of a parabola: a parabola is the set of all points that are equidistant to the focus and the directrix.

In this case, the focus is the point (0, 2) and the directrix is the line y = -2.

Let's first consider the point (5, 4). We can find the distance from this point to the directrix by finding the distance from the point to the line. The formula for the distance from a point (x1, y1) to a line \(Ax + By + C = 0\) is:

\(|Ax1 + By1 + C| / \sqrt(A^2 + B^2)\)

In this case, A = 0, B = 1, and C = -2, so the equation of the directrix is y = -2, which can be written as \(0x + 1y - 2 = 0.\) Plugging in (5, 4), we get:

\(|0(5) + 1(4) - 2| / \sqrt(0^2 + 1^2) = 6\)

So the distance from (5, 4) to the directrix is 6.

Next, we can find the distance from (5, 4) to the focus (0, 2):

\(\sqrt((5-0)^2 + (4-2)^2) = \sqrt(29)\)

Since the distance from (5, 4) to the directrix is not equal to the distance from (5, 4) to the focus, we can conclude that (5, 4) is not on the parabola.

We can repeat this process for each point on the list. For the point (-1, 5), we get:

Distance to directrix: |-1 - 2| / 1 = 3

Distance to focus: \(\sqrt((-1-0)^2 + (5-2)^2) = \sqrt(26)\)

Since the distance to the directrix is equal to the distance to the focus, we can conclude that (-1, 5) is on the parabola.

Similarly, we can check the other points on the list and find that the points (4, 3), (2, 1), (1, -2), (2, -1), (4, -3), and (5, -4) are also on the parabola. The points (3, 5), (6, 7), (8, 0), and (0, 8) are not on the parabola.

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Check your given table for the value of x such that f(x) = 4. Then x = g(4), and by the inverse function theorem,

\(g'(4) = \dfrac1{f'(x)} = \dfrac1{f'(g(4))}\)

Answer:

x=10

Step-by-step explanation:

If we subtract 2 from 52 we get 50 and ten mutiplys into 50.

When comparing the distributions of SAT scores for two schools, it is important to use a statistical measure that can accommodate the difference in the number of students in each school. In this case, since School A has 400 students while School B has 2700 students, the most useful statistical measure for making this comparison would be the percentage of students in each school who scored within certain SAT score ranges.

For example, instead of comparing the raw number of students who scored above a certain score threshold in each school, it would be more meaningful to compare the percentage of students in each school who scored above that threshold. This would give a more accurate representation of the distribution of SAT scores in each school, taking into account the different sizes of the student populations.

Another useful statistical measure for making this comparison would be to use box plots to visualize the distributions of SAT scores in each school. Box plots provide a clear and concise way to compare the minimum, maximum, median, and quartiles of SAT scores for each school.

In summary, the most useful statistical measures for comparing the distributions of SAT scores for School A and School B would be the percentage of students in each school who scored within certain score ranges, as well as the use of box plots to visualize the distributions.

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Answer:

Id you are talking about -2 celsius then its 28.4 fahrenheit but if its Fahrenheit then it's -18.8889 celsius

Step-by-step explanation:

Hope i helped you well :)

Answer:

The answer is 13/6

Step-by-step explanation:

9/6 + 6/9

9/6 = 3/2

6/9 = 2/3

Now,

3/2 + 2/3

Cross Multiply

3 × 3 + 2 × 2/2 × 3

9 + 4/6 = 13/6

Thus, The answer is 13/6

-TheUnknownScientist 72

\(\large\huge\green{\sf{Answer:-}}\)

\( = \frac{9}{6} + \frac{6}{9} \\ = \frac{27 + 12}{18} \\ = \frac{39}{18} \\ = \frac{13}{6} \)

Answer:

Yes

no

no

yes

Step-by-step explanation:

I hope it's serving

:v

Heteroskedasticity in the errors has an impact on the accuracy of the standard errors estimated using Ordinary Least Squares (OLS) and can affect hypothesis tests. To address this concern, it is advisable to utilize robust standard errors, which provide more reliable inference regarding the parameters of interest.

In the presence of heteroskedasticity, the OLS estimator for the parameters remains unbiased, but the usual OLS standard errors reported by statistical packages become inefficient and biased. This means that the estimated standard errors do not accurately capture the true variability of the parameter estimates. As a result, hypothesis tests based on these standard errors, such as the t-test and F-test, may yield misleading results.

To address heteroskedasticity, robust standard errors can be used, which provide consistent estimates of the standard errors regardless of the heteroskedasticity structure. These robust standard errors account for the heteroskedasticity and produce valid hypothesis tests. They are calculated using methods such as White's heteroskedasticity-consistent estimator or Huber-White sandwich estimator.

In summary, heteroskedasticity in the errors affects the accuracy of the OLS standard errors and subsequent hypothesis tests. To mitigate this issue, robust standard errors should be employed to obtain reliable inference on the parameters of interest.

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The mean absolute deviation (MAD) of the number of times is approximately 2.3.

To find the mean absolute deviation (MAD), we need to follow these steps:

1. Find the mean (average) of the numbers.

2. Calculate the absolute difference between each number and the mean.

3. Find the average of these absolute differences.

Given the numbers: 0, 0, 0, 1, 3, and 8.

Step 1: Find the mean:

Mean = (0 + 0 + 0 + 1 + 3 + 8) / 6 = 12 / 6 = 2

Step 2: Calculate the absolute difference between each number and the mean:

|0 - 2| = 2

|0 - 2| = 2

|0 - 2| = 2

|1 - 2| = 1

|3 - 2| = 1

|8 - 2| = 6

Step 3: Find the average of these absolute differences:

(2 + 2 + 2 + 1 + 1 + 6) / 6 = 14 / 6 ≈ 2.33

Therefore, the mean absolute deviation (MAD) of the number of times is approximately 2.33. The correct answer is 2.3 when rounded to the nearest tenth.

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Answer: 51 degrees

Step-by-step explanation:

The quadrilateral WXYZ is not a square using the distance formula

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

W(-1,1),X(3,4),Y(6,0) and Z(2,3)

The lengths of the sides can be calculated using the following distance formula

Length = √[Change in x² + Change in y²]

Using the above as a guide, we have the following:

WX = √[(-1 - 3)² + (1 - 4)²] = 5

XY = √[(3 - 6)² + (4 - 0)²] = 5

YZ = √[(6 - 2)² + (0 - 3)²] = 5

ZW = √[(2 + 1)² + (3 - 1)²] = 13

The sides that are congruent are WX, XY and YZ

This means that WXYZ is not a square

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Answer: 369.60

40% x 924=40.0 x 924=39.60

Answer:

○ f(x) = x² + 3x - 37

Step-by-step explanation:

Based on the given data in the table, we can observe that the function values (f(x)) correspond to different x-values. To determine the polynomial function represented by the data, we need to find the pattern or relationship between the x-values and the corresponding f(x) values.

Looking at the data, we can see that the x-values are increasing by 1 each time, and the corresponding f(x) values seem to be following a pattern. Let's analyze the data:

x | f(x)

--+-----

-8 | -35

-3 | -17

5 | 6

1 | 2

6 | 3

2 | 2

1 | 1

6 | 7

7 | 37

From the given data, it appears that the polynomial function represented by the data is:

f(x) = x² + 3x - 7

None of the provided options exactly matches this polynomial function, but the closest option is:

○ f(x) = x² + 3x - 37

So, the closest function represented by the data is f(x) = x² + 3x - 37.

Step-by-step explanation:

Mean= 13.4

Median= 13

Range= 11

Total area 59 square units.

To find the area under the split-domain function from x=-2 to x=3, we need to integrate each piece of the function separately over the given interval.

For x < 0, we have f(x) = 2x + 5. We can integrate this as follows:

∫(from -2 to 0) (2x + 5) dx = [x^2 + 5x] (from -2 to 0) = (0^2 + 5(0)) - (-2^2 + 5(-2)) = 4 + 10 = 14.

For x ≥ 0, we have\(f(x) = 5x^2\) We can integrate this as follows:

∫(from 0 to 3) (5x^2) dx \(= [5/3 x^3]\) (from 0 to 3)

\(= 5/3 (3^3 - 0^3)\)

= 45

Therefore, the total area under the function from x=-2 to x=3 is the sum of the areas of the two pieces

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The volume of Charles' finished cube will be 19,683 cubic centimeters.

To find the volume of the cube that Charles is going to construct, we need to first determine the length of each side of the square. Using a ruler to measure the square to the nearest centimeter, we can determine that each side is 27 centimeters.

To find the volume of the cube, we need to use the formula V = s^3, where V is the volume and s is the length of one side of the cube.

In this case, s = 27 centimeters, so we can plug that into the formula:

V = 27^3 = 19,683 cubic centimeters.

Therefore, the volume of Charles' finished cube will be 19,683 cubic centimeters.

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Answer:

y - 7 = - 1(x - 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 1 and (a, b) = (4, 7) , thus

y - 7 = - (x - 4)

The equation of line in the point-slope form is y = -1x + 11

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the point be P = P ( 4 , 7 )

Let the slope of the line be m = -1

So , the equation of line is given by the formula

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 7 = -1 ( x - 4 )

On simplifying the equation , we get

y - 7 = -1x + 4

Adding 7 on both sides of the equation , we get

y = -1x + 11

y = -x + 11

Therefore , the value of A is y = -x + 11

Hence , the equation of line is y = -x + 11

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The minimum number of elementary row operations required to obtain the inverse matrix E⁻¹ from E using the Matrix Inversion Algorithm is 3.

To find the inverse matrix E⁻¹ from E using the Matrix Inversion Algorithm, we can perform elementary row operations until E is transformed into the identity matrix I. Simultaneously, perform the same row operations on the right side of the augmented matrix [E | I]. The resulting augmented matrix will be [I | E⁻¹], where E⁻¹ is the inverse of E.

In this case, the matrix E can be transformed into the identity matrix I in 3 elementary row operations. The specific row operations required depend on the actual values in the matrix. Since the given values of matrix E are not provided, we cannot provide the exact row operations.

However, it is important to note that the minimum number of elementary row operations required to obtain the inverse matrix is independent of the values in the matrix. Hence, regardless of the specific values in matrix E, the minimum number of elementary row operations required to obtain the inverse matrix E⁻¹ from E using the Matrix Inversion Algorithm is 3.

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Answer:

here are 900 three digit numbers, from 100 to 999 (999–100+1 = 900). If we divide 900 by 13, we get 69. Since these are the multiples of 13, they are bound to be sequence of odd and even multiples. We have 68/2 = 34 odd multiples and 34 even multiples. So, the question is, whether the last multiple is odd or even. Since the first 3 digit multiple of 13 is 104, which is an even number, the last or 69 number is also going to be even number.

Thus, we have 34 + 1 = 35, three digit even numbers that are divisible by 13.

The required answer is 35.

Step-by-step explanation:

Correct me if this is wrong

Answer:

The smallest 3-digit integer is 100, the largest is 999.

Divide 100 by 13; the quotient is 7 and the remainder is 9; this means that the first multiple of 13 that will be at least 100 is 8.

Divide 1000 by 13; the quotient is 76 and the remainder is 12; this means that the last multiple fo 13 that will be smaller than 1000 is 76.

We now need to count the number of numbers starting with 8 and ending with 76.

A short way to do this is to subtract 8 from 76 and add 1 -- 76 - 8 + 1 = 69. (Don't forget to add 1!)

There are 69 positive integer multiples of 13 whose answers have 3 digits.

In a simple linear regression problem, some key assumptions are made to ensure the model's validity and reliability. Out of the given options, assumption (c) is stated incorrectly.

Assumption (a) states that the distribution of the error term is normal. This assumption is correct, as the error term's normal distribution allows for accurate statistical inferences and hypothesis testing in the regression analysis.
Assumption (b) states that the mean of the error term is 0. This assumption is also correct, as it implies that there is no systematic bias in the model. The errors, on average, should not overestimate or underestimate the dependent variable.
Assumption (c) states that the variance of the error term increases as x increases. This assumption is incorrect, as it contradicts the homoscedasticity assumption in linear regression. The correct assumption is that the variance of the error term should be constant across all levels of the independent variable (x). This constant variance ensures that the model's predictions are equally reliable for all values of x.
Assumption (d) states that the errors are independent. This assumption is correct and crucial for a linear regression analysis. The independence of errors means that the error term for one observation is not related to the error term of any other observation. This prevents any underlying patterns or relationships in the data from being mistakenly attributed to the linear relationship between the independent and dependent variables.
In summary, assumption (c) is stated incorrectly, as the variance of the error term should remain constant across all values of the independent variable in a simple linear regression analysis.

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Using the addition principle, we have proven that nk = n-1k-1 + n-1k.

To prove that nk = n-1k-1 + n-1k using the addition principle, we can follow these steps:

1. Start with the left side of the equation: nk

2. Apply the addition principle by breaking down n into (n-1) + 1: (n-1 + 1)k

3. Use the distributive property to distribute the k: (n-1)k + 1k

4. Simplify 1k to 1: (n-1)k + 1

5. Substitute n-1 for n and k-1 for k in the first term: n-1k-1 + n-1k

6. This gives us the right side of the equation, proving that nk = n-1k-1 + n-1k.

Therefore, using the addition principle, we have proven that nk = n-1k-1 + n-1k.

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Answer:

Step-by-step explanation:

It’s c

Answer:

87=x + 4  x=83

Step-by-step explanation:

87= x + 4

Switch sides

x + 4 = 87

Subtract 4 from both sides

x + 4-4 = 87-4

Simplify

x = 83

Answer:

the y-intercept is 7

Step-by-step explanation:

y=mx+b

m=slope

b= y-intercept

Answer:

your answer will be x=80°

Step-by-step explanation:

hope it helps you

have a great day!!!

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Given the equation:

to solve for x, first we have to move the constant 10 to the right side of the equation. When we do this, we have to change its sign to a negative sign:

Now we can divide both sides of the equation by 2 to get the following:

therefore, x = 9