Write an equation of the line satisfying the given conditions. Express numbers as integers or simplified fractions. The line is parallel to the x-axis and passes through (1, 2). The equation of the line is

The linear function (A) c(x) = 5.50 + 20.50x represents the total cost when x tickets are applied.

The term "linear function" in mathematics applies to two different but related ideas:

A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

So, c ⇒ the overall expense.

The quantity (x) of tickets

The price of one ticket without a service charge.

The fact that:

108 = 5.50 + 5z

5z = 108 - 5.50

5z = 102.5

z = 102.5/5

z = $20.5

Equating the linear function is:

c(x) = 5.50 + 20.50x

Therefore, the linear function (A) c(x) = 5.50 + 20.50x represents the total cost when x tickets are applied.

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Correct question:
Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in dollars for ordering 5 tickets is $108.00. Which linear function represents c, the total cost, when x tickets are ordered? (A service fee is a single fee applied to the total, no matter the number of tickets purchased).

a c(x) = 5.50 + 20.50x

b c(x) = 5.50x + 20.50

c c(x) = 5.50 + 21.60x

d c(x) = 5.50x + 21.60

Answer:

Convection

Step-by-step explanation:

The correct option is  C Radiation.

Conduction means transfer of energy (heat) arising from temperature differences between adjacent parts of a body.

Convection is the transfer of thermal energy by the physical movement of fluid (liquid, gas, or plasma) from one location to another.

Radiation is an electromagnetic radiation that is emitted by a body as a result of its temperature. All objects with a temperature above absolute zero emit thermal radiation in a spectrum of wavelength.

Sublimation is the process of changing a solid into a gas without passing through the liquid phase. To sublime a substance, a certain energy must be transferred to the substance via heat (q) or work (w).

Hence from all the above definitions it is clear that every phenomenon except  radiation transfer some amount of thermal energy.

Hence through Radiation thermal energy is not transferred.

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Answer:

(a) What percentage of women would not be able to use the original ejection seats designed for men?

To answer this question, we need to find the percentage of women whose weight is outside the range of 140 lb to 201 lb, which is the weight range for which the original ejection seats were designed. We can do this by standardizing the weight distribution of women using the formula:

z = (x - μ) / σ

where z is the standard score, x is the weight of a woman, μ is the mean weight of women, and σ is the standard deviation of the weight of women.

Substituting the given values, we get:

z = (140 - 162) / 46 = -0.478

z = (201 - 162) / 46 = 0.848

Using a standard normal table or a calculator, we can find that the percentage of women whose weight is below 140 lb (corresponding to a z-score of -0.478) is 31.45%. Similarly, the percentage of women whose weight is above 201 lb (corresponding to a z-score of 0.848) is 19.34%. Therefore, the percentage of women who would not be able to use the original ejection seats designed for men is:

31.45% + 19.34% = 50.79%

(b) What weight range would accommodate 99.7% of the female pilots?

To find the weight range that would accommodate 99.7% of the female pilots, we need to find the z-scores that correspond to the 0.15% and 99.85% percentiles of the standard normal distribution. Using a standard normal table or a calculator, we can find that these z-scores are approximately -2.97 and 2.97, respectively.

Substituting these z-scores into the standardization formula, we get:

-2.97 = (x - 162) / 46

x = 63.88 lb

and

2.97 = (x - 162) / 46

x = 260.12 lb

Therefore, the weight range that would accommodate 99.7% of the female pilots is approximately 63.88 lb to 260.12 lb.

(c) What percentage of women would need ejection seats redesigned for them?

To find the percentage of women who would need ejection seats redesigned for them, we need to find the percentage of women whose weight is outside the weight range that would accommodate 99.7% of the female pilots. Using the values from part (b), we can see that the weight range that would accommodate 99.7% of the female pilots is approximately 63.88 lb to 260.12 lb. Therefore, the percentage of women who would need ejection seats redesigned for them is:

100% - 99.7% = 0.3%

Answer:

sure so quadrant one is top right and its positive positive and quadrant 2 top left and is negative positive quadrant 3 is bottom left and negative negative quadrant 4 is bottom right and its positive negative

Step-by-step explanation:

The probability of obtaining a sum less than or equal to 4 is:  1/12

An experiment consists of tossing two ordinary dice and adding their numbers together. To determine the probability of obtaining a sum of 8, we need to first count the number of ways we can get a sum of 8. We can do this by listing all the possible combinations of dice rolls that add up to 8:

2+6, 3+5, 4+4, 5+3, 6+2

So there are 5 ways to get a sum of 8.

Next, we need to determine the total number of possible outcomes for this experiment. Each die has 6 sides, so there are 6 x 6 = 36 possible outcomes.

Therefore, the probability of obtaining a sum of 8 is:

Number of ways to get a sum of 8 / Total number of possible outcomes = 5/36

Now let's determine the probability of obtaining a sum less than or equal to 4. We can use the same method as before:

1+1, 1+2, 2+1

So there are 3 ways to get a sum less than or equal to 4.

The probability of obtaining a sum less than or equal to 4 is:

Number of ways to get a sum less than or equal to 4 / Total number of possible outcomes = 3/36 = 1/12

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The different two-letter initials can people have using the upper case characters in the English alphabet is 676 (if no specifications are given)

The question has not specified other conditions so we have assumed it by cases and solved it

Case 1 -

“Everything” allowed, means that we are considering solutions like “AA” and “BA, AB”

If this is the case then there are => 26 x 26 = 676 Combinations,

Case 2-

No repetition allowed

Here, we are excluding cases like “AA, BB” etc so here we have

26 x 25 = 650 as our answer

Case 3-

no repetition allowed + unique set every time, So

here we will have ²⁶C₂ (this is basic combinatorics formula )

= (26 x 25)/2

= 325 combinations possible

Case 4 -

Repetition allowed + unique set every time

here we will assume along with the uniqueness of each combination we will add Repeated combinations, Here we have “AA, BB, CC,……..ZZ” 26 new combinations along with unique ones So,

²⁶C₂+ 26 = 325 + 26 = 391 possible cases.

and I would recommend adding more detail to your question specifying the conditions in a better way, but the technically correct answer to your questions if no conditions are CASE 1.

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The solution is, 35, lists of three elements can we make using the numbers 1, 2, 3, 4, and 5, if repetition is allowed.

In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.

here, we have,

Given data:

{1 ,2, 3 ,4, 5}

Formula for combinations is used since the order does not matter and repetition is allowed.

nCr = (n + r -1) /(r! * (n-1)!)

where n is the total number of items and r is the items to be picked

now, we get,

5C3 = (5 + 3 - 1)! /(3! * (5 -1)!

5C3 = 7!/(3! *4!) Simplifying the factorials)

5C3 = 5040/(6*24)

5C3 =5040/144

5C3 = 35

Hence, The solution is, 35, lists of three elements can we make using the numbers 1, 2, 3, 4, and 5, if repetition is allowed.

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1. The trend in an exponential trend model is also known as:
c. Exponential growth

2. Based on the above information, please select the right statement below:
b. Polynomial Trend + Seasonality model has learned the systematic components better than others

One should be concise and not provide extraneous amounts of detail, and ignore any typos or irrelevant parts of the question. Additionally, it is important to use the terms provided in the question in your answer.In the provided student question, the trend in an exponential trend model is also known as exponential growth. The correct statement based on the information provided about the three models and their respective training and validation periods is that the Exponential Trend + Seasonality model has learned the systematic components better than the others. This is because the Exponential Trend + Seasonality model has the lowest error values for both the training and validation periods, indicating that it is better at predicting future values based on the systematic components. Therefore, option A is the correct answer.

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The unit vector in the same direction as vector \( v = 4d - j \) is \( \frac{4d\sqrt{16d^2 + 1}}{16d^2 + 1} - \frac{j}{\sqrt{16d^2 + 1}} \).

To find the unit vector in the same direction as vector \( v \), we need to normalize the vector \( v \).

Given \( v = 4d - j \), the magnitude of vector \( v \) can be calculated as:

\[

\|v\| = \sqrt{(4d)^2 + (-1)^2} = \sqrt{16d^2 + 1}

\]

To obtain the unit vector, we divide each component of \( v \) by its magnitude:

\[

\text{Unit vector of } v = \frac{4d}{\sqrt{16d^2 + 1}} - \frac{j}{\sqrt{16d^2 + 1}}

\]

Simplifying the expression further, we can rationalize the denominator:

\[

\text{Unit vector of } v = \frac{4d}{\sqrt{16d^2 + 1}} \cdot \frac{\sqrt{16d^2 + 1}}{\sqrt{16d^2 + 1}} - \frac{j}{\sqrt{16d^2 + 1}} = \frac{4d\sqrt{16d^2 + 1}}{16d^2 + 1} - \frac{j}{\sqrt{16d^2 + 1}}

\]

Therefore, the unit vector in the same direction as \( v \) is \( \frac{4d\sqrt{16d^2 + 1}}{16d^2 + 1} - \frac{j}{\sqrt{16d^2 + 1}} \).

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Answer:

4.5

 miles

Step-by-step explanation:

Well, he runs

3

miles in

28

minutes. Also, see that

42

=

28

⋅

1.5

.

So, his journey would just be running

1.5

times, with each time running

28

minutes.

So, he runs a total of

1.5

⋅

3

=

4.5

miles

Answer:

4.5 miles

Step-by-step explanation:

You divide 28/3 then the answer you get multiply it to 42 = 4.5.

Answer:

Your answer would be 6, -4, and 3

Step-by-step explanation:

The roots of the original polynomial equation are 6, -4 and 3

The polynomial equation is given as:

P(x) = (x - 6)(x + 4)(x - 3)

Set the polynomial to 0

(x - 6)(x + 4)(x - 3) = 0

Split the equation

(x - 6) = 0, (x + 4) = 0 and (x - 3) = 0

Solve for x in each split

x = 6, x = -4 and x = 3

Hence, the roots of the original polynomial equation are 6, -4 and 3

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Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the required number line is not included in the question.

A general explanation is as follows:

An open circle means > or <

A closed circle means >= or <=

Take, for instance, the attached number line:

The open dot on -3 means >-3 or <-3

The arrow points to the right direction, means >-3 i.e. greater than -3

Hence, the inequality is:

\(x > -3\)

Answer:

It's D

Step-by-step explanation:

Stay frosty

Answer:

D

NO STEP BY STEP!

Answer:

I'm not completely sure, but I hope this helps.

Answer:

Slope = 3

y-intercept: 0

Step-by-step explanation:

(1,3) and (2,6)

Slope: (6-3)/(2-1) = 3/1 = 3

y-intercept: 3 - (3)(1) = 3-3 = 0

y = 3x

the equation of the plane that passes through the point (2, - 14) and is parallel to the vector (1, 1, 4) is given by:r.(1, 1, 4) = p.(1, 1, 4) => x + y + 4z = 2 + 14 + 4( - 2) => x + y + 4z = 6. Therefore, the equation of the required plane is x + y + 4z = 6.

Given equation of plane are:x - z = 2 ....(1)y + 4z = 2 ....(2)xy - 4z = 4 ....(3)We are supposed to find an equation of the plane that passes through the line of intersection of the planes (1) and (2) and is perpendicular to the plane (3).To find the line of intersection of the planes (1) and (2), we solve the two planes simultaneously. The solution is the line of intersection of the two planes.To find the solution, we first eliminate x by adding equations (1) and (2) to obtain:y + x + 4z = 4 ...(4)Similarly, we eliminate x from equations (1) and (3) to obtain:xy - z - 4z = 4 => y(z + 1) = z + 4 => y = \(\frac{(z + 4)}{(z + 1)}\) ...(5)Now, we eliminate y from equations (4) and (5) to get an expression for z. Substituting that value of z in any of the equations, we can obtain the corresponding values of x and y. Once we have two such points, we can write the equation of the line that passes through them. That will be the line of intersection of the planes (1) and (2).Solving equations (4) and (5), we get z = - 4 or z = 2. Putting z = - 4 in equation (5), we get y = - 2.5 and putting z = - 4 and y = - 2.5 in equation (4), we get x = 0.5. Therefore, the line of intersection of the planes (1) and (2) is (0.5, - 2.5, - 4).Similarly, putting z = 2 in equation (5), we get y = 2 and putting z = 2 and y = 2 in equation (4), we get x = - 2. Therefore, the line of intersection of the planes (1) and (2) is (- 2, 2, 2).We know that the equation of the plane that passes through a point A(x₁, y₁, z₁) and is perpendicular to a vector n = (a, b, c) is given by:a(x - x₁) + b(y - y₁) + c(z - z₁) = 0Therefore, the equation of the plane that passes through the line of intersection of the planes (1) and (2) and is perpendicular to the plane (3) is:x - 0.5y - 2z = 1 ...(6)To obtain the above equation, we first find a vector that is parallel to the line of intersection of the planes (1) and (2). For that, we take the cross-product of the normals to the planes (1) and (2) as follows:n₁ × n₂ = (1, 0, - 1) × (0, 4, 1) = (4, 1, 4)Now, we find a point on the line of intersection of the planes (1) and (2). One such point is (0.5, - 2.5, - 4).Therefore, the required plane is 4x + y + 4z = 14.Therefore, we found the required equation of the plane. The equation of the plane is x + y + 4z = 6.

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To solve for the distance covered in the first two hours, we need to calculate the velocity at time t = 0 and t = 2.The car will have covered 44 miles during the first 2 hours of driving.

The velocity of the car t hours after leaving Austin is given by the equation V = 12 + 5t - 32. To solve for the distance covered in the first two hours, we need to calculate the velocity at t = 0 and t = 2.

At t = 0, V = 12 - 32 = -20. This means that the car was travelling at -20 miles per hour when it left Austin. Since velocity and distance are inversely proportional, the car had covered 0 miles when it left Austin.

At t = 2, V = 12 + 10 - 32 = -10. This means that the car was travelling at -10 miles per hour after 2 hours. Since velocity and distance are inversely proportional, the car had covered 44 miles after 2 hours by time.

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The number of different groups of subjects possible when randomly selecting from a group of subjects can be determined using the concept of combinations. The total number of possible groups can be calculated by finding the number of combinations of subjects that can be formed from the given group.

When selecting subjects from a group, the order of selection doesn't matter. We can use the combination formula to calculate the number of different groups. If there are 'n' subjects in the group and we want to select 'r' subjects, the number of different groups can be calculated as C(n, r), which is given by

n! / (r! * (n - r)!).

For example, if there are 10 subjects in the group and we want to select 3 subjects, the number of different groups of subjects possible would be

C(10, 3) = 10! / (3! * (10 - 3)!),

which simplifies to 10! / (3! * 7!).

Evaluating this expression will give you the total number of different groups of subjects that can be formed through random selection.

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The length of the rectangle with a perimeter of 24 inches and a width of 7 inches is 5 inches.

The perimeter of a rectangle is given by the formula: P = 2l + 2w where P is the perimeter, l is the length, and w is the width. We know that the perimeter of the rectangle is 24 inches and the width is 7 inches.

Substituting the given values in the formula for the perimeter of the rectangle, we have:

24 = 2l + 2 × 7

Simplifying, 24 = 2l + 14

Subtracting 14 from both sides, we get:

10 = 2l

Dividing both sides by 2, we get: l = 5

Therefore, the length of the rectangle is 5 inches.

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x+(3x+10-4)+(3x+ 10)=72

Quit parenthesis:

x+3x+10-4+3x+10=72

Combine like terms:

x+3x+3x+10-4+10=72

7x +16 =72

Subtract 16 from both sides of the equation:

7x+16-16 = 72-16

7x= 56

Finally divide both sides by 7:

7x/7 =56/7

x= 8

Answer:

21,845

Step-by-step explanation:

The sum of geometric sequence:

S n = a 1 * ( q^n - 1 ) / ( q - 1 )

where:  a 1 = 1,

q = a 2 : a 1 = 4 : 1 = 4

S 8 = 1 * ( 4^(8) - 1 ) / ( 4 - 1 ) =

= ( 65,536 - 1 ) / ( 4 - 1 ) = 65,535 / 3 = 21,845

Answer: X <0

Step-by-step explanation: 2(x+3)<x+6

Use the distributive property to multiply 2 by x+3.

2x+6<x+6

Subtract x from both sides.

2x+6−x<6

Combine 2x and −x to get x.

x+6<6

Subtract 6 from both sides.

x<6−6

Subtract 6 from 6 to get 0.

x<0

Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

To find dw/ds and dw/dt using the Chain Rule, we need to differentiate the function w with respect to s and t, respectively. Given the function w = y^3 - 10x^2y and the values s = -5 and t = 10, we can proceed as follows:

(a) Finding dw/ds:

Using the Chain Rule, we have dw/ds = (dw/dx) * (dx/ds) + (dw/dy) * (dy/ds).

Taking the partial derivatives, we have:

dw/dx = -20xy

dx/ds = e^s

dw/dy = 3y^2 - 10x^2

dy/ds = e^t

Substituting the values s = -5 and t = 10 into the derivatives, we can evaluate dw/ds.

(b) Finding dw/dt:

Using the Chain Rule, we have dw/dt = (dw/dx) * (dx/dt) + (dw/dy) * (dy/dt).

Taking the partial derivatives, we have:

dw/dx = -20xy

dx/dt = e^s

dw/dy = 3y^2 - 10x^2

dy/dt = e^t

Substituting the values s = -5 and t = 10 into the derivatives, we can evaluate dw/dt.

In summary, to find dw/ds and dw/dt using the Chain Rule, we differentiate the function w with respect to s and t, respectively, by applying the appropriate partial derivatives. By substituting the given values of s and t into the derivatives, we can evaluate dw/ds and dw/dt.

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Answer:

Select two points

7/-2 and 5/-1

subtract y1 from y2 to figure out y's change

7 - 5 = 2 change in y

now we subtract x1 from x2 to figure out x's change

-2 - ( -1 ) = -1 change in x

The slope will just be the results of the change in y and x but in the order of rise/run

2/-1 = -2 is the slope

Answer:

y=-1x+1

Step-by-step explanation:

The remaining side is 16.9 and remaining angles are 83.1 and 34.9.

The cosine formula to find the side of the triangle is given by:

c = √[a² + b² – 2ab cos C] Where a,b and c are the sides of the triangle.

Given:

m∠B = 62°, a = 11, and c = 19

Now, b² = a² + c² - 2ac cos B.

b = √ a² + c² - 2ac cos B

b = √ 11² + 19² - 2x 11  x 19 cos 62

b= 16.9

Now. a/ sin A = b/ sin B= c/ sin C

So, <C = arc sin ( c sin B /b)

<C = arc sin ( 19 sin 62 /16.9)

<C = 83.1

and, <A = arc sin ( a sin B /b)

<A = arc sin ( 11 sin 62 /16.9)

<A = 34.9

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The PHP function commonly used to send an SQL query to a MySQL database is "mysqli_query()." The general form of the return value of this function is a result object, which represents the outcome of the query execution.

In PHP, the "mysqli_query()" function is commonly used to send SQL queries to a MySQL database. It takes two parameters: the first parameter is the database connection object, and the second parameter is the SQL query string. When the "mysqli_query()" function is executed, it sends the SQL query to the MySQL database for execution. The function returns a result object, which represents the outcome of the query execution.

The specific contents of the result object depend on the type of query executed. For SELECT queries, the result object contains the retrieved data from the database, which can be fetched using other functions like "mysqli_fetch_assoc()" or "mysqli_fetch_array()." For INSERT, UPDATE, DELETE, or other types of queries, the result object typically indicates the success or failure of the query execution.

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Answer:

\(\Large \boxed{h(g(f(x)))=-8x^2-40x-50}\)

Step-by-step explanation:

\(f(x)=2x+5 \\\\ g(x)=x^2 \\\\h(x)=-2x\)

\(h(g(f(x)))=-2((2x+5)^2)\)

Expanding and solving for brackets.

\(h(g(f(x)))=-2(4x^2+20x+25)\)

Distributing -2 to the terms in the brackets.

\(h(g(f(x)))=-8x^2-40x-50\)

Answer:

-8x^2 - 40x - 50

Step-by-step explanation:

f(x) = 2x + 5

g(x) = x^2

h(x) = -2x

h(g(f(x))) =

First find g(f(x))

g(f(x)) = (2x+5) ^2 = 4x^2 + 10x + 10x +25

                            = 4x^2 + 20x + 25

The stick this in for g(f(x)

h(g(f(x))) = -2 (4x^2 + 20x + 25)

             = -8x^2 - 40x - 50