Which ordered pair is a solution of the equation?

5x−2y=18

Answer:

my bad yall, I seen the comments!! it's 12

Step-by-step explanation:

I'm so sorry!!

Answer:

Okay, i'm not being jugy but it it is super easy... it is 12 only because 1x12=12, 2x12=24, 3x12=36, and 4x12=48!!

it is most definately 12 DON'T WORRY

Answer:

285 students were in school.

Step-by-step explanation:

5%=0.05

0.05*300=15

300-15=285

There were 285 students in school.

Given that 5% of the 300 students were absent, we can calculate it as follows:

= 5% of 300

= (5/100) x 300

= 0.05 x 300

= 15

Therefore, there were 15 students absent from school.

Now, the In school students

Total students - Absent students = In-school students

300 - 15 = 285

So, there were 285 students in school.

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The general solution of the given second-order linear ordinary differential equation is y = (c1 + c2x)e^(5x) + 22/25, where c1 and c2 are arbitrary constants.

The given differential equation is y'' - 10y' + 25y = 22. To find the general solution, we first need to find the complementary function by solving the associated homogeneous equation, which is y'' - 10y' + 25y = 0.

Assuming a solution of the form y = e^(rx), we substitute it into the homogeneous equation and obtain the characteristic equation r^2 - 10r + 25 = 0. Solving this quadratic equation, we find that r = 5 is a repeated root.

Therefore, the complementary function is of the form y_c = (c1 + c2x)e^(5x), where c1 and c2 are arbitrary constants.

Next, we find a particular solution for the non-homogeneous equation y'' - 10y' + 25y = 22. Since the right-hand side is a constant, we can assume a constant solution y_p = a.

Substituting y_p = a into the differential equation, we find that 25a = 22, which gives a = 22/25.

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Answer:

-15

Step-by-step explanation:

I think

A confidence interval estimate of the population mean rating for Miami is:

Confidence interval:

(Mean - E) ≤ μ ≤ (mean + E)

(7.52 - 0.6578) ≤ μ ≤ (7.52 + 0.6578)

6.8622 ≤μ≤ 8.1778

Now, According to the question:

Given the data:

2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9

6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9

7 10 7 9 9 9 9

Assume a confidence interval of 95%

Using calculator :

The mean of the distribution (m) = 7.52

Standard deviation (s) = 2.314

Sample size),

Obtaining the t score ;

Degree of freedom (df) = (n-1) = 50 - 1 = 49

t(1-α/2), 49 = t(0.025, 49) = 2.01 ( t distribution table)

Margin of Error :

2.01 * s/√n = 2.01 * 2.314/7.0710678

Margin of Error (E) = 0.6578

Confidence interval:

(Mean - E) ≤ μ ≤ (mean + E)

(7.52 - 0.6578) ≤ μ ≤ (7.52 + 0.6578)

6.8622 ≤μ≤ 8.1778

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The complete question is this:

The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of business travelers follow.

2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9

6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9

7 10 7 9 9 9 9

Required:

Develop a confidence interval estimate of the population mean rating for Miami.

(2x + 5)² in the denominator represents the total number of gallons of gas purchased in the whole trip squared.

Annabella spends $2.25 per gallon on gas at the gas station. After driving a certain distance, she stops at a second gas station and spends $2.15 per gallon on gasoline.

Annabella can express her average cost per gallon of gasoline as 2.25 × 2.15(x + 5)/(2x + 5)²

The meaning of the parts of this rational expression in the context of the situation are as follows: 2.25 and 2.15 are the cost per gallon of gas at the two different gas stations.

x represents the number of gallons of gas bought at the first station.

5 is the number of miles driven between the first and second gas stations. And 2x + 5 is the total number of gallons of gas used in the entire trip (from the first gas station to the second).

Therefore, (x + 5) is the amount of gasoline bought from the second gas station, and 2x is the amount of gasoline bought from the first gas station.

The expression (x + 5)/(2x + 5) represents the weighted average of the cost per gallon of gas at the two gas stations.

Finally, (2x + 5)² in the denominator represents the total number of gallons of gas purchased in the whole trip squared.

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Answer:

$5,843.9

Step-by-step explanation:

2016

Total health care cost in US = $1.7 trillion

= $1,700,000,000,000

Population in US = 290.9 million.

= 290,900,000

Average amount spent per person on health care = Total health care cost in US / Population in US

= 1,700,000,000,000 / 290,900,000

= $5843.9326228944

Approximately,

$5,843.9

To the nearest whole number

= $5,844

Answer:

Average Speed

C.) 19.6 m/s

Instantaneous Speed

D.) 39.2 m/s

Step-by-step explanation:

Given the function to represent the distance traveled by the object in \(t\) seconds:

\(y = 4.9t^2\)

To find:

Object's average speed during the first 4 seconds ?

Instantaneous speed at t = 4 seconds

Solution:

Average speed of a moving object is given by, Total Distance covered divided by Total time taken.

\(\text{Average Speed = }\dfrac{\text{Total Distance traveled}}{\text{Total Time Taken}}\)

Let us find the distance traveled in 4 seconds by putting t = 4 in the equation \(y = 4.9t^2\)

\(y = 4.9\times 4^2 = 78.4\ m\)

Now, let us put the values in the formula:

\(\text{Average Speed = }\dfrac{78.4}{4} = \bold{19.6\ m/s}\)

For instantaneous speed, we need to differentiate y w.r.to t:

\(Speed = \dfrac{d}{dt}y = 4 \times 4.9 t^{2-1}\\\Rightarrow Speed = \dfrac{d}{dt}y = 4 \times 4.9 t\)

Now, let us put t = 4 seconds

Speed = \(4\times 4.9\times 4\) = 39.2 m/s

The answers are:

Average Speed

C.) 19.6 m/s

Instantaneous Speed

D.) 39.2 m/s

Answer:

(1, 4)

Step-by-step explanation:

After making a $150 deposit in the bank in one year, two years, and three years, Homer will have a total of $689 in the bank in four years, considering the interest rate of 5.6%.

Let's break down the problem step by step. In one year, Homer makes a $150 deposit. After one year, his initial deposit will earn interest at a rate of 5.6%. Therefore, after one year, his account balance will be $150 + ($150 * 0.056) = $158.40.

After two years, Homer makes another $150 deposit. Now, his initial deposit and the first-year balance will both earn interest for the second year. So, after two years, his account balance will be $158.40 + ($158.40 * 0.056) + $150 = $322.46.

Similarly, after three years, Homer makes another $150 deposit. His account balance at the beginning of the third year will be $322.46 + ($322.46 * 0.056) + $150 = $494.62.

Finally, after four years, Homer's account balance will be $494.62 + ($494.62 * 0.056) = $689.35, which rounds down to $689. Therefore, Homer will have $689 in the b in four years, considering the interest rate of 5.6%.

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D) The example (2x^2 + 5x) + (4x^2 - 4x) = (4x^2 - 4x) + (2x^2 + 5x) illustrates the commutative property of addition for polynomials.

The commutative property of addition for polynomials states that the order in which polynomials are added does not affect the result of the sum. In other words, it states that if we have two polynomials A and B, the result of adding A and B (A+B) will be the same as adding B and A (B+A).

For example, consider the polynomials (2x^2 + 5x) and (4x^2 - 4x). If we add these two polynomials in the order given, (2x^2 + 5x) + (4x^2 - 4x) = 6x^2 + x. Now, if we add these two polynomials in the reverse order, (4x^2 - 4x) + (2x^2 + 5x) = 6x^2 + x. We can see that the order of the polynomials does not affect the result of the sum, and thus it holds the commutative property of addition.

Option (2x^2 + 5x) + (4x^2 - 4x) = (4x^2 - 4x) + (2x^2 + 5x) illustrates the commutative property of addition for polynomials, because it shows that the order of the polynomials does not matter and it gives the same answer.

It is important to note that the other options does not illustrate the commutative property.

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Answer:

yep

Step-by-step explanation:

Answer:

y = -x + 6

Step-by-step explanation:

We can plug the given point and slope into the point-slope formula and solve for the y-intercept formula.

y - y = m(x - x)  <-- Point-Slope Formula

m = -1

(x,y) = (1, 5)

y - 5 = -1(x - 1)

y - 5 = -x + 1

y = -x + 6   <-- Y-intercept Formula

Answer: $9.05

Step-by-step explanation:

divide 135.75 by 15 in order to find the cost of one album.

135.75 / 15 = 9.05

answer: $9.05

Answer:

SAS similarity

Step-by-step explanation:

The two triangles MON and MQP are such that

Angle M = Angle M

MO/MQ = MN/MP

Therefore, Triangle MON ~ Triangle MQP (SAS similarity)

Step-by-step explanation:

\(\dfrac{d(e^x+ln~x)}{dx}\\\\ \dfrac{d(e^x)}{dx}+\dfrac{d(ln~x)}{dx}\\\\ \implies{\boxed{\sf{e^{x}+\dfrac{1}{x}}}}\)

The value of x for the two expressions will be 0.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the two equations are (-x+2y= 6) and 6y =x+18. The equations can be solved as below,

-x+2y= 6 or x = 2y - 6

6y = x + 18

Substitute the value of x in the second equation,

6y = 2y - 6 + 18

4y = 12

y = 3

x = 2y - 6

x = ( 2 x 3 ) - 6

x = 0

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Answer:

Your answer is 20

Step-by-step explanation:

as the formula 1/2*4*10=20.

hope it help you if yes then please make me the brainiest.

Thank you

parshv

In  linear equation, 21 phone calls does Tanner have to route to spend a total of 42 minutes on the phone

What is linear equation?

Tanner spent total min on phone = 24 min

total  phone calls = 12

Tanner have to route to spend a total of 42 minutes on the phone

                                                    =  12/24 * 42

                                                    =  1/2 * 42

                                                        = 21

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The y-intercept is approximately 191.15, which is closest to option B) 191.1.

To compute the y-intercept, we need to use the formula of the regression line:

y = a + bx

where a is the y-intercept, b is the slope, x is the independent variable (in this case, x-bar), and y is the predicted value of the dependent variable (in this case, y-bar).

The slope can be computed as:

b = r(sy/sx)

where r is the correlation coefficient, sy is the standard deviation of y, and sx is the standard deviation of x.

Substituting the given values, we get:

b = 0.341(37/12) = 1.05025

Now, we can use the formula of the regression line to find the y-intercept:

y = a + bx

251 = a + 1.05025(57)

a = 191.08875

Therefore, the y-intercept is approximately 191.1, which is answer choice B).
To compute the y-intercept, we will first need to find the slope (b) of the regression line using the given correlation coefficient (r), standard deviations (sx and sy), and means (x-bar and y-bar). Then, we will use the point-slope form of a linear equation to find the y-intercept.

Step 1: Calculate the slope (b)
b = r * (sy/sx)
b = 0.341 * (37/12)
b ≈ 1.05

Step 2: Use the point-slope form to find the y-intercept
y - y-bar = b * (x - x-bar)

Plug in the values for x-bar, y-bar, and b:
y - 251 = 1.05 * (x - 57)

Since we want the y-intercept, we will set x to 0:
y - 251 = 1.05 * (0 - 57)

Solve for y:
y - 251 = 1.05 * (-57)
y - 251 ≈ -59.85
y ≈ 251 - 59.85
y ≈ 191.15

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Answer:

To convert 2 Bigha into Kattha:

If 1 Bigha = 20 Kattha:

2 Bigha = 2 * 20 Kattha = 40 Kattha

If 1 Bigha = 16 Kattha:

2 Bigha = 2 * 16 Kattha = 32 Kattha

The integer that represents where he is now is -5.

What is the whole number?

Whole numbers are numbers without fractions and it is a collection of positive integers and zeros. It is represented by the symbol “W” and the set of numbers is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,……………}.

After diving 5 feet down into the swimming pool, Damian is at a depth of -5 feet, because he is underwater and the number is negative.

An integer is a positive or negative whole number, such as -5.

The negative sign denotes that Damian is underwater and the 5 is the distance he dove below the surface.

Hence, the integer that represents where he is now is -5.

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The measure of angle ABP is 90° and the measure of angle APB is 48°.

In the given figure, the measure of arc AB is 108° and the measure of angle ACB is (x+3)°.

Tangent and radius of a circle meet at 90°. If we draw a radius that meets the circumference at the same point, the angle between the radius and the tangent will always be exactly 90°.

Question 6:

Here, The measure of arc AB = 2×The measure of angle ACB

108 = 2(x+3)

⇒ x+3=54

⇒ x =51°

Question 7:

Given that, ∠PAB=42° and line PB is tangent to circle A

Now, ∠ABP =90° (Angle formed by tangent and radius is 90°)

Here, ∠ABP+∠PAB+∠APB=180°

⇒ 90°+42°+∠APB=180°

⇒ 132°+∠APB=180°

⇒ ∠APB=180°-132°

⇒ ∠APB=48°

Therefore, the measure of angle ABP is 90° and the measure of angle APB is 48°.

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When an arch is extended overhead into a half cylinder, it is known as a barrel vault.

A barrel vault is a curved architectural structure that resembles the shape of a half-cylinder. It is created by placing a series of arches side by side, forming a continuous and uninterrupted vaulted ceiling. The term "barrel" refers to the resemblance of the vault to the shape of a barrel or a tunnel.

Barrel vaults have been used in architecture for centuries and are often found in historical buildings and structures. They provide a sturdy and durable construction method, distributing the weight of the ceiling evenly along the arches. This allows for the creation of large and open interior spaces without the need for additional support columns.

Barrel vaults are commonly used in churches, cathedrals, and other monumental structures, where they serve both functional and aesthetic purposes. The sweeping and graceful curves of the barrel vaults add a sense of grandeur and elegance to architectural designs, making them a popular choice in various architectural styles throughout history.

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Answer:

Im pretty sure its 5

Step-by-step explanation:

5:1 due to 20/4 would be 5. I can give you more of an explaination if needed.

Answer:

5 triangles to 4 circles.

The surface given by the equation \(4x^2 - 16y^2 + z^2 = 16\) is a hyperboloid of two sheets. It consists of two distinct surfaces that intersect along the z-axis and open upwards and downwards.

To identify the surface defined by the equation \(4x^2 - 16y^2 + z^2 = 16,\) we can analyze the equation and determine its geometric properties.

First, let's rewrite the equation in a standard form:

\(4x^2 - 16y^2 + z^2 = 16\)

By rearranging terms, we have:

\((x^2/4) - (y^2/1) + (z^2/16) = 1\)

Comparing this equation to the standard form of a hyperboloid, we can see that the x and z terms have positive coefficients, while the y term has a negative coefficient. This indicates that the surface is a hyperboloid of two sheets.

The trace of the surface can be obtained by setting one variable constant and examining the resulting equation. Let's consider the traces in the xz-plane (setting y = 0) and the xy-plane (setting z = 0).

When y = 0, the equation becomes:

\(4x^2 + z^2 = 16\)

This represents an ellipse in the xz-plane centered at the origin, with the major axis along the x-axis and the minor axis along the z-axis.

When z = 0, the equation becomes:

\(4x^2 - 16y^2 = 16\)

This represents a hyperbola in the xy-plane centered at the origin, with the branches opening along the x-axis and the y-axis.

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identify the surface from the following equation \(4x^2-16y^2 z^2=16\)

Answer: a = 12, b = 2, c = 11

Step-by-step explanation:

Using exponent rules we can distribute the exponent of 3 to the xyz.

This results in the numerator now being. \(x^{5*3}+y^{1*3}+z^{4*3}\\\) This can be simplified to, \(x^{15}y^{3}z^{12}\\\).

Now divide the numerator by the denominator subtracting the exponents.

Which equals, \(x^{12}y^{2}z^{11}\)

So a = 12

b = 2

and

c = 11

The values of \(a, \ b,\ c\) are  \(12,\ 2,\ 11\) .

Exponent indicates that the base is to be raised to a certain power. So, it is the power of the base.

We have,

\(\frac{(x^5yz^4)^3}{x^3yz}=x^ay^bz^c\)

Now simplify the above given equation;

\(\frac{(x^5*3y^1*3z^4*3)}{x^3yz}=x^ay^bz^c\)

\(\frac{(x^{15}y^3z^{12})}{x^3yz}=x^ay^bz^c\)

Now, Using the exponent rule;

\(\frac{a^n}{a^m} = a^{n-m}\)

So,

\((x^{15-3}y^{3-1}z^{12-1})=x^ay^bz^c\)

\((x^{12}y^{2}z^{11})=x^ay^bz^c\)

Now,

As we see variables on both sides of equation are same (i.e. bases of powers are same), so now compare the powers of sides of variables;

⇒    \(x^{12}=x^a\)

       \(a=12\),

And, \(y^2=y^b\)

         \(b=2\)

And, \(z^{11}=z^c\)

         \(c=11\)

So, the values of \(a, \ b,\ c\) are \(12,\ 2,\ 11\) which are find out using the  exponent rule.

Hence, we can say that the values of \(a, \ b,\ c\) are \(12,\ 2,\ 11\) .

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Answer: 25

Step-by-step explanation: simplified the equation