What are the slope and the y-intercept of the graph of the linear function shown on the grid
a. slope = -1/4 , y-intercept = -1.5
b. slope = 1/4 , y-intercept = -6
c. slope = -4 , y-intercept = -1.5
d. slope = 4 , y-intercept = -6
PLEASE ANSWER SOON LOL​

The answer is  True, the percentile rank identifies the percentile of a particular value within a set of data.

The percentile rank is a measure that identifies the percentage of scores in a distribution that are equal to or lower than a given score. It is calculated by dividing the number of scores that are equal to or lower than the given score by the total number of scores in the distribution, and multiplying the result by 100 to obtain a percentage. The percentile rank can be used to compare individual scores to the rest of the distribution, and can provide useful information about the relative standing of a score within a particular group or population. Therefore, it is true that the percentile rank identifies the percentile of a particular value within a set of data.

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If Sam says that 2/7 to the power of 2 times 1/3 to the power of 5 can be rewritten as 2/21 to the power of 7 Sarah says it can be rewritten as 2/21 to the power of 10 Steve says it cannot be rewritten as either of these expression. The person that is correct is: Steve.

2/7 to the power of 2 times 1/3 to the power of 5 can be rewritten or express as [(2/7²)× (1/3^5)].

This implies that both Sam and Sarah are wrong, Only Steve is correct because  2/7 to the power of 2 times 1/3 to the power of 5 can either of the two expression that was mentioned by Sam and Sarah.

Therefore if Steve says it cannot be rewritten as either of these expression. The person that is correct is: Steve.

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Given :

The ordered pair (10, 4) is solution to the equation 3x - 5y = 10.

To Find :

Which one is the solution and which is not.

Solution :

Two pairs are (10,4) and (4,10) :

Putting ( 10,4 ) in given equation, we get :

LHS = 3( 10 ) - 5( 4 ) = 30 - 20 = 10 = RHS

So, ( 10,4 ) is the solution of the equation.

Now, putting, ( 4, 10 ) in given equation, we get :

LHS = 3( 4 ) - 5( 10 ) = 12 - 50 = -38 ≠ RHS

Therefore, (10,4) is the solution and (4,10 ) is not the solution.

Hence, this is the required solution.

Answer: Yes, (10,4) is a solution

Step-by-step explanation: Took the test

Answer:

it's A and C

(4, -8) and (-1,7)

Step-by-step explanation:

y = -3x + 4

A. works

x = 4

y = -8

-3(4) + 4

-12 + 4 = -8

B. doesn't work

x = 2

y = -10

-3(2) + 4

-6 + 4 = -2

C. works

x = -1

y = 7

-3(-1) + 4

3 + 4 = 7

D. doesn't work

x = -3

y = 4

-3(-3) + 4

9 + 4 = 13

it's A and C

(4, -8) and (-1,7)

Therefore, the standard deviation of the data set is approximately 4.14.

The standard deviation is calculated by taking the square root of the variance, which is the sum of the squared deviations divided by the sample size minus 1.

So, first we need to calculate the variance:

variance = sum of squared deviations / (sample size - 1)

variance = 103 / (7 - 1)

variance = 17.17

Now we can find the standard deviation:

standard deviation = √(variance)

standard deviation = √(17.17)

standard deviation = 4.14 (rounded to two decimal places)

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The first step used in the elimination method is to align the coefficients of one chosen variable in both equations.

To solve a system of equations using elimination, the first step is to align the coefficients of one variable in both equations.

This involves multiplying one or both equations by a constant to create equal coefficients for the chosen variable.

This allows for easy elimination when adding or subtracting the equations.

Once the coefficients are aligned, you can proceed to the next step of eliminating one variable by adding or subtracting the equations.

After eliminating one variable, the resulting equation will have only one variable, which can then be solved for its value.

This value can be substituted back into either of the original equations to find the value of the other variable. Finally, the solution to the system of equations is the values of both variables.

In conclusion, the first step used in the elimination method is to align the coefficients of one chosen variable in both equations.

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The surface area of the cone is 628 in²

A cone is a shape formed by using a set of line segments or the lines which connects a common point, called the apex or vertex.

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of cone is expressed as;

SA = πr( r+l)

where l is the slant height and r is the radius

SA = 3.14 × 10( 10+ 10)

SA = 31.4 × 20

SA = 628 in².

Therefore the surface area of the cone is 628 in²

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Answer:

78

Step-by-step explanation:

The exchange rate of the euro/pound expressed to four decimal places is 1.0100 euro/pound.

To find the exchange rate of the euro/pound, we can use the given exchange rates of dollar/pound and dollar/euro.

Let's denote the exchange rate of euro/pound as E.

Given:

Exchange rate of dollar/pound = 1.21 dollar/pound

Exchange rate of dollar/euro = 1.22 dollar/euro

To find the exchange rate of euro/pound, we can divide the exchange rate of dollar/euro by the exchange rate of dollar/pound:

E = (Exchange rate of dollar/euro) / (Exchange rate of dollar/pound)

E = 1.22 dollar/euro / 1.21 dollar/pound

Simplifying this expression, we get:

E = 1.01 euro/pound

Therefore, the exchange rate of the euro/pound, is 1.0100 euro/pound.

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Answer:

pi ≈ 3,141593

Step-by-step explanation:

I think this is the right answer

Answer:

Shaylee's work is correct

Step-by-step explanation:

lisa's work is not correct because -7+5 is -2 not -12

Answer: 360 - 44 - 80 = 236

236 ÷ 2 = 118

both angle equal to 118

Step-by-step explanation:

The measure of angle 1 is 118 degrees and the measure of angle 2 is 118 degrees.

It is defined as the four-sided polygon in geometry having four edges and four corners.

We know that kite is quadrilateral, having :

It has one pair of opposite congruent angles.

One diagonal is bisected.

The top and bottom angles are bisected but

As we know from the kite properties it has one pair of opposite congruent angles

From the properties of the quadrilateral the sum of the interior angles is 360 degrees

44 + angle 1 + angle 2 + 80 = 360

Angle 1 = angle 2 = x(say)

44 + x + x + 80 = 360

2x + 124 = 360

2x = 236

x = 118 degrees

Angle 1 = angle 2 = 118 degrees

Thus, the measure of angle 1 is 118 degrees and the measure of angle 2 is 118 degrees or m∠1 = 118° and m∠2 = 118°.

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The number of independent people (X) who view the ad until someone clicks on it (including the person who clicked on the ad), then X follows a geometric distribution with a probability of success p = 0.22.

Question 1: What is the probability that the first person who views the ad clicks on it?

Answer: Since X follows a geometric distribution, the probability that the first person who views the ad clicks on it is equal to the probability of success, which is p = 0.22.

Question 2: What is the probability that at least three people need to view the ad until someone clicks on it?

Answer: To find the probability that at least three people need to view the ad until someone clicks on it, we need to calculate the probability that it takes three or more people. This is equal to 1 minus the cumulative probability up to two people. The cumulative probability of X less than or equal to 2 is given by:

P(X ≤ 2) = P(X = 1) + P(X = 2)

Since X follows a geometric distribution, the probability mass function is given by:

P(X = k) = \(1-p^{(k-1)}\) × p

Using this formula, we can calculate:

P(X ≤ 2) = P(X = 1) + P(X = 2) = \(1-0.22^{(1-1)}\) × 0.22 + \(1-0.22^{(2-1)}\)× 0.22

Question 3: What is the expected value (mean) of X?

Answer: The expected value (mean) of a geometric distribution with probability of success p is given by E(X) = 1/p. Therefore, the expected value of X in this case is:

E(X) = 1/0.22

Question 4: What is the standard deviation of X?

Answer: The standard deviation of a geometric distribution with probability of success p is given by σ(X) = √(q/p²), where q = 1 - p. Therefore, the standard deviation of X in this case is:

σ(X) = √((1 - 0.22)/(0.22²))

Question 5: What is the probability that it takes exactly five people to click on the ad?

Answer: Since X follows a geometric distribution, the probability of X = 5 is given by:

P(X = 5) = \(1-p^{(5-1)}\) × p

Using this formula, we can calculate the probability that it takes exactly five people to click on the ad.

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The Taylor series of the function is given by;

\(\frac{Z}{1-Z}=1+Z+Z^{2}+Z^{3}+Z^{4}+Z^{5}+Z^{6}+...\)

The formula of Taylor series is given by;

\(f(x)=f(a)+\frac{f^{'}(a)}{1!}(x-a)+\frac{f^{''}(a)}{2!}(x-a)^{2}+....+\frac{f^{n}(a)}{n!}(x-a)^{n}+R_{n}\)

To calculate the Taylor series of the given function,

\(f(x)=\frac{Z}{1-Z}\)

We need to first differentiate the function to find the nth derivative of the function at some point a. We can do this using the quotient rule.

\(\frac{d}{dx}\frac{Z}{1-Z}=\frac{(1-Z)\frac{dZ}{dx}-Z\frac{d(1-Z)}{dx}}{(1-Z)^{2}}\)

We can now simplify this expression by using the product rule to find the second derivative of Z and the first derivative of 1-Z,

\(\frac{dZ}{dx}=1\)\(\frac{d}{dx}(1-Z)=\frac{d}{dx}(1)-\frac{d}{dx}(Z)=0-1=-1\)

Substituting these derivatives into the equation above gives,

\(\frac{d}{dx}\frac{Z}{1-Z}=\frac{(1-Z)-Z(-1)}{(1-Z)^{2}}=\frac{1}{(1-Z)^{2}}\)

We can continue this process of differentiation to find the third, fourth, fifth, and sixth derivative of the function.

\(\frac{d^{2}}{dx^{2}}\frac{Z}{1-Z}=\frac{2}{(1-Z)^{3}}\)

\(\frac{d^{3}}{dx^{3}}\frac{Z}{1-Z}=\frac{6}{(1-Z)^{4}}\)

\(\frac{d^{4}}{dx^{4}}\frac{Z}{1-Z}=\frac{24}{(1-Z)^{5}}\)

\(\frac{d^{5}}{dx^{5}}\frac{Z}{1-Z}=\frac{120}{(1-Z)^{6}}\)

\(\frac{d^{6}}{dx^{6}}\frac{Z}{1-Z}=\frac{720}{(1-Z)^{7}}\)

To find the Taylor series of the function, we now substitute these values into the formula of the Taylor series at the point a=0

\(\frac{Z}{1-Z}=1+Z+Z^{2}+Z^{3}+Z^{4}+Z^{5}+Z^{6}+...\)

Therefore, the Taylor series is,

\(\frac{Z}{1-Z}=1+Z+Z^{2}+Z^{3}+Z^{4}+Z^{5}+Z^{6}+...\)

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Applying the exterior angle theorem, the measure of the exterior angle to angle X is: B 112.55°.

In other to find the measure of the exterior angle to angle X, we have to recall the theorem known as the exterior angle theorem, which states that the measure of an exterior angle is equal to the two interior remote angles that are opposite to it.

In triangle XYZ, angle Y and Z are the remote interior angles. We are given the following:

Measure of angle Y = 38.25°

Measure of angle Z = 74.3°

Therefore:

The measure of the exterior angle to angle X = measure of angle Y + measure of angle Z

Substitute

The measure of the exterior angle to angle X = 38.25° + 74.3°

The measure of the exterior angle to angle X = 112.55°

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The equation that can be used to find the number of seconds in a number is [60s = m].

So, an equation that finds the number of seconds in a number of minutes.

We know that:

Then, the equation will be:

Therefore, the equation that can be used to find the number of seconds in a number is [60s = m].

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Answer:

well u should always know that a sum of angles in a triangle add up to 180 degrees it never changes

Answer:

The three angles in a triangle always add up to 180 degrees. This is a property that is widely accepted as true and is not needed to be proved. However, if a proof is required, see attached images for proof of property.

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Answer: 56.52 meters squared i took the test :)

Step-by-step explanation:

ALSO ITS MY NAME LOL

Answer:

Step-by-step explanation:

Answer:

11259.5

Step-by-step explanation:

25×386+3219÷2

Multiply 25 and 386 to get 9650.

9650+3219/2

Convert 9650 to fraction 19300/2.

19300/2+3219/2

Since 19300/2 and 3219/2 have the same denominator, add them by adding their numerators.

19300+3219/2

Add 19300 and 3219 to get 22519.

22519/2

Divide 22519 by 2 to get 11259.5.

11259.5

The value of n in the expression is approximately equal to 269.33.

We have,

To find the value of n, we can simplify the given equation using logarithmic properties and then solve for n.

Using logarithmic properties:

3log₁.₂ + 2log₁/₃√10 - log₂₀ = log n

Applying the power rule of logarithms and converting the radicals to fractional exponents:

log₁.₂³ + log₁/₃(10)² - log₂₀ = log n

Simplifying the logarithmic expressions:

log₁.₂(8) + log₁/₃(100) - log₂₀ = log n

Converting the logarithmic expressions into the exponential form:

1.₂⁸ + 1/₃(100) - 20 = n

Simplifying the expression:

256 + 100/₃ - 20 = n

Evaluating the expression:

n = 256 + 33.33 - 20

n ≈ 269.33

Therefore,

The value of n in the expression is approximately equal to 269.33.

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The complete question:

If 3log₁.₂ + 2log₁/₃√10 - log₂₀ = log(n), what is the value of n?

Assuming a constant growth factor, the population of Gotham City grew by approximately 4.287% each year.

This can be calculated using the formula for exponential growth, which is:
y = a * (1 + r)^t
Where: y = final value of the population
a = initial value of the population
r = annual growth rate expressed as a decimal
t = number of years

For this problem, let's assume that the initial population of Gotham City was 100,000 and that the population grew for 10 years.

Using these values, we can calculate the annual growth rate as follows:

100,000 * (1 + r)^10 = final population
r = (final population / 100,000)^(1/10) - 1

Plugging in a final population of 148,644 (which is a 48.644% increase from the initial population),

r = (148,644 / 100,000)^(1/10) - 1r = 0.04287 (rounded to 5 decimal places)

Therefore, the annual growth rate (or percentage increase) is approximately 4.287% (rounded to 3 decimal places).

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Answer:

1)4 41/50

2)7 7/10

By applying the linear equation concept, it can be concluded that:

A. The slope of the line is 15

B. The standard form of the equation is 15x - y + 325 = 0

C. The function notation of the equation is g(x) = 15x + 325

D. The balance in the bank account after 12 days is $505

Linear equation is an equation that contains one or more variables, where each variable has the power of one.

The standard form of a linear equation is y - y₁ = m(x - x₁) or ax + by + c = 0, where m is the slope of the function.

Slope of the function represents the change in y (Δy) over the change in x (Δx). m = Δy / Δx

We have the following table:

x         0       5       10

g(x)   325   400   475

A. To find the slope of the line, we calculate the value of Δy  dan Δx:

Δy = y₂ - y₁

    = 400 - 325

    = 75

Δx = x₂ - x₁

     = 5 - 0

     = 5

m = Δy / Δx

   = 75 / 5

   = 15

B. To find its standard form, we can input the value of one point into y - y₁ = m(x - x₁):

            y - y₁ = m(x - x₁)

        y - 325 = 15 (x - 0)

        y - 325 = 15x - 0

15x - y + 325 = 0

C. function notation changes the y to g(x), so we get:

   15x - y + 325 = 0

15x - g(x) + 325 = 0

                  g(x) = 15x + 325

D. The balance in the bank account after 12 days can be calculated by substituting the value of x = 12 into the function:

g(x) = 15x + 325

      = 15 · 12 + 325

      = 180 + 325

      = $505

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Answer:

50

Step-by-step explanation:

A full circle is 360. The half circle you're looking at is 180.

So 180-65-65

The predicted height is close to the actual height of the plant by 0.69 cm

The equation of the height function of the plant is given as:

y = 1.44x + 1.55

The height on day 7 is calculated as:

y = 1.44 * 7 + 1.55

Evaluate

y = 11.63

The recorded height is given as 12.32

The residual is calculated as:

Residual = Recorded - Predicted

So, we have:

Residual = 12.32 - 11.63

Evaluate

Residual = 0.69

Hence, the predicted height is close to the actual height of the plant by 0.69 cm

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The exact volume of the first object is approximately 992.05 cubic units, and the exact volume of the second object is (3π/14) cubic units.

Volume of the first object:

Volume =\(\int\limits^0_7 {1/2*(6-(6/49)x^{2})^{2} } \, dx\)

Volume = \(\frac{1}{2} \int\limits^0_7 {36-(72/49)x^{2} +(36/2401)x^{4} } \, dx\)

Volume = 1029 - (1836/7) + (10.347/7)

Volume ≈ 992.05 cubic units

Therefore, the volume of the first object is approximately 992.05 cubic units.

Volume of the second object:

Volume = \(\int\limits^0_1{2\pi *y^{3}*(1-y^{3} ) } \, dy\)

Integrating term by term:

Volume = 2π [(1/4) - (1/7)]

Volume = 2π [(7 - 4)/28]

Volume = 2π * (3/28)

Volume = 3π/14

Therefore, the volume of the second object is (3π/14) cubic units.

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The general solution of the damped spring-mass system with the given parameters is y(t) = e^(-t/2) [c1cos((√7/2)t) + c2sin((√7/2)t)]. By applying the initial conditions y(0) = 1 and y'(0) = 0, the specific solution can be obtained as y(t) = (2/7)e^(-t/2)cos((√7/2)t) + (3/7)e^(-t/2)sin((√7/2)t).

The equation for the damped spring-mass system can be expressed as my'' + cy' + ky = 0, where m is the mass, c is the damping coefficient, and k is the spring constant. In this case, m = 1 kg, c = 3 kg/s, and k = 2 kg/\(s^2\).

To find the general solution, we assume a solution of the form y(t) = e^(rt). By substituting this into the equation and solving for r, we get \(r^2\) + 3r + 2 = 0. Solving this quadratic equation gives us the roots r1 = -2 and r2 = -1.

The general solution is then given by y(t) = c1e^(-2t) + c2e^(-t). However, since we have a damped system, the general solution can be rewritten as y(t) = e^(-t/2) [c1cos((√7/2)t) + c2sin((√7/2)t)], where √7/2 = √(3/4).

By applying the initial conditions y(0) = 1 and y'(0) = 0, we can solve for the coefficients c1 and c2. The specific solution is obtained as y(t) = (2/7)e^(-t/2)cos((√7/2)t) + (3/7)e^(-t/2)sin((√7/2)t). This satisfies the given initial value problem.

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