A line has a slope of Negative one-fourth and passes through point (Negative five-fourths, 1). What is the equation of the line? y = negative one-fourth x + StartFraction 21 Over 16 EndFraction y = negative one-fourth x + StartFraction 11 Over 16 EndFraction y = negative one-fourth x minus one-fourth y = negative one-fourth x minus five-fourths

Answer:

Step-by-step explanation:

-8+x-4+9x = -8-4+x+9x

= -12+10x

PLEASE MARK BRAINLIEST.

Answer:

4 days

Step-by-step explanation:

15x4=60

The Cartesian coordinate system is also referred to as a plane because it represents a two-dimensional space.

In mathematics, a plane is a flat surface that extends infinitely in all directions. The Cartesian coordinate system consists of two perpendicular lines, known as the x-axis and y-axis, which intersect at a point called the origin. These axes divide the plane into four quadrants.

The term "plane" in the context of the Cartesian coordinate system originates from the concept of a geometric plane, which is a fundamental concept in Euclidean geometry. In Euclidean geometry, a plane is a flat, two-dimensional surface that extends infinitely in all directions.

The Cartesian coordinate system borrows this concept and applies it to represent points, lines, curves, and shapes in a two-dimensional space.

By using the Cartesian coordinate system, we can assign coordinates (x, y) to any point in the plane, where the x-coordinate represents the horizontal position and the y-coordinate represents the vertical position.

This system allows us to precisely locate and describe objects or phenomena within the two-dimensional space, making it a valuable tool in various fields such as mathematics, physics, engineering, and computer graphics.

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Answer:

width = 5 in

length = 17 in

Step-by-step explanation:

Area of a rectangle = length x width

width = w

length = 2 + 3w

85 = (w) x (2 + 3w)

85 = 2w + 3w³

this can be solved using quadratic equation

3w³ + 2w - 85 = 0

factors of 3w³ x -85 that add up to 2w are : +17 w and -15w

(3w³ - 15w) (17w - 85) = 0

3w(w - 5) 17(w - 5) 0

w = 5

or w = - 17/3

the width cannot be a negative number. the correct width is 5 in

Length = 2 x 3(5) = 17 inches

The matrix A [2194] cannot be expressed as a product of elementary matrices since it is a single-element matrix.

Elementary matrices are square matrices obtained by performing a single elementary row operation on the identity matrix. They are used in matrix operations, such as matrix multiplication and finding inverses.

However, the matrix A [2194] you provided is a 1x1 matrix, meaning it has only one element, which is 2194. Since elementary matrices are square matrices, they have dimensions greater than 1x1.

In order to express a matrix as a product of elementary matrices, it typically needs to have more than one element and be of a suitable dimension for matrix operations.

Therefore, in the case of the matrix A [2194], it cannot be expressed as a product of elementary matrices since it does not meet the requirements in terms of size and structure for elementary matrix operations.

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Hey there!

Answer:

After solving for x, our final solution is \(x=8\).

__________________________________

1. Expand \(4(2x-13)\).

\(8x-52\)

\(8x-52=4+x\)

2. Move 52 to the right side.

\(8x=x+56\)

3. Move x to the left side.

\(7x=56\)

4. Divide both sides by 7.

\(\frac{7x}{7} =\frac{56}{7}\)

5. Simplify.

\(x=8\)

________________________________________

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The profit P the company makes can be represented as: P = R - C. We can substitute the values of R and C in this formula to find the profit in terms of x.

Given that the revenue R is represented by 9x and the cost C is represented by 2x + 4500. The profit P can be represented by the formula P = R - C. To find the profit in terms of x, we substitute the values of R and C into this formula. P = 9x - (2x + 4500) P = 7x - 4500.

Therefore, the profit made by the company can be represented as P = 7x - 4500. Since the company sells each pen for $9, the number of pens they sell is represented by x. Hence, we can find the profit made by the company based on the number of pens sold. By knowing the profit made on each pen sold, the company can make informed decisions about the number of pens they should produce to maximize their profit.

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The theoretical probability of getting C is 0.4, and the practical probability of getting C is 12.

a) For the given case total outcomes are 5

The desired outcome is getting C thus the desired outcome is 2

So, The theoretical probability of choosing C is 2/5

b) The experimental probability of choosing a C can be calculated as the ratio of the number of times a C was actually chosen to the total number of trials.

From the table, we see that a C was chosen 5 + 7 = 12 times out of a total of 50 trials.

Therefore, the experimental probability of choosing a C is 12/50 or 0.24.

We can compare the experimental probability to the theoretical probability to see if they are similar.

In this case, the experimental probability of 0.24 is slightly higher than the theoretical probability of 0.4.

This could be due to chance or it could suggest that the letter C is slightly more likely to be chosen than expected. However, with only 50 trials, it is difficult to draw any definitive conclusions.

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1. Total revenue formula: Rx = 10,000x^(3/2)/(2+√x). 2. Marginal revenue formula: MR(x) = R′(x). 3. MR(9) calculation.


To find the marginal revenue (MR) and evaluate MR(9), we first need to understand the total revenue formula and how to calculate the derivative of this formula.

1. Total revenue formula (Rx):
The total monthly revenue from the sale of x automobiles of a certain model is given by:
Rx = 10,000x^(3/2)/(2+√x)
2. Marginal revenue formula (MR):
The marginal revenue (MR) is calculated by taking the derivative of the total revenue formula, Rx.
3. MR(9) calculation:
To find MR(9), we substitute x = 9 into the derivative formula of Rx.

Now, let's calculate the MR(9) step by step:
Step 1: Find the derivative of Rx:
To find the derivative, we need to apply the power rule and chain rule.
The derivative of Rx with respect to x is given by:
R′(x) = (d/dx) [10,000x^(3/2)/(2+√x)]
Step 2: Simplify the derivative:
To simplify the derivative, we can use the quotient rule and the power rule.
R′(x) = [10,000 * ((2+√x) * (3/2) * x^(1/2)) - (10,000 * x^(3/2) * (1/2) * (√x))] / (2+√x)^2
Simplifying further:
R′(x) = [15,000x^(3/2) + 5,000x - 10,000x^(3/2)√x] / (2+√x)^2
Step 3: Calculate MR(9):
Substitute x = 9 into the derivative formula.
MR(9) = [15,000(9)^(3/2) + 5,000(9) - 10,000(9)^(3/2)√9] / (2+√9)^2
Simplifying:
MR(9) = [15,000(27) + 5,000(9) - 10,000(27)√9] / (2+3)^2
MR(9) = [405,000 + 45,000 - 270,000] / 25
MR(9) = 180,000 / 25
MR(9) = 7200
Therefore, MR(9) = 7200.

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Answer:

6+1.25t

Step-by-step explanation:

W(in the 1st month)=6+1.25

W(in the 2nd month)=6+1.25+1.25

W(in the 3rd month)=6+1.25+1.25+1.25

W(in the t months)=6+t(1.25)

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

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Enter cost and tip percent to get a tip amount and total dinner amount. ... how many people? ... Calculate a tip or gratuity and get the total amount to pay. ... If you are splitting the cost at a restaurant among several people you can divide by the ... To calculate a gratuity or tip on any calculator it is a simple multiplication.

Answer:

Step-by-step explanation:

a) , The probability of winning the lottery when the order is unimportant is 1/8008.

b) The probability of winning the lottery when the order matters is 1/5765760.

a. Assuming that order is unimportant:

To calculate the probability of winning the lottery when the order is unimportant, we need to use the concept of combinations. The formula for calculating combinations is:

C(n, r) = n! / (r! * (n - r)!)

where n is the total number of options and r is the number of choices.

In this case, we have 16 numbers to choose from, and we need to select 6 numbers. So the probability of winning can be calculated as:

C(16, 6) = 16! / (6! * (16 - 6)!)

Calculating this expression gives us:

C(16, 6) = 8008

Therefore, the probability of winning the lottery when the order is unimportant is 1/8008.

b. Assuming that the order matters:

When the order matters, we need to use the concept of permutations to calculate the probability of winning.

The formula for calculating permutations is:

P(n, r) = n! / (n - r)!

Using the same numbers as before, we have:

P(16, 6) = 16! / (16 - 6)!

Calculating this expression gives us:

P(16, 6) = 5765760

Therefore, the probability of winning the lottery when the order matters is 1/5765760.

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Answer:

2/3

Step-by-step explanation:

-2x+3=-1+x+2

-2x-x+3=-1+2

-3x+3=1

-3x=1-3

-3x=-2

3x=2

x=2/3

Answer:

Step-by-step explanation:

Let the box tops collected by Mrs Goby be represented by x.

Since Mrs William's collected 4 more then mrs. Goby, Mrs Williams will have: = x+4

Miss Williams and mrs Laplant had the same number of box tops. They both had x+4 box tops.

To calculate the number of box tops that mrs. William's collect will be:

x + (x + 4) + (x + 4) = 64

3x + 8 = 64

3x = 64 - 8

3x = 56

x = 56/3

x = 18 1/3

Therefore, box too collected by Miss Williams will be:

= x + 4

= 18 1/3 + 4

= 22 1/3

= 22 approximately

The impact propensity can be interpreted as the slope coefficient for the tax personal exemption (pe) or its first lag in

the regression equation.

To determine the impact propensity in the regression of the general fertility rate (GFR) on the tax personal exemption

(PE) and its first lag, you should follow these steps:

Estimate the regression model using the available data. The model should look like this:

GFR = β0 + β1 × PE + β2 × PE_lag + ε

Where GFR is the general fertility rate, PE is the tax personal exemption, PE_lag is the tax personal exemption's first

lag, and ε is the error term.

Obtain the estimated coefficients (β0, β1, and β2) from the fitted regression model.

These coefficients will help you determine the impact propensity.

Calculate the impact propensity. The impact propensity in this context refers to the change in the general fertility rate

resulting from a one-unit increase in the tax personal exemption, taking into account both its current and lagged

effects.

To find the impact propensity, sum the coefficients for the tax personal exemption and its first lag:

Impact propensity = β1 + β2

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The area of the triangle JHI is 8.75 square units.

From the given figure,

Area of a ΔJHI = Area of a rectangle - (Area of 3 triangles)

= 5×4 - (1/2 ×3×4 + 1/2 ×2×3 + 1/2 ×1×5)

= 20 - (6+3+2.5)

= 20 - 11.25

= 8.75 square units

Therefore, the area of the triangle JHI is 8.75 square units.

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Answer:

Step-by-step explanation:

A teacher buys a yogurt cup for $2.00 and a textbook for $13.00 for each student in their classroom. The teacher spends a total of $405.00 for all of the yogurt cups and textbooks. How many students are in the teacher's class?

expenditure for each student 2 + 13 = 15.

We divide the total expenditure by the number of students

405: 15 = 27 $ (your answer)

Answer:

27

Step-by-step explanation:

Answer:

3.) 0.894

Step-by-step explanation:

✔️First, find BD using Pythagorean Theorem:

BD² = BC² - DC²

BC = 17.89

DC = 16

Plug in the values

BD² = 17.89² - 16²

BD² = 64.0521

BD = √64.0521

BD = 8.0 (nearest tenth)

✔️Next, find AD using the right triangle altitude theorem:

BD = √(AD*DC)

Plug in the values into the equation

8 = √(AD*16)

Square both sides

8² = AD*16

64 = AD*16

Divide both sides by 16

4 = AD

AD = 4

✔️Find AB using Pythagorean Theorem:

AB = √(BD² + AD²)

AB = √(8² + 4²)

AB = √(64 + 16)

AB = √(80)

AB = 8.9 (nearest tenth)

✔️Find sin x using trigonometric ratio formula:

Reference angle = x

Opposite side = BD = 8

Hypotenuse = AB = 8.944

Thus:

\( sin(x) = \frac{opp}{hyp} = \frac{8}{8.944} = 0.894 \) (nearest thousandth)

Answer:

Hey! The correct answer is the third option, I just took the test and it was correct

Step-by-step explanation:

3.) 0.894

In anova, by dividing the mean square between groups by the mean square within groups, a(n) Analysis of variance  statistic is computed.

What is Analysis of variance ?

What are some instances where ANOVA has been applied?

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The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

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Answer:

The area is 12.56 units^2 (same as circumference?)

Step-by-step explanation:

Assuming pi is 3.14, the equation for the circumference is C = 2 pi r

Fill it out for the radius (r)

12.56 = 2 3.14 r

12.56 = 6.28 r

r = 2

With the radius, the equation for the area is A = pi r^2

Fill it out for the area

A = 3.14 2^2

A = 3.14 4

A = 12.56

The answer to the question "difference of -72 and a product of -720?" is -9.

To find the sum of the two numbers, we can set up the following equations based on the given information:

Let the two numbers be x and y, where x > y.

x - y = -72 (since the difference between the numbers is -72)

xy = -720 (since the product of the numbers is -720)

We can solve these equations simultaneously using algebraic methods. One way to do this is to isolate one of the variables in one of the equations and substitute it into the other equation. For example, we can isolate y in the first equation by rearranging it to y = x + 72, and then substitute this into the second equation:

x(x + 72) = -720

Expanding the left-hand side, we get:

x^2 + 72x = -720

Rearranging the equation, we get:

x^2 + 72x + 720 = 0

Now we can solve for x using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 1, b = 72, and c = 720. Plugging in these values, we get:

x = (-72 ± √(72^2 - 4(1)(720))) / (2(1))

Simplifying further, we get:

x = (-72 ± √(5184 - 2880)) / 2

x = (-72 ± √2304) / 2

x = (-72 ± 48) / 2

Now we have two possible values for x:

x1 = (-72 + 48) / 2 = -12

x2 = (-72 - 48) / 2 = -60

Since x > y, we take x = -12 and y = -72 - (-12) = -60 + 12 = -48.

Thus, the sum of the two numbers is -9, which is obtained by adding x and y:

-12 + (-48) = -9.

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Answer:

Step-by-step explanation:500

a) the probability of  exactly 3 heads when flipping a coin 6 times is 0.25. b) the probability that there will not be more than one failure during a particular month is approximately 0.7788.

(a) To calculate the probability of obtaining exactly 3 heads when flipping a coin 6 times, we can use the binomial probability formula. The formula is given by P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful outcomes, p is the probability of success on a single trial, and C(n, k) represents the binomial coefficient.

In this case, n = 6 (number of coin flips), k = 3 (number of heads), and p = 0.5 (since the coin is fair). Plugging these values into the formula, we get P(X = 3) = C(6, 3) * (0.5)^3 * (1-0.5)^(6-3).

The binomial coefficient C(6, 3) can be calculated as C(6, 3) = 6! / (3! * (6-3)!) = 20.

Substituting these values, we have P(X = 3) = 20 * (0.5)^3 * (0.5)^3 = 20 * 0.125 * 0.125 = 0.25.

Therefore, the probability of obtaining exactly 3 heads when flipping a coin 6 times is 0.25.

(b) The Poisson distribution can be used to model the number of events occurring in a fixed interval of time or space, given the average rate of occurrence. In this case, the average rate is given as 3 failures every 12 months, which can be interpreted as an average rate of 3/12 = 0.25 failures per month.

To find the probability that there will not be more than one failure during a particular month, we can use the Poisson probability formula. The formula is given by P(X = k) = (e^(-λ) * λ^k) / k!, where λ is the average rate and k is the number of events.

In this case, λ = 0.25 (average rate) and we want to find P(X ≤ 1).

P(X ≤ 1) = P(X = 0) + P(X = 1) = (e^(-0.25) * 0.25^0) / 0! + (e^(-0.25) * 0.25^1) / 1!

Simplifying, we have P(X ≤ 1) = e^(-0.25) + (e^(-0.25) * 0.25) = 0.7788.

Therefore, the probability that there will not be more than one failure during a particular month is approximately 0.7788.

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The 2 equations which can be used to solve the given situations of the numbers are:

So, the equations that can be formed are:

Let, Ronan's number be 'x' and '4x' be Kelsey's number.

Now, solve as follows:

Ronan's number be: -2/3

Kelsey's number be: 4 × 2/3 = -8/3

Let, let, Kelsey's number be 'x' and Ronan's number be '3x'.

Now, solve as follows:

Ronan's number be: 72.75

Kelsey's number be: 24.25

Therefore, the 2 equations which can be used to solve the given situations of the numbers are:

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