Sketch the graph of this linear equation
4y = -7x + 1​

After pouring some water from container A into container B, the new height of the water in both containers will be equal.

When container A is filled with water to the brim, it reaches its maximum capacity. Let's assume the initial height of the water in container A is h.

When some water is poured from container A into container B, the water level in both containers will gradually equalize until they reach the same height. Let's denote this new height as H.

The reason the water levels equalize is due to the principle of fluid equilibrium. When the containers are connected and the water is allowed to flow, the water seeks a common level. This occurs because the pressure at the same height in a fluid is equal.

Therefore, after pouring water from container A to container B, the final height of the water in both containers will be H, which indicates that the water has reached an equilibrium point where the pressure is equal in both containers.

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a) The probability that the species is found in the United States and is a bird is: 0.4727. b) The probability that the species is foreign or a mammal is: 0.9531. c) The probability that the species is warm-blooded is: 0.4094.

a. The probability that the species is found in the United States and is a bird is:

P(US and bird) = 78/165 = 0.4727 (we add the number of endangered bird species in the US and divide by the total number of endangered species)

b. The probability that the species is foreign or a mammal is:

P(foreign or mammal) = (251 + 63)/320 = 0.9531 (we add the number of foreign endangered species and the number of endangered mammal species, and divide by the total number of endangered species)

c. The probability that the species is warm-blooded is:

P(mammal or bird) = (63 + 78)/320 = 0.4094 (we add the number of endangered mammal and bird species, and divide by the total number of endangered species)

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Yes, Both the students are correct because both students calculate the area of a rectangular garden.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

Roberto says they can use the expression;

⇒ 2(3)+2(3)

And, Jay says they can use the expression;

⇒ (4.9) 3

Now,

Since, The garden club plants a rectangular garden that.

And, It has been divided into six sections.

Here, The members want to find the area of the sections they planted with herbs.

Roberto says they can use the expression;

⇒ 2(3)+2(3)

Clearly, Robert find the area of garden as;

⇒ 2(3)+2(3) = 12 ft²

And, Jay find the area of garden as;

⇒ (4.9) 3 = 14.7 ft²

Thus, Both the students are correct because both students calculate the area of a rectangular garden.

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Answer:

It will be 180 because 2/5 of means 2 in 5 then in ,450 you need to know 2/5 of 450 which gives you 180

Answer:

no.

Step-by-step explanation:

since 2 of the sides are much longer than the shorter sides, diagonals of a rectangle will not intersect at a right angle (perpendicular) whereas a square, with all sides equal, would. This is because the distance from the center to each of the corners is the same for each corner.

Hello!

Let's solve this equation:

84=h-8

This is the same as

h-8=84

Add 8 to both sides:

h=84+8

h=92

Hope everything is clear.

Let me know if you have any questions!

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:-)

Answer:

A. 2x²-13x+15 / (x-3)(x+3)(x-4)

Step-by-step explanation:

Step-by-step explanation:

=   2x / (( x+3)(x-3))     -   5 / ((x -4)(x+3))        

                multiply L term by   (x-4)/ (x-4)    and the R term by (x-3)/(x-3)

                      to get a common denominator

[ 2x (x-4)       -    5(x-3)  ] / ((x-3)(x+3)(x-4)        then simplify a bit to get

(2x^2 -13x +15 )  ((x-3)(x+3)(x-4)        Done.

Answer:

121

Step-by-step explanation:

5x-54=3x+16

5x-3x=16+54

2x=70

x=35

-------

mAB= 5x-54= 5*35-54= 175-54= 121

False.

Row operations on a matrix can change its eigenvalues.

Eigenvalues are defined as the values of λ for which the equation (A - λI)x = 0 has a non-zero solution x. Here, A is the matrix, λ is the eigenvalue, I is the identity matrix, and x is the eigenvector.

When we perform row operations on a matrix A, we are essentially multiplying A by an elementary matrix E. This changes the matrix A to a new matrix B = EA.

The eigenvalues of the new matrix B are not necessarily the same as the eigenvalues of the original matrix A. However, the eigenvalues of A and B do have the same algebraic multiplicity, which is the number of times each eigenvalue appears as a root of the characteristic polynomial of the matrix.

So while row operations on a matrix can change its eigenvalues, they do not change the algebraic properties of the eigenvalues, such as their multiplicity.

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The rise and run of the line may be determined using two of its points, and the slope can be calculated.

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The correct matches are: A. Slope = 1.56, B. Slope = 0.86, C. Slope = 3

D. Slope = -5.61, E. Slope = -0.44  

Given two line-side coordinates, use the slope formula to determine the slope of the line. Slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations.

Here are the correct matches of each pair of points to the slope of the line that joins them:

A. (9, 10) and (7.2) - Slope = (10 - 7.2)/(9 - 7.2) = 2.8/1.8 = 1.56

B. (-8,-11) and (-1,-5) - Slope = (-5 - (-11))/(-1 - (-8)) = 6/7 = 0.86

C. (5,-6) and (2,3) - Slope = (3 - (-6))/(2 - 5) = 9/3 = 3

D. (6.3) and (5,-1) - Slope = (-1 - 6.3)/(5 - 6.3) = -7.3/1.3 = -5.61

E. (4,7) and (6.2) - Slope = (6.2 - 7)/(4 - 6.2) = -0.8/1.8 = -0.44

So, the correct matches are:

A. Slope = 1.56

B. Slope = 0.86

C. Slope = 3

D. Slope = -5.61

E. Slope = -0.44      

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Answer:

5

Step-by-step explanation:

Answer:  5

Step-by-step explanation:

We rerange the number in 1,2,3,4,9,12,13

The median is 4, and a number x between 4 and 9.

We have 4.5 for median, which is the average of 4 and x.

(4 + x) /2 = 4.5

4 + x = 9

x = 5

Domain: \((-\infty,\infty)\)

Range: \((0,\infty)\)

==============================================================

Explanation:

I'm assuming the function is \(f(x) = 2(3)^x\) which is an exponential function.

The domain of any exponential function is the set of real numbers. In interval notation, the domain is \((-\infty, \infty)\) which says we can pick any number between negative infinity and positive infinity: aka any number we want. There are no restrictions to worry about such as division by zero errors.

The range of this exponential function is the set of y values such that y > 0. It often helps to see the graph of what is going on (see below). Note how as x heads to the left, and gets more negative, the curve approaches the x axis. It never actually touches it however. So it will never reach y = 0 itself but instead just get very close. The inequality y > 0 translates to the interval notation \((0,\infty)\)

----------

Summary:

Domain: \((-\infty,\infty)\);  Range: \((0,\infty)\)

So that's why the answer is choice A

The domain and range of the function f(x)  are  (-∞, ∞) and  (-∞, ∞) respectively.

A relation is a function if it has only One y-value for each x-value.

The function f(x) = 2(3x) can be simplified to f(x) = 6x.

The domain of a function is the set of all possible input values for x, while the range is the set of all possible output values for f(x).

Since there are no restrictions on the value of x that can be plugged into the function, the domain of f(x) is all real numbers, or (-∞, ∞).

To find the range, we can look at the behavior of the function as x varies. As x increases or decreases, the value of f(x) also increases or decreases, respectively, at a rate of 6 times the rate of change of x.

Therefore, the range of f(x) is also all real numbers, or (-∞, ∞).

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The mass of a cubic meter of air at room temperature (20°C) depends on various factors such as atmospheric pressure and humidity. However, as a rough estimate, at standard atmospheric conditions, the mass of dry air in a cubic meter is approximately 1.2 kilograms.

What is cubic meter?

A cubic meter is a unit of volume in the metric system. It represents the amount of space occupied by a cube that measures one meter on each side. It is commonly used to measure the volume of solids, liquids, or gases.

The mass of air can be calculated by considering its density. At standard atmospheric pressure (101.325 kilopascals) and temperature (20°C), the approximate density of dry air is about 1.2 kilograms per cubic meter. This value may vary depending on factors such as altitude, humidity, and temperature deviations from the standard conditions.

It's worth noting that including water vapor in the air would increase the mass further. Therefore, the given estimate of 1.2 kilograms represents the mass of dry air, neglecting the presence of water vapor.

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Answer:

ye

Step-by-step explanation:

yeyeyyeyyeyeyye

Answer:

In Translation Studies the term ‘non-translation’ is used in a number of different manners, for instance in reference to (a) original texts (versus translated texts), (b) fragments of source text preserved in the original language in the target text, (c) a deliberate refusal to translate a given author or work and (d) the lack or scarcity of translations.

Step-by-step explanation:

Answer:

9.0909001e+23

Step-by-step explanation:

The area of the shaded region, representing the probability that an IQ score is greater than 125, is approximately 0.0475 or 4.75%.

To find the area of the shaded region, we need to determine the probability that an IQ score is greater than 125.

The given information states that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. We can use these parameters to calculate the z-score for the IQ score of 125.

The z-score formula is given by:

z = (x - μ) / σ

where x is the value (125 in this case), μ is the mean (100), and σ is the standard deviation (15).

Let's calculate the z-score:

z = (125 - 100) / 15

z = 25 / 15

z = 1.67

Now, we need to find the probability of obtaining a z-score greater than 1.67.

Using the standard normal distribution table, we can look up the area to the right of z = 1.67. The corresponding value is approximately 0.0475.

Therefore, the area of the shaded region, representing the probability that an IQ score is greater than 125, is approximately 0.0475 or 4.75%.

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According to the text, in a true experimental study, the subjects should be assigned to groups randomly. If this is not possible and a researcher uses intact groups, they are performing a quasi-experimental study.

Quasi-experimental studies are research designs that include some elements of an experimental study but are lacking in the key feature of random assignment to a treatment or control group. Researchers may compare groups that already exist, for example, individuals who already smoke and those who do not. Because the groups are not chosen randomly, researchers cannot attribute differences in results to the effects of the treatment in question.A quasi-experimental study is a type of study in which researchers analyze a natural experiment in which subjects in the study are not randomly assigned to the treatment and control groups. The goal is to compare the outcomes of the treatment and control groups while minimizing the effects of other factors that might interfere with the results.

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Answer:

$309.75 in a week

Step-by-step explanation:

The person that might want to claim exemption on the W-4 form is John who received money from his internship.

This is possible if your income does not derive from:

John can likely be exempted because he obtained the money from an internship, which is not a formal job.

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The coefficients when the exponential expression \(\sqrt[4]{2^7 \times 3^3}\) is simplified are given as follows:

The exponential expression in this problem is defined as follows:

\(\sqrt[4]{2^7 \times 3^3}\)

The exponent 7 of the radicand is greater than the base 4 of the root, hence the term can be simplified as follows:

\(\sqrt[4]{2^7} = 2\sqrt[4]{2^3} = 2\sqrt[4]{8}\)

Then the simplified expression is going to have the following format:

\(\sqrt[4]{2^7 \times 3^3} = 2\sqrt[4]{8 \times 3^3}\)

As 3³ = 27, the expression is written as follows:

\(2\sqrt[4]{8 \times 3^3} = 2\sqrt[4]{8 \times 27}\)

The product of 8 and 27 is of 8 x 27 = 216, hence the expression is given as follows:

\(2\sqrt[4][216]\)

The coefficient a is the outer term of the expression, hence it's value is given as follows:

a = 2.

The coefficient b is the radicand of the expression, hence it's value is given as follows:

b = 216.

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=========================================================

Explanation:

Points Q and R have the same y coordinate of 6.

This means they're on the same horizontal level and we can form a number line through these points. Think of Q and R being on the x axis.

Going from -4 to 8 is a distance of 12 units because either

-4-8 = -12 which flips to +12 or 12

8-(-4) = 8+4 = 12

Effectively I used absolute value for the first part to go from -12 to 12. Distance cannot be negative.

Alternatively, you can count out the number of horizontal spaces from -4 to 8 and you should count out 12 units.

--------------------------------

If you need to use the distance formula, then this is what the steps may look like:

\(Q = (x_1,y_1) = (-4,6) \text{ and } R = (x_2, y_2) = (8,6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-4-8)^2 + (6-6)^2}\\\\d = \sqrt{(-12)^2 + (0)^2}\\\\d = \sqrt{144 + 0}\\\\d = \sqrt{144}\\\\d = 12\\\\\)

In my opinion, the distance formula is overkill because we can simply apply subtraction or count out the number of spaces. It's up to you which you prefer you like better. Of course be sure to follow all instructions your teacher mentions.

If the two points weren't on the same horizontal level, then we would have no choice and have to use the distance formula. Or you could use the pythagorean theorem which is effectively what the distance formula is derived from.

a) The probability that the bank is empty is approximately 0.0026.

b) the average time the customer spends waiting to be called is approximately -0.25 c) hours the average number of customers in the bank is -1.5 d) the average number of customers waiting to be served is approximately 9.

To answer these questions, we can use the M/M/4 queuing model, where the arrival rate follows a Poisson distribution and the service time follows an exponential distribution. In this case, we have four bank tellers, so the system is an M/M/4 queuing model.

Given information:

Arrival rate (λ) = 12 customers per hour

Service rate (μ) = 1 customer every 15 minutes (or 4 customers per hour)

(a) To calculate the probability that the bank is empty, we need to find the probability of having zero customers in the system. In an M/M/4 queuing model, the probability of having zero customers is given by:

P = (1 - ρ) / (1 + 4ρ + 10ρ² + 20ρ³)

where ρ is the traffic intensity, calculated as ρ = λ / (4 * μ).

ρ = (12 customers/hour) / (4 customers/hour/teller) = 3

Substituting ρ = 3 into the formula, we have:

P = (1 - 3) / (1 + 4 * 3 + 10 * 3² + 20 * 3³) ≈ 0.0026

Therefore, the probability that the bank is empty is approximately 0.0026.

(b) The average time the customer spends waiting to be called is given by Little's Law, which states that the average number of customers in the system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In this case, we want to find W.

L = λ * W

W = L / λ

Since the average number of customers in the system (L) is given by L = ρ / (1 - ρ), we can substitute this into the equation to find W:

W = L / λ = (ρ / (1 - ρ)) / λ

W = (3 / (1 - 3)) / 12 ≈ -0.25

Therefore, the average time the customer spends waiting to be called is approximately -0.25 hours, which is not a meaningful result. It seems there might be an error in the given data.

(c) The average number of customers in the bank (L) can be calculated as:

L = ρ / (1 - ρ) = 3 / (1 - 3) = -1.5

Therefore, the average number of customers in the bank is -1.5, which is not a meaningful result. It further suggests an error in the given data.

(d) The average number of customers waiting to be served can be calculated as:

\(L_q\) = (ρ² / (1 - ρ)) * (4 - ρ)

Substituting ρ = 3, we have:

\(L_q\\\) = (3² / (1 - 3)) * (4 - 3) ≈ 9

Therefore, the average number of customers waiting to be served is approximately 9.

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Step-by-step explanation:

Given the conditions:

1. ∠HGJ ≅ ∠JFH (Given)

2. GH ≅ FJ (Given)

3. FH ≅ GJ (Given)

Wherein,

1. ∠HGJ and ∠JFH are right angles, proving they are congruent (∠HGJ ≅ ∠JFH) by the definition of perpendicular lines (lines GH and JH are perpendicular, as are lines FJ and JH).

2. Lines GH and FJ are congruent (GH ≅ FJ) given as a condition.

3. Lines FH and GJ are also congruent (FH ≅ GJ), as provided.

On comparing these conditions with the postulates of triangle congruence, the given conditions align with the Hypotenuse-Leg (HL) Congruence Postulate, confirming that triangle GJH is congruent to triangle FHJ. This is because the HL postulate states that "If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent."

In this case:

- The hypotenuses FH and GJ are congruent.

- One set of legs, GH and FJ are also congruent.

- And both triangles have a right angle.

Thus, the proof demonstrates that triangle GJH is congruent to triangle FHJ by the Hypotenuse-Leg Congruence Postulate (HL).

The distance between two opposite corners of the floor is 9.4 meters. The result is obtained by using Pythagorean theorem.

A diagonal is a straight line that connects the opposite corners of a polygon.

The floor of a storage unit is 8.5 meters long and 4.1 meters wide.

Find the distance between two opposite corners of the floor!

We have

It means that the shape of the floor is a rectangle. See the illustration picture in the attachment! The distance between two opposite corners is called diagonal.

We can determine the diagonal length by using Pythagorean theorem.

a² + b² = c²

c is the longest side of a triangle.

In this case, c is the diagonal of the rectangle. So,

8.5² + 4.1² = c²

72.25 + 16.81 = c²

c² = 89.06

c = 9.437

c ≈ 9.4 m

Hence, the diagonal length of the rectangle floor is 9.4 meters.

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Answer:

16 oz, 15.3 oz, 9oz

Step-by-step explanation:

these are the highest to lowest in price write in the form of oz.

Answer:

-300

Step-by-step explanation:

Answer: The answer is D. Since all values have the same denominator, simply arrange them by least to greatest by referring to the numerator.

Answer:

Step-by-step explanation:   since there are 9s on all of the bottom it would be 1/9 ,4/9, 5/9, 8/9

The absolute maximum value is at x = 4. The absolute minimum value is at x = 5.

Given function is f(x) = x² - 10x - 9 and the interval is [4, 7].

Here, f(x) is a quadratic function which means that the graph of the function is a parabola. For finding the absolute maximum and minimum values of the function, we have to check the critical points, that is where f'(x) = 0 and the endpoints of the interval which is given, that is 4 and 7 respectively.

Calculating the first derivative of the given function, we get:

f(x) = x² - 10x - 9f'(x) = 2x - 10

Critical point : f'(x) = 0 => 2x - 10 = 0=> x = 5

When x = 5, f(x) = f(5) = 16 - 50 - 9 = -43.

The critical point x = 5 doesn't fall in the interval [4, 7].

Hence, we need to calculate the values of the function at endpoints of the interval i.e. at x = 4 and x = 7.

When x = 4,f(x) = f(4) = 16 - 40 - 9 = -33

When x = 7,f(x) = f(7) = 49 - 70 - 9 = -30

From the above values, it is clear that the absolute maximum value is at x = 4 and the absolute minimum value is at x = 5.

Hence, the answer is as follows: The absolute maximum value is at x = 4. The absolute minimum value is at x = 5.

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Answer:

68°

Step-by-step explanation:

Equations:

To solve for y we have to use the sine rule which is defined as:

\(\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}\)

Side a is opposite from angle A, side b is opposite from side B, etc.

Solving for y:

Let's say angle A was the angle we are trying to find. Then we can re-write the sine rule as:

\(\frac{sin(y)}{250} =\frac{sin(48)}{200}\)

Let's re-arrange this for the angle y:

\(sin(y)=250 * \frac{sin(48)}{200} \\y=sin^-1(250 * \frac{sin48}{200} )\)

Typing this into a calculator gives the answer: \(y = 68.26...\) which is 68 degrees rounded to the nearest whole degree.