A= l . w
x is 3 and y is 7
(xy+1) (xy-1) ​

The largest factor of the sum of y and z is 24.

The replacement approach has the advantage of providing the precise values for the variables (x and y), which correspond to the site of intersection.

When using the "by substitution" method, you must first solve one of the equations provided (you must choose which one) for one of the variables (you must choose which one), after which you must plug this value back into the other equation provided (you must "substitute" for the chosen variable and solve for the other value). The first equation is then used to back-solve for the first variable. The many procedures required in using the replacement approach to solve problems have been described in full above. Use those to discover the solution to a given system of linear equations.

We are given with three equations having three unknowns:

x = z/4

x + y + z = 26

y = 2z

Using the method of substitution, we can now solve for each of the three unknowns.

Since the first equation, x = z/4, is an equation for x in terms of z, and the third equation, y = 2z, is an equation for y in terms of z, we can replace x and y in the second equation by their equivalent expressions as follows:

x + y + z = (z/4) + (2z) + z = 26

We are left with an equation with just one unknown z. We can now solve for z:

(z/4) + (2z) + z = 26

z/4 + 8z/4 + 4z/4 = 13z/4 = 26

z/4 = 2

z = 8

Now that we know z, we can easily solve for y, then compute y + z (note: we can also solve for x, but since we are not interested in the value of x there is no need to do so):

y = 2z = 2(8) = 16

y + z = 16 + 8 = 24

Since the largest factor of any number is the number itself, the largest factor of the sum of y and z is 24.

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(a) Yes, the air in the house would exceed the long-term health standard if the groundwater is in equilibrium with the air in the house.

(b) The budget equation for TCE is dct/dt = k(c+ - CT) - Q(ca - CT).

(c) The characteristic time t for TCE to build up in the house from zero to unhealthful (long-term exposure) if there is no ventilation is given by t = Ahk/Q. For the given values, t = 1.4 years. A large value of t indicates a significant TCE problem.

(d) The minimum value of Q to keep CT below 20 ppm is 160 cfm. This is more than the residential requirement of 40 cfm.

(a) The Henry's Law constant for TCE is 0.4, which means that the concentration of TCE in air at equilibrium with water is 40% of the concentration in water. The groundwater concentration is 110 ppm, so the equilibrium air concentration would be 44 ppm. This exceeds the long-term health standard of 25 ppm.

(b) The flux of TCE through the floor is given by FT = k(c+ - CT), where k is a measured constant, c+ is the concentration of TCE in the groundwater, and CT is the concentration of TCE in the air in the house. The normal strategy for remediating vapor intrusion is to install fans in the house that ventilate the house with outside air. The outside ambient air has a concentration of ca. The budget equation for TCE is dct/dt = k(c+ - CT) - Q(ca - CT), where dct/dt is the rate of change of the concentration of TCE in the house, k is the flux constant, c+ is the concentration of TCE in the groundwater, CT is the concentration of TCE in the air in the house, Q is the ventilation rate, and ca is the concentration of TCE in the outside air.

(c) The characteristic time t for TCE to build up in the house from zero to unhealthful (long-term exposure) if there is no ventilation is given by t = Ahk/Q, where Ah is the area of the house, k is the flux constant, and Q is the ventilation rate. For the given values, t = 1.4 years. A large value of t indicates a significant TCE problem.

(d) The minimum value of Q to keep CT below 20 ppm is 160 cfm. This is more than the residential requirement of 40 cfm. The difference is due to the fact that the groundwater concentration is much higher than the ambient air concentration.

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Answer:

y=(7/5)x + 34/5

Step-by-step explanation:

All straight lines generally follow the equation format of: y=mx+c

Where m is the slope/gradient of the line, and c is a constant, the y-intercept, the y value when x=0.

To start, we need to find the slope, which we do by dividing the rise of the line by the run, that is the difference between the y value of two points divided by the different between the x value of two points.

We can use the two given points on the graph: (-7,-3) and (-2,4).

The rise is 7 because 4-(-3)=7, and the run is 5 because -2-(-7)=5.

Therefore the slope is 7/5.

so our equation so far is:

y=(7/5)x + c, (It is positive because the line is 'going upwards'.)

Now to find the c, we can just substitute in a pair of coordinates, we can use (-2,4):

4= (7/5)(-2) + c

4 = -14/5 + c

4 + 14/5 = c

c= 34/5

Therefore our full equation is:

y=(7/5)x + 34/5

Hope this helped!

Answer:

I think the answer is d

Step-by-step explanation:

Answer:

It shows you are giving us 18 points not 30 :(

The function of differentiable parameterization of arc length 2 in space is ∫√(1)² + (2t)² + (cos(t))² dt.

To set up a differentiable parameterization of arc-length 2 in space, we can use the arc-length formula:

s = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt

where s is the arc length, t is the parameter, and (x, y, z) is the position vector.

We want the arc length to be 2, so we can set up the following equation:

2 = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt

We can then choose a function for each component of the position vector, such as:

x = t

y = t²

z = sin(t)

We can now find the derivatives with respect to t:

dx/dt = 1

dy/dt = 2t

dz/dt = cos(t)

We can substitute these into the arc-length formula:

2 = ∫√(1)² + (2t)² + (cos(t))² dt

Solving this integral for t will give us the desired parameterization of arc-length 2 in space. However, this integral may not have a closed-form solution, so numerical methods may need to be used to approximate the solution.

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The question is -

Differentiable parameterization of arc-length 2 in space ( not in a plane) how would you set up the function?

An example of a geometric formula that contains pi(π) is the formula for the circumference of a circle, which is

C = 2πr. This formula is used to calculate the distance around a circle.

A geometric formula is a mathematical equation that describes a relationship between geometric figures or their properties.

Geometric formulas are used to calculate the area, perimeter, volume, surface area, and other properties of shapes such as circles, triangles, rectangles, spheres, cubes, and cylinders. For example, the formula for the area of a triangle is

A = 1/2 b×h, where b is the base of the triangle and h is its height.

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A slow-moving barge moves through the sea at a speed of 4 km/h. It travels 8 miles upstream in the same amount of time as a barge traveling 24 miles downstream with the current. The current moves at a 2 km/h rate.

Let’s start by using the formula for distance, rate, and time:

Distance = rate x time

Let’s assume that the rate of the current is r km per hour.

Going upstream (against the current), the effective rate of the barge is:

4 – r km per hour

Going downstream (with the current), the effective rate of the barge is:

4 + r km per hour

We are told that the time it takes the barge to travel 8 miles upstream is the same as the time it takes to travel 24 miles downstream. Using the formula, we can set up the following equation:

8 / (4 – r) = 24 / (4 + r)

We can simplify this equation by cross-multiplying:

8(4 + r) = 24(4 – r)

Expanding and simplifying, we get:

32 + 8r = 96 – 24r

Adding 24r and subtracting 32 from both sides, we get:

32r = 64

Dividing both sides by 32, we get:

R = 2

Therefore, the rate of the current is 2 km per hour.

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56 employees chose purple as their favorite color choice for sales tags.

The circle graph is a visual representation of the data, where each sector's angle is proportional to the percentage of the total number of employees who chose that color. This graph is an effective way to communicate complex data quickly and easily.

From the circle graph, we can see that the sector for purple covers 20% of the total circle, which represents the percentage of employees who chose purple as their favorite color choice for sales tags. To find the actual number of employees who chose purple, we need to calculate 20% of the total number of employees surveyed.

20% of 280 is equal to (20/100) x 280 = 56.

Therefore, 56 employees chose purple as their favorite color choice for sales tags.

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The width of each class interval from the given grouped frequency distribution table is 9.

In a frequency distribution, the numerical width of a class is referred to as the class interval. Data is organised into classes in a grouped frequency distribution. The class interval is determined by the difference between the upper and lower class limits.

The give class intervals are 20-29, 30-39, 40-49 and 50-59.

The size, or width, of a class interval is the difference between the lower and upper class boundaries and is also referred to as the class width, class size, or class length.

So, class width = Upper class - Lower class

29-20=9

39-30=9

Therefore, the width of each class interval is 9.

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The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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To make the points in the scatterplot easier to find, the geom jitter() function method first builds a scatterplot and then adds a little amount of random noise to each point in the plot.

A scatterplot is produced using the ggplot2 function in R called geom jitter(). Each point in the plot receives a small bit of random noise to make them simpler to locate. The link between two variables in a dataset is visualised using this function.

The geom jitter() function can help to make data points easier to differentiate in a scatterplot by adding a small amount of random noise to each point. This is particularly useful when there is a lot of overlap between data points in the plot. The amount of jitter can be adjusted to ensure that the data points are still distinguishable, while still providing a more accurate representation of the data. Additionally, it can be used to adjust the size, color, and shape of the data points, allowing for a more customized visualization.

# Example of geom_jitter()

# Load ggplot2

library(ggplot2)

# Create data

x <- c(1,2,3,4,5,6,7,8,9,10)

y <- c(4,5,6,7,8,9,10,11,12,13)

# Plot data

ggplot(data = data.frame(x,y), aes(x, y)) +

geom_jitter()

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Answer:

I don't know the answer for sure, if you maybe sent a picture? But I think it's 150 feet...

Step-by-step explanation:

Answer:

x+3= 2x when x = 3

3+3 = 2*3

6= 6

They are not equal when x is any other number rather than 3

Answer:

Step-by-step explanation:

n + 1 = 4(n - 8)

n + 1 = 4n - 32      [Multiply 4 times (n-8)]

1 = 3n - 32           [Subtract 1n from both sides]

33 = 3n               [Add 32 to both sides]

3n = 33

CHECK:

Does n + 1 = 4(n - 8) when n = 11?

n + 1 = 4(n - 8)

11 + 1 = 4(11 - 8)

11 + 1 = 4(3)

12 = 12   YES

Answer:

7/21=3/9 is the proportion of 7:21=3:9

Answer:

$1560

Step-by-step explanation:

x = salary

y = weekly

255 = 1/12 x + 125

3060 = x + 1500

x = 1560

The equivalent expression of 5\(x^{3/2}\) is  5√(x³). The correct option is last one.

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given:

An expression,

5\(x^{3/2}\)

To find the equivalent expression:

We have to simplify the expression,

5\(x^{3.1/2}\)

= 5(x³)\(){1/2}\)

= 5√(x³)

The above expression is an equivalent expression.

Therefore, 5√(x³) is an equivalent expression.

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All four interior angles of a square are 90°

Therefore,

The measure of ∠VWT will be

Hence,

∠VWT = 90°

Step2:measure the angle CWV

Sum of angles in a triangle is

Therefore,

Hence,

∠ CWV = 45°

Since the perimeter of the square WVJT

Then

All sides of a square are equal, therefore,

Hence, we will have that

Using the Pythagoras theorem,we will have

Therefore,

Length CW = 3

The perimeter of CBAZ IS

Recall, that all sides of a square are equal,

Hence,

Therefore, perimeter of CBAZ will be

Hence,

Perimeter of CBAZ =24

The probability value become is 2c/(N-1).

According to the statement

we have given that If P and Q are both neighbors of R, and by considering unstructured network in which each node randomly chooses c neighbors.

we have to find that the probability of neighbors that they are also neighbors of each other.

So, For this purpose to find the probability is

Consider a network of N nodes unstructured and let

If each node chooses c neighbors at random,

then the probability that P will become by choose Q, or Q chooses P is roughly 2c/(N-1).

And the probability outcomes value become is 2c/(N-1).

So, The probability value become is 2c/(N-1).

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The sample may not be perfectly representative of the entire U.S. population, and any differences observed between men and women in the sample may not necessarily reflect gender differences in the population as a whole.

Random sample of U.S. residents, while the comparison of responses between men and women is a comparison of subgroups within the sample.

By using a random sample of U.S. residents, the study aims to obtain a representative sample of the population's opinions on stem cell research. This is important because it allows the study to draw conclusions about the opinions of the entire population rather than just a specific group of people.

Comparing the responses of men and women within the sample can provide insights into any gender differences in opinions about stem cell research. However, it is important to note that the sample may not be perfectly representative of the entire U.S. population, and any differences observed between men and women in the sample may not necessarily reflect gender differences in the population as a whole.

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Answer:

5^8/5^6 = 5^(8-6) = 5^2 = 25. Therefore, 5^8/5^6 simplified to a single power of 5 is 25.

Step-by-step explanation:

Answer:

the answer for that is 5^6-3 = 5^3 = 125

Step-by-step explanation:

Answer:

\(12\sqrt{30}\)

Step-by-step explanation:

Given:

\(\sqrt{45} \times \sqrt{96}\)

Rewrite 45 as 9 · 5 and 96 as 16 · 6:

\(\implies \sqrt{9 \cdot 5} \times \sqrt{16 \cdot 6}\)

\(\textsf{Apply radical rule} \quad \sqrt{a \cdot b}=\sqrt{a}\sqrt{b}:\)

\(\implies \sqrt{9}\sqrt{5} \times \sqrt{16}\sqrt{6}\)

Rewrite 9 as 3² and 16 as 4²:

\(\implies \sqrt{3^2}\sqrt{5} \times \sqrt{4^2}\sqrt{6}\)

\(\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0\)

\(\implies 3\sqrt{5} \times 4\sqrt{6}\)

Multiply 3 and 4:

\(\implies 12\sqrt{5}\sqrt{6}\)

\(\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{b}=\sqrt{a \cdot b}\)

\(\implies 12\sqrt{5 \cdot 6}\)

Multiply 5 and 6:

\(\implies 12\sqrt{30}\)

\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

Let's get it done ~

\(\qquad \sf  \dashrightarrow \: \sqrt{45} \times \sqrt{96} \)

\(\qquad \sf  \dashrightarrow \: \sqrt{ {3}^{2} \times 5 } \times \sqrt{2 {}^{4} \times 2 \times 3} \)

\(\qquad \sf  \dashrightarrow \: 3 \sqrt{5} \times 2 {}^{2} \sqrt{6} \)

\(\qquad \sf  \dashrightarrow \: 3 \sqrt{5} \times 4\sqrt{6} \)

\(\qquad \sf  \dashrightarrow \: 12 \sqrt{30} \)

well, let's move like the crab, backwards, let's start with b), then we'll do a)

b)

\({\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=2\\ y=75 \end{cases}\implies 75=ab^2 \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=5\\ y=9375 \end{cases}\implies 9375=ab^5\implies 9375=ab^{2+3}\implies 9375=ab^2 b^3\)

\(\stackrel{\textit{substituting from the 1st equation}}{9375=\underset{ab^2}{(75)} b^3}\implies \cfrac{9375}{75}=b^3\implies 125=b^3 \\\\\\ \sqrt[3]{125}=b\implies \boxed{5=b}\hspace{5em}\stackrel{\textit{we know that}}{75=ab^2}\implies 75=a5^2\implies 75=25a \\\\\\ \cfrac{75}{25}=a\implies \boxed{3=a}\hspace{5em} {\Large \begin{array}{llll} y = 3(5^x) \end{array}}\)

a)

\(\begin{cases} x=0\\ y=j \end{cases}\implies j=3(5^0)\implies j=3(1)\implies j=3 \\\\\\ \begin{cases} x=4\\ y=k \end{cases}\implies k=3(5^4)\implies k=3(625)\implies k=1875\)

Answer:

\(26.68\ \text{feet}\)

Step-by-step explanation:

a = 100 feet

\(\angle B=20^{\circ}\)

\(\angle C=45^{\circ}\)

\(\angle A=180-(20+45)=115^{\circ}\)

From sine rule we have

\(\dfrac{\sin B}{b}=\dfrac{\sin A}{a}\\\Rightarrow b=\dfrac{\sin B}{\sin A}a\\\Rightarrow b=\dfrac{\sin 20^{\circ}}{\sin 115^{\circ}}\times 100\\\Rightarrow b=37.73\ \text{feet}\)

\(\sin C=\dfrac{h}{b}\\\Rightarrow h=b\sin C\\\Rightarrow h=37.73\times \sin 45^{\circ}\\\Rightarrow h=26.68\ \text{feet}\)

The is seagull is \(26.68\ \text{feet}\) above the ground.

Answer: A) 1/2

Step-by-step explanation:

Answer:

If you flip a coin three times in the air, what is the probability that tails lands up all three times?

Step-by-step explanation:

1/2

Answer:

1 1/2 pizzas

Step-by-step explanation:

2 (pizzas) x 8/8 (8 full slices)

=16/8 - 4/8 (2 slices times two(2 from each pizza))

=12/8

=1 4/8 (12/8 = 1 remainder 4)

= 1 1/2 (simplify by dividing both parts by two)

Answer:

47,141

Step-by-step explanation:

I'm pretty sure that's right. Hope I helped <3

Answer:

Its this $47,141