(b) If the lines y=x+1 and x+2y=8 intersect at R, find the coordinates of R.
(c) Hence, calculate the area of △PQR.

This is the expression for ∂z/∂u using the Chain Rule.

To find ∂z/∂u using the Chain Rule, we first need to find the partial derivative of z with respect to r and θ.
∂z/∂r = e^(r cos θ) cos θ
∂z/∂θ = -e^(r cos θ) r sin θ
Next, we can use the Chain Rule to find ∂z/∂u:
∂z/∂u = (∂z/∂r) * (∂r/∂u) + (∂z/∂θ) * (∂θ/∂u)
We know that r= 6 uv and θ = √(u^2+v^2 ), so we can substitute those values in:
∂z/∂u = (e^(r cos θ) cos θ) * (6v) + (-e^(r cos θ) r sin θ) * (u/√(u^2+v^2 ))
Simplifying this expression, we get:
∂z/∂u = 6ve^(6uv cos(√(u^2+v^2 )))cos(√(u^2+v^2 )) - (u/√(u^2+v^2 ))e^(6uv cos(√(u^2+v^2 )))r sin(√(u^2+v^2 ))
We have z = e^(r cos θ), r = 6uv, and θ = √(u^2 + v^2). We need to find ∂z/∂u.
Using the Chain Rule, we get:
∂z/∂u = (∂z/∂r)(∂r/∂u) + (∂z/∂θ)(∂θ/∂u)
First, let's find the partial derivatives of z:
∂z/∂r = e^(r cos θ) cos θ
∂z/∂θ = -e^(r cos θ) r sin θ
Now, find the partial derivatives of r and θ with respect to u:
∂r/∂u = 6v
∂θ/∂u = u / √(u^2 + v^2)
Now, substitute these partial derivatives back into the Chain Rule formula:
∂z/∂u = (e^(r cos θ) cos θ)(6v) + (-e^(r cos θ) r sin θ)(u / √(u^2 + v^2))
This is the expression for ∂z/∂u using the Chain Rule.

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Answer:

4,234 dekaliters converted to milliliters is 42340000.

Step-by-step explanation:

Answer: Your answer is going to be 42340000 millimeters.

Step-by-step explanation:

Find out how much one dekaliter is worth; multiply by that amount.

The answer is that \($\bar{X}-\bar{Y}$\) is normal with mean 0 and standard deviation \($5 / 9$\). None of the given options match this result exactly, but the closest one is "normal with mean 0 and standard deviation \($5 / 6^{\prime \prime}$\).

The mean of \($\bar{X}$\) and \($\bar{Y}$\) are:

\(E(\bar{X})=E\left(\frac{1}{16} \sum_{i=1}^{16} X_i\right)=\frac{1}{16} \sum_{i=1}^{16} E\left(X_i\right)=\frac{1}{16}(16 \times 15)=15\)

and

\($$E(\bar{Y})=E\left(\frac{1}{9} \sum_{i=1}^9 Y_i\right)=\frac{1}{9} \sum_{i=1}^9 E\left(Y_i\right)=\frac{1}{9}(9 \times 15)=15$$\)

The variance of \($\bar{X}$\) and \($\bar{Y}$\) are:

\($$\{Var}(\bar{X})=\{Var}\left(\frac{1}{16} \sum_{i=1}^{16} X_i\right)=\frac{1}{16^2} \sum_{i=1}^{16} \{Var}\left(X_i\right)=\frac{1}{16^2}(16 \times 4)=\frac{1}{4}$$\)

and

\($$\{Var}(\bar{Y})=\{Var}\left(\frac{1}{9} \sum_{i=1}^9 Y_i\right)=\frac{1}{9^2} \sum_{i=1}^9 \{Var}\left(Y_i\right)=\frac{1}{9^2}(9 \times 4)=\frac{4}{81}$$\)

Now, we have:

\(E(\bar{X}-\bar{Y})=E(\bar{X})-E(\bar{Y})=0\)

and

\(\{Var}(\bar{X}-\bar{Y})=\{Var}(\bar{X})+\{Var}(\bar{Y})=\frac{1}{4}+\frac{4}{81}=\frac{25}{81}\)

Therefore, \($\bar{X}-\bar{Y}$\) follows a normal distribution with a mean 0 and a standard deviation:

\($$\sqrt{{Var}(\bar{X}-\bar{Y})}=\sqrt{\frac{25}{81}}=\frac{5}{9}$$\)

So, the answer is that \($\bar{X}-\bar{Y}$\) is normal with mean 0 and standard deviation \($5 / 9$\). None of the given options match this result exactly, but the closest one is "normal with a mean 0 and standard deviation \($5 / 6^{\prime \prime}$\).

Definition: To distribute a product is to make it available to a wide audience so that they can purchase it. These actions are involved in distribution: 1. A reliable transportation system to deliver the commodities to various locations.

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Answer:

sure

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The number of cubes used in the third, fourth, and fifth figures of the pattern are 17 cubes, 21 cubes, and 25 cubes, respectively.

The recursive function f(n + 1) = f(n) + 4 states that each subsequent figure in the pattern will have 4 more cubes than the previous figure.

To determine the number of cubes in each figure, we start with the given values and add 4 to each subsequent figure.

In Figure 1, there are 9 cubes. Adding 4 cubes, we get Figure 2 with 13 cubes. Continuing this pattern, we add 4 cubes to each subsequent figure.

Figure 3: Figure 2 + 4 = 13 + 4 = 17 cubes
Figure 4: Figure 3 + 4 = 17 + 4 = 21 cubes
Figure 5: Figure 4 + 4 = 21 + 4 = 25 cubes

Therefore, the number of cubes used in the third, fourth, and fifth figures of the pattern are 17 cubes, 21 cubes, and 25 cubes, respectively.

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QUESTION - Luis uses cubes to represent each term of a pattern based on a recursive function. The recursive function defined is f(n + 1) = f(n) + 4, where n is an integer and n ≥ 2. The number of cubes used in each of the first two figures is shown below. How many cubes does Luis use in the third, fourth, and fifth figures of the pattern? Fill in the blanks.
Figure 1: 9 cubes
Figure 2: 13 cubes
Figure 3:
Figure 4:
Figure 5:

Answer:

If it's not what You are looking for type in the equation solver your own ... is 12 percent of 912.6 - step by step solution || 2x-9=2x-9 || 2(x-3)=4(x+2) ...

Step-by-step explanation:

sorry if im wrong

Answer:

c, 4/3

Step-by-step explanation:

you need to isplate y so subtract 5 from both sides then divide both sides by 3, the coefficient of x is now 4/3 and x coefficient is the slope

There are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

In this problem, we want to find the number of ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

Since every man must be diametrically opposite a woman, we can pair each man with one woman. There are 5 men and 9 women, so there are 5 pairs. We need to find the number of ways to seat these 5 pairs of people in a circle.

To do this, we can first seat one pair in any position. Then, we can seat the second pair anywhere but opposite the first pair. This gives us 11 positions for the second pair. Continuing in this way, we see that there are 11 * 6 * 5 * 4 * 3 = 7920 ways to seat the 5 pairs of people in a circle.

So, there are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

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Assuming 14 people, 5 men and 9 women, how many ways can they sit in a circle such that every man is diametrically opposite a woman?

Answer:

x=3

Step-by-step explanation:

substitute into the equation

Answer:

x = 3

Step-by-step explanation:

x = -b/2a  for a = 1 & b = -6

x = 6/2

x = 3

Answer:2 45833333333/50000000000

The number of seats in the front row of the theater is a = [2y/(n(n-1)) - x/(n-1)]/2

Let's call the number of seats in the first row "a". We can use the information given in the problem to set up an equation in terms of "n", "d", "x", and "y"

y = a + (a + d) + (a + 2d) + ... + (a + (n-1)d) (1)

We can simplify this equation by using the formula for the sum of an arithmetic series

y = [n/2][2a + (n-1)d] (2)

We can solve this equation for "a" in terms of "n", "d", and "x"

2a = (2y/n) - (n-1)d - 2xd

a = [(2y/n) - (n-1)d - 2xd]/2

Since we know that the number of seats in the last row is "x", we can substitute that into the equation

x = a + (n-1)d

x = [(2y/n) - (n-1)d - 2xd]/2 + (n-1)d

Simplifying this equation gives us

2x = (2y/n) + (n-1)d

2d = (2x - (2y/n))/(n-1)

Now we can substitute this value of "d" into the equation we found for "a"

a = [(2y/n) - (n-1)d - 2xd]/2

a = [(2y/n) - x - (2x - (2y/n))/(n-1)]/2

a = [2y/(n(n-1)) - x/(n-1)]/2

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Answer:

1/3

Because 1/3 if divide into two, it'll be 0.5/3 but if the question says that the answer have to be in whole number, that means it must be 1/6.

Answer:12

Step-by-step explanation:

because it will take 2 to make a cup

The taxicab distance formula between two points (x1, y1) and (x2, y2) is expressed as

distance = Ix1 - x2I + Iy1 - y2I

From the information given,

x1 = 7, y1 = 5

x2 = 8, y2 = 6

Distance = I7 - 8I + I5 - 6)

Distance = I- 1I + I- 1I = 1 + 1

Distance = 2

If the null hypothesis was true, the probability or percentage of obtaining the sample evidence that one has is typically referred to as the p-value.

The p-value is a statistical measure that quantifies the strength of evidence against the null hypothesis based on the observed data. To understand the concept of the p-value, let's consider a hypothesis testing scenario. In hypothesis testing, we start with a null hypothesis (H₀) that represents the default assumption or belief. The alternative hypothesis (H₁) contradicts or challenges the null hypothesis. The goal is to assess the evidence in favor of or against the null hypothesis using sample data.

The p-value is calculated by determining the probability of obtaining a test statistic as extreme as or more extreme than the one observed, assuming the null hypothesis is true. If the p-value is small (below a predetermined significance level, often denoted as α), it suggests that the observed data is unlikely to occur by chance if the null hypothesis is true. In this case, we reject the null hypothesis in favor of the alternative hypothesis.

However, if the p-value is large (greater than or equal to α), it suggests that the observed data is reasonably likely to occur by chance even if the null hypothesis is true. In this case, we fail to reject the null hypothesis and do not find strong evidence against it. It's important to note that the p-value does not directly measure the probability that the null hypothesis is true or false. Instead, it quantifies the probability of obtaining the observed data or more extreme data if the null hypothesis is true.

In summary, if the null hypothesis is true, the p-value represents the probability of obtaining the sample evidence or more extreme evidence that one has. A small p-value indicates strong evidence against the null hypothesis, while a large p-value suggests that the observed data is reasonably likely to occur by chance even if the null hypothesis is true.

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Answer:

(5s + 8) is the missing factor.

Step-by-step explanation:

The given expression is 5s² + 23s + 24

We have to convert the given expression into the factored form.

One factor of the expression has been given as (x + 3)

5s² + 23s + 24 = 5s²+ 15s + 8s + 24

                        = 5s(s + 3) + 8(s + 3)

                        = (5s + 8)(s + 3)

So the factors of the expression will be (s + 3) and (5s + 8)

Therefore, the missing factor of the given expression is (5s + 8).

The first and third rectangular prisms have the same volume of 30 cubic units.

The second rectangular prism has a volume of 350 cubic units, and the fourth rectangular prism has a volume of 24 cubic units.

The volume of each of the rectangular prisms can be calculated as follows:

1.   length: 1; width: 10; height: 3

volume = 1 x 10 x 3 = 30

2.  length: 5; width: 10; height: 7

volume = 5 x 10 x 7 = 350

3.   length: 2; width: 5; height: 3

volume = 2 x 5 x 3 = 30

4.   length: 4; width: 2; height: 3

volume = 4 x 2 x 3 = 24

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Answer:

Step-by-step explanation:True, the product of any five consecutive integers is divisible by 120. We can prove this statement using a direct proof rather than a proof by contradiction.

Let's consider five consecutive integers: n, n+1, n+2, n+3, and n+4.

We know that 120 is divisible by 2, 3, 4, 5, and 6. So, we need to show that the product of these consecutive integers is divisible by each of these numbers.

Divisible by 2: Among these five consecutive integers, there will always be at least one even number. Hence, the product will be divisible by 2.

Divisible by 3: If we sum up the five consecutive integers (n + n+1 + n+2 + n+3 + n+4), we get a multiple of 5. So, the product is divisible by 5, and one of the consecutive integers will be divisible by 3, making the product divisible by 3.

Divisible by 4: If we consider the last two digits of any five consecutive integers, we can observe that there will always be at least two even numbers. Thus, the product is divisible by 4.

Divisible by 5: As mentioned earlier, the sum of the five consecutive integers is a multiple of 5. Therefore, the product is divisible by 5.

Divisible by 6: Since the product is divisible by 2 and 3 (as shown above), it is also divisible by 6.

By satisfying the divisibility conditions for 2, 3, 4, 5, and 6, we can conclude that the product of any five consecutive integers is divisible by 120.

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Is "perimeter". The perimeter is the sum of all the sides of a two-dimensional figure. For example, if you have a rectangle with sides of length 3 and 5, then the perimeter would be 3+3+5+5 = 16.

In explanation, the perimeter is an important measure of a two-dimensional figure because it gives us an idea of how much boundary or fence we would need if we were to enclose the figure. Additionally, the perimeter can be used to calculate other properties of a figure such as its area or volume.

the perimeter is an essential concept in geometry that helps us measure the boundaries of two-dimensional figures.


Perimeter refers to the total length of the sides or edges of a two-dimensional shape. To calculate the perimeter, you simply add the lengths of all the sides of the figure.

Conclusion: In summary, the term you are looking for is "perimeter," which represents the total length of the sides of a two-dimensional figure.

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Answer:

m<E = \(77^{o}\)

Step-by-step explanation:

From the diagram, ΔACE and ΔBDE are similar. So that comparing its angles, we have;

(8x + 4) = (9x - 5)

8x + 4 = 9x - 5

5 + 4 = 9x - 8x

x = 9

Thus,

(8x + 4) = 8(9) + 4 = 76

(9x - 5) = 9(9) - 5 = 76

3x = 3(9) = 27

From ΔACE,

3x + (8x + 4) + m<E = 180 (sum of angles in a triangle)

27 + 76 + m<E = 180

m<E = 180 - 103

m<E = \(77^{o}\)

A system of equation is 1680mi3hr = p−w×600×2hr -p + w  for a jet airliner travels 1680 miles in 3hours with a tail wind.

Let p be  the speed of the jet airliner

and w  be the speed of the tail wind

It takes the plane 3 hours to go 1680 miles when a jet airliner travels with a tail wind and and 3.5 hours to go 1680 miles against the wind.. So, using system of equations we get

1680mi3hr = p−w×600×2hr = p + w

Solving for the left sides we get:

200mph = p - w

300mph = p + w

Now solve for one variable in either equation, we use

200mph = p - w

Add w to both sides:

p = 200mph + w

Using the value of x, we can found the value of w using system of equations.

300mph = (200mph + w) + w

Combine like terms:

300mph = 200mph + 2w

Subtract 200mph on both sides:

100mph = 2w

On dividing by 2:

50mph = w

So the speed of the tail wind is 50mph.

Therefore, 200mph = p - 50mph

Add 50mph on both sides:

250mph = p

Hence, speed of jet airliner is 250mph.

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The problem can be solved by using the binomial distribution, since there are a fixed number of trials (300 students) and each trial (student) has two possible outcomes (asleep or not asleep) with a fixed probability (50%). The mean number of students asleep at the end of class is 150 and the variance is 75.

Let X be the number of students asleep at the end of class. Then X is a binomial random variable with parameters n = 300 (number of trials) and p = 0.5 (probability of success).The mean of a binomial distribution is given by:μ = npSo, the mean number of students asleep at the end of class is:μ = np = 300 × 0.5 = 150The variance of a binomial distribution is given by:σ² = np(1 - p)So, the variance of the number of students asleep at the end of class is:σ² = np(1 - p) = 300 × 0.5 × (1 - 0.5) = 75Therefore, the mean number of students asleep at the end of class is 150 and the variance is 75.

The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent trials, each with the same probability of success. The mean and variance of a binomial distribution are given by:μ = np and σ² = np(1 - p)where n is the number of trials, p is the probability of success, μ is the mean, and σ² is the variance.In this problem, we are given that 300 students are takings introductory physic from a boring professor, and each student has a 50% chance of falling asleep at some point during lecture and staying asleep until the end of class. We want to find the mean and variance of the number of students asleep at the end of class.Let X be the number of students asleep at the end of class. Then X is a binomial random variable with parameters n = 300 and p = 0.5. The probability mass function of X is given by:P(X = k) = (300 choose k)(0.5)^k(0.5)^(300-k)where (300 choose k) is the binomial coefficient, which is the number of ways to choose k items from a set of 300 items. We can use this probability mass function to find the mean and variance of X.The mean of a binomial distribution is given by:μ = npSo, the mean number of students asleep at the end of class is:μ = np = 300 × 0.5 = 150The variance of a binomial distribution is given by:σ² = np(1 - p)So, the variance of the number of students asleep at the end of class is:σ² = np(1 - p) = 300 × 0.5 × (1 - 0.5) = 75Therefore, the mean number of students asleep at the end of class is 150 and the variance is 75.

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The algebraic expression that represents the given sentence is:

8 (x + 5).

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. The values a expressed in an unknown number using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression.

In mathematics, a number that is obtained by multiplying two or more distinct variables together is referred to as the product.

Let us suppose the "a number", as x.

The sum of a number and 5 is represented as follows:

(x + 5)

The product of 8 and sum of a number and 5 is represented as follows:

8 (x + 5)

Hence, the algebraic expression that represents the given sentence is:

8 (x + 5)

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I can help you with that problem i just did that on my own.

The answer is b, my teacher explained it to me on a test. Don't know if he's right because he was a substitute.

The equation of the sinusoidal function is y = -2sin(x + 1.5) - 3 and the Amplitude  is A = -2 and the period is 2π

A sine wave, sinusoidal wave, or simply sinusoid refers to a symmetric wave reflecting one complete cycle of a single-frequency oscillation; mass movement over time defined by a trigonometric function, the sine.

The sinusoidal function

The minimum and the maximum of the function are

Minimum = -1

Maximum = -5

The amplitude (A) is calculated as:

A = 0.5 * (Maximum - Minimum)

So, we have:

A = 0.5 * (-5 + 1)

A = -2

The vertical shift (d) is calculated as:

d = 0.5 * (Maximum + Minimum)

So, we have:

d = 0.5 * (-5 - 1)

d = -3

The period (P) is calculated as:

P = 2π/B

From the graph,

B = 1

So, we have:

P = 2π/1

P = 2π

So, the amplitude is -2 and the period is 2π.

The equation of the sine function

In (a), we have:

A = -2

B = 1

d = -3

A sine function is represented as:

y = A sin(Bx + C) + D

So, we have:

y = -2sin(x + C) - 3

The graph passes through the point (0, -5)

So, we have

-5 = -2sin(0 + C) - 3

Solve for C, we have

C = 1.5

So, we have:

y = -2sin(x + 1.5) - 3

Hence, the equation of the sinusoidal function is y = -2sin(x + 1.5) - 3

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Answer:

Step-by-step explanation: