Find the equation for the plane through the points P_0 (2,−5,−2),Q_0 (−1,1,3), and R_0 (−4,5,2). Using a coefficient of −13 for x, the equation of the plane is (Type an equation.)

Answer:

Linear algebra is flat differential geometry and serves in tangent spaces to manifolds.

Step-by-step explanation:

Linear algebra is the study of lines and planes, vector spaces and mappings that are required for linear transforms. It is a relatively young field of study, having initially been formalized in the 1800s in order to find unknowns in systems of linear equations.

Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations. Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science, computer animation, and the social sciences (particularly in economics).

The solution to the system of equations graphed below is,

⇒ (0, 1)

Since, We have to given that;

Two system of equations are,

⇒ g (x) = 3x + 2

⇒ f (x) = |x - 1| + 1

Here, The graph of both system of equation are shown in graph.

We know that;

In a graph, the solution of system of equation are represented by a intersection point of both graph.

Here, In the graph of system of equation,

Intersection point is,

⇒ (0, 1)

Hence, The solution to the system of equations graphed below is,

⇒ (0, 1)

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These two points on the number line describe that she descended by 70 units.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,
She started at –5 and descended to –75.
On the number line, the difference between  -75 and -5 is given as
= -5 - (-75)
= 70

Thus, these two points on the number line describe that she descended by 70 units.

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Answer:

x=24 y=15

step by step solution:

Answer:

The answer is below

Step-by-step explanation:

La distancia entre dos puntos A(x₁, y₁) y B(x₂, y₂) en el plano cartesiano se da como:

\(AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

El paralelogramo que se muestra en el diagrama tiene vértices en P (3, 6), Q (7, 6), R (9, 2) y S (1, 2)

a) La distancia entre Q y R viene dada por:

\(QR=\sqrt{(9-7)^2+(2-6)^2} =\sqrt{20}=2\sqrt{5} \ units\)

b) La distancia entre P y R viene dada por:

\(QR=\sqrt{(9-3)^2+(2-6)^2} =\sqrt{52}=2\sqrt{13} \ units\)

Answer:

B) =−7j−k−1

Step-by-step explanation:

10k+17-7j-18-11k what we have

=(−7j)+(10k+−11k)+(17+−18) combine like terms

=−7j−k−1

Answer:

-7j-k-1

Step-by-step explanation:

for this problem you have to subtract the like terms while following the order of the equation (start with the terms on the left and move terms)

Step 1:

-7j has no like terms

= -7j

Step 2:

10k and -11k are like terms

10k-11k

= -1k

Step 3:

17 and -18 are like terms

17-18

= -1

Step 4:

put all simplified terms together

=-7j-k-1

Answer:

Step-by-step explanation:

2.5

4 quarts per gallon

8 quarts per 2 gallons

2 quarts is half a gallon since 4 quarts is a full gallon

answer: 2.5

Answer: Only once.

Step-by-step explanation:

Given: Sara goes to the mall every 6th day. Andy goes to the same shopping mall every 7th day.

Then, from starting the first day , the number of day when they meet = L.C.M of (6,7)

Since 7 is a prime number , so the least common multiple of 6 and 7 = 6 x 7 = 42

So, every 42th day they will meet.

Both December and January have 31 days.

Starting from 1st December , they will meet on 11th January because 42 = 31 +11 , where 31 days are of December and next 11 days of January.

next time they will meet 42 days after Also 20 + 22 , where 20 remaining days of January and 22 of February, so next time they will meet on 22nd February.

So, they will meet only once at 11th January in the month of December and January .

Sara and Andy would meet once if counting is started from 1st of December

The number of days in December and January are:

\(\mathbf{December = 31}\)

\(\mathbf{January = 31}\)

So, the total number of days in both months.

\(\mathbf{Total = January + December}\)

So, we have:

\(\mathbf{Total = 31 + 31}\)

\(\mathbf{Total = 62}\)

Next, we list out the multiples of 6 and 7, up to 62.

The list is as follows:

\(\mathbf{6: 6, 12, 24, 30, 36, 42, 48, 54, 60}\)

\(\mathbf{7: 7, 14 ,21, 28, 35, 42, 49, 56}\)

The common term between both multiples is

\(\mathbf{Common = 42}\)

This means that they would meet 42 days since the beginning of December.

Hence, they would meet just once if counting is started from 1st of December

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1.15 percentile of people would be expected to score 115 or more

What is Standard Deviation?

A standard deviation (or σ) is a measure of how widely distributed the data is in reference to the mean. A low standard deviation suggests that data is grouped around the mean, whereas a large standard deviation shows that data is more spread out.

Solution:

Mean = 100

Standard Deviation = 13

To solve the given problem we need to calculate the Z - Score

Z = X - Mean / Standard Deviation

P(X > 115)

Z = 115 - 100 / 13

Z = 15 / 13

Z = 1.15 Percentile

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1. The factoring step is

sin²θ - cos²θ sin²θ = sin²θ (1 - cos²θ)

Then the Pythagorean identity is invoked:

cos²θ + sin²θ = 1   →   1 - cos²θ = sin²θ

so that

sin²θ - cos²θ sin²θ = sin²θ sin²θ = sin⁴θ

(third option)

2. Recall that a ² - b ² = (a - b) (a + b). The numerator here is such a difference of squares:

csc²x - 1 = (cscx - 1) (cscx + 1)

Then

(csc²x - 1) / (1 + sinx) = ((cscx - 1) (cscx + 1)) / (1 + sinx)

Recall that cscx = 1/sinx, so rewrite this as

… = ((1/sinx - 1) (1/sinx + 1)) / (1 + sinx)

In the numerator, pull out a factor of 1/sinx from both terms:

… = (1/sinx (1 - sinx) × 1/sinx (1 + sinx)) / (1 + sinx)

… = ((1 - sinx) (1 + sinx)) / (sin²x (1 + sinx))

Cancel the common factor of 1 + sinx :

… = (1 - sinx) / sin²x

Expand the fraction and rewrite sin in terms of csc :

… = 1/sin²x - sinx/sin²x

… = 1/sin²x - 1/sinx

… = csc²x - cscx

Factor out cscx to get the second option,

… = cscx (cscx - 1)

Answer:

7

Step-by-step explanation:

i got it correct on my test

We can compute various descriptive statistics such as the mean, median, mode, range, variance, standard deviation, sum of values, and sum of squared deviations.

The sample mean, also known as the average, provides information about the central tendency of the variable X. It represents the typical or average number of coupons used by the shoppers in the sample. In this case, calculating the mean of the given data would provide an estimate of the average number of coupons used over the 6-month period.

The sample standard deviation measures the dispersion or variability of the data points around the mean. It indicates how much the individual observations deviate from the mean value. A higher standard deviation implies greater variability, indicating a wider range of coupon usage among the shoppers in the sample.

By computing the sample mean and standard deviation, we can understand the average coupon usage and the degree of variability in the data. These statistics help us summarize and interpret the characteristics of the variable X, allowing us to make comparisons, identify outliers, assess the spread of the data, and make inferences about the larger population from which the sample was drawn.

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Answer:

D-Square

Step-by-step explanation:

That describes a square, so the answer a square.

Answer:

D

Step-by-step explanation:

Answer:

45 degrees

Step-by-step explanation:

The first angle of the triangle is 45 degrees. This can be determined by the given information that the second angle is 30 degrees larger than the first and the third angle is 3 times the second. Since the second angle is 30 degrees larger than the first, the first angle must be 15 degrees, and the third angle must be 3x15=45 degrees.

\(\pi \int\limits^6_0 {\frac{26}{3} } \, x^{2} -\frac{1}{9} x^{4} dx\) is the integral that uses the method of disks/washers to find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified lines.

A method for determining the volume of a solid of revolution of a solid-state material while integrating along an axis "parallel" to the axis of revolution is known as disc integration, also known as the disc method in integral calculus.

This technique stacks an endless number of discs with varied radii and minuscule thickness to produce the final three-dimensional form. To create hollow solids of revolutions, the same ideas may also be applied when using rings in place of discs (this is known as the "washer technique").

As opposed to this, shell integration integrates along an axis that is parallel to the axis of revolution. The solution can be seen in the attached images below.

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To solve the initial value problem y" + 4y = 4u_n(t), where y(0) = 0 and y'(0) = 1, we will follow these steps:

a. Find the Laplace transform of the solution y(t).

The Laplace transform of the given differential equation can be obtained using the properties of the Laplace transform. Taking the Laplace transform of both sides, we get:

s^2Y(s) - sy(0) - y'(0) + 4Y(s) = 4U_n(s),

where Y(s) represents the Laplace transform of y(t) and U_n(s) is the Laplace transform of the unit step function u_n(t).

Since y(0) = 0 and y'(0) = 1, the equation becomes:

s^2Y(s) - s(0) - 1 + 4Y(s) = 4U_n(s),

s^2Y(s) + 4Y(s) - 1 = 4U_n(s).

Taking the inverse Laplace transform of both sides, we obtain the solution in the time domain:

y''(t) + 4y(t) = 4u_n(t).

b. Find the solution y(t) by inverting the transform.

To find the solution y(t) in the time domain, we need to solve the differential equation y''(t) + 4y(t) = 4u_n(t) with the initial conditions y(0) = 0 and y'(0) = 1.

The homogeneous solution to the differential equation is obtained by setting the right-hand side to zero:

y''(t) + 4y(t) = 0.

The characteristic equation is r^2 + 4 = 0, which has complex roots: r = ±2i.

The homogeneous solution is given by:

y_h(t) = c1cos(2t) + c2sin(2t),

where c1 and c2 are constants to be determined.

Next, we find the particular solution for the given right-hand side:

For t < n, u_n(t) = 0, and for t ≥ n, u_n(t) = 1.

For t < n, the particular solution is zero: y_p(t) = 0.

For t ≥ n, we need to find the particular solution satisfying y''(t) + 4y(t) = 4.

Since the right-hand side is a constant, we assume a constant particular solution: y_p(t) = A.

Plugging this into the differential equation, we get:

0 + 4A = 4,

A = 1.

Therefore, for t ≥ n, the particular solution is: y_p(t) = 1.

The general solution for t ≥ n is given by the sum of the homogeneous and particular solutions:

y(t) = y_h(t) + y_p(t)

y(t) = c1cos(2t) + c2sin(2t) + 1.

Using the initial conditions y(0) = 0 and y'(0) = 1, we can determine the values of c1 and c2:

y(0) = c1cos(0) + c2sin(0) + 1 = c1 + 1 = 0,

c1 = -1.

y'(t) = -2c1sin(2t) + 2c2cos(2t),

y'(0) = -2c1sin(0) + 2c2cos(0) = 2c2 = 1,

c2 = 1/2.

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A regression analysis was performed to analyze the cost behavior of operating costs. The output was saved as a new worksheet, the cost equation was formulated, and the statistical significance of the relationship was assessed.

a. To run a regression, the monthly expense data for operating costs and the corresponding total cases should be input into statistical software that supports regression analysis. The output should be saved as a new worksheet, which can be renamed as "Output" for easy reference.

b. The cost equation formula can be written as: Operating Costs = Intercept + (Slope * Total Cases). The intercept represents the estimated baseline level of operating costs, while the slope represents the change in operating costs associated with a one-unit change in total cases.

c. The amount of change in operating costs that can be explained by the change in total cases can be determined by examining the coefficient of determination (R-squared) in the regression output. R-squared represents the proportion of the variation in operating costs that can be explained by the variation in total cases.

d. The statistical significance of the relationship between operating costs and total cases can be assessed using the p-values associated with the coefficients in the regression output. At the 0.05 significance level, a p-value less than 0.05 indicates statistical significance, implying that the relationship is unlikely to be due to chance. Similarly, at the 0.01 significance level, a p-value less than 0.01 indicates statistical significance with an even stricter criterion. The specific p-value used for significance testing should be mentioned in the question or provided in the regression output.

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Answer: 26 child tickets were sold that day.

Step-by-step explanation:

Let's say the number of child tickets sold is "x".

According to the problem, the number of adult tickets sold is four times the number of child tickets sold. So, the number of adult tickets sold would be 4x.

6.10x + 9.90(4x) = 1188.20

6.10x + 39.60x = 1188.20

45.70x = 1188.20

x = 26

Answer:

10x + 15

Step-by-step explanation:

Answer:

I dont know what the question is asking you but im assuming it was asking you what is the equation:

Slope = 10.

Equation: y=10x+15

Y-intercept: 15

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

Hope this helps!

Step by step? Just ask.

Doubt? --> comment section.

Happy Holidays! (✿◡‿◡)

Answer:

Step-by-step explanation:

If you don't know how to use your calculator to find a regression equation, that is much too much to try and teach you in a forum such as this (it takes all hour to teach Algebra 2 students during the school year and they are sitting in class watching a demonstration!). I entered the data in my calculator and got the equation to be

y = 18.9x + 850 with a correlation coefficient of only .8 so this is not a very good model for this data anyway. However, we will proceed with the question as it asks. Year 0 is 2008, so the year in question, 2016, is year 8. We fill in the model with 8 for x and solve for y, the cases in NY of crime in that year:

y = 18.9(8) + 850 and

y = 151.2 + 850 so

y = 1001 cases of crime

Answer:

The length of the rectangular field is 77 meters.

Step-by-step explanation:

We can use the formula for the area of a rectangle to solve this problem:

Area = length x width

We are given that the area is 4235 m² and the width is 55 m. We can substitute these values into the formula and solve for the length:

4235 = length x 55

To isolate the variable "length" on one side of the equation, we can divide both sides by 55:

4235/55 = length

Simplifying the right side gives:

77 = length

The function G(t)=(2⋅t)4 is not an exponential function. So, the value of a and b are none.

Exponential function:

In an exponential function, a variable appears in the place of an exponent.

The general form of an exponential function is:  y = abx where x is the variable of the exponent, and a and b are constants with a ≠ 0, b > 0, and b ≠ 1.

The function G(t) = (2t)^4 can be rewritten as G(t) = 16t^4, which is a polynomial function, not an exponential function. The value of "a" and "b" cannot be determined for the given function since the function is not exponential.

Therefore, the value of a = NONE, b = NONE.

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The fact that certain neurons might respond only to your mother's face but not your father's face highlights the importance of facial recognition and the specificity of neural responses.

Facial recognition is a complex cognitive process that involves the ability to distinguish and identify different faces. The specificity of neural responses to different faces, such as responding exclusively to one's mother's face but not the father's face, highlights the importance of neural specialization and the intricate nature of face perception.

The brain possesses specialized neurons known as face-selective neurons or face cells that are specifically tuned to detect and process facial features. These neurons play a crucial role in facial recognition and contribute to our ability to differentiate and remember faces.

The fact that certain neurons respond selectively to specific faces, like the mother's face, suggests that our brains have developed specialized mechanisms to encode and process important social stimuli, such as faces of close family members. This phenomenon emphasizes the significance of early experiences, bonding, and the formation of neural representations associated with familiar faces, particularly those with strong emotional connections.

In summary, the specificity of neural responses to the mother's face highlights the importance of facial recognition and the specialized neural mechanisms involved in processing and distinguishing familiar faces, contributing to our understanding of social cognition and the complexities of human brain function.

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Answer:

a) 20

Step-by-step explanation:

Use similar triangles.

2/3 = x/30

3x = 2 * 30

3x = 60

x = 20

Answer: a) 20

The correct answer is b. we know the standard deviation of the population.

The Nearly Normal condition, also known as the Central Limit Theorem, states that the sampling distribution of the sample mean tends to be approximately normal, even if the population distribution is not normal, under certain conditions. One way to meet the Nearly Normal condition is by knowing the standard deviation of the population.

When the standard deviation of the population is known, the sample size does not have to be large for the sampling distribution of the sample mean to be approximately normal. This is because the standard deviation provides information about the variability of the population, allowing for a more accurate estimation of the sample mean distribution.

While the other options (a, c, and d) may be relevant in specific scenarios, they are not directly related to meeting the Nearly Normal condition as defined by the Central Limit Theorem.

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Answer:hi there!that same guy did that w my question too :( i’m reporting his answers. i will help u out tho ahah. the answer is 470(32-n). i hope this helps :). have a good dayyy

Step-by-step explanation:

Given, f(x) = x + 1 and g(x) = 2x.The inverses of these functions are f⁻¹(x) = x - 1 and g⁻¹(x) = x/2Now, let us solve the given function by using the BODMAS Rule.f(g⁻¹(f⁻¹(f⁻¹(g(f(5))))))

First, calculate f(5)

f(5) = 5 + 1 = 6

Now, calculate g(f(5))

g(f(5)) = g(6) = 2 × 6 = 12.

Now, calculate f⁻¹(f⁻¹(g(f(5)))).For this, we need to find the value of g(f(5)).So,

g(f(5)) = 12.f⁻¹(12) = 12 - 1 = 11.

Now, calculate f(g⁻¹(11))For this, we need to find the value of g⁻¹(11).

g⁻¹(11) = 11/2

Now, f(g⁻¹(11)) = f(11/2)f(11/2) = 11/2 + 1 = 13/2

Therefore, the answer is 13/2.

Therefore, the function f(g⁻¹(f⁻¹(f⁻¹(g(f(5)))))) is equal to 13/2.

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Answer: The answer is (d) 700 miles. 35 inches on the map represents 700 miles in actual distance

Step-by-step explanation:

This is a Unitary method problem.

If 25 inches on the map represents 500 miles in actual distance, then we can write:

25 inches / 500 miles = 35 inches / x miles

where x is the number of miles represented by 35 inches on the map.

To solve for x, we can cross-multiply and simplify:

25 inches * x miles = 500 miles * 35 inches

25x = 17500

x = 700

Therefore, 35 inches on the map represents 700 miles in actual distance.

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