Find an equation for the set of points in an xy-plane that are equidistant from the point P and the line l. P(−9, 2); l: x = −3

Answer:

(-2, 2)          

Step-by-step explanation:

x= -2  y= 2      

Answer: ..

Step-by-step explanation:

Wed: 0%

Thu: 30%

Fri: 50%

Sat: 80%

Sun: 100%

I got these answers by taking 100, and subtracting the rain percentage from it. For instance, if it was a 45% to rain, and a unknown amount for it to not rain, I would take 100 and subtract 45 from it, resulting in a 55% chance of it not raining.

Answer: 3:50b>765.00+0.75 279 Burritos

Step-by-step explanation:

The width of the rectangular walkway is 15 yards. This is determined by finding the product of the length and width to match the given area of 11 1/4 square yards.

To find the width of the rectangular walkway, we can use the formula for the area of a rectangle: length multiplied by width.

Given:

Area = 11 1/4 square yards

Length = 9/12 yard

Let's convert the mixed fraction for the area to an improper fraction:

11 1/4 = 44/4 + 1/4 = 45/4

Now, we can set up an equation:

Area = Length * Width

Substituting the given values:

45/4 = 9/12 * Width

To simplify the equation, we can convert all fractions to a common denominator:

45/4 = 9/12 * Width

45/4 = 3/4 * Width

Now, we can solve for the width:

Width = (45/4) / (3/4)

Width = (45/4) * (4/3)

Width = 45/3

Width = 15

Therefore, the width of the rectangular walkway is 15 yards.

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The rectangular walkway has an area of 11 1/4 square yards. The length of the walkway is given as 9/12 yards.

To find the width of the walkway, we can use the formula for the area of a rectangle: Area = Length x Width.

Let's proceed with finding the width of the walkway.

Answer: We on da same question i do not know

Step-by-step explanation:

The 95% confident interval for the true mean length of stay of all hospital patients is (3.716, 5.284) days.

To find a 95% confident interval for the true mean length of stay of all hospital patients, we can use the formula:

Confidence interval = sample mean ± margin of error

The margin of error is calculated as the product of the critical value and the standard error, where the critical value is determined based on the desired confidence level and the standard error is the standard deviation divided by the square root of the sample size.

Given:

Sample mean  = 4.5 days

Standard deviation (σ) = 4 days

Sample size (n) = 100

Confidence level = 95%

First, let's calculate the critical value. Since the sample size is large (n > 30), we can use the Z-table to find the critical value for a 95% confidence level. The critical value corresponds to a 2-tailed test, so we need to find the value that leaves 2.5% in each tail.

Looking up the Z-table, the critical value for a 95% confidence level is approximately 1.96.

Next, let's calculate the standard error:

Standard error (SE) = σ / sqrt(n)

SE = 4 / sqrt(100)

SE = 4 / 10

SE = 0.4

Now, we can calculate the margin of error:

Margin of error = critical value * standard error

Margin of error = 1.96 * 0.4

Margin of error = 0.784

Finally, we can construct the confidence interval:

Confidence interval = sample mean ± margin of error

Confidence interval = 4.5 ± 0.784

Confidence interval = (3.716, 5.284)

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Answer: LM = 11

because L is between N and M => we have:

NL + LM = NM

⇔ 6x - 5 + 2x + 3 = 30

⇔ 8x -2 = 30

⇔ 8x = 32

⇔ x = 4

with x = 4, => LM = 2.4 + 3 = 11

Step-by-step explanation:

The scenario that match this graph is 12 gallons are presently in the bath tube draining at 3 gallons per minute.

An equation is an expression that shows the relationship between two or more numbers and variables.

From the graph using points (0, 12) and (4, 0):

y intercept = 12; slope = (0 - 12)/(4 - 0) = -3

The scenario that match this graph is 12 gallons are presently in the bath tube draining at 3 gallons per minute.

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Answer:

A median of a triangle is a line segment that passes through a vertex and bisects the midpoint of the opposite that vertex .

The line segment joining the first point (-1, -5, 4) to the second point (-6, 4, -2) can be represented by parametric equations.  The parametric equations are: x = -1 + t(-5) y = -5 + t(9) z = 4 + t(-6)

To derive the parametric equations, we use the concept of parameterization. Let's introduce a parameter t that varies from 0 to 1 to represent the distance along the line segment.

We can find the direction vector of the line segment by subtracting the coordinates of the first point from the coordinates of the second point:

Direction vector = (-6, 4, -2) - (-1, -5, 4) = (-5, 9, -6)

Now, we can express the parametric equations by adding the direction vector multiplied by the parameter t to the coordinates of the first point:

x = -1 + t(-5)

y = -5 + t(9)

z = 4 + t(-6)

These parametric equations allow us to generate points along the line segment by plugging in different values of t. When t = 0, we get the first point (-1, -5, 4), and when t = 1, we get the second point (-6, 4, -2). As t varies between 0 and 1, we traverse the line segment connecting the two points.

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Answer:

Hayley is correct.

Step-by-step explanation:

81 can have a base of 9, as 9*9 = 81. However, it can also have a base of 3, as 3*3*3*3 = 81. 81 can be shown as a power with a base of 3 or 9.

The evaluated definite integrals using right Riemann sums are:

a) ∫[0, 2] (2x + 1)dx = 9.

b) ∫[3, 7] (4x + 6)dx is divergent.

c) ∫[1, 5] (1 - x)dx = 4.

d) ∫[0, 2] (x^2 - 1)dx = 2.

To evaluate the definite integrals using right Riemann sums, we partition the interval into subintervals and approximate the area under the curve using the right endpoints of each subinterval.

a) ∫[0, 2] (2x + 1)dx:

Let's partition the interval [0, 2] into n subintervals of equal width. The width of each subinterval is Δx = (2 - 0) / n = 2/n.

The right endpoints of the subintervals are: x1 = 2/n, x2 = 4/n, x3 = 6/n, ..., xn = 2. The right Riemann sum is given by: R_n = Σ[(2x + 1) * Δx] from i = 1 to n.

Expanding the sum, we have:

R_n = [(2(2/n) + 1) * (2/n)] + [(2(4/n) + 1) * (2/n)] + ... + [(2(2) + 1) * (2/n)]

= [4/n + 1] * (2/n) + [8/n + 1] * (2/n) + ... + [5] * (2/n)

= 2[4/n + 1 + 8/n + 1 + ... + 5] * (2/n)

= 2[(4 + 8 + ... + 5n)/n + n] * (2/n)

R_n = 2[(n/2)(4 + 5n)/n + n] * (2/n)

= (4 + 5n + 2n) * (4/n)

= (9n + 4) * (4/n)

Taking the limit as n approaches infinity, we have:

∫[0, 2] (2x + 1)dx = Lim(n->∞) (9n + 4) * (4/n)

= Lim(n->∞) 9 + (4/n)

= 9.

Therefore, ∫[0, 2] (2x + 1)dx = 9.

b) ∫[3, 7] (4x + 6)dx:

The right Riemann sum is given by: R_n = Σ[(4x + 6) * Δx] from i = 1 to n.

Expanding the sum and simplifying, we find:

R_n = 4[(3 + 4n/n) + (3 + 4(2n)/n) + ... + (3 + 4(n)/n)] * (4/n)

= 4[(3 + 4 + ... + (3 + 4n))/n] * (4/n)

= 4[(3n + 4(1 + 2 + ... + n))/n] * (4/n)

= 4[(3n + 4(n(n+1)/2))/n] * (4/n)

= 4[(3n + 2n(n+1))/n] * (4/n)

= 4[3 + 2(n+1)] * (4/n)

= 4[6 + 2n] * (4/n)

= 8 + 8n

Taking the limit as n approaches infinity, we have:

∫[3, 7] (4x + 6)dx = Lim(n->∞) (8 + 8n)

= Lim(n->∞) 8n

= ∞.

Therefore, ∫[3, 7] (4x + 6)dx is divergent.

c) ∫[1, 5] (1 - x)dx:

Using the same approach, we have:

R_n = [(1 - 1/n) * (4/n)] + [(1 - 2/n) * (4/n)] + ... + [(1 - n/n) * (4/n)]

= [(1 + 1 + ... + (n-1))/n] * (4/n)

= [(n-1)/n] * (4/n)

= (4(n-1))/n^2

Taking the limit as n approaches infinity, we have:

∫[1, 5] (1 - x)dx = Lim(n->∞) (4(n-1))/n^2

= Lim(n->∞) (4 - 4/n)

= 4.

Therefore, ∫[1, 5] (1 - x)dx = 4.

d) ∫[0, 2] (x^2 - 1)dx:

Using the same approach, we have:

R_n = [(0^2 - 1/n) * (2/n)] + [(1^2 - 2/n) * (2/n)] + ... + [(2^2 - n/n) * (2/n)]

= [(0^2 + 1^2 + ... + (n-1)^2)/n] * (2/n)

= [(0^2 + 1^2 + ... + (n-1)^2)/n] * (2/n)

= [(0 + 1 + 4 + ... + (n-1)^2)/n] * (2/n)

= [(n(n-1)(2n-1))/6n] * (2/n)

= [(n-1)(2n-1)]/3n

Taking the limit as n approaches infinity, we have:

∫[0, 2] (x^2 - 1)dx = Lim(n->∞) [(n-1)(2n-1)]/3n

= Lim(n->∞) (2n^2 - 3n + 1)/3n

= Lim(n->∞) (2n^2/n - 3n/n + 1/n)

= Lim(n->∞) (2 - 3/n + 1/n)

= 2.

Therefore, ∫[0, 2] (x^2 - 1)dx = 2.

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Answer:

B

Step-by-step explanation:

I got it right on edge2020, 160-40= 120

120/2 = 60 because the angle was gonna be half way between the two angles

The expression that represent | r+s| is Option B

A vector is an object that has both magnitude and direction.

It is given that

|r| = 17 at an angle of 40 degree

|s| = 14 at an angle of 160 degree

| r + s| = ?

The magnitude will be determined by the cosine law

and the angle will be 60 degree , obtained from the figure attached with the answer.

\(\rm |r + s| = \sqrt{ 17^2 + 14 ^2 -2 * 14 *17 cos 60\)

Therefore , the expression that represent | r+s| is Option B.

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The statement, "A statistic is a formula calculable with data," is True. A statistic is a mathematical calculation that uses data to summarize, organize, analyze, and interpret data.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. In summary, a statistic is a numerical value that represents a piece of information about a particular data set. It is calculated using mathematical formulas, statistical models, or algorithms.

The purpose of using statistics is to provide objective and accurate descriptions of the data, measure the degree of variability, identify patterns and trends, make inferences, and test hypotheses. In conclusion, statistics are used in different fields such as social sciences, business, finance, medicine, engineering, and environmental studies, to name a few, to make informed decisions based on data analysis.

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Store B sells 12591 products.

An equation is a mathematical statement that demonstrates the equality of two mathematical expressions.

Let the number of products Store A sells be x, the number of products store B sells be y, and the number of products store C be z.

Now,

Store C sells 125910 products.

z = 125910 products

Store A sells one-half as many as store C.

x = ( 1/2 )z

x = ( 1/2) × 125910

x = 62955 products

Store A sells five times as many products as store B can be expressed as the equation,

x = 5y

62955 = 5y

Dividing each side by 5,

y = 62955 / 5

y = 12591 products

Store A, B, and C sell 62955, 12591, and 125910 products.

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Check the picture below.

well, ∡CED is the same as ∡CEA and those are right-angles so those are pretty much given, now

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{29}\\ a=\stackrel{adjacent}{20}\\ o=\stackrel{opposite}{CE} \end{cases} \\\\\\ CE=\sqrt{ 29^2 - 20^2}\implies CE=\sqrt{ 841 - 400 } \implies CE=\sqrt{ 441 }\implies \boxed{CE=21} \\\\\\ \stackrel{\textit{since we know the radius CB=29}}{CB-CE = EB\implies }\boxed{EB=8}\)

Answer:

angle CED 90°. CE = 21. EB = 8.

Step-by-step explanation:

angle CED = 90° (right angle).

the radius (centre to edge) is the same right around the circle.

so that means that distance CD = 29.

draw a line from C to D. notice how that has just become an hypotenuse?

we know that DE = 20.

we have a right-angled triangle.

CE² = hypot² - DE²

       = 29² - 20²

       = 841 - 400

       = 441

CE = √441 = 21.

EB must be radius subtract CE. that is, 29 - 21 = 8.

The area of the surface is 0.5 square meters.

Force is an external agent capable of changing a body's state of rest or motion

The pressure, P, is defined as the force, F, per unit area, A:

P = F / A

We can rearrange this equation to solve for the area:

A = F / P

Substituting the given values, we have:

A = 55 N / 110 Pa

Simplifying this expression gives:

A = 0.5 square meters.

Therefore, the area of the surface is 0.5 square meters.

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3.1 Sociomathematical norms can be defined as These norms are constructed through social processes, classroom interactions, and are enforced through the use of language and gestures. 2. During Teacher Lee's class, it appeared that there were different notions on what constitutes an acceptable mathematical explanation and justification compared to sociomathematical norms at play during the lesson. This impression was created in the following ways:3.2.1 Acceptable Mathematical .

Teacher Lee and the learners seem to have different ideas about what makes an acceptable mathematical explanation. The learners expected Teacher Lee to provide concise and precise explanations, with a focus on the answer. Teacher Lee, on the other hand, expected learners to provide detailed explanations that showed their reasoning and understanding of the mathematical concept. This difference in expectations resulted in a lack of understanding and frustration.3.2.2 Acceptable Mathematical Justifications:

Similarly, Teacher Lee and the learners had different ideas about what constituted an acceptable mathematical justification. The learners seemed to think that providing the correct answer was sufficient to justify their reasoning, whereas Teacher Lee emphasized the importance of explaining and demonstrating the steps taken to reach the answer. This led to different understandings of what was considered acceptable, resulting in confusion and misunderstandings.

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To orthogonally diagonalize the matrix A, we will follow these steps:
1. Find the eigenvalues of matrix A.
2. Find the eigenvectors corresponding to each eigenvalue.
3. Normalize the eigenvectors to form an orthogonal basis.
4. Construct the orthogonal matrix Q and the diagonal matrix D.

To orthogonally diagonalize the matrix A, we need to find the eigenvalues and eigenvectors of A.

A = [[3, -1], [-1, 3]]

The characteristic polynomial of A is:

det(A - λI) = det([[3-λ, -1], [-1, 3-λ]]) = (3-λ)² - 1 = λ² - 6λ + 8 = (λ-2)(λ-4)

So the eigenvalues are λ₁ = 2 and λ₂ = 4.

To find the eigenvectors, we need to solve the system of equations:

(A - λ₁I)x = 0 and (A - λ₂I)x = 0

For λ₁ = 2, we have:

(A - 2I)x = [[1, -1], [-1, 1]]x = 0

This system has two linearly independent solutions:

v₁ = [1, 1] and v₂ = [-1, 1]

For λ₂ = 4, we have:

(A - 4I)x = [[-1, -1], [-1, -1]]x = 0

This system has one linearly independent solution:

v₃ = [1, -1]

To orthogonalize the eigenvectors, we need to normalize them and put them as columns of an orthogonal matrix Q.

Q = [[1/√2, -1/√2, 0], [1/√2, 1/√2, 0], [0, 0, 1]]

The diagonal matrix D has the eigenvalues on the diagonal:

D = [[2, 0], [0, 4]]

Finally, we can check that QTAQ = D:

QTAQ = [[1/√2, -1/√2, 0], [1/√2, 1/√2, 0], [0, 0, 1]]T[[3, -1], [-1, 3]][[1/√2, -1/√2, 0], [1/√2, 1/√2, 0], [0, 0, 1]] = [[2, 0, 0], [0, 4, 0], [0, 0, 4]] = D

Therefore, matrix A is orthogonally diagonalized by Q and D.

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1. Identify the total value for each row by adding up the numbers in each cell of that row. 2. Divide the value of each cell in a specific row by the corresponding row total to get the probability for that cell. 3. Repeat this process for all the cells in each row to obtain the conditional probabilities for the entire table.

The probabilities you calculate represent the likelihood of an event occurring given the row condition. By dividing each cell by the row total, you're essentially normalizing the data to account for different row totals. This allows for easier comparisons between probabilities and ensures that the sum of probabilities in a row is equal to 1.
Some values may have already been completed for you in the table. In that case, verify the accuracy of the given probabilities by performing the calculations yourself. If they match your calculations, you can confidently proceed to fill in the remaining probabilities using the steps outlined above.
By following this method, you'll obtain a table with conditional probabilities, allowing for more informed analysis and decision-making based on the data provided.

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After answering the presented question, we can conclude that As a result, the simple interest (I) earned on a $425.00 principal amount at a 6% annual interest rate for three years is $76.50.

In mathematics, interest is the amount of money earned or payable on an original investment or loan. You can use either simple or compound interest. Simple interest is calculated as a percentage of the initial amount, whereas compound interest is calculated on the principal amount plus any previously earned interest. If you invest $100 at a 5% annual simple interest rate, you will get $5 in interest every year for three years, for a total of $15.

We can use the following formula to solve for I (simple interest):

I = P * r * t

where P is the principle amount of $425.00

r = 6% annual interest rate = 0.06 (as a decimal)

t = time span = 3 years

When we enter the given values into the formula, we get:

I = $425.00 * 0.06 * 3 \sI = $76.50

As a result, the simple interest (I) earned on a $425.00 principal amount at a 6% annual interest rate for three years is $76.50.

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Answer:The vertex form is -y=a(x-h)2+k

Step-by-step explanation:

Answer:

3(x-2)^2-7

Step-by-step explanation:

expanding gives you: 3(x^2-4x+4)-7=3x^2-12x+12-7=3x^2-12x7+5

Therefore , the solution of the given problem of unitary method comes out to be the location where the light is fixed, the ladder must be 25 feet long.

The task can be finished by applying what was learned, using this varied strategy, and merging all important variables from past researchers who used a specific methodology. If the desired assertion outcome occurs, the entity represented in the statement can either also be detected or both important processes will actually miss the expression. For fifty pens, a refundable payment of Rupees ($1.21) might be required.

Here,

We are aware that the hypotenuse of a right triangle with seven and twenty-four foot legs is AB.

To utilise the Pythagorean theorem, then:

=>  AB² = 7² + 24²

=> AB²= 49 + 576

=> AB² = 625

=> AB = 25

In order for the electrician to reach the location where the light is fixed, the ladder must be 25 feet long.

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Hence, the cost of fencing the garden is ₹9485. Hence, the cost of plowing the garden is ₹756.

Perimeter is the total distance around the outside of a closed two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the lengths of all its four sides, whereas the perimeter of a circle is found by multiplying the diameter by π (pi). Perimeter is usually expressed in units of length, such as meters, centimeters, feet, or inches.

Here,

The perimeter of the rectangular garden is twice the sum of its length and width. So, the length of the fence needed to enclose the garden is:

2 × (length + width) = 2 × (175 m + 96 m) = 542 m

Therefore, the cost of fencing the garden at 17.50 per meter is:

Cost of fencing = length of fence × cost per meter

= 542 m × 17.50

= 9485

Hence, the cost of fencing the garden is ₹9485.

To find the cost of plowing the garden, we need to first calculate its area, which is given by:

Area = length × width

= 175 m × 96 m

= 16800 m²

Therefore, the cost of plowing the garden at 4.50 paise per square meter is:

Cost of plowing = area of garden × cost per square meter

= 16800 m² × 0.045

= 756

Hence, the cost of plowing the garden is ₹756.

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the solution w = -36 is correct

The given equation is w/4 + 16 = 7.The main objective here is to solve for the variable w. Let us see the step-by-step process to solve for w:

Step 1: Simplify the left side of the equation by subtracting 16 from both sides. w/4 + 16 = 7 ⇒ w/4 = -9The justification for subtracting 16 from both sides is the additive inverse property of equality, which states that if a = b, then a - c = b - c for any real number c.

Step 2: Multiply both sides of the equation by 4 to isolate w. w/4 = -9 ⇒ (4)(w/4) = (4)(-9) ⇒ w = -36The justification for multiplying both sides of the equation by 4 is the multiplication property of equality, which states that if a = b, then ac = bc for any real number c.

Step 3: Check the solution. Substitute -36 for w in the original equation to make sure it satisfies the equation. w/4 + 16 = 7 ⇒ (-36)/4 + 16 = 7 ⇒ -9 + 16 = 7 ⇒ 7 = 7Since 7 = 7 is a true statement, . The justification for this step is that it ensures that the solution obtained in the previous step is valid.

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Answer:

Both are true

Answer:  14,533.79 don´t take my word for it

Step-by-step explanation:

Future Value of Annuity Due

P = 2,000

r = 5.5% (0.055)

n = 6

1.055 * (2,000 * [(1 + 0.055)^6 - 1)/(0.055)])

= 14,533.79

The correct identification of the dependent variable and the independent variable for the experiment is valid experiment.

Independent variable: The variable that is being changed or manipulated in an experiment is called the independent variable. The experimenter modifies the independent variable to observe its effect on the dependent variable.

Dependent variable: The dependent variable is the variable that is being measured and observed in an experiment. It is dependent on the independent variable because it changes as a result of the manipulation of the independent variable.

Therefore, To carry out a valid experiment, it is crucial to accurately identify the dependent variable and independent variable.

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