What is the equation of a line passing through the points (2, -6) and (4, -16) in slope-intercept form

Perimeter of a hexagon: Side length (s) x 6

Replacing with the value given:

49 1/2 = 6 s

Solve for s ( side length)

(49 1/2) /6 = s

s= 33/4 ft

The difference in elevation between the height of mountain and height of valley measuring from sea level is equal to 6594 feet.

Since it is given that the height of mountain from the sea level is 6874 feet and the height of valley is 280 feet. Therefore to calculate the difference in elevation, the heights will be subtracted from one another to get a value which will show the elevation. Since both the heights are measured from the sea level which is taken as constant, so no extra calculations will be needed.

Elevation difference = Height of mountain - height of valley

Elevation difference = 6874 - 280 = 6594 feet

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Answer:

A. 8(3 + 8x)

Step-by-step explanation:

Hope it helps you in your learning process

To find the x-coordinate of the point where the line l intersects the plane x - 3y - z = 9, we need to find the value of x when the coordinates (x, y, z) satisfy both the equation of the line and the equation of the plane.

Since the line l is parallel to the line with vector equation r(t) = 〈2, 4, 1〉 + t〈2, 3, -2〉, we can write the equation of line l as:

x = 2 + 2t

y = 4 + 3t

z = 1 - 2t

Substituting these equations into the plane equation x - 3y - z = 9, we have:

(2 + 2t) - 3(4 + 3t) - (1 - 2t) = 9

Simplifying the equation, we solve for t:

2 + 2t - 12 - 9t - 1 + 2t = 9

-5t - 11 = 9

-5t = 20

t = -4

Substituting t = -4 into the equation x = 2 + 2t, we find:

x = 2 + 2(-4) = -6

Therefore, the x-coordinate of the point where the line l intersects the plane is -6.

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A basis for the subspace is given by the three vectors consisting of all vectors of the form [x1, -2x1+x2, -9x1+4x2, -5x1-7x2]:

[1, 0, 0, -5], [0, 1, 4, -7], and [0, 0, 0, 1].

To find a basis for the given subspace, we need to determine the linearly independent vectors that span the subspace.

Let's rewrite the given vector as a linear combination of the standard basis vectors in R4:

[x1, -2x1+x2, -9x1+4x2, -5x1-7x2] = x1[1, 0, 0, -5] + x2[0, 1, 4, -7] + 0[0, 0, 0, 1]

Thus, the subspace is spanned by the vectors [1, 0, 0, -5], [0, 1, 4, -7], and [0, 0, 0, 1].

To check for linear independence, we can set up the following augmented matrix and row reduction:

[ 1 0 0 | 0 ]

[ 0 1 4 | 0 ]

[ 0 -2 -9 | 0 ]

[-5 -7 0 | 0 ]

Using row operations, we can reduce this to:

[ 1 0 0 | 0 ]

[ 0 1 0 | 0 ]

[ 0 0 1 | 0 ]

[ 0 0 0 | 0 ]

Since the only solution is the trivial solution, the vectors are linearly independent.

Therefore, a basis for the subspace is given by the three vectors:

[1, 0, 0, -5], [0, 1, 4, -7], and [0, 0, 0, 1].

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Answer:

760

Step-by-step explanation:

5 times 6 is 30 and 30 + 8 = 38. 38 times 20 = 760

Hope this helps

Answer:

I assume you meant that the total length of the train is 86.8m.

Let ’n’ be the length of a carriage.

Then the length of the engine is (2/3)n.

4n+(2/3)n = 86.8

(14/3)n = 86.8

n =18.6. (2/3)n = 12.4.

Each carriage is 18.6 meters long.

The engine is 12.4 meters long.

Step-by-step explanation:

Mak me brainliest

Answer:

10 is the answer

Step-by-step explanation:

6 times what equals 60?

10

Answer:

3

Step-by-step explanation:

(4-10)/(6-8)

-6/-2=3

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

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Step-by-step explanation:

1. 572/1000,

2. 0.50, 0.5

3. 22/7 , 1/(7/22), 3.14, 3.140

4. √16, 4, 4.00, 4.0

5. √1/√1, 1.0, 1.00 etc.

Given that profits decrease by 13.8% when the degree of operating leverage (DOL) is 3.8.

The decrease in sales is: We have to determine the percentage decrease in sales Let the percentage decrease in sales be x.

Degree of Operating Leverage (DOL) = % change in Profit / % change in Sales3.8

= -13.8% / x Thus, we have: x

= -13.8% / 3.8

= -3.63%Therefore, the decrease in sales is 3.63%.Hence, the correct option is C) 3.63%. Percentage decrease in sales = % change in profit / degree of operating leverage

= 13.8 / 3.8

= 3.63% The percentage decrease in sales is 3.63%.

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Answer:

Broken =16.67%

Not broken=83.33%

Step-by-step explanation:

In terms of percentage the total amount of eggs =100%

ie 30=100%

Amount of eggs broken=5

Amount of eggs not broken=30-5

Using proportion

30=more

5=less

to find for percentage of eggs broken ie 5

first let x represent eggs broken

If less more divide×100%

and 5 is less than 30

x=5/30×100%

simplify

x=1/6×100%

x= 16.66%or16.67%

Eggs not broken=30-5

=25

Using proportion again

25=less

30=more

if less more divide

x=25/30×100%

simplify

x=2500%/30

Step-by-step explanation:

2b - 3/3 - 5 = 10

2b - 1 - 5 = 10

2b - 6 =10

2b -6 +6 = 10 +6

2b = 16

b = 8

If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

For this question we need to subtract and multiply the numbers. We know that 2 = 25% of 8 so:

\(\boxed{8-2=6}\\\boxed{6/2=3}\)

We are going to take that 25% and multiply it with 3 to get are final answer.

\(\boxed{25*3=75}\\\boxed{So,2=75}\)

Therefore, If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

Answer:

Step-by-step explanation:

Since a is parallel to b , taking CE as transversal

m< CED = m<3 = 58° (alternate interior angles)

Answer:

Step-by-step explanation:

Since line A is parallel to line B, then angle 1 and angle D are alternate interior and are congruent. That means that angle 1 is 60. Angle 2 can be found by  subtracting 60 + 58 from 180:

180 - 60 - 58 = 62. Now to find angle 3, we just subtract angle 1 and angle 2 from 180:

180 - 60 - 62 = 58 (which works out perfectly because angle 3 and angle E are congruent as we just found out!)

a. Probability of completing the exam in one hour or less is 0.0228. b. Probability of completing the exam in more than 60 minutes but less than 75 minutes is 0.2857. c. About 10 students are expected to be unable to complete the exam in the allotted time.

a. To find the probability of completing the exam in one hour or less, we need to convert one hour (60 minutes) into a z-score using the formula:

z = (x - μ) / σ

where x is the value we want to convert, μ is the mean, and σ is the standard deviation. So, we have:

z = (60 - 80) / 10 = -2

Using a standard normal distribution table or a calculator, we find that the probability of a z-score being less than or equal to -2 is 0.0228 (to 4 decimals). Therefore, the probability of completing the exam in one hour or less is 0.0228.

b. To find the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes, we need to convert both values into z-scores:

z1 = (60 - 80) / 10 = -2

z2 = (75 - 80) / 10 = -0.5

Then, we can find the probability between these two z-scores using a standard normal distribution table or a calculator. The probability is:

P(-2 < z < -0.5) = P(z < -0.5) - P(z < -2)

= 0.3085 - 0.0228

= 0.2857 (to 4 decimals)

Therefore, the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes is 0.2857.

c. We know that the mean time to complete the exam is 80 minutes and the standard deviation is 10 minutes. To find the number of students who will be unable to complete the exam in the allotted time of 90 minutes, we need to find the number of students whose completion time is greater than 90 minutes.

We can convert 90 minutes into a z-score using the formula:

z = (x - μ) / σ = (90 - 80) / 10 = 1

Using a standard normal distribution table or a calculator, we find that the probability of a z-score being greater than 1 is 0.1587.

So, the proportion of students who will be unable to complete the exam in 90 minutes is 0.1587. To find the actual number of students, we can multiply this proportion by the total number of students:

0.1587 x 60 ≈ 9.52

Therefore, we can expect about 10 students to be unable to complete the exam in the allotted time.

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We know that

• You have 2 1/2 yards of fabric.

• You want to make 3 pillows.

To find the number of yards of fabric you can use for each pillow, we just have to divide. We know that 2 1/2 is equivalent to 5/2 yards.

The maximum number of functions that can be defined from the power set of A, P(A), to the power set of B, P(B) is 4096.

The Collection of well-defined objects or elements is known as a set. The objects in a set are called elements. The Set contains a finite number of elements. The Set is denoted by any capital letter like A, B etc. Elements of the set can be numbers, alphabets etc.

The elements of the set are listed inside the curly brackets { ..... }. There are various types of sets. The set of all subsets of the set X is called a Power set including the null set, empty set and the set itself. Cardinal number or cardinality denotes the number of elements in the set. Cardinality is denoted by n( X ) where X is a set. The number of subsets of the set is given by 2^n.

As per the question,

⇒  n ( A )   =   3 elements

Number of subsets of A   =   2³

                                          =   8 subsets

⇒   n ( B )   =   2 elements

Number of subsets of B   =   2²

                                          =   4 subsets

By using the product rule,

Total number of functions from P ( B ) to P ( A )   =   8 × 8 × 8 × 8

                                                                                =   4096

Therefore, 4096 is the maximum number of functions that can be defined from the power set of A, P(A) to the power set of B.

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Fuzzy logic is commonly utilized in computer science, artificial intelligence, engineering, and other fields that require imprecise or ambiguous information to be handled.

The mathematical method of handling imprecise or subjective information is fuzzy logic.What is the mathematical method of handling imprecise or subjective information?The mathematical method of handling imprecise or subjective information is fuzzy logic. It is a form of reasoning that allows for the management of approximate, subjective, or ambiguous information to be carried out using a mathematical model. It is a soft computing technique that uses artificial intelligence to model uncertainty and imprecision in data. Fuzzy logic is commonly utilized in computer science, artificial intelligence, engineering, and other fields that require imprecise or ambiguous information to be handled.

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Answer:

B&E

Step-by-step explanation:

Realized that I didn't actually "answer it" hahaha! Using a online calculator is always helpful in finding answers like these.

A fundamental identity is an equation that relates the values of the trigonometric functions for a given angle. The equation cot θ = cos θ/sinθ is an example of a fundamental identity.

This identity states that the cotangent of an angle is equal to the cosine of the angle divided by the sine of the angle. The equation sec θ = 1/cosθ is another example of a fundamental identity. This identity states that the secant of an angle is equal to the reciprocal of the cosine of the angle. The equation sec^2 + 1 = tan^2θ is also a fundamental identity. This identity states that the square of the secant of an angle plus one is equal to the square of the tangent of the angle. The equation 1 + cot^2θ = csc^2θ is not a fundamental identity. This equation states that one plus the square of the cotangent of an angle is equal to the square of the cosecant of the angle. This equation is not a fundamental identity because it does not relate the values of the trigonometric functions for a given angle.

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the probability that a student, answering each question at random, will answer at least 14 questions correctly is approximately 0.0000039 rounded to seven decimal places.

To calculate the probability that a student, answering each question at random, will answer at least 14 questions correctly, we can use the binomial probability formula.

The probability of answering a question correctly by random chance is 1 out of 5, which can be expressed as 1/5 or 0.2.

Let's denote:

n = number of trials (number of questions) = 20

p = probability of success (probability of answering a question correctly) = 0.2

x = number of successful outcomes (number of questions answered correctly)

We want to calculate the probability of answering at least 14 questions correctly, which means we need to find the probability of getting 14, 15, 16, 17, 18, 19, or 20 questions correct.

Using the binomial probability formula, we can calculate the probability for each case and sum them up:

P(X ≥ 14) = P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18) + P(X = 19) + P(X = 20)

P(X = k) = (n choose k) * \(p^k * (1 - p)^{(n - k)\)

Using this formula for each value of k and adding them up, we find:

P(X ≥ 14) ≈ 0.0000039

Therefore, the probability that a student, answering each question at random, will answer at least 14 questions correctly is approximately 0.0000039 rounded to seven decimal places.

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Complete question is below

A student takes a multiple choice test with 20 questions. Each question has 5 possible answers, only one of which is correct. { a) If a student answers each question at random, what is the probability that they will answer at least 14 questions correctly? Round your answer to seven decimal places.

Answer:

Personally its a negative real‼️‼️

i hope you guys didn't have to suffer thru the rest like I did c,:

here is THE REST OF THE ANSWERS!

Step-by-step explanation:

THE ENTIRE PICTURE ABOVE IS CORRECT, BUT AFTER THAT THE NEXT ANSWERS ARE.....

8. angle LNO is congruent to angle NLM because of CPCTC

9. segment ON is parallel to segment LM because of converse of the alt. int. angles theorem

10. segment LO is parallel to segment MN because of converse of the alt. int. angles theorem

11. LMNO is a parallelogram because of the def. of a parallelogram

I just did all of these on edg. 2022 and they're correct. have a great day/night you guys and good luck!

We will use the converse of alternate interior angles theorem  to prove LMNO is a Parallelogram.

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length, and the opposite angles of a parallelogram are of equal measure.  

The proof is as follows:

Statements                                                   Reasons

1) LO ≅ MN                                                        Given

2) ON ≅ LM                                                       Given

3) LN ≅ LN                                                     Reflexive property

4) Δ LON ≅ Δ NML                                       SSS congruency rule

5) ∠ NLO ≅ ∠ LNM                                         CPCTC

and ∠ MLN ≅ ∠ LNO              

6) LM ║ ON and LO ║ MN   converse of alternate interior angles theorem

7) LMNO is a Parallelogram                  Property of Parallelogram  

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Answer:

A. & E.

Step-by-step explanation:

Pizza Truck Mean: 800

400 + 800 + 1,000 + 1,000 = 3,200

3,200/ 4 = 800

Burger Truck Mean: 800

800 + 700 + 900 + 800 = 3,200

3,200/ 4 = 800

They have the same mean; answer A.

Pizza Truck Median: 900

400, 800, 1000, 1000,

800, 1000

900

Burger Truck Median: 800

700, 800, 800, 900

800, 800

800

The pizza truck median is larger; answer E.

Answer:

x  ≥  21

Hope this helps!

Answer:

plz give the other person brain thingy :D

Step-by-step explanation:

Answer:6

Step-by-step explanation:

-7=s+(-13)

Open bracket

-7=s-13

Collect like terms

s=-7+13

s=6