How Do I solve -7(2v-2)+4v=4(v+1)

Answer:

Step-by-step explanation:

Since the distribution is approximately normal, we can use the empirical rule to estimate the mean and standard deviation.

According to the empirical rule:

Approximately 68% of the data falls within 1 standard deviation of the mean

Approximately 95% of the data falls within 2 standard deviations of the mean

Approximately 99.7% of the data falls within 3 standard deviations of the mean

From the information given in the problem, we know that:

10% of women are less than 60.8 inches tall

10% of women are more than 67.6 inches tall

So, we can estimate the mean height as the midpoint between 60.8 and 67.6:

mean = (60.8 + 67.6) / 2 = 64.2 inches

We also know that 80% of women are between 60.8 and 67.6 inches tall. Since this is approximately 1 standard deviation from the mean (on either side), we can estimate the standard deviation as:

standard deviation = (67.6 - 64.2) / 1 = 3.4 inches

Therefore, the mean height is approximately 64.2 inches and the standard deviation is approximately 3.4 inches.

Answer:

5/7

Step-by-step explanation:

When you reduce 150/210 you get 5/7, this is the reduced form

Using basic arithmetic operations, we concluded that a) Bryony wrote more words in total than Arthur.

b) Bryony wrote 220 more words than Arthur.

The four basic mathematical operations are addition, subtraction, multiplication, and division.

a) In order to establish who wrote more words overall, we must total the words that each participant wrote. By dividing the typical words per minute by the total number of minutes each person worked, we may determine this:

Arthur: 65 minutes × 16 words/minute = 1040 words

Bryony: 90 minutes × 14 words/minute = 1260 words

Therefore, Bryony wrote more words in total than Arthur.

b) To find out how many more words Bryony wrote than Arthur, we can subtract Arthur's total from Bryony's total:

1260 words - 1040 words = 220 words

Hence, Bryony wrote 220 more words than Arthur.

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a. The vector equation of the line passing through points A(4, −5, 3) and B(3, −7, 1) is r = (4 − t)i − 5j + (3 − t)k, where t is any real number.

b. The vector equation of the line parallel to the y-axis and passing through point (1, 3, 5) is r = i + (3 + t)j + 5k, where t is any real number.

c. The scalar equation of the plane is:ax + by + cz = dwhere a, b, and c are the components of the normal vector, and d is the distance of the plane from the origin.

a) The vector equation of a line passing through points A and B can be written as: r = a + tb,

where r is the position vector of any point P(x, y, z) on the line, a is the position vector of point A, b is the direction vector of the line, and t is a parameter representing the distance of the point P from point A

.r = a + tb = (4, −5, 3) + t (3 − 4, −7 + 5t, 1 − 3t) = (4 − t, −5 + 2t, 3 − t)

Thus, the vector equation of the line passing through points A(4, −5, 3) and B(3, −7, 1) is r = (4 − t)i − 5j + (3 − t)k, where t is any real number.

b) Any line parallel to the y-axis has direction vector d = (0, 1, 0).

The line passes through the point (1, 3, 5).

The vector equation of the line can be written as:

r = a + td = (1, 3, 5) + t(0, 1, 0) = (1, 3 + t, 5)

Thus, the vector equation of the line parallel to the y-axis and passing through point (1, 3, 5) is r = i + (3 + t)j + 5k, where t is any real number.

c) A line perpendicular to the y-plane must have a direction vector parallel to the y-axis, i.e., d = (0, 1, 0). The line passes through point (0, 1, 2).

The vector equation of the line can be written as:

r = a + td = (0, 1, 2) + t(0, 1, 0) = (0, 1 + t, 2)

Thus, the vector equation of the line perpendicular to the y-plane and passing through point (0, 1, 2) is

r = ti + (1 + t)j + 2k, where t is any real number.5)

The vector equation of the plane can be written as: r = r0 + su + tv, where r is the position vector of any point P(x, y, z) on the plane, r0 is the position vector of the point where the normal vector intersects the plane, u and v are vectors in the plane and s and t are parameters.

r = [2, 1, 4] + i[-2, 5, 3] + s[1, 0, -5]r = [2, 1, 4] - 2i + 5j + 3i + s[1, 0, -5]r = (2 + s)i + j - 2s + (4 - 2i + 5j + 3i) + t[1, 0, -5]r = (2 + s)i - i + 6j + (4 + 3i) - 2s + t[1, 0, -5]r = (s + 2)i + 6j - 2s + (3i + 4) + t[-5, 0, 1]r = (s - 2)i + 6j - 2s + 3it + 4 + t * [-5, 0, 1]

The scalar equation of the plane is:ax + by + cz = dwhere a, b, and c are the components of the normal vector, and d is the distance of the plane from the origin.

To find the components of the normal vector, we can take the cross product of the vectors in the plane:n = u x v = [1, 0, -5] x [-2, 5, 3] = [-5, -13, -5]

The components of the normal vector are a = -5, b = -13, and c = -5.

To find the distance of the plane from the origin, we can use the fact that the position vector of any point on the plane is perpendicular to the normal vector.

The position vector of the point [2, 1, 4] is:r = [2, 1, 4] = (s - 2)i + 6j - 2s + 3it + 4 + t * [-5, 0, 1]

Equating the dot product of r and n to zero gives:-5(s - 2) - 13(6) - 5(-2s + 3t + 4) = 0

Simplifying this equation gives:24s - 15t - 67 = 0

Thus, the distance of the plane from the origin is |67/24|. The scalar equation of the plane is:-5x - 13y - 5z = 67/24.

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The vector equation of the line is:

r = (4, -5, 3) + t(-1, -2, -2)

The vector equation of the line is:

r = (1, 3, 5) + t(0, 1, 0)

The vector equation of the line is:

r = (0, 1, 2) + t(1, 0, 0)

25(x - 2) + 13(y - 1) + 5(z - 4) = 0

Simplifying this equation gives the scalar equation of the plane.

a) To find the vector equation of the line through the points A(4, -5, 3) and B(3, -7, 1), we can use the direction vector given by the difference between the two points:

Direction vector: AB = B - A = (3, -7, 1) - (4, -5, 3) = (-1, -2, -2)

Now, we can write the vector equation of the line as:

r = A + t(AB)

where r is the position vector of any point on the line and t is a parameter.

Therefore, the vector equation of the line is:

r = (4, -5, 3) + t(-1, -2, -2)

b) To find the vector equation of the line parallel to the y-axis and containing the point (1, 3, 5), we can use the direction vector (0, 1, 0) since it is parallel to the y-axis.

Therefore, the vector equation of the line is:

r = (1, 3, 5) + t(0, 1, 0)

c) To find the vector equation of the line perpendicular to the y-plane and passing through the point (0, 1, 2), we can use a direction vector that is perpendicular to the y-plane. One such vector is (1, 0, 0) which points along the x-axis.

Therefore, the vector equation of the line is:

r = (0, 1, 2) + t(1, 0, 0)

5. To write the scalar equation of the plane given by the vector equation [x, y, z] = [2, 1, 4] + i[-2, 5, 3] + s[1, 0, -5], we can use the point-normal form of the equation of a plane.

The normal vector of the plane can be found by taking the cross product of the two direction vectors given:

n = [-2, 5, 3] × [1, 0, -5]

  = [(-5)(-5) - (3)(0), (3)(1) - (-2)(-5), (-2)(0) - (-5)(1)]

  = [25, 13, 5]

The scalar equation of the plane is given by:

n · ([x, y, z] - P) = 0

where n is the normal vector and P is a point on the plane. Using the given point [2, 1, 4]:

25(x - 2) + 13(y - 1) + 5(z - 4) = 0

Simplifying this equation gives the scalar equation of the plane.

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The solution of the system by using elementary row operations on the equations or on the augmented matrix following systemic elimination procedure is x1 = −8 and x2 = 3.

The complexity of the algebra required to solve a linear system rises as the number of equations and unknowns grows. By streamlining the nomenclature and standardizing processes, the necessary computations may be made easier to handle.

The procedures listed below should be followed in order to solve a system of linear equations using the row operations:

1. As a matrix equation, write the equations as AX = B.

2. Create an augmented matrix by converting the matrix equation to the following form: [A | B] (the word "augmented" refers to the vertical line we create to remind us where the equals sign belongs).

3. Reduce the augmented matrix using row operations to arrive at the answer.

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The 28th term in the sequence of positive rationals produced by the counting process described in Theorem 5.3.1 is 3/2.

Theorem 5.3.1 describes a counting process in which positive rationals are listed in increasing order. The process starts with 1/1, followed by all rationals of the form m/1, 1/m, where m is a positive integer.

Next, all rationals of the form m/(m+1), (m+1)/m are listed, where m is a positive integer. This process continues, with all remaining rationals listed in increasing order.

To find the 28th term in this sequence, we need to determine which rational number is listed in the 28th position. Following the described counting process, we can list out the first few rationals in the sequence:

1/1, 1/2, 2/1, 1/3, 3/1, 2/3, 3/2, 1/4, 4/1, 3/4, 4/3, 2/5, 5/2, 3/5, 5/3, 4/5, 5/4, ...

Counting through this list, we see that the 28th term is 3/2.

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Answer:

acute angle

Step-by-step explanation:

acute angle because it is under 90°

If the angle measure is less than 90 degrees then it's acute, if it is equal to 90 degrees it's right or square, if it's more than 90 degrees it's obtuse, and if it's equal to 180 degrees it's a straight angle but in this case it's straight and obtuse since 180 is greater than 90.

The correct answer is (D) The full length to which it can be extended.

The size classification of an extension ladder indicates the full length to which it can be extended.
An extension ladder's size classification indicates the total length the ladder can reach when its fly section is fully extended.

This helps users determine if the ladder will be long enough for their specific needs when working at height.

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Answer:

4x-15+6x-35=180

Step-by-step explanation:

4x−15+6x−35=180

Step 1: Simplify both sides of the equation.

4x−15+6x−35=180

4x+−15+6x+−35=180

(4x+6x)+(−15+−35)=180(Combine Like Terms)

10x+−50=180

10x−50=180

Step 2: Add 50 to both sides.

10x−50+50=180+50

10x=230

Step 3: Divide both sides by 10.

10x/10=230/10

Answer:10x

Step-by-step explanation: 6x+4x=10x

Answer:

x = 50; 2x = 100

Step-by-step explanation:

x + 2x = 150

3x = 150

x = 50

2x = 2(50)

2x = 100

Answer:

7x + 7y is the product of 7 & (x + y)

Step-by-step explanation:

\(7x + 7y = 7(x + y)\)

Hence 7 & (x + y) are the factors of 7x + 7y

Therefore, there are 53,248 different super subs that can be made if there are 8 toppings, 6 condiments, and 6 types of homemade bread to choose from at Sandwich Station.

The super sub at Sandwich Station consists of 4 different toppings and 3 different condiments. The question is asking how many different super subs can be made if there are 8 toppings, 6 condiments, and 6 types of homemade bread to choose from.

To solve this problem, we can use the multiplication principle of counting. The multiplication principle states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things.

Let's use the multiplication principle to solve this problem. There are four different toppings, and we can choose any of the eight toppings for each of the four spots.

Using the multiplication principle, there are

8 x 8 x 8 x 8 = 4096

ways to choose the toppings. Similarly, there are

6 x 6 x 6 = 216

ways to choose the condiments. Lastly, there are 6 different types of homemade bread to choose from. Using the multiplication principle again, there are

4096 x 216 x 6 = 53,248,

which means there are 53,248 ways to make the super subs.

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Answer:

y= 1/2x + 2.5

Step-by-step explanation:

We already have the point-slope form of the line.

Convert into Slope Intercept form:

y-3=1/2(x-1)

\(y-3=\frac{1}{2}x -0.5\leftarrow \text {Distribute}\\y-3+3=\frac{1}{2}x-0.5+3\leftarrow \text {Subtraction Property of Equality} \\\boxed{y=\frac{1}{2}x+2.5} \text { OR } \boxed{y=\frac{1}{2}x+\frac{5}{2}}\)

The general solution in both vector and scalar form is as follows:

Vector form:

\(\[\mathbf{x} = c_1\mathbf{v}_1e^{\lambda_1t} + c_2\mathbf{v}_2e^{\lambda_2t}\]\)

Scalar form:

\(\[\begin{aligned}x &= c_1v_{11}e^{\lambda_1t} + c_2v_{21}e^{\lambda_2t} \\y &= c_1v_{12}e^{\lambda_1t} + c_2v_{22}e^{\lambda_2t}\end{aligned}\]\)

What are eigenvalues?

Eigenvalues are a concept in linear algebra that are used to analyze the properties of linear transformations or matrices. In simple terms, eigenvalues represent the scaling factors by which a vector is stretched or compressed when it is transformed by a linear transformation or multiplied by a matrix.

To find the general solution for the given system of differential equations:

\(\[\begin{aligned}x' &= -6x + 5y \\y' &= -5x - 4y\end{aligned}\]\)

We can rewrite the system in matrix form as follows:

\(\[\mathbf{x'} = \begin{bmatrix} -6 & 5 \\ -5 & -4 \end{bmatrix} \mathbf{x}\]\)

where \($\mathbf{x} = \begin{bmatrix} x \\ y \end{bmatrix}$.\)

To find the general solution, we need to find the eigenvalues and eigenvectors of the coefficient matrix\($\begin{bmatrix} -6 & 5 \\ -5 & -4 \end{bmatrix}$.\)

The characteristic equation is given by:

\(\[\det(\mathbf{A} - \lambda \mathbf{I}) = 0\]\)

where \($\mathbf{A}$\) is the coefficient matrix,\($\lambda$\)is the eigenvalue, and \($\mathbf{I}$\)is the identity matrix.

Substituting the values, we have:

\(\[\begin{aligned}\det \begin{pmatrix} -6-\lambda & 5 \\ -5 & -4-\lambda \end{pmatrix} &= 0 \\(-6-\lambda)(-4-\lambda) - (5)(-5) &= 0 \\\lambda^2 + 10\lambda + 6 &= 0\end{aligned}\]\)

Solving this quadratic equation, we find the eigenvalues \(\lambda_1$ and $\lambda_2$.\left \{ {{y=2} \atop {x=2}} \right.\)

Once we have the eigenvalues, we can find the corresponding eigenvectors\($\mathbf{v}_1$ and $\mathbf{v}_2$\) by solving the equation:

\(\[(\mathbf{A}-\lambda\mathbf{I})\mathbf{v} = 0\]\)

Substituting the eigenvalues, we solve for the eigenvectors.

Let's denote the eigenvalues as \(\lambda_1$ and $\lambda_2$,\) and the corresponding eigenvectors as \(\mathbf{v}_1$ and $\mathbf{v}_2$.\)

Once we have the eigenvalues and eigenvectors, we can express the general solution in both vector and scalar form as follows:

Vector form:

\(\[\mathbf{x} = c_1\mathbf{v}_1e^{\lambda_1t} + c_2\mathbf{v}_2e^{\lambda_2t}\]\)

Scalar form:

\(\[\begin{aligned}x &= c_1v_{11}e^{\lambda_1t} + c_2v_{21}e^{\lambda_2t} \\y &= c_1v_{12}e^{\lambda_1t} + c_2v_{22}e^{\lambda_2t}\end{aligned}\]\)

wherec_1 andc_2 are arbitrary constants\(, $v_{ij}$\) that represent the \(i$-th\)component of the jth eigenvector and \($e^{\lambda_it}$\) represent the exponential term with the eigenvalue.

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Solution:

We are required to determine which is a geometric sequence.

Firstly, let us look at what a Geometric sequence is .

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

In summary, a Geometric sequence has a common ratio.

Let us take a look at the options one after the other

A. -5,0,10,25,45

B. 1,2,4,8,16

C.-3,1,5,9

D. 4,8,24,96,480

Thus, the answer is B. 1,2,4,8,16

Answer:

Step-by-step explanation:

We will approach this problem by doing a check

Say the diameter of a circle is 4 cm

Hence the radius is 3 cm

We know that the circumference is \(C=2\pi r\)

\(C=2*3.142*2= 12.57cm\)

The circumference is about 3 time bigger than the diameter

Let us try another case say the diameter is 6 cm

The radius is 3 cm

\(C=2*3.142*3= 18.85cm\)

Answer:

N = 27

Step-by-step explanation:

The total value would be 90 , as it is a right triangle . Starting from the aforementioned number and subtracting it by the given values above shall reward you with the correct answer .

90 - ( 6 + 3 ) = 81

81 / 3 = 27

ALSO GIVE ME BRAINLIEST PLEASE :)

Answer:

i think 27??

Step-by-step explanation:

n+6 +90+2!+3=180

Answer:

I think it's B) Alloy X

Answer:

16

Step-by-step explanation:

Angles on a straight line add to 180°.

\(5x+1+6x+3=180 \\ \\ 11x+4=180 \\ \\ 11x=176 \\ \\ x=16\)

the distance between the tree and the flagpole is approximately 23.29 feet.

To find the distance between the tree and flagpole, we can use the Pythagorean theorem, which states that the square of the distance between the two points (the hypotenuse of the right triangle) is equal to the sum of the squares of the other two sides.

In this case, the distance between the tree and flagpole (the hypotenuse of the triangle) is equal to the square root of (20^2 + 12^2) = square root of (400 + 144) = square root of 544.

So the distance between the tree and the flagpole is approximately 23.29 feet.

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The average participation score after dropping the lowest 4 participation scores is = 83.33%

In order to calculate the average participation score after dropping the lowest 4 participation scores, we need to first calculate the participation score for each class.

For the first class, the student answered 2 out of 3 quizzes correctly, so the participation score is (2/3) x 100 = 66.67%.

For the second class, the student answered 1 quiz correctly, so the participation score is 100%.

Now we need to find the average participation score after dropping the lowest 4 scores. Since the student only participated in 2 classes, we don't need to drop any scores, the average participation score is (66.67 + 100)/2 = 83.33%

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option C. Rejecting a true null hypothesis. The level of significance in hypothesis testing is the probability of rejecting a true null hypothesis.

In hypothesis testing, the null hypothesis is a statement that there is no significant difference between two populations or variables, while the alternative hypothesis is a statement that there is a significant difference. The level of significance, denoted by alpha (α), is the probability of rejecting the null hypothesis when it is actually true.

In other words, if the level of significance is set at 0.05 (or 5%), this means that there is a 5% chance of rejecting the null hypothesis when it is actually true. This is known as a type I error, or a false positive.

The level of significance is usually set by the researcher or statistician before conducting the hypothesis test, and is typically based on the desired balance between the risk of making a type I error and the risk of making a type II error (failing to reject a false null hypothesis).

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The level of significance in hypothesis testing is the probability of

a. accepting a true null hypothesis

b. accepting a false null hypothesis

c. rejecting a true null hypothesis

d. could be any of the above, depending on the situation

Answer:

I'd say the answer is A or B

Step-by-step explanation:

Since the colonists overtime had so many laws passed over that were cruel and unfair they went against the British with acts like the Tea Act which were preformed to turn against the British. (sorry if im wrong ^-^)

A) The distance increases between starting and 6 seconds.

B) The distance is constant between seconds 6 and 8.

C) The distance decreases between seconds 8 and 12

Answer:

Robert can make 16 packages

Answer:

True. The statement is also equivalent to: If m<B + m<C does not equal m<D, then m<A does not equal m<B and m<A + m<C is not equal to m<D.

Answer:

3 / 16

Step-by-step explanation:

Let The total amount = x

Fraction eaten on first day = 1/4x

Fraction left = x - 1/4x = 3/4x

Fraction of amount left eaten on second day = 3/4 of 3/4x

3/4 * 3/4x = 9/16x

Fraction left :

3/4x - 9/16x = (12x - 9x) /16 = 3/16x

Hence, fraction left = 3/16

Answer:

34/50 or 17/25

Step-by-step explanation:

trust

Answer: I think the problem is telling you to add the fractions, so 4/50 + 3/5 = 34/50 which simplifies to 17/25

Step-by-step explanation: First in order to add the fractions, you need to make the both of the fractions denominators the same. So 5*10=50, and whatever you do to the bottom you have to do to the top, so 3*10=30. So the problem will now be 4/50 + 30/50 = 34/50, and 34/50 silified is 17/25.