Need help with question 12.

The equation of a line passing through the terminal point of a vector a and in the direction of vector b is  r = a + λb.

In math the equation of a straight line is y = m x + c

where m is the gradient and c is the height at which the line crosses the y -axis, also known as the y -intercept.

Here we need to find the equation of a line (or a set of lines) passing through the terminal point of a vector a and in the direction of vector b.

Based on the general form of the equation of the line, the vector form of the equation of a line passing through a point having a position vector a, and parallel to a vector line b is written as,

=> r = a + λb.

Where λ refers the constant term.

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The length of RV is 14, SV is 7, TP is 15 and VP is 10. The solution has been obtained using centroid theorem.

What is centroid theorem?

According to the centroid theorem, the centroid of a triangle is located at a distance of 2/3 between the vertex and the midpoint of the sides.

In the given figure, V is the centroid of the triangle

The medians RS and PT intersect at V.

Now, since V divides each median in the ratio 2:1, therefore,

⇒VT = 1/3 of PT

⇒PT = 3*VT

Since, VT=5

⇒PT = 15 = TP

So, VP = PT - VT

⇒VP = 15-5

⇒VP = 10

Similarly,

⇒RV = 2/3 of RS

Since, RS = 21, therefore,

⇒RV = 2/3 of 21

⇒RV = 14

So, SV = RS-RV

⇒SV = 23-14

⇒SV = 7

Hence, the length of RV is 14, SV is 7, TP is 15 and VP is 10.

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The complete question is attached below

The formula the ratio of the displacement thickness to the boundary layer thickness is u = δ / 2

The term displacement thickness is defined as the distance by which the body surface should be shifted in order to compensate for the reduction in mass flow rate on account of boundary layer formation.

Here we need to find the way to determine the ratio of the displacement thickness to the boundary layer thickness.

As we all know that the boundary layer thickness. ideal fluid viscous force is neglected but in actual viscous stresses are prominent within the boundary layer.

AS we all also know that when fluid flows past a solid body the fluid particles adhere to the boundary and the condition of no-slip occurs.

Here the term non-slip conditions means the velocity of the fluid at body surface will be same as the velocity of body.

Then it can be calculated by using the following formula,

=> u = δ / 2

Complete Question:

Here by using the equation  u/U = y/δ and to determine the ratio of the displacement thickness to the boundary layer thickness.

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A sample of 5 backpacks will be chosen from a population of backpacks whose weights are normally distributed with mean 19.7 pounds with a 3.1-pound standard deviation. Each backpack's weight will be noted.

A sample of 5 backpacks will be chosen from a population of backpacks whose weights are normally distributed with mean 19.7 pounds with a 3.1-pound standard deviation. Each backpack's weight will be noted.. The weight of each backpack will be recorded in order to calculate the mean and standard deviation of the sample. To calculate the mean, the total weight of the five backpacks will be added together and then divided by the number of backpacks in the sample (5). To calculate the standard deviation, the weight of each backpack will be subtracted from the mean and the resulting difference will be squared. All of the squared differences will then be added together, divided by the number of backpacks in the sample (5), and the square root of this result will be taken. This will give us the standard deviation of the sample. These calculations will provide us with valuable information about the weights of the backpacks in the sample, which can then be compared to the weights of the backpacks in the population.

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No, these data do not allow us to infer that the mean number of commercials watched is greater than 15.

To make such an inference, we would need to know the population mean number of commercials watched, along with the population standard deviation. We can use the sample data to calculate the sample mean and sample standard deviation. The sample mean (X) is the sum of the data values divided by the number of observations. The sample standard deviation (s) is calculated using the equation s = √(sum of (x-X)² / (n-1)) , where n is the number of observations. With the sample mean and standard deviation we can then use a t-test to determine if the population mean is significantly greater than 15.

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The expression for the simplified polynomial would be - x² - 10x - 24.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the polynomial ( x + 5 )² is subtracted from 1. The simplified polynomial can be written as:-

Polynomial = 1 - ( x + 5 )²

Polynomial = 1 - ( x² + 10x + 25 )

Polynomial = 1 - x² - 10x - 25

Polynomial = -x² - 10x - 24

Hence, the polynomial can be written as -x² - 10x - 24.

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Given that IJ = 2, we know that IJ is the radius of the circle.

The area of the shaded sector is given as . Since the area of a sector is given by (angle of sector/360) * pi * r^2, we can set up the equation:

(x/360) * pi * 2^2 =

Solving for x:

x = (180/pi)*

We know that the arc JLK corresponds to the angle x, thus the length of JLK is (x/360)2pi*IJ = (x/180)*IJ * T = (180/pi) * T.

The probability that 1 battery in a pack of 16 is defective is approximately 0.3706 or 37.06%.

The binomial model can be used to calculate the probability of a specific number of successful outcomes (in this case, defective batteries) in a fixed number of trials (in this case, 16 batteries) with a constant probability of success (in this case, 5%) for each trial.

The probability of 1 defective battery in a pack of 16 can be calculated using the formula:

P(X = 1) = (¹⁶C₁) × (0.05)¹ × (0.95)⁽¹⁶⁻¹⁾

where (¹⁶C₁) is the binomial coefficient, which is equal to 16.

So;

P(X = 1) = (¹⁶C₁) × (0.05)¹ × (0.95)⁽¹⁶⁻¹⁾

P(X = 1) = 16 × 0.05 × 0.95¹⁵

P(X = 1) = 0.3706

Therefore, the probability that 1 battery in a pack of 16 is defective is approximately 0.3706 or 37.06%.

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The eastbound airplane has traveled 16 miles.

This can be determined using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the distance the northbound airplane has traveled (12 miles) is one side of the triangle, the distance the eastbound airplane has traveled is the other side, and the distance between the two airplanes (20 miles) is the hypotenuse.

So, we can set up the equation as:

(distance eastbound airplane)^2 + 12^2 = 20^2

Solving for the distance eastbound airplane, we get:

distance eastbound airplane = sqrt(20^2 - 12^2) = sqrt(256 - 144) = sqrt(112) = 16 miles

The perimeter of a rectangle is 700 feet. A quadratic function for its area in terms of its width is A(w) = 350w - w²

The formula for the perimeter of a rectangle is given by:

p = 2w + 2l

While its area is:

A = w x l

Where:

w = width

l = length

Substitute p = 700 ft.,

700 = 2w + 2l

700 = 2(w + l)

w + l = 350

l = 350 - w

Substitute l = 350 - w into the formula of area:

A = w x l

A = w (350 - w)

A(w) = 350w - w²

Hence, the expression is: A(w) = 350w - w²

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Answer: The answer is 3

Step-by-step explanation:

No, new atoms are not created in a chemical reaction. Atoms are rearranged or combined to form new compounds. The total number of atoms before and after the reaction is the same. This is known as the law of conservation of mass.

The law of conservation of mass states that in a closed system, the total mass of the reactants (the substances before the reaction) is equal to the total mass of the products (the substances after the reaction). This means that the atoms present in the reactants must also be present in the products, but in different combinations or arrangements.

Therefore, It's important to note that in some reactions, atoms can be transformed into different forms, for example, a carbon atom can be transformed into a carbon dioxide molecule, but the mass of the atoms remains the same.

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The exponent form that represents the side length of the square is √x

From the question, we have the following parameters that can be used in our computation:

Area = x in.²

The area of a square is calculated as

Area = Side length²

substitute the known values in the above equation, so, we have the following representation

Side length² = x

Take the square root of both sides

Side length = √x

Hence, the expression is √x

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The altitude of the second beetle above the first beetle when they are 72 cm apart horizontally is 14.4 cm.

In order to find the altitude of the second beetle, let x be the altitude of the second beetle above the first beetle.

The horizontal distance between the two beetles is 72 cm.

The first beetle moves twice as fast as the second beetle, so the vertical distance between them is 2x.

Therefore, the equation for the problem is:

3x + 2x = 72

5x = 72

x = 14.4 cm

Therefore, the altitude of the second beetle above the first beetle when they are 72 cm apart horizontally is 14.4 cm.

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Answer:111

Step-by-step explanation:

1111

answer

no

steps

February ends on the 28th this year 2023

leap year February ends on the 29th

The image that gives the translation of the polygon six units to the left and two units upward is given as follows:

The fourth graph.

(which is the third graph if we consider that the first is the original image).

A translation is a movement to a graph or figure in which only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.

The translations are represented as follows:

For the translation 5 units left, we have that:

The bottom segment of x = 1 to x = 4 will assume coordinates of x = -5 to x = -2.

For the translation 2 units up, we have that:

The vertical segment from y = 1 to y = 3 will assume coordinates from y = 3 to y = 5.

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Answer:

The value of z can be found using the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. In other words, if a, b, and c are the lengths of the sides of a triangle opposite angles A, B, and C, respectively, and A, B, and C are the angles opposite sides a, b, and c, respectively, then: a/sin(A) = b/sin(B) = c/sin(C). This can be used to solve for the unknown side length.

Answer: Maybe if you post the question

Step-by-step explanation:

The coordinates of point p along the directed line segment ab are [tex]$p(-1,-2)$[/tex]

Let the coordinates of point p be (x,y)

The ratio of ap to pb is 2 to 6, so we have [tex]$$\frac{|ap|}{|pb|} = \frac{2}{6}$$[/tex]

We can calculate the distances between points $a$ and $p$ and points $p$ and $b$ using the distance formula as follows:

[tex]$$|ap| = \sqrt{(x+3)^2+(y-2)^2}$$$$|pb| = \sqrt{(5-x)^2+(y+4)^2}$$[/tex]

We can use the ratio of the distances to set up a proportion to solve for $x$ and $y$:

[tex]$$\frac{|ap|}{|pb|} = \frac{2}{6} \implies \frac{\sqrt{(x+3)^2+(y-2)^2}}{\sqrt{(5-x)^2+(y+4)^2}} = \frac{2}{6}$$\\[/tex]

Solving for $x$ and $y$, we get $x = -1$ and $y = -2$.

Therefore, the coordinates of point $p$ along the directed line segment $ab$ are [tex]$p(-1,-2)$[/tex]

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$52 hundred is introduced to the December 31, 20Y6.

A proportion is a unit of fairness possession in the capital inventory of a corporation, and may discuss with devices of mutual funds, restrained partnerships, and actual property funding trusts. Share capital refers to all the stocks of an enterprise. The proprietor of stocks in a employer is a shareholder (or stockholder) of the corporation.

Note that proportion is an indivisible unit of capital, expressing the possession dating among the employer and the shareholder.

Given that bond indenture for the 10-year, 9% debenture bonds issued January 2, 20Y5, required working capital of $100,000, a current ratio of 1.5, and a quick ratio of 1.0 at the end of each calendar year until the bonds mature.

The profits acquired from the possession of stocks is a dividend. There are extraordinary varieties of stocks consisting of fairness stocks, bonus stocks, proper stocks, and worker inventory choice plan stocks.

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Answer:

3. f

4. b

5. a, x

Step-by-step explanation:

3.

a/f = f/c

f² = ac

f = √ac

Answer: f

4.

x/b = b/c

b² = cx

b = √cx

Answer: b

5.

x/k = k/a

k² = ax

k = √ax

Answer: a, x

Answer:

The area of a circle is pi multiplied by the radius squared (A = π r²)

The radius (r) is the distance from the center of the circle, to the edge of the circle.

Example:

if you have a circle with radius 2, the area would be:

r = 2

A = π (2)²

A = π(4)

A = 4π

Answer:

Area can be calculated by the formula = [tex]\pi r^{2}[/tex]

Step-by-step explanation:

We can calculate the area of a circle with the formula,

Area of Circle = [tex]\pi r^{2}[/tex]

Where r replicates the radius of the circle

Answer: 13:6

Ratio of length to width = 39:18

Divide both by 3 to simplify

13:6

A perimeter longer than 50 for any point, C satisfies the area requirement.

Consequently, we have a base-10 triangle whose area is 100. Since the area is equal to half the product of base and height, the object's height is then 20.

The next two sides. If one of the sides is exactly 20 inches tall (when it coincides with the height, forming a right triangle), the other side must be strictly greater than 20 inches tall (being the hypotenuse), in which case the perimeter must be greater than 50.

Alternately, both sides could be longer than 20 because neither side is a height. Once more, the perimeter exceeds 50.

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The full question

In a given plane, points A and B are 10 units apart. How many points C are there in the plane such that the perimeter of triangle ABC is 50 units and the area of triangle ABC is 100 square units?

The number of papers that Ms. Motley will grade in five days would be = 46 papers (approximately).

The number of papers Ms. Motley graded in first day = 9 papers

The number of papers Ms. Motley graded in the second day = 27 papers

The number of papers Ms. Motley graded in the third day = 31 papers

The average number of she graded for the three days is calculated as follows;

9+27+31 = 67/3 = 27.3 papers.

If in 3 days = 27.3 papers

5. days = X papers

Make X papers the subject of formula;

X papers = 5× 27.3/3

= 136.5/3

= 45.5 papers

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The students expected to like soda are 324

from the question, we have the following parameters that can be used in our computation:

150 students out of a total of 800 students on campus did not like soda.

This means that

650 students out of a total of 800 students on campus like soda.

i.e. 800 - 150 = 650

When half of the students are considered, we have

Soda = 650/2

Evaluate

Soda = 325

Hence, the number of students is 325

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