a vector has initial point 1=(−3,1) and terminal point 2=(,7). find all numbers so that has length 10

Answer:

70%

Step-by-step explanation:

56 / 80 x 100 = 70%

The rate of return on the $10,000 bond purchased at $8750 with a 10% coupon is 24.29%. The answer closest to this value is option C, 11.43%.

The rate of return on a bond is determined by the coupon rate and the difference between the purchase price and face value of the bond.

The coupon rate is the amount of interest paid annually on a bond expressed as a percentage of the face value of the bond.

In this case, the coupon rate is 10%, and the bond was purchased at $8750.

The face value of the bond is $10,000,

So the difference between the purchase price and face value is $1250.

The rate of return can be calculated as follows:

rate of return = (coupon rate + (face value - purchase price) / purchase price) * 100

rate of return = (0.10 + ($10,000 - $8750) / $8750) * 100

rate of return = (0.10 + ($1250 / $8750)) * 100

rate of return = (0.10 + 0.1429) * 100

rate of return = 0.2429 * 100

rate of return = 24.29%

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The probability that a data value is less than two standard deviations from the mean is 95.45%.

In a normal distribution, approximately 68% of the data values fall within one standard deviation from the mean. This means that about 68% of the data values lie between the mean minus one standard deviation and the mean plus one standard deviation.

If we extend this to two standard deviations from the mean, we find that approximately 95.45% of the data values fall within two standard deviations from the mean. This means that about 95.45% of the data values lie between the mean minus two standard deviations and the mean plus two standard deviations.

Therefore, the probability that a data value is less than two standard deviations from the mean is 95.45%.

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The probability that a data value is less than two standard deviations from the mean is 95.45%.

In a normal distribution, approximately 68% of the data values fall within one standard deviation from the mean. This means that about 68% of the data values lie between the mean minus one standard deviation and the mean plus one standard deviation.

If we extend this to two standard deviations from the mean, we find that approximately 95.45% of the data values fall within two standard deviations from the mean. This means that about 95.45% of the data values lie between the mean minus two standard deviations and the mean plus two standard deviations.

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Victor, a recent high school student, took the sat exam, then the probability (given as a percentage) is 53.8%

Let's start defining the random variable X.

X : '' SAT critical reading scores from the 2019 school year for high school students in the United States ''

We know that X ~ N (μ,σ)

Where μ is the mean and σ is the standard deviation.

⇒ X ~ N (497,115)

If we want to calculate probabilities related to X we need to standardized the random variable. We do this by subtracting the mean to X and then dividing by the standard deviation. This new random variable will be ''Z'' and Z ~ N (0,1)

We can find the probabilities of ''Z'' in any standard normal table.

The cumulative distribution of ''Z'' is the function Φ where  :

P ( Z ≤ a ) = Φ (a)

Now, we need to calculate the following probability :

= P ( 120 < [tex]X[/tex] < 513 )

If we standardized this :

= P ( [tex]\frac{120-497}{115}[/tex] < [tex]\frac{X-497}{115}[/tex] <  [tex]\frac{513-497}{115}[/tex] )

We know that [tex]\frac{X-497}{115}[/tex]≅ Z ⇒

= P ( [tex]\frac{120-497}{115}[/tex] < [tex]Z[/tex] <  [tex]\frac{513-497}{115}[/tex] )

= P ( [tex]\frac{120-497}{115}[/tex] < [tex]Z[/tex] <  [tex]\frac{513-497}{115}[/tex] )

= P ( -3.27 < [tex]Z[/tex] <  0.139 )

= Φ(-3.27) - Φ(0.139)

= 0.9898 - 0.4509

= 0.5389

= 53.89% ≅ 53.8%

Therefore,

Victor, a recent high school student, took the sat exam, then the probability (given as a percentage) is 53.8%

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Victor, a recent high school student, took the sat exam, then the probability (given as a percentage) is 53.8%

Let's start defining the random variable, X.

X: '' SAT critical reading scores from the 2019 school year for high school students in the United States ''

We know that X ~ N (μ,σ)

Where μ is the mean and σ is the standard deviation.

⇒ X ~ N (497,115)

If we want to calculate probabilities related to X we need to standardize the random variable. We do this by subtracting the mean from X and then dividing by the standard deviation. This new random variable will be ''Z'' and Z ~ N (0,1)

We can find the probabilities of ''Z'' in any standard normal table.

The cumulative distribution of ''Z'' is the function Φ where  :

P ( Z ≤ a ) = Φ (a)

Now, we need to calculate the following probability :

= P ( 120 <  < 513 )

If we standardized this :

= P (  <  <   )

We know that ≅ Z ⇒

= P (  <  <   )

= P (  <  <   )

= P ( -3.27 <  <  0.139 )

= Φ(-3.27) - Φ(0.139)

= 0.9898 - 0.4509

= 0.5389

= 53.89% ≅ 53.8%

Therefore,

Victor, a recent high school student, took the sat exam, then the probability (given as a percentage) is 53.8%

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The equivalent fractions, with a common numerator of 6, are given as follows:

A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:

Fraction = x/y.

The terms are named as follows:

Equivalent fractions are fractions for which the ratio of the numerator and the denominator is the same.

For fraction 2/5, the numerator is of 2, hence 6/2 = 3 and the equivalent fraction is obtained as follows:

(2 x 3)/(5 x 3) = 6/15.

For fraction 3/10, the numerator is of 3, hence 6/3 = 2 and the equivalent fraction is obtained as follows:

(2 x 3)/(2 x 10) = 6/20.

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The probabilities of the individual outcomes are the same.

The probability model for this situation is uniform.

A mathematical illustration of a random event is a probability model. Its sample space, occurrences therein, and associated probability for each event serve as its definition.

The collection of all potential outcomes is the sample space S for a probability model.

Hence, it can be seen that there is 2 of each number so there is an equal chance. when there is an equal chance that is uniform.

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Elena's total score for the two games is 478, with her score in the first game being 224 and her score in the second game being 254.

Let 'x' be Elena's score in the first game and 'y' be Elena's score in the second game.

We know that the total score for the two games is 478, so we can write the following equation:

x + y = 478

We also know that the score in the second game is 30 more than 3/4 of Elena's score in the first game. We can write this as:

y = x + 30

Substituting this into the first equation gives:

x + x + 30 = 478

Simplifying gives:

2x + 30 = 478

Subtracting 30 from both sides gives:

2x = 448

Dividing both sides by 2 gives:

x = 224

So, Elena's score in the first game is 224. Substituting this value into the equation for the second game gives:

y = 224 + 30

So, Elena's score in the second game is 254.

In summary, Elena's total score for the two games is 478, with her score in the first game being 224 and her score in the second game being 254.

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Using the concept of sine rule and cosine rule, the value of angle ACB is

36.64°

The sine rule is a mathematical formula used in trigonometry to find the relationship between the sides and angles of a triangle. It states that the sine of one of the angles in a triangle is equal to the ratio of the length of the side opposite that angle, divided by the length of the hypotenuse. The formula can be written as:

sin(A) = a / c

where A is one of the angles in the triangle, a is the length of the side opposite angle A, and c is the length of the hypotenuse. The sine rule is commonly used to find the length of one side of a triangle when the lengths of the other two sides and one angle are known. Another form of the sine rule is the "ambiguous case" formula, which can be used to find one of the angles in a triangle when the lengths of all three sides are known:

a / sin(A) = b / sin(B) = c / sin(C)

where A, B, and C are the angles in the triangle, and a, b, and c are the lengths of the sides.

In the given problem, we can simply substitute the values into the formula and then solve for the unknown angle.

a / sin A = b / sin B = c / sin C

But since we don't know the value of BC, we can find that first using cosine rule.

a² = b² + c² - 2(bc) cos A

a² = 9² + 6² -2(9)(6)cos80

a² = 98.23

a = √98.23

a = 9.9

Going back to using sine rule;

a / sin A = b / sin B = c / sin C

9.9 / sin 80 = 6 / sin C

sin C = (6 sin 80) / 9.9

sin C = 0.5968

C = sin⁻¹(0.5968)

C = 36.64°

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Answer:A 1.23 x 102hr

Step-by-step explanation:

It will take 1.23 x 10^2 hours to fill a cylinder-shaped vat.

What is the volume of the cylinder?

A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².

The volume of the cylinder-shaped vat can be calculated as follows:

V = π * r^2 * h

= π * 32.5^2 * 33.9 ft^3

The mass of the liquid in the vat can be calculated as the product of its volume and density:

m = d * V

= 1.77 g/mL * π * 32.5^2 * 33.9 ft^3

The time it takes to fill the vat can be calculated as the ratio of the mass of the liquid to the rate at which it is spilling out of the hose:

t = m / (12,757.9 g/s)

Converting the volume to liters, the density to kg/m^3, and the time to hours, the answer is approximately 1.23 x 10^2 hours.

Hence, it will take 1.23 x 10^2 hours to fill a cylinder-shaped vat.

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Hello!

The following common fractions converted into percentages...

[tex]\frac{5}{8}=[/tex] 62.5%

[tex]\frac{8}{9} =[/tex] 88.8% repeating

Step-by-step explanation:

To convert a common fraction into a percentage you must first convert the fraction to a decimal and then multiply by 100

Hope this helps!

The correct expression for the given scenario is,

⇒ y = 6 × 4³

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

A population has a beginning number is 6.

Now, A population has a beginning number is 6.

Hence, The population if it expands at a rate of 4 for 3 years is,

⇒ y = 6 × 4³

Thus, The correct expression for the given scenario is,

⇒ y = 6 × 4³

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P ( A or B ) ≠ P(A) + P(B) Hence, A and B are not mutually exclusive. hence  is not true for events

therefore the given condition is not true and hence statement is not true for the given events

Two events are called mutually exclusive they are independent to each other.

Also, If A and B are any two events,

Then they are called mutually exclusive,

If P(A ∪ B ) = P(A) + P(B)

Or P ( A or B ) = P(A) + P(B)

Here, P(A) = 0.37, P(B) = 0.38 and P(A or B) = 0.27

Since,

0.27 ≠ 0.37 + 0.38

⇒  P ( A or B ) ≠ P(A) + P(B)

Hence, A and B are not mutually exclusive.

therefore the given condition is not true and hence statement is not true

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A complex number is the product of a real number and an imaginary number in the form of a + bi. Complex numbers are used to solve equations that don't have real solutions, such as [tex]x^{2}[/tex] + 1 = 0.

How to solve a complex number?

Given:

When solving and reasoning with complex numbers, it's important to keep the following properties in mind:

1. The sum of two complex numbers is the sum of their real and imaginary parts.

For example, (a + bi) + (c + di) = (a + c) + (b + d)i

2. The product of two complex numbers is the product of their real and imaginary parts.

For example, (a + bi).(c + di) = (ac - bd) + (ad + bc)i

3. The magnitude (or absolute value) of a complex number is the distance from the origin to the point (a,b) on the complex plane.

For example, |a + bi| = √a^2 + b^2

4. The conjugate of a complex number is its mirror image across the real axis.

For example, the conjugate of (a + bi) is (a - bi).

These properties can be used to solve and reason with complex numbers. For example, to find the quotient of two complex numbers, one could divide the product of their conjugates by the product of their magnitudes.

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Answer:

Let x be the number of bottles of water that Yui buys, and y be the number of sports drinks. The first equation represents the total number of bottles:

x + y = 6

The second equation represents the total cost:

1.5x + 2.5y = 10

To solve for x and y, we can use substitution. Solving the first equation for y in terms of x:

y = 6 - x

Substituting this expression for y into the second equation:

1.5x + 2.5(6 - x) = 10

Expanding and simplifying the right side:

1.5x + 15 - 2.5x = 10

-x + 15 = 10

Subtracting 15 from both sides:

-x = -5

Dividing both sides by -1:

x = 5

Substituting this value for x back into y = 6 - x:

y = 6 - 5

y = 1

So Yui buys 5 bottles of water and 1 bottle of sports drink.

Step-by-step explanation:

The mass of the salt in the tank after t minutes is t kg. The tank begins to overflow after 300 minutes, and the mass of the salt in the tank is 300 kg.

a. To determine x(t), the mass of the salt in the tank after t minutes, we can use the principle of mass balance:

x(t) = 0.5 * [Vin(t) - Vout(t)]

where

Vin(t) = the volume of brine solution that flows into the tank after t minutes

Vout(t) = the volume of brine solution that flows out of the tank after t minutes.

Vin(t) = 4t

Vout(t) = 2t

Therefore:

x(t) = 0.5 * [4t - 2t] = 0.5 * 2t = t

So, the mass of the salt in the tank after t minutes is t kg.

b. To determine the mass of the salt when the tank begins to overflow, we need to find the time when the volume of brine solution in the tank reaches 600l.

Vin(t) - Vout(t) = 600

4t - 2t = 600

2t = 600

t = 300

So, the tank begins to overflow after 300 minutes, and the mass of the salt in the tank is 300 kg.

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Cosecant, Secant, and Cotangent are the three trigonometric functions that are, respectively, abbreviated as Csc sec cot.

The three trigonometric functions for cosecant, secant, and cotangent are, respectively, denoted as Csc sec cot. Due to the fact that these functions are the reciprocals of the sine, cosine, and tangent functions, respectively, they are also known as the reciprocal trigonometric functions.

Secant or sec is expressed as 1/cos, cotangent or cot is represented as 1/tan, or cos/sin, and cosecants or Csc are represented as 1/sin, [tex]$$Cos^{-1[/tex] and 1/cos should not be mistaken with one another because they are significantly different. The reciprocal of cos is 1/cos, and inverse cos is used to find angles.

The relationship between the sides and angles of a right-angled triangle is known as a trigonometric ratio. The ratio of the neighboring side to the opposite side is known as a cotangent.

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Answer:

Step-by-step explanation:

76

Answer:

Step-by-step explanation:I don’t know u nerdy boy

An experimental unit treats a person (also known as a subject), an object, or another clearly defined object.

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The value of the expression when x = 2 is

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

10(x + 2) + 10 • 2

The expression 10(x + 2) + 10 * 2 for x = 2 is:

10(2 + 2) + 10 * 2

So, we have the following representation

10 * 4 + 10 * 2 =

So, we have the following representation

40 + 20

Lastly, we have

= 60

So, the answer is B. 60.

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A graph of the points with its ordered pair to show the number of cereal boxes there are for shipment of 4, 8, 10, 14, and 16 cases is shown in the image attached below.

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the relationship between the x-values and y-values in this table as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 144/24

Constant of proportionality, k = 6.

When x= 4, the number of cereal boxes y is given by:

y = 6x

y = 6(4)

y = 24 ⇒ ordered pair (4, 24).

When x= 8, the number of cereal boxes y is given by:

y = 6x

y = 6(8)

y = 48 ⇒ ordered pair (8, 48).

When x= 10, the number of cereal boxes y is given by:

y = 6x

y = 6(10)

y = 60 ⇒ ordered pair (10, 60).

When x = 14, the number of cereal boxes y is given by:

y = 6x

y = 6(14)

y = 84 ⇒ ordered pair (14, 84).

When x = 16, the number of cereal boxes y is given by:

y = 6x

y = 6(16)

y = 96 ⇒ ordered pair (16, 96).

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Answer: The last graph

Step-by-step explanation:

i did the test on flvs .

The last graph shows the relationship given in the table

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Slope = 11.50-8.5/4-2

=1.5

Let us take a point (5, 13), let us check this point which correctly matches the graph

Hence, the last graph shows the relationship given in the table

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The value of the angle is ∠MLN = 21°

What is an angle? In-Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The word “angle” is derived from the Latin word “angulus”, which means “corner”. The two rays are called the sides of an angle, and the common endpoint is called the vertex. The angle that lies in the plane does not have to be in Euclidean space. In case the angles are formed by the intersection of two planes in Euclidean or other space, the angles are considered dihedral angles. The angle is represented using the symbol “∠”. The angle measurement between the two rays can be denoted using the Greek letter θ, α, β etc. If the angles are measured from a line, we can find two different types of angles, such as a positive angle and a negative angle.

Positive Angle: If the angle goes in counterclockwise, then it is called a positive angle.

Negative Angle: If the angle goes clockwise direction, then it is called a negative angle.

∠MLN = ∠MLO - ∠OLN

= 52° - 31°

= 21°

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It will take Dionne 60 minutes and Elia 70 minutes to fold 210 packing boxes.

To find the unit rate for each person, divide the number of boxes they can fold by the time it takes them to fold them:

Dionne: 175 boxes / 50 minutes = 3.5 boxes/minute

Elia: 120 boxes / 40 minutes = 3 boxes/minute

Next, divide the total number of boxes to be folded (210) by each person's unit rate:

Dionne: 210 boxes / 3.5 boxes/minute = 60 minutes

Elia: 210 boxes / 3 boxes/minute = 70 minutes

So, it will take Dionne 60 minutes and Elia 70 minutes to fold 210 packing boxes.

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Answer:

Step-by-step explanation:

x = -2

F(x)=1.5(2)^x=0.375 , G(x)=-3(1/4)^x=-48

x=0

F(x)=1.5(2)^x=3, G(x)=-3(1/4)^x=-3

x=1/2

F(x)=1.5(2)^x=1.06 , G(x)=-3(1/4)^x=-6

AUC - B = 17 and AUB = 1, 2, 8, 9, 10, The partition of S formed by A, B, and C is not Au(B-C) = 1, 2, 8, 9, 10, or 17.

Finding the union of A and B requires us to identify every element that is either in A, B, or both. Here, A = 17 and B = 8, 9, and 10 respectively. So AUB = {1, 2, 8, 9, 10, 17}.

Finding (AUC) - B requires us to identify the components of the union of A and C minus the components of B. Here, A equals 17, B equals 8, 9, and 10, and C equals 17. Therefore, (AUC) - B = 17.

To determine Au(B-C), we must first identify the components of the union of A and the difference between B and C. Here, A equals 17, B equals 8, 9, and 10, and C equals 17. Therefore, Au(B-C)=1, 2, 8, 9, 10, and 17.

d. S cannot be partitioned by A, B, or C since S includes items that are not present in any of those three. As an illustration, elements 1 and 2 are present in S but not in A, B, or C. Therefore, S cannot be divided into A, B, and C.

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The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 30%.

The probability that a randomly selected school or district uses digital content is 72%. To find the probability that a randomly selected school uses digital content and uses it as part of their curriculum, we need to divide the number of schools that use digital content and use it as part of their curriculum (6) by the total number of schools (20). This gives us 6/20 or 30%. Therefore, the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 30%.

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