Order the following set of numbers in ascending order (least to greatest): 2.007; 2.714; 2.09; 2.741; 2.07

So the answer is: the first arc should pass through point B (not A). All other elements in the diagram appear to be correct.

The elements or members of a set are the parts that make it up. To divide the components of a set, commas and two curly (idle) braces are typically employed. Capital letters are always used to print the set's name. The set "A" in this context consists of the letters v, w, x, y, and z.

Based on the given diagram and instructions, it appears that the error in the construction is that the first arc is centered at point C instead of point A. The correct procedure for constructing a line parallel to line AB and passing through point P is as follows:

1.Draw a line AB and mark point P not on line AB.

2.From point P, draw an arc that intersects line AB at points D and E.

3.Draw another arc, centered at point D, with the same radius as the first arc. This arc should intersect the first arc at point F.

4.Draw a line through point P and point F. This line is parallel to line AB and passes through point P.

So the answer is: the first arc should pass through point B (not A). All other elements in the diagram appear to be correct.

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The third arc should be drawn centred at F.

What is an arc?

In geometry, an arc is a curved segment of a circle or any curved line. It is a part of a curve that is bounded by two distinct endpoints and is characterized by its length, its curvature, and its central angle.

Constructing a parallel line to line AB and passing through point P.

To find:

The error occurred in the construction.

The procedure is,

The first arc must be drawn centred at C.

The second must be drawn centred at P.

Finally, the third arc must be drawn centred at F.

But here, the third arc is drawn centred at D. This is wrong.

The correct step is that the third arc must be centred at F.

Hence, The third arc should be drawn centred at F.

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The car salesperson made $62,000 in sales for the month

Let us say the amount of sales the car salesperson made in a month is x. Then, the total income can be represented as:

$1,400 + 0.05x = $4,500

The equation represents the total income of the car salesperson as the base salary of $1,400 per month plus a commission of 5% on sales. To find the amount of sales made, we have to solve x.

Subtracting $1,400 from both sides:

0.05x = $4,500 - $1,400 = $3,100

Dividing both sides by 0.05:

x = $3,100 / 0.05 = $62,000

So the car salesperson made $62,000 in sales for the month.

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Answer:

4 white horses.

Step-by-step explanation:

First, you need to find the total of the first set of horses (basically how many total were in the table).

~ 3+2+9+1 = 15

Next we need to find how many horses were white horses out of these 15 horses. In short the proportion would be White Horses/Total Horses.

~  \(\frac{3}{15}\) (or  \(\frac{1}{5}\), simplified)

Now, all we need to do is create the proportion with 20 as the denominator (in this case, 20 will be the total horses, and we just need to find X, or how many horses are expected to be white out of all of those horses). The proportion will look somewhat like this:

~  \(\frac{1}{5}\) = \(\frac{x}{20}\)

The final step is to multiply across (1x20) then divide that number by the 5 to find X.

~ 20÷5 = 4

Anyways, that means it would be expected to have 4 white horses out of 20 total. Hope this helped ^-^

Answer: Yes

Step-by-step explanation:

\(\frac{123}{2}=\frac{246}{4}=\frac{369}{6}=\frac{492}{8}=61.5\).

Since the ratio of distance in miles and the time in hours is constant, the relationship is proportional.

Time taken to walk across 100 yard field is 60 minutes.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

Speed of Slauson = 5 ft./min

That is, in 1 minute, Slauson can walk 5 feet.

We have to find the time taken to walk 100 yard.

1 yard = 3 feet

100 yard = 300 feet

Speed = Distance / Time

Time = Distance / Speed

Time = 300 / 5 = 60 minutes

Hence it will take 60 minutes to walk across a 100 yard field.

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There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

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Answer:

The slopes of parallel lines are equal.

Step-by-step explanation:

Two lines are parallel if their slopes are equal and they have different y-intercepts.

Based on the given information, the question is asking about the apparent relationship between two variables: study hours and test score. The correct answer is c.

Test score tends to increase as the number of study hours increases. This suggests a positive correlation between the two variables, meaning that as one variable (study hours) increases, the other variable (test score) also tends to increase.
The apparent relationship between the two variables under consideration, which are study hours and test score, can be described as follows:
Your answer: c. Test score tends to increase as the number of study hours increases.
This is because, generally, the more time a person spends studying, the better their understanding of the material, which often leads to a higher test score.

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ANSWER:

Selling more than 0 and less than 20 units will give positive revenue.

STEP-BY-STEP EXPLANATION:

We have the following function:

Now, we propose the following inequality:

Since negative units cannot be sold, we are then interested in the range from 0 to 20, therefore, if more than 0 and less than 20 units come in, the revenue will be positive.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The difference between −9 4/5 and −3 2/3 is -6 2/15.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The difference between −9 4/5 and −3 2/3 is,

−9 4/5 − (−3 2/3)

= −9 4/5 + 3 2/3

= (−9+3) + (−4/5 + 2/3)

= −6 + (-2/15)

= -6 2/15

Hence, The difference between −9 4/5 and −3 2/3 is -6 2/15.

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Answer:

D.(1,-2)

Step-by-step explanation:

y= -3x+1

when x=1

y= -3*1 +1

y=-3+1

so

y=-2

Given the expression:

2.5x

Let's determine the situation which best represents the expression.

Let's start from the first statement:

• A. The total amount of change received to pay for an item that cost $2.50:

The best representation for this is: C = A - 2.50

Where A is the amount paid, C is the amount of change.

• B. The area of a rectangle with side lengths 2.5 and x:

The best representation for this situation is:

2.5x

• C. The total cost of an item that is 2.50 more than x dollars:

T = 2.50 + x

• D. The total square footage of a yard when 2.50 yards is divided into equal parts:

This expression cannot be represented by 2.5x

Therefore, the situation which can be represented by the expression 2.5 is:

The area of a rectangle with side lengths 2.5 and x

ANSWER:

B. The area of a rectangle with side lengths 2.5 and x

Part A. The Volume of the tent is 96 ft²;    Part B: The Surface area of the tent is 152 ft².

Surface area of a triangular prism = 2(½ × b × h) + (a + b + c)H, where: a, b, and c are the lengths of the sides of the triangular base, b is the length of the base of the triangular face and h is the height; and H is the length of the prism.

Volume = ½ × b × h × l, where l is the length of the prism, b is the length of the base of the triangular face and h is the height.

Part A: Volume of the tent:

b = 6 ft

h = 4 ft

l = 8 ft

Volume of the tent = ½ × 6 × 4 × 8 = 96 ft²

Part B: Surface area of the tent:

b = 6 ft

h = 4 ft

a + b + c = 6 + 5 + 5 = 16 ft

H = 8 ft

Surface area of the tent = 2(½ × 4 × 6) + (16)8 = 152 ft²

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The value of Y0 for which the solution of the initial value problem y′−2=8 + 9sint, y(0)=y0 remains finite as to infinity is -5/2.

In mathematics, the y-intercept of a function is indicated by the beginning value of the function. Understanding the y-intercept is beneficial for graph functions.

Employ the first-order linear differential equation's solution formula, which I've lately demonstrated numerous times here.

\(y = e^t[e^{-t}(1+3sin(t)) dt + c] = -(\frac{1}{2})(3sin(t) + 3cos(t) + 2) + ce^t\)

After doing integration by parts twice.

Since lim{t->oo} y is finite, c = 0.

So, y(0) = -(1/2)(3+2) = -5/2

Therefore, the value of Y0 for which the solution is -5/2.

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Answer:

M1=35, M2=77, M3=49, M4=77, M5=62, M6=28

Step-by-step explanatio

Answer:

Angle 1) 35

Angle 2) 77

Angle 3) 49

Angle 4) 77

Angle 5) 62

Angle 6) 28

Step-by-step explanation:

Start with angle 3)

You have 2 angles for this one already, 90 and 41

All angles in a triangle have the sum of 180, therefore

Angle 3 = 180 - 90 - 41

Angle 3 = 49

Next is Angle 6)

You have Angle 3 and 103

Angle 6 = 180 - 49 - 103

Angle 6 = 28

Now Angle 2)

Angle 2 is on the same line as 103 and are supplementary, the sum is 180

Angle 2 = 180 - 103

Angle 2 =  77

Angle 4)

2 and 4 are vertical opposites with the same measurement, so 77

Angle 1)

Using Angles 1 and 2 and 68, they have a sum of 180

Angle 1 = 180 - 77 - 68

Angle 1 = 35

Angle 5)

Now with Angle 4 and 41 thats given, Angle 5 is

180 - 77 - 41 = 62

Answer:

x-intercept: (2,0)

y-intercept: (0,-4/3)

vertical asymptote: x = -3

Step-by-step explanation:

To find the x-intercepts, we can set f(x) to 0, which is y=0:

2x-4/x+3 = 0

2x-4 = 0

2x = 4

x = 2

To find the y-intercepts, we can set x to 0:

2(0)-4/(0)+3 = y

y = -4/3

To find the vertical asymptote, we can set the denominator equal to 0:

x+3 = 0

x = -3

Answer:

D

Step-by-step explanation:

Answer:

\(b = 72\)

Step-by-step explanation:

The variable "b" can be found by applying the "vertical angles theorem" or "opposite angles theorem".

For example, in the image provided on this answer we can see that m∠C = 62 (measure of angle C) is equal to the m∠A = 62 (measure of angle A).

The same can be said for ∠B and ∠D; both of which have the same angle measure of 118 degrees due to the vertical angles theorem.

The size of the the matrix B if a matrix A is 5x3 and the product AB is 5x7 is B =[3x7].

Two matrices can only be multiplied if the first matrix has the same number of columns as the second matrix has. If the first matrix has dimensions of a x b and the second matrix has dimensions of c x d, then b = c and their product will have dimensions of a x d.

Let A is a 3 x 5 matrix and B is a 5 x 7 matrix

We know that matrix multiplication of A and B is possible if

Number of columns of A = Number of rows of B

Since in the given problem

Number of columns of A = Number of rows of B = 5

So the product is possible

Now the product AB is a matrix of order 3 × 7

Now the order of the product AB is 3 × 7

If a 3 x 5 matrix is multiplied by a 5 x 7 matrix then their product is a matrix of order 3 × 7.

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Answer:

6.2

Step-by-step explanation:

15+16=31

31/5=6.2

Step-by-step explanation:

\(15 + 16 \div 5 \\ calculate \: the \: sum \: of \: 15 \: and \: 16 \\ 31 \div 5 = 6 \frac{1}{5} \\ or \: 6.2\)

There are 30 films entered in a movie festival, and a team of judges must pick the first, second, and third place winners. The number of possibilities for the winners is the subject of this question.

The number of ways to choose the first place winner is 30. After that, there are 29 films remaining to choose the second place winner, and 28 films left to choose the third place winner. However, the order in which the second and third place winners are chosen does not matter, since the two winners will still have the same ranks. Therefore, the number of ways to choose the second and third place winners is the number of ways to choose two out of the remaining 28 films, which is 28 choose 2 or (2827)/(21) = 378.

To find the total number of possibilities, we multiply the number of ways to choose the winners for each place: 303781 = 11,340. Therefore, there are 11,340 ways to choose the first, second, and third place winners from 30 films entered in the movie festival.

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The flux of the vector field F through the portion of the plane 3x + 2y + z = 6 in the first octant with the downward orientation cannot be determined due to the lack of a finite area on the given portion of the plane in the x-y plane.

To compute the flux of the vector field F = (xy, 3yz, 2zx) through the portion of the plane 3x + 2y + z = 6 in the first octant with the downward orientation, we need to evaluate the surface integral of the vector field over the given portion of the plane.

First, we need to parameterize the surface that lies on the plane. Since the equation of the plane is given as 3x + 2y + z = 6, we can express z in terms of x and y as z = 6 - 3x - 2y.

Next, we need to determine the bounds for the variables x and y. Since we are considering the portion of the plane in the first octant, we need to find the values of x and y that satisfy the conditions x ≥ 0, y ≥ 0, and 3x + 2y + z ≤ 6.

Substituting the expression for z in the inequality, we have 3x + 2y + 6 - 3x - 2y ≤ 6, which simplifies to 0 ≤ 0. This condition is always satisfied and does not provide any useful bounds.

Therefore, the portion of the plane in the first octant does not have any boundaries in the x-y plane that define a finite area. As a result, the surface integral and, consequently, the flux of the vector field through this portion of the plane cannot be calculated.

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the ratio is the relation(division) between 2 number

Step 1

Let

number 1= number of apples=8

number 2=total fruit = number of pears+ number of apples=5+8

number 2=13

Step 2

so, the ratio of apples to total fruit is 8/13

The geometric sequence for \(a_{1} = -8\), r = 1/2, and n=9 is -1/32.

The geometric sequence formula has the general form \(a_{n} = a_{1} * r^{n-1}\), where r denotes the common ratio, \(a_{1}\) denotes the first term, and n denotes the term's position in the series.

To find the geometric sequence, we can use the formula,

\(a_{n} = a_{1} * r^{n-1}\)

where \(a_{n}\) is the geometric sequence of n term

           \(a_{1}\) = first term

           n = term number

In given problem \(a_{1}\) = -8, r = 1/2, n=9

Put all values in the above equation,

\(a_{n} = (-8) * (\frac{1}{2})^{8-1} \\a_{n} = (-8) * (\frac{1}{2})^{7} \\a_{n} = (-8) * \frac{1}{2^{7} } \\a_{n} = (-8) *\frac{1}{128} \\a_{n} = \frac{-1}{32}\)

Therefore the \(9^{th}\) term of the geometric sequence is -1/32.

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The proposed solution y = xr leads to r = -2 for the given differential equation.

By substituting the proposed solution y = xr into the differential equation \(x^2y'' + 5xy' + 4y = 0\), we can find the value of r that satisfies the equation.

First, we differentiate y = xr twice to find the first and second derivatives.

\(y' = rx^(r-1)\)and \(y'' = r(r-1)x^(^r^-^2^).\)

Substituting these derivatives into the differential equation, we have:

\(x^2(r(r-1)x^(^r^-^2^)) + 5x(rx^(^r^-^1^)) + 4xr = 0\).

Simplifying the equation, we get:

\(r(r-1)x^r + 5rx^r + 4xr = 0\).

Factoring out the common term \(x^r\), we have:

\(x^r(r(r-1) + 5r + 4) = 0\).

For this equation to hold true for all x, the coefficient in front of \(x^r\) must be zero. Thus, we have:

r(r-1) + 5r + 4 = 0.

Simplifying the equation further, we get:

\(r^2 - r + 5r + 4 = 0,r^2 + 4r + 4 = 0,(r + 2)^2 = 0\).

From this equation, we find that r = -2. Therefore, the proposed solution y = xr leads to r = -2 as the solution for the given differential equation.

The proposed solution method for solving differential equations is based on the assumption that the solution can be expressed in a specific form. In this case, the proposed solution y = xr assumes that the solution is a power function of x. By substituting this solution and its derivatives into the differential equation, we can determine the value of r that satisfies the equation.

The process involves substituting the proposed solution and its derivatives into the differential equation, simplifying the equation, and identifying the condition under which the equation holds true. In this case, after simplifying the equation, we obtain a quadratic equation in terms of r. Solving this quadratic equation leads to the value r = -2, which satisfies the original differential equation.

The proposed solution method is a powerful technique used in solving linear homogeneous differential equations, where the equation can be expressed as a linear combination of the derivatives of the dependent variable with respect to the independent variable. By substituting the proposed solution, we can determine the values of the constants or exponents that satisfy the equation and find the general solution.

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The equivalent expression to the -49y - 14 are as follow,

7(-7y -2) , -7(7y + 2) ,-1(49y + 14), -14(3.5y + 1), -98/7 - 49y and -7(7y + k₁) + k₂ where -14 = -k₁ + k₂.

Expression is equal to

-49y - 14

The equivalent expressions are ,

By taking -1 as common factor

-(49y + 14)

By taking -7 as common factor

-7(7y + 2)

By taking 7 as common factor .

7(-7y -2)

By taking -14 as common factor

-14(3.5y + 1)

By replacing -14  as -98/7

-98/7 - 49y

By replacing -14 = -21 + 7

-7(7y + 3) + 7

By replacing -14 = -28 + 14

-7(7y + 4) + 14

By replacing -14 = -35 + 21

-7(7y + 5) + 21

By replacing -14 = -42 + 28

-7(7y + 6) + 4

and many more.

All of these expressions are equivalent to -49y -14.

Therefore, the expression which are equivalent to the given expression are 7(-7y -2) , -7(7y + 2) ,-1(49y + 14), -14(3.5y + 1), -98/7 - 49y and -7(7y + k₁) + k₂ where -14 = -k₁ + k₂.

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The dimensions 36 x 27 inches are too small to allow a 48-inch piece of glass to fit through it.

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Answer: B^5

Step-by-step explanation: truss

To determine if the point is a solution or not, we have to substitute the x-value and see if the y-value is correct:

*For x=5

For x=2

For x=-1

For x=-3

Then, the point that is NOT a solution for the equation is D. (-3, 2). The solution for x=-3 is -5.5.