when 100 engines are​ shipped, all of them are free of defects. select a written description of the complement of the given event.

A system of three linear equations: for the total number of tickets sold is 215 is f + s + t = 215, for the total revenue from ticket sales is $1214 is 7f + 5.25s + 5.5t = 1214, for three times as many senior citizen tickets were sold as full-price tickets is s = 3f.  

There were approximately 11 full-price tickets sold. There were 33 senior citizen tickets sold. There were 171 student tickets sold.

Let f, s, t be the number of full-price tickets sold, senior citizen tickets sold, student tickets sold.

Firstly, write a system of three linear equations based on the given information and mark the equation number.

f + s + t = 215      (1)        (the total number of tickets sold is 215)

7f + 5.25s + 5.5t = 1214   (2)  (the total revenue from ticket sales is $1214)

s = 3f          (3)           (three times as many senior citizen tickets were sold as full-price tickets)

solve this system by substitution. Using equation (3), we can substitute 3f for s in equations (1) and (2):

f + 3f + t = 215

7f + 5.25(3f) + 5.5t = 1214

Simplifying these equations gives:

4f + t = 215           (4)

24.75f + 5.5t = 1214   (5)

We can solve equation (4) for t to get:

t = 215 - 4f

We can substitute this expression for t in equation (5) and solve for f:

24.75f + 5.5(215 - 4f) = 1214

24.75f + 1182.5 - 22f = 1214

2.75f = 31.5

f = 11.45 ≈ 11

Therefore, approximately 11 full-price tickets were sold. Using equation (3), we can find the number of senior citizen tickets sold:

s = 3f = 3(11) = 33

Therefore, 33 senior citizen tickets were sold. Finally, we can use equation (1) to find the number of student tickets sold:

f + s + t = 215

11 + 33 + t = 215

t = 171

Therefore, 171 student tickets were sold.

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Answer:

60 Kilometers per hour

Step-by-step explanation:

To solve for how long it took Molly to get home, we can use this equation:

So, Molly took an hour and 30 minutes, or 90 minutes to travel 90km.

To get the number of km she traveled every hour, we can use this equation:

We multiply by [tex]\frac{2}{3}[/tex] because if we need to figure out the average speed for every hour (60) we need to convert 90 to 60, and to do that we multiply the 90 by [tex]\frac{2}{3}[/tex].

Therefore, Molly travels 60km every hour.

The interpretation of the slope is that it represents the additional cost per mile driven, beyond the initial charge of $30.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

The equation for the total cost of renting the truck is:

C = 30 + 2.50m

where C is the total cost

m is the number of miles driven.

The slope of the equation is the coefficient of "m", which is 2.50. The slope represents the rate of change of the total cost with respect to the number of miles driven.

In this case, the slope of 2.50 means that for each mile driven, the total cost of renting the truck increases by $2.50.

So, the interpretation of the slope is that it represents the additional cost per mile driven, beyond the initial charge of $30.

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The slope of the line passing through the points (-1, 2) and (2, -3) is -5/3

From the question, we are to determine the slope of the line that passes through the points (-1, 2) and (2, -3)

To find the slope of the line passing through the points (-1,2) and (2,-3), we can use the formula

m = (y₂ - y₁)/(x₂ - x₁)

Where m is the slope of the line

and (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Substituting the given values into this formula, we get

m =(-3 - 2)/(2 - (-1))

m = -5/(2 + 1)

m = -5/3

Hence, the slope is -5/3

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The quarts to Oz conversion is simple and can be done through the formula - Quantity in ounces or oz = quantity in quarts × 32

Quart and oz are the units used to get an information on the volume. The two units are related and can be easily converted to each other through the relation. The equivalent amount of one over the other is -

1 quart is equal to 32 fluid ounces.

Now, to find the amount of quarts in oz, students can simply use this formula -

Quantity in ounces or oz = quantity in quarts × amount of ounces equivalent to one quart

The value of amount of ounces equivalent to one quart will be kept 32. So, let us find the 0.03 quart equivalent in ounces.

Quantity in ounces = 0.03 × 32

Performing multiplication on Right Hand Side of the equation

Quantity of fluid in ounces = 0.96 ounces.

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Answer:

y = - 3x + 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

x - 3y = 3 ( subtract x from both sides )

- 3y = - x + 3 ( divide through by - 3 )

y = [tex]\frac{1}{3}[/tex] x - 1 ← in slope- intercept form

with slope m = [tex]\frac{1}{3}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3 , then

y = - 3x + c ← is the partial equation

to find c substitute (5, - 9 ) into the partial equation

- 9 = - 3(5) + c = - 15 + c ( add 15 to both sides )

6 = c

y = - 3x + 6 ← equation of perpendicular line

True. System developers can initiate a formal project as early as the preliminary investigation stage, or later on, as analysis, design, and implementation activities occur.

When considering the initiation of a formal project, system developers need to assess the risks, costs, benefits, and constraints associated with the project. During the preliminary investigation stage, they conduct a feasibility study to determine whether the project is technically feasible, economically viable, and socially and legally acceptable. If the feasibility study shows that the project is feasible, the developers can initiate the project by defining its scope, objectives, deliverables, and requirements.

Once the project is initiated, the developers can proceed with the analysis, design, and implementation activities. The analysis phase involves gathering and documenting the requirements, analyzing the existing system, and identifying the functional and non-functional requirements of the new system.

True. System developers can initiate a formal project as early as the preliminary investigation stage, or later on, as analysis, design, and implementation activities occur. The decision on when to initiate a formal project depends on several factors, such as the complexity of the system, the available resources, and the level of certainty about the feasibility of the project.

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Answer:

15/4 is a prime number so that's the answer to this question

Step-by-step explanation:

4/5 = 3/a

4•a = 5•3

4a = 15

4a/4 = 15/4

a = 15/4

A regression line is a line of​ means, and outliers have a big effect on the regression line.

Regression:

Regression is a statistical method used in finance, investing, and other disciplines that attempts to determine the strength and character of the relationship between a dependent variable (usually denoted by Y) and a set of other variables (called variables independent). Also known as simple regression or ordinary least squares (OLS), linear regression is the most common form of this technique. Linear regression establishes a linear relationship between two variables based on a line of best fit. So the linear regression is plotted with a straight line and the slope defines how changes in one variable affect changes in the other variable.

Regression Line:

Regression lines are very useful for the forecasting process. The purpose of this line is to describe the relationship between the dependent variable (variable Y) and one or more independent variables (variable X). Using the equation obtained from the regression line, the analyst can predict the future behavior of the dependent variable by entering different values ​​for the independent variable. Regression lines are widely used in the financial industry and in business in general.

The regression line formula is like the following:

Y = a + bX + u

The multiple regression formula looks like this:

Y = a + b₁X₁ + b₂X₂ + b₃X₃ + … + btXt +u.

Y is the dependent variable

X is the independent ones

a is the interception point

b is the slope

u is the residual regression.

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For each point, their position with respect to its location on the circle are as follows;

(4, 0) will be located inside the circle.

(-3, 3) will be located outside the circle.

(-2, -2) will be located on the circle.

In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;

(x - h)² + (y - k)² = r²

Where:

In this exercise, we would use an online graphing calculator to plot the equation of this circle as shown in the image attached below.

(x - 2)² + (y - 1)² = 25

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Answer:

(a^2+2)(a+2)

Step-by-step explanation:

Factor a^3+2a+2a^2+4.

Using Factoring by grouping

a^3+2a   +    2a^2+4

Factor out a from the first two terms and 2 from the last two terms.

a( a^2 +2) + 2 ( a^2+2)

Factoring out a^2+2.

(a^2+2)(a+2)

A measure of variation that includes spread, variance, and spread from the mean is the standard deviation.

The skewness of the data is expressed as standard deviation. It measures how far each observation is from the mean. Approximately 95% of the values ​​in each distribution fall within 2 standard deviations of the mean.

Standard deviation is a measure of spread, variance, and deviation from the mean given spread.

The standard deviation represents the "typical" deviation from the mean. This is a popular measure of volatility because it preserves the original units of the data set.

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Because the exchange rate between the US dollar (USD) and the euro (EUR) changes over time, the exact conversion from $100 US to euros will be determined by the current exchange rate.

As of the 21 Feb 2023 cutoff date, the exchange rate was around 1 USD = 0.94 EUR.

Using this exchange rate, we can calculate the value of $100 US in euros:

$100 US x 0.94 EUR/USD = 94 EUR

Therefore, as of 21 Feb 2023, $100 US was equivalent to approximately 94 euros.

However, it's important to note that exchange rates are subject to change, and the exact conversion may differ depending on the current rate.

The price at which one currency can be exchanged for another is referred to as the currency exchange rate. Exchange rates fluctuate constantly and are determined by the global foreign exchange market's supply and demand for currencies.

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Answer:

Step-by-step explanation:

15a6b4/5a2b

you can scrap the a and b

15*6*4/ 5*2=

now you keep simplifying the fraction

3*6*4/2=

3*6*2=

36

Answer: I believe the answer would be 20 dollars spent at the movies.

Step-by-step explanation:

The given function,[tex]Y=40(1-0.4)^x[/tex]  is an exponential decay

What is an exponential function?

An exponential function is a mathematical function of the form [tex]f(x) = a^x[/tex], where "a" is a constant and "x" is the input variable. These functions are commonly used to model situations that involve continuous growth or decay.

In the given example you provided,[tex]Y=40(1-0.4)^x[/tex] represents an exponential decay function where the initial value is 40 and the common ratio is (1-0.4), which is 0.6. As x increases, the value of the function approaches zero, but never reaches it.

Hence, the given function,[tex]Y=40(1-0.4)^x[/tex]  is an exponential decay.

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trueeeeeeeeeeeeeeeee

The equation of the normal line to the curve is y = -x + π

To find the equation of the normal line to the curve y = sin(sinx) at x = π, we need to find the slope of the tangent line at x = π and then use that to determine the slope of the normal line. We can find the slope of the tangent line by taking the derivative of y with respect to x and evaluating it at x = π.

y = sin(sinx)

Taking the derivative with respect to x, we get:

dy/dx = cos(sinx) * cosx

At x = π, we have:

dy/dx = cos(sin(π)) * cos(π) = -1 * (-1) = 1

So the slope of the tangent line at x = π is 1. Since the normal line is perpendicular to the tangent line, its slope is the negative reciprocal of 1, which is -1.

Now we need to find the y-intercept of the normal line, which is the point where the line intersects the y-axis. To do this, we can plug in the values of x = π and y = sin(sinx) = sin(sin(π)) = 0 into the equation of the line:

y = mx + b

0 = -1 * π + b

b = π

So the equation of the normal line is:

y = -x + π

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The completed table in the question used to prove the proportional BD/AB = BC/(AB + AC), when AD is an angle bisector can be presented as follows;

Statement                      [tex]{}[/tex]                   Reason

1. EB ║ AD, AD bisects ∠ABC   [tex]{}[/tex]      1. Given

2. ∠BEC = ∠DAC              [tex]{}[/tex]                2. Corresponding angles theorem

3. ∠C = ∠C   [tex]{}[/tex]                                     3. Reflexive property of congruence

4. ΔBEC = ΔDAC [tex]{}[/tex]                             4. AAA similarity postulate

5. DC/AC = BC/EC [tex]{}[/tex]                      5. Similar triangles have equivalent ratios

6. EC = EA + AC    [tex]{}[/tex]                             6. Segment addition postulate

7. DC/AC = BC/(EA + AC)[tex]{}[/tex]           [tex]{}[/tex] 7. Similar triangles have equivalent ratios

8. AD/AB = DC/AC [tex]{}[/tex]                           8. Triangle angle bisector theorem

9. BD/AB = DC/AC    [tex]{}[/tex]                         9. Substitution property

10. ∠EBA = ∠DAB [tex]{}[/tex]                             10. Alt int. angles theorem

11. ∠DAB = ∠DAC        [tex]{}[/tex]                      11. Definition of a bisector

12. ∠EBA = ∠BEC   [tex]{}[/tex]                           12. Alt int. angles theorem

13. ΔEBA is isosceles [tex]{}[/tex]                       13. Definition of isosceles triangles

14. CA = AB [tex]{}[/tex]                                       14. Side length of isosceles

15. BD/AB = BC/EC [tex]{}[/tex]                           15. Similar triangles have equal ratios

16. BD/AB = BC/(EA + AC) [tex]{}[/tex]                16. Substitution property

17. EA = AB [tex]{}[/tex]                                   17. Definition of isosceles triangle ΔEBA

18. BD/AB = BC/(AB + AC)  [tex]{}[/tex]               18. Substitution property

An angle bisector is an line that divides an angle into two angles of the same measure.

The details of the some of the reasons useds to prove the specified proportion are presented as follows;

Corresponding angles theorem

The corresponding angles theorem states that the corresponding angles formed between parallel lines and a transversal are congruent

Reflexive property of congruence

The reflexive property of congruence states that a geometric figure, such as an angle is congruent to itself

AA similarity postulate

The AA similarity postulate states that triangles are similar two angles in one triangle are congruent to two angles in the other triangles.

Similar triangles have equivalent ratios

Segment addition postulate

The segment addition postulate states that the point B is located between the points A and C on a segment, only if AC = AB + BC.

Ratios of corresponding sides ar

Triangle angle bisector theorem

The triangle angle bisector theorem states that an angle bisector of a triangle divides the side facing the bisected angle in the ratio of the lengths of the other two sides.

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Total cost with pass = $20a

Total cost without pass = $12a + 40

According to the information

We can write a system of equations for this problem,

Equation 1:

Cost with season pass = 12a + 40

Equation 2:

Cost without season pass = 20a

Therefore,

The system of equations that represents this problem is:

12a + 40 = c  ...(i)

20a = c   ...(ii)

Now making table for it:

Cost     Number     Amount Spent    Total Cost With   Total Cost Without

Ad.          Ad.            Pass ($)               Season Pass      Season Pass

20            a                      0                        20a + 0                   20a

12             a                     40                       12a + 40                 12a + 40

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The center of the dilation, point C, is located at the same point as it was before the dilation. This is because the center of dilation is the point from which the dilation occurs, and it does not change during the dilation process.

To find the coordinates of point C, we can use the properties of dilations. The coordinates of the vertices of the dilated triangle are found by multiplying the coordinates of the original triangle by the scale factor.

So, if the coordinates of point X are (x1, y1), the coordinates of point X' will be (0.5x1, 0.5y1). Similarly, the coordinates of point Y' will be (0.5x2, 0.5y2) and the coordinates of point Z' will be (0.5x3, 0.5y3), where (x2, y2) and (x3, y3) are the coordinates of points Y and Z, respectively.

Since point C is the center of dilation, the coordinates of point C will be the same as the coordinates of the midpoint of the line segment connecting points X and X', points Y and Y', and points Z and Z'. The midpoint of a line segment is found by averaging the coordinates of the endpoints. So, the coordinates of point C will be:

C = ((x1 + 0.5x1)/2, (y1 + 0.5y1)/2) = (0.75x1, 0.75y1)

Therefore, the center of the dilation, point C, is located at (0.75x1, 0.75y1).

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C) The ordered pair that represents the initial value of the function is of (0,3840), meaning that the graph of the function crosses the y-axis at the value of y = 3840.

D) The rate of change of the equation is of -128, meaning that when x increases by one, y is decreased by 128.

The following is the definition of a linear function's slope and intercept:

y = mx + b.

In which:

m is the slope, representing the rate of change, that is, by how much y changes when x is increased by one.

The value of y at x=0 is represented by the intercept, b. Hence the ordered pair is of (0,b).

The function is defined as follows for this problem:

y = -128x + 3840.

The slope and intercept are therefore given as follow:

m = -128, b = 3840.

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Based on the arithmetic sequence with the first term −5 and the common difference 4 is 660, we could find m = 20.

To find the sum of the first m terms of an arithmetic sequence, we can use the formula:

sum = (m/2)(2a + (m-1)d),

where a is the first term,

d is the common difference,

and m is the number of terms.

In this case, we are given a = −5, d = 4, and sum = 660. We can plug these values into the formula and solve for m:
660 = (m/2)(2(-5) + (m-1)(4))
660 = (m/2)(-10 + 4m - 4)
660 = (m/2)(4m - 14)
1320 = m(4m - 14)
0 = 4m^2 - 14m - 1320

Now we can use the quadratic formula to solve for m:
m = (-b ± √(b^2 - 4ac))/(2a)
m = (-(−14) ± √((−14)^2 - 4(4)(-1320)))/(2(4))
m = (14 ± √(196 + 21120))/8
m = (14 ± √21316)/8
m = (14 ± 146)/8

Now we have two possible values for m:
m = (14 + 146)/8 = 160/8 = 20
m = (14 - 146)/8 = -132/8 = -16.5

Since m must be a positive integer, we can conclude that m = 20. Therefore, the sum of the first 20 terms of the arithmetic sequence is 660.

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If a bee can fly at an average rate of 7 miles per hour and it flew nonstop for 18 hours, we can find the distance it traveled by multiplying its average speed by the time it flew:

distance = speed x time

distance = 7 miles/hour x 18 hours

distance = 126 miles

Therefore, the bee would have traveled 126 miles in 18 hours.

Answer:

126 m (Miles)

Step-by-step explanation:

distance travelled = speed×time = 7×18 = 126 miles

The null space of A is spanned by the vector x = (t, -t, -t, -t), where t is a real number

Vectors are an important mathematical tool for representing data, equations, and other mathematical objects. In this problem, we are given a matrix A and asked to find a non-zero vector x in the null space of A.

The matrix A = | | 1-1-1-1 | can be reduced to row-echelon form using row operations. The resulting matrix is A = | | 1 0 0 0 | , which has a single non-zero row, indicating that the null space of A is one-dimensional.

Therefore, the non-zero vector x in the null space of A can be written as x = (t, -t, -t, -t), where t is a real number.

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The amount would $10,000 due in 50 years be worth today if the discount rate were 7.5% is,

P = $7,042

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

We know that;

The formula is,

⇒ Amount = P (1 + r)ⁿ

Hence, We get;

10,000 = P (1 + 0.75)⁵⁰

10,000 = P (1.75)⁵⁰

10,000 = P × 1.42

P = 10,000 / 1.42

P = $7,042

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