See attached image and answer questions.

See Attached Image And Answer Questions.

Answers

Answer 1

The properties of the polynomial are

Degree = oddLeading coefficient = NegativeOdd multiplicity = 3Even multiplicity = 1

How to determine the properties of the polynomial

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

The graph

On the graph, we have the following readings:

A root of multiplicity 1 at x = -5A root of multiplicity 1 at x = -2A root of multiplicity 2 at x = 1A root of multiplicity 1 at x = 4y-intercept = 2

Using the above as a guide, we have the following:

Degree = sum of multiplicities

Degree = 1 + 1 + 2 + 1

Degree = 5

The leading coefficient is negative

This is so because the graph opens down

There are 3 zeros with odd multiplicities and 1 zero with even multiplicity

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Related Questions

Data analysts pay attention to sample size in order to achieve what goals? select all that apply.

Answers

The practise of extracting information from data to guide better business decisions is known as data analysis. Five iterative phases typically comprise the data analysis process:

Choose the data you want to examine.

gather the data

Clean up the data before analysis.

Study the information

Interpret the analysis' findings

It is common knowledge that data analysts focus on the sample size in order to

To prevent a few outlier responses from distorting the results

ensuring that the data reflects a variety of viewpoints

to prevent making erroneous conclusions due to a tiny sample size

An analyst of data is who?

An individual involved in the handling of data is referred to by this phrase.

Such a person aids in the analysis, retrieval, and drawing of conclusions from the information at hand.

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Help me with my last question…..

Answers

Answer:

C

Step-by-step explanation:

An irrational number cannot be shown as a simple fraction. If the number has decimals that are non-repeating (so not 7.85555555... or. 9.121212121...), cannot be shown as fractions (not 1.50000000... as it can be written as 3/2), and does not terminate (aka end).  C is the answer you're looking for, as it cannot be shown as a fraction, the numbers after the decimal go on indefinitely,  and the number's don't follow a noticeable repeatable pattern.

Answer:

Step-by-step explanation:

The table shows a linear relationship between the variables x and y. What is the slope? X y 3 6 9 24 12 6 12 288 18 8​

Answers

The slope of the line with the points (6, 3) and (12, 6) is equal to 1/2.

How to calculate the slope of a line?

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (6, 12).

Points on y-axis = (3, 6).

Substituting the given data points into the slope formula, we have the following;

Slope, m = (6 - 3)/(12 - 6)

Slope, m = 3/6

Slope, m = 1/2.

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the division or the multiplication property of equality to solve 1,145 = y
-——
224

Answers

Answer:

26.it is all about thinking

the ratio of the number of students playing basketball to soccer at a local middle school is 5:2. what percent of the students at the middle school play soccer?(round to the nearest percent)

Answers

Answer: Let's say there are a total of 100 students at the middle school. Then, 5 parts out of 7 are playing basketball and 2 parts out of 7 are playing soccer. The percent of students playing soccer can be calculated as follows:

(2/7) * 100 = 28.57% (rounded to the nearest percent)

So, approximately 28.57% of the students at the middle school play soccer.

Step-by-step explanation:

riya wants to buy a mirror which one of these shapes has only one line of symmetry

Answers

Answer:

Of the shapes you mentioned (circle, square, triangle, rectangle), the only one that has only one line of symmetry is the triangle. All other shapes have multiple lines of symmetry.

Step-by-step explanation:

Timothy, Laurence and Mike went to a bookstore to buy some books. The ratio of the number of books bought by Laurence and Mike were 2: 7. Timothy and Laurence bought a total of 20 books while Timothy and Mike bought a total of 35 books. How many books did Timothy buy?

Answers

Answer:

[tex]\mbox{\large \textsf{Timothy bought 14 books}}[/tex]

Step-by-step explanation:

Let's use first letters of names to represent the number of books bought by that person. This makes it easier to explain.

Therefore, the books bought by each of the three persons are T(imothy), L(aurence) and M(ike)

We will now convert each of the word description into math equations and solve

We are given that the ratio of the number of books bought by Laurence and Mike were 2: 7

We can write this as:
[tex]\dfrac{L}{M} = \dfrac{2}{7}\\\\[/tex]

Multiplying both sides by M:
[tex]L = \dfrac{2}{7}M\cdots\cdots(1)[/tex]  

Timothy and Laurence bought a total of 20 books can be represented as
[tex]T + L = 20\cdots\cdots(2)[/tex]

Timothy and Mike bought a total of 35 books can be represented as
[tex]T + M = 35\cdots\cdots(3)[/tex]


Eq (3) - Eq (2):

[tex]T + M - (T + L) = 35 - 20\\\\T + M - T - L = 15\\\\M - L = 15 \cdots\cdots (4)[/tex]

Substituting for [tex]\displaystyle L = \frac{2}{7}M[/tex]  from equation (1) into equation (4) we get

[tex]M - \dfrac{2}{7}M = 15\\\\\dfrac{5}{7}M = 15\\\\M = \dfrac{7}{5} \times 15\\\\M = 21\\\\[/tex]

Given [tex]\displaystyle M = 21[/tex] using equation (3), [tex]\displaystyle T + M = 35[/tex] we get

[tex]T + 21 = 35\\\\T = 35 - 21\\\\\textrm{or}\\\\T = 14[/tex](Answer)

If we wanted to find out how many books Laurence bought use Eq(1)
[tex]L = \dfrac{2}{7}M\\\\L = \dfrac{2}{7} \times 21\\\\L = 6\\\\[/tex]

Select the independent pair(s) of events.
=break your pencil lead while writing, and = feel overly stressed.
=put together a swing set correctly, and =read the directions.
=make an error on your income tax return, and =file Form 1040 long.
=have a salad with dinner, and =work on a home project.

STATS 2332

Answers

=break your pencil lead while writing, and = feel overly stressed.

=put together a swing set correctly, and =read the directions.

These are independent events because the occurrence of one event does not affect the occurrence of the other event. Breaking a pencil lead while writing and feeling overly stressed may happen at the same time, but one event does not cause the other. Similarly, putting together a swing set correctly and reading the directions are independent events because one action (reading the directions) does not determine the outcome of the other action (assembling the swing set correctly).

=make an error on your income tax return, and =file Form 1040 long.

These are dependent events because the occurrence of one event (making an error on the tax return) affects the occurrence of the other event (filing Form 1040 long). If you make an error on your tax return, you may need to file a longer form to correct it.

=have a salad with dinner, and =work on a home project.

These are also dependent events because one event (having a salad with dinner) does not determine the outcome of the other event (working on a home project). These events may happen at the same time, but one does not cause the other.

Can someone please help me with this equation

Answers

The measure of the angles m∠BOX = 77.5° and  m∠AOX = 77.5°.

What is the angle bisector of an angle?

The angle bisector of an angle is a line or line segment that divides the angle into two equal parts, creating two smaller angles that are congruent (i.e., have the same measure). The angle bisector starts from the vertex of the angle and extends to the opposite side or ray of the angle, dividing the angle into two smaller angles that have the same number of degrees.

By the definition of the angle bisector of an angle, the angle bisector divides the angle in two equal measures.

As m∠AOB = 155°

m∠BOX = 1/2 * m∠AOB

m∠BOX = 1/2 * 155

m∠BOX = 77.5°

also m∠AOX = 77.5°

Hence, the measure of the angles m∠BOX = 77.5° and m∠AOX = 77.5°.

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How can the statement be rewritten as a conditional statement in if-then form? the sum of the digits of a two-digit number is less than the value of the original two-digit number.

Answers

The statement "the sum of a two-digit number is less than the value of the original two-digit number" can be rewritten as conditional statement. If the sum of two digits of a two-digit number is less than the value of the original two-digit number, the number is valid.

A conditional statement, "if p, then q," with p representing the hypothesis and q representing the conclusion. We can identify the hypothesis and conclusion by rewriting the statement "the sum of the digits of a two-digit number is less than the value of the original two-digit number" as an if-then conditional statement.

The hypothesis is the condition that must be satisfied in order to valid the conclusion. In this case, the hypothesis is "the sum of the digits of a two-digit number is less than the value of the original two-digit number".

By combining these, we can rewrite the statement as follows:

If the sum of a two-digit number's digits is less than the value of the original two-digit number, the number is valid.

The hypothesis (the sum of the digits of a two-digit number is less than the value of the original two-digit number) is a sufficient condition for the conclusion, according to this conditional statement (the number is valid). In other words, if the hypothesis is correct, we can be certain that the conclusion is correct as well.

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20% discount on $365 purchase

Answers

Answer:

To find the amount of the discount, we need to multiply the purchase price by 20% or 0.20.

Discount = $365 × 0.20 = $73

So, the discount on a $365 purchase is $73.

The price after the discount would be $365 - $73 = $292.

To calculate the discount on a $365 purchase with a 20% discount, you can follow these steps:

1. Calculate the discount amount:

Discount = 20% x $365 = $73

2. Subtract the discount from the original price:

Final price = $365 - $73 = $292

Therefore, the final price of the $365 purchase with a 20% discount is $292.

For a fishing trip, Henry is going to choose lures to put in his tackle box. He has 4 lures that are crankbaits and 9 that are Jigs. In how many ways can he choose
7 lures if more than 5 must be jigs?

Answers

The number of ways for which he can choose 7 lures if more than 5 must be jigs is of:

372 ways.

What is the combination formula?

The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The possible combinations are given as follows:

Six jigs from a set of 9 and one crankbait from a set of 4.Seven jigs from a set of 9.

Hence the number of ways is given as follows:

n = 9!/(6! x 3!) x 4!/(1! x 3!) + 9!/(7! x 2!)

n = 372 ways.

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the quotient of twice the difference of five less than a number and six
what's the algebraic expression

Answers

Hi there, here's your answer:

Given:

The quotient of twice the difference of five less than a number and six.

Let the number be x.

By this, it is understood that the algebraic equation is in a fractional form, with the numerator being

Twice the difference of five less than a number, i.e.

2(x - 5)

And the denominator is 6.

Therefore, we get the algebraic equation to be:

[tex]\frac{2(x-5)}{6}[/tex]

Hope it helps! Please mark as brainliest!

Quadrilateral ABCD has the following angle measures:

m∠A = ?°, m∠B = 97°, m∠C = 47°, m∠D = 90°

What is m∠A?

306°
234°
126°
54°

PLEASE HELP!

Answers

Answer:

126

Step-by-step explanation:

360-97-47-90=126

so 126

Answer: C) 126

Step-by-step explanation: first, you need to use this equation...

m∠A + m∠B + m∠C + m∠D = 360°

=> m∠A + 97° + 47° + 90° = 360°    add all of the numbers...

=> m∠A + 234° = 360°                  subtract both sides by 234

=> m∠A = 360°- 234°

=> m∠A = 126°

Hope you've understood...

Riding equation of the line that has the same slope as 3X minus 2Y equals 12 in the same y-intercept as 5Y +21 equals 4X

Answers

The linear equation can be written as:

y = (3/2)*x - 21/5

How to write the linear equation?

A general linear equation can be written as:

y = m*x + b

Where m is the slope and b is the y-intercept.

First, we know that our line has the same slope than:

3x - 2y = 12

Rewriting that we will get:

3x - 2y = 12

3x - 12 = 2y

(3/2)x - 12/2 = y

So the slope of this line is (3/2).

And our lie has the same y-intercept as 5y + 21 = 4x

We can rewrite that to get:

5y = 4x - 21

y = (4/5)x - 21/5

The y-intercept is -21/5

Then the linear equation is:

y = (3/2)*x - 21/5

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PLEASE HELP QUICKLY

Answers

Ok I don’t understand why it’s 4 ft that’s labeled instead of 3.75 ft but I’m going to assume it’s 4 you’re using.

The pythagorean theorem is basically the 1 leg squared + 2nd leg squared = slanted side (hypotenuse) squared. Or a squared + b squared = c squared

Plug in.

4^2 + 10^2 = c^2
16 + 100 = 116
Square root of 116 (rounded): 10.77 or 10.8

Answer: 10.7 or 10.8

Step-by-step explanation:

so, first  [tex]a^{2} +b^{2} =c^{2}[/tex]

while [tex]a = 3.75[/tex] and [tex]b=10[/tex] and [tex]c=?[/tex]

so, it will be written as,

[tex]3.75^{2} +10^{2} =c^{2} \\[/tex]

[tex]14.0625+100=c^2[/tex]

[tex]114.0625=c^2[/tex] then square root both sides to have an answer of:

[tex]10.7=c[/tex]

That's if you are going to use the [tex]a=3.75[/tex]. as written in the question...

while if you're going to use [tex]a=4[/tex] (as shown in the figure) then only change the 3.75 with 4.

which will equal to...

[tex]4^2+10^2=c^2[/tex]

[tex]16+100=c^2[/tex]

[tex]116=c^2[/tex] then square root both sides to have an answer of:

[tex]10.77=c[/tex]

[tex]10.8[/tex] ≈ [tex]c[/tex]

hope you've understanded.!

statements about -27 that are true

Answers

The statements about the number -27 that are true are given as follows:

-27 is an integer number.-27 is a rational number.

What are rational and irrational numbers?

Rational numbers are numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.

Irrational numbers are numbers that cannot be represented by fractions, being non-terminating and non-repeating decimals, such as non-exact square roots.

Integer numbers are numbers that have no decimal part, hence -27 is an example of an integer number, which are also rational numbers.

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The circumferrence of the circle at the center of a basketball court is 37.68 feet. Find the area of the circle at center court. Use 3.14 for pi. Please answer.​

Answers

113.097 is the area (i used 3.14) pls comment for explanation :)

Find the value of X , Y, and z in the parallelogram below.

Answers

Answer:

[tex]x = -64\\\\y = -63\\\\z = -57[/tex]

Step-by-step explanation:

Diagonally opposite angles of a parallelogram are equal

Therefore

-y - 3 = 60

Add 3 to both sides; -3 terms on left side cancel out

- y = 60 + 3

- y = 63

Multiply both sides by -1

-1(-y) = -1(63)

y = - 63

Another property of a parallelogram is that the angles formed on either end by a side must equal 180°.

Rephrased,

The consecutive or adjacent angles are supplementary which means they add up to 180°

We see that -2z + 6 and 60° are adjacent angles
So

- 2z + 6 + 60 = 180

-2z + 66 = 180

-2z = 180 - 66

-2z = 114

z = 114/-2

z = -57

Similarly

-2x - 8 + 60 = 180

-2x + 52 = 180

-2x = 180 - 52

-2x = 128

x = 128/-2

x = -64

Her little sister's birthday is next week, so Brittany is planning a bubble-themed birthday party! She buys a big bottle of bubble solution and divides it equally among 6 small bottles. Each small bottle holds 1/8 of a gallon of bubble solution.

Use an equation to find the amount of bubble solution in the big bottle.

Answers

There is 3/4 of a gallon of bubble solution in the big bottle.

What is an equation?

In mathematics, an equation is a statement that asserts the equality of two expressions, typically separated by an equal sign (=). An equation contains one or more variables, which are symbols that represent unknown values, and may also contain constants, coefficients, and arithmetic operations such as addition, subtraction, multiplication, and division.

Let's use "x" to represent the amount of bubble solution in the big bottle, in gallons.

According to the problem, the big bottle was divided equally among 6 small bottles, and each small bottle holds 1/8 of a gallon of bubble solution. Therefore, the total amount of bubble solution in the big bottle is equal to the sum of the amounts in the 6 small bottles:

x = 6 * (1/8)

Simplifying the right-hand side of the equation, we get:

x = 3/4

Therefore, there is 3/4 of a gallon of bubble solution in the big bottle.

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There are 3 swimmers in a race. There will be a first-place and a second-place prize awarded. In how many different ways can the 2 prizes be awarded?

Answers

Answer:

Step-by-step explanation:

6

Which expression is equivalent to

Answers

The expression equivalent to 5x +10y -15 by taking the common factor is 5(x + 2y - 3).

What is taking out common factors?

The takeout of the common factor is the procedure, ab + ac = a(b + c). Think about how the expression 5x + 10 gets factored. The common factor 5, which was previously in front of the brackets, has been removed.

Figuring out what to multiply to create an expression. It is comparable to "splitting" an expression into numerous smaller expressions.

Given, the expression is 5x + 10y -15

So, 5x +10y -15 = 5x + 5*2y - 5*3

                         = 5(x + 2y - 3)

Hence, the required answer is 5(x + 2y - 3).

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Please Explain and solve this problem. What trigonometric function would you use based upon the given information in the triangle shown below? ASAP

Answers

To solve the problem we would use tangent as a trigonometric function and find the unknown value.

What are trigonometric functions?

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

From the given triangle we observe that the given values are:

Angle B, side a and side b.

To find any of the unknows in the three we use the trigonometric function tangent.

Tan α = opposite side / adjacent side

For the given figure:

Tan B = b / a

Hence, to solve the problem we would use tangent as a trigonometric function and find the unknown value.

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Choose all of the values that are solutions to inequality x < -2

Answers

Answer:

The solution to the inequality x < -2 is all real numbers that are less than -2. This means that any number that is less than -2 will satisfy the inequality, but any number that is greater than or equal to -2 will not.

So, the solution set for x < -2 is all real numbers that are less than -2. This solution set can be expressed as (-∞, -2).

Therefore, the values that are solutions to the inequality x < -2 are:

• all real numbers less than -2, such as -3, -4, -5, etc.

Note that -2 itself is not part of the solution set, since it is not less than -2.

here are the first four terms of a number sequence 1 5 13 29.
The rule to continue this sequence is mutiply the previous term by 2 then add 3
work out the 5th term of this sequence

Answers

Answer:

61

Step-by-step explanation:

using the rule to find the fifth term from the fourth term 29

5th term = 2 × 29 + 3 = 58 + 3 = 61

Supervisor: "Your average time to process a sale is 14 minutes. You have to decrease
that by 25% this month in order to meet your goals."
Employee: "Thank you for the feedback. I will work on lowering my processing time to
minutes by the end of the month."
3.5
7
10.5
12
17.5

Answers

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{25\% of 14}}{\left( \cfrac{25}{100} \right)14}\implies \text{\LARGE 3.5}[/tex]

A distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population is called

Answers

Answer:

sampling distribution

Step-by-step explanation:

:)

Find the perimeter of the triangle as both a decimal and in simplest
radical form

Answers

Add the sides' lengths to find a triangle's perimeter. As an illustration, the perimeter of a triangle with sides a, b, and c is given by P = a + b + c.

What is meant by perimeter?The radius of a shape's edge is known as the perimeter. Discover how to calculate a shape's perimeter by multiplying its side lengths.It is measured from the object's edge to its perimeter. Like the yard that is fenced in at your home. The distance around anything is called its perimeter. The fence is 200 feet long for a yard that is 50 feet by 50 feet.The measurement of a shape's perimeter is its length. It takes adding the lengths of all four sides to determine a rectangle's or square's perimeter.The length of a two-dimensional shape's perimeter is referred to as its perimeter. The total length of all the sides of the thing is also a definition for it.

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i need help with this question ASAP

Answers

In the image of the trapezoid the value of angle C is 82 degrees

What is a trapezoid?

A trapezoid is a quadrilateral with one pair of parallel sides.

Opposite angles of a trapezoid are angles that are located across from each other, with a side of the trapezoid between them.

In a trapezoid, opposite angles are always congruent, meaning they have the same measure. This is a result of the fact that a trapezoid is a parallelogram, which means that its opposite sides are parallel and equal in length.

When opposite sides of a parallelogram are parallel, it follows that opposite angles are congruent.

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Find the value of x that makes each sentence true.
If (5 1/5)^5=25x then x =
If (8 1/3)^2= 4x, then x =

Answers

The first equation is:

(5 1/5)^5 = 25x

To solve for x, we need to simplify the left side of the equation first.

(5 1/5)^5 = (5 + 1/5)^5 = 6^5 = 7776

So,

7776 = 25x

Therefore,

x = 7776/25 = 311.04

For the second equation:

If (8 1/3)^2 = 4x, then x =

We need to simplify the left side of the equation first.

(8 1/3)^2 = (8 + 1/3)^2 = 9^2 = 81

So,

81 = 4x

Therefore,

x = 81/4 = 20.25

So the values of x that make each sentence true are 311.04 and 20.25, respectively.

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The other end of the string is attached to a large vertical conducting plate that has a charge density of o = 30 x 10-6C/m. + + + + + + L m, A 25% Part (a) Write an expression for the magnitude of the electric field due to the charge distribution on the conductive plate. E = 0 Grade Summary Deductions 0% Potential 100% 0 B 0 Y b 0 Submissions Attempts remaining: 20 (% per attempt) detailed view d h ( 789 HOME 1456 1 23 + 0 END VO BACKSPACE GEL CLEAR g k j m n P S Submit Hline Feedback I give up! Hints: for a 0% deduction. Hints remaining: 0 Feedback: 0% deduction per feedback. Date Submission History All Date times are displayed in Eastern Standard Time Red submission date times indicate late work. Time Answer Hints Feedback 24 25% Part (b) Write an expression for the horizontal component of the net force acting on the charged sphere in terms of the tension T in the string, the electric field, and the given variables. A 25% Part (c) Write an expression for the vertical component of the net force acting on the charged sphere in terms of the tension T in the string and the given variables. 425% Part (d) What is the angle in degrees that the string makes with respect to the vertical? 1. Find f(4) f(1)=8 f(n)=-2f(n-1)-4 when planning activities for school-age children, the nurse organizes games that include competition. at which age are these kinds of games preferred by children? Newington Town Manager Tanya Lane proposed a $124.2 million budget Monday night -- a 4.7 percent increase over the previous year." [R141] What was Newington's budget in the "previous year"? Costs of Starting Your Own BusinessSHORT ANSWERYou are looking at a potential location to open your first spa. The rent is $21 per square(annually), and the space is 1,800 square feet. How much rent would you pay each year? Eachfootmonth? Unit 8 Review of Perfect Tenses1. The salesperson _______________________ (assure) the couple that if they _______________ (buy) the new furnace, it ___________(be) guaranteed for 15 years.2. The wildfire __________ already ____________________ (burn) 1,000 acres of forest before the firefighters _____________________(can) put out the fire.3. Carlos ____________________________ (live) in Manitoba for 2 years before he ____________________ (move) south to Hamilton.4. Vanessa __________________________(work) at the Vietnamese restaurant since she ________________ (be) a student in EAP Level 2.5. Samir __________________ (attend) a Formula 1 race in Bahrain when he _______________ (live) in the region. 6. Hayaam _______________________ (arrive) late for the meeting because she _____________________ (miss) her regular GO train. 7. Cee __________________ (meet) Vanessa when he ____________________(start) to work at Pho Binh Minh restaurant, but he _________________________________(not realize) she was his classmate for 2 weeks.8. The companys profits ______________________ (decline) for 2 years before it __________________________________________ (decide) to replace the president.9. Even though Fatimah and Jessica __________________________ (live) in the same building for 2 years, they never _______________(meet) each other until they _________________ (join) the painting class at the community centre.10. Abdul _____________________________ (be employed) at the company for 20 years, when they ____________________ (promote) him to manager.11. Even though Celma _____________________________ (enjoy) living in Italy for more than 10 years, she and her husband ________________________ (decide) to move to Canada 4 years ago. 12. Sylvia _____________________ (be) a student in the LINC ESL classes for 2 months, when her teacher ___________________ (suggest) she join the EAP program. 13. Havel _________________________(enjoy) hiking in the mountains near his home town, but he ____________________(worry) about encountering a bear while hiking.14. Khitam usually _______________(give) Jessica a ride home after class, but one day she ____________________________(drive) over a cat, so Jessica ____________________ (stop) driving with her. 15. Paloma _______________________(be) a lawyer for 2 years before she _______________(have) to present a case before a judge in court.16. Her grandparent ________________________________(be married) for over 50 years, when her grandfather ____________________(fall) one day on some ice and _____________(die) because of his head injury. 17. Needa _______________________(live) in Canada for 3 years when she __________________(decide) to return to Palestine. 18. Although the company ____________________________________________(assure) my friends that their house would be built on time, it _______________________ (take) 8 months longer tan promised.