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Question at position 4
Marcus has a circuit that uses a battery to light up a light bulb. He needs three wires to make his circuit. He changes the circuit to have a paper clip attached to wire 2 as shown in the picture below.






Marcus has a circuit that uses a battery to light up a light bulb. He needs three wires to make his circuit. He changes the circuit to have a paper clip attached to wire 2 as shown in the picture below.






A. The battery will die.


B. The light bulb will light up.


C. The light bulb will break.


D. The paper clip will turn black.

2.62 seconds before the ball Martin threw hits the ground.

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared component must be included. These are also known as quadratic equations.

Let t be the time in seconds

h(t) be he height of the ball, in feet

we have

h(t) = −16t² + 40t + 5

we know that

When the ball hits the ground, the height is equal to zero

so

−16t² + 40t + 5=0

The equation solving formula for a quadratic equation of the type

at²+bt+c=0

is equal to

t=(-b±√(b²-4ac))/2a

in this problem we have

−16t² + 40t + 5=0

so

a=-16

b=40

c=5

substitute in the formula:

t = (-40±√(40²-4×40×5))/2×-16

t = (-40±√(1600-800))/-32

t=2.62sec

therefore, 2.62 seconds before the ball Martin threw

hits the ground.

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Thus, the length of the other side of Ross's garden is 18 feet.

Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

To find the length of the other side of Ross's garden, we can use the Pythagorean theorem.

In this case, let's assume the length of the other side of Ross's garden x.

We can set up the following equation:

x² + 30² = 33²

Solving for x, we get:

x² = 33² - 30²

x² = 1089 - 900

x² = 289

x = √289

x = 17.

Thus, the length of the other side of Ross's garden is 18 feet.

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Answer:

b

d

.  ._-_-_-__---_--_--_----___-_--------_--------------------------__-_______--_-__-________---_-_--___-----__--

The solution to the equation is x = 22.5.

To solve the equation x-9 = (3/5)x, we can first simplify the right-hand side by multiplying both sides by 5 to get rid of the fraction:

5(x-9) = 3x

An equation is a mathematical statement that indicates the equality of two expressions. Equations typically contain variables, which are represented by letters, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on either side of the equals sign are called the left-hand side and right-hand side of the equation.

Expanding the left-hand side, we get

5x - 45 = 3x

Next, we can simplify by subtracting 3x from both sides:

2x - 45 = 0

Adding 45 to both sides, we get:

2x = 45

Finally, dividing both sides by 2, we get:

x = 22.5

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Jorge needs to sell at least $88.89 worth of products for the week in order to be able to purchase the new tire and cover his commission.

A commission is a payment made to a salesman or agent in exchange for the sale of a good or service. Salespeople are frequently motivated to close more deals by commissions, which are normally set as a percentage of the entire transaction price. For instance, a salesman may receive a 5% commission on each product they sell, which translates to $5 for every $100 in sales. Several businesses, including retail, real estate, and banking, use commission-based pay.

Let us suppose the amount he needs to sell = x.

Thus, for 5% commission on his sales to purchase a $80 tire we have the equation:

x * 0.95 - 0.05x >= 80

0.9x >= 80

x >= 80/0.9

x >= 88.89

Therefore, Jorge needs to sell at least $88.89 worth of products for the week in order to be able to purchase the new tire and cover his commission.

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Answer:

Step-by-step explanation:

<ATC+90+60=180

<ATC=30

we know that,

if 30-------x

60--------[tex]x\sqrt{3}[/tex]

90---------2x

so,  x\sqrt{3}=10

x=10/sqrt{3}

Answer:

54

Step-by-step explanation:

if you look at the ratios between the values of A and B. you will see that the successive values of A increase by 10 while B increase by 12

Therefore for A

35 + 10 = 45

for B

42 + 12 = 54

The investor's stock balance has decreased by a total of [tex]24.36[/tex]%.

You aren't a property owner; you are a lending investor. You have invested in ownership if you purchase stock in a corporation. Your proportionate part of the company's profits will be deducted from the return you get. The original investment sum will continue to be correlated to the overall worth of the business.

The investors is someone or something that makes investments in other persons or groups with the intention of profiting to them in the future. On principle, everyone who invests money for something qualifies as an investor.

The decrease in stock A,

[tex]= 1300 * 22[/tex]%

[tex]= 286[/tex]

Decrease in stock B,

[tex]= 4820 * 25[/tex]%

[tex]= 1205[/tex]

Total decrease [tex]= 286+1205[/tex]

[tex]= 1491[/tex]

Total percentage decrease,

[tex]= (1491 / (1300 + 4820) ) * 100[/tex]%

[tex]= 1491 / 6120 * 100[/tex]%

[tex]= 24.36[/tex]%

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The monthly percent decrease in average weekly crate production from Month A to Month B is 40%.

A number can be expressed as a fraction of 100 using a percentage. The word "%" stands for it. Percentages are frequently used to represent change or growth over time and to compare two values. Finding the proportion of the quantity you are interested in to the total is necessary before you can compute a percentage. The percentage is then calculated by multiplying the ratio by 100.

For Month A the production is:

2000 + 3000 + 2000 + 3000 = 10,000

Thus, average weekly production is:

A = 10,000 / 4

A = 2500

For month B we have:

2000 + 1000 + 3000 + 0 = 6000

Average weekly crate production is:

= 6000 / 4

= 1500

The percentage decrease is given by:

percent decrease = [(original value - new value) / original value] x 100%

= [(2500 - 1500) / 2500] x 100%

= 40%

Therefore, the monthly percent decrease in average weekly crate production from Month A to Month B is 40%.

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According to the slope, the angle 3 also has a measure of 143 degrees.

To find the measure of angle 3, we first need to understand how angles 2 and 3 are related.

In other words, angles 2 and 3 are congruent (have the same measure). Therefore, if we can find the measure of angle 2, we can determine the measure of angle 3.

We know that angle 2 has a measure of 143 degrees. We also know that angles 2 and 3 are alternate interior angles, which means they are congruent.

Now, let's justify why this is true using the concept of slopes. Since the power lines are parallel, they have the same slope. This means that the angle between each power line and the horizontal is the same.

Since angle 2 is the angle between one of the power lines and the horizontal, we know that angle 3 must also have the same measure because it is the angle between the other power line and the horizontal.

Therefore, we can confidently say that the measure of angle 3 is also 143 degrees.

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Complete Question:

A pair of parallel power lines in Mohamed Bin Zayed City is installed on a slope. Find m∠3 if m∠2= 143 degrees . Justify your answer

The number of jars of raspberry jam filled is required.

The number of jars of raspberry jam is 1/24

Fraction:

A fraction represents a part of a whole, or more generally, any number of equal parts. In common English, a fraction describes the number of parts of a certain size, such as half, eight-fifths, three-quarters. A common, vulgar, or simple fraction consists of a numerator that appears above (or before a slash, such as 1⁄2) a line, and a non-zero denominator that appears. Multipliers and denominators are also used in less common fractions, including complex, complex, and mixed fractions.

According to the Question:

The number of jars of strawberry jam is 1/8 jars.

The number of jars of raspberry jam is half of the number of jars of strawberry jam.

So,

1/8 × 1/3

= 1/24

The number of jars of raspberry jam is 1/24.

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(a) Yes, the player makes the shot; (b) A quadratic function in standard form that models the path of the shot is: [tex]f(x) = -\frac{3}{50} (x-13)(x-3)[/tex]

(a) We need to find the x-int to see if he makes the shot at (3,0).

    so, first we factor!

[tex]y=-\frac{1}{20} (x-6)(x-3)[/tex]

0 = (x - 6) = (6, 0)

0 = (x - 3) = (3, 0)

This shows that the player makes the shot.

(b) x- int = (13, 0) and (3, 0)

    random point = (10, 1.4)

    f(x) = a(x - 13) (x - 3)

    1.4 = a(10 - 13) (10 - 3)

    1.4 = a(-3) (7)

   [tex]\frac{1.4}{-21} = \frac{-21a}{-21}[/tex]

       a = 0.06 ≈ [tex]\frac{-3}{50}[/tex]

the Quadratic function is [tex]f(x) = -\frac{3}{50} (x-13)(x-3)[/tex]

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Full Question:

A professional basketball player's shot is modeled by the function shown, where x and y are measured in feet.

a. Does the player make the shot?

b. The basketball player releases another shot from the point (13,0) and makes the shot. The shot also passes through the point (10, 1.4). Write a quadratic function in standard form that models the path of the shot.

After answering the prοvided questiοn, we can cοnclude that Therefοre, equatiοn there are 26 twο-pοint questiοns and 16 three-pοint questiοns οn the test.

In mathematics, an equatiοn is a statement that implies the unity οf twο traits. An equatiοn cοnsists οf twο sides separated because οf an analytical sοlutiοn (=). Fοr instance, the debate "2x + 3 = 9" asserts that the remark "2x + 3" equals the valuatiοn "9". The gοal οf sοlving equatiοns is tο determine the amοunt οr values οf the variable in the mοdel) that wοuld allοw the equatiοn tο really be true.

Fοrmulae can be simple οr cοmplex, regular οr nοnlinear, and cοntain οne οr mοre variables. Fοr example, in the equatiοn "x² + 2x - 3 = 0," the variable x is elevated tο the secοnd pοwer. Lines are used extensively in mathematics, including algebra, equatiοns, and geοmetry.

Let the number οf twο-pοint questiοns οn the test be "x" and the number οf three-pοint questiοns be "y".

[tex]x+y=42[/tex]

[tex]2x+3y=100[/tex]

[tex]x+y=42[/tex]

[tex]x=42-y[/tex]

[tex]2(42-y)+3y=100[/tex]

[tex]84-2y+3y=100[/tex]

[tex]Y=16[/tex]

[tex]x+y=42[/tex]

[tex]x+16=42[/tex]

[tex]x=26[/tex]

Therefore, there are 26 two-point questions and 16 three-point questions on the test.

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(u - 5 + (7))(u - 5 - (7)) = 0 is the equation we created in u that simplifies to 2u2 - 20u + 36 = 0.

The two forms of equations are identity equations and conditional equations. The variables all have the same identity for all conceivable values.

Creating an equation in u that can be solved for 2u² - 20u + 36 = 0

It indicates that the following are the solutions for x for a quadratic equation of the form ax² + bx + c = 0:

x = (-b±√(b²-4ac))/2a

By dividing both sides by 2, we can rewrite the equation 2u2 - 20u + 36 = 0 as follows:

u² - 10u + 18 = 0

u = (-(-10) ± √((-10)² - 4(1)(18))) / 2(1)

Simplifying this expression, we get:

u = (10 ± √(100 - 72)) / 2

u = (10 ± √(28)) / 2

u = (10 ± 2√(7)) / 2

u = 5 ± √(7)

A quadratic equation with roots r1 and r2 can be expressed as: This allows us to merge the two solutions into a single equation.

(x - r1)(x - r2) = 0

By substituting in the two answers we discovered for u, we obtain:

(u - 5 + √(7))(u - 5 - √(7)) = 0

Extending this phrase results in:

u² - 10u + 18 = 0

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The linearization of the function √????(x,y)=18−2x2−3y2 at the point (1, -2) is (x,y)≈6.4−4(x−1)−6(y+2). Using this linear approximation, we can estimate the value of (0.9,−1.9) to be approximately 6.1.

To explain further, linear approximation is a method used to approximate a function with a linear equation near a given point. We use linear approximation to estimate the value of a function at a certain point without actually having to evaluate it.

First, we find the linearization of the function √????(x,y)=18−2x2−3y2 at the point (1, -2). We do this by finding the derivative of ????(x,y) with respect to x and y and substituting the coordinates of the given point.

Taking the partial derivative of ????(x,y) with respect to x, we get ????x(x,y)=4x−4 and substituting x = 1 and y = -2, we get ????x(1,−2)=−4.

Similarly, taking the partial derivative of ????(x,y) with respect to y, we get ????y(x,y)=−6y−6 and substituting x = 1 and y = -2, we get ????y(1,−2)=18.

Therefore, the linearization of the function √????(x,y)=18−2x2−3y2 at the point (1, -2) is ????(x,y)≈6.4−4(x−1)−6(y+2).

Using this linear approximation, we can estimate the value of ????(0.9,−1.9) to be approximately 6.1. We do this by substituting x = 0.9 and y = -1.9 in the linear approximation, which gives us ????(0.9,−1.9)≈6.1.

Hence, the value of ????(0.9,−1.9) is estimated to be approximately 6.1 using the linear approximation of the function ????(x,y)=18−2x2−3y2 at the point (1, -2).

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Answer:

429

Step-by-step explanation:

The proof that line segment PR is greater than the line segment PF is shown below

Given that

The above statements mean that we have a right triangle PFR such that

In a right triangle, the longest side is the hypotenuse

This means that

PR is greater than PF

This proves that if R is any point on line l that is different from F, then PR > PF.

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Answer:  960 eggs are not sold.

Step-by-step explanation:

Let t be the number of total eggs.

36%(t) = 540

0.36(t) = 540

         t = 1500

1500 - 540 = 960

Answer:

Gradient of the line segment:

The gradient of a line segment is given by the formula:

m = (y2 - y1) / (x2 - x1)

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

In this case, (x1, y1) = (6, 4) and (x2, y2) = (8, 3). Substituting into the formula, we get:

m = (3 - 4) / (8 - 6) = -1/2

Therefore, the gradient of the line segment is -1/2.

Midpoint of the line segment:

The midpoint of a line segment is given by the formula:

((x1 + x2) / 2, (y1 + y2) / 2)

In this case, (x1, y1) = (6, 4) and (x2, y2) = (8, 3). Substituting into the formula, we get:

((6 + 8) / 2, (4 + 3) / 2) = (7, 3.5)

Therefore, the midpoint of the line segment is (7, 3.5).

Length of the line segment:

The length of a line segment is given by the distance formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, (x1, y1) = (6, 4) and (x2, y2) = (8, 3). Substituting into the formula, we get:

d = sqrt((8 - 6)^2 + (3 - 4)^2) = sqrt(2^2 + (-1)^2) = sqrt(5)

Therefore, the length of the line segment is sqrt(5).

Answer:

To find the gradient of the line segment, we use the formula:

gradient = (change in y) / (change in x)

So, gradient = (3 - 4) / (8 - 6) = -1/2

To find the midpoint of the line segment, we use the formula:

midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

So, midpoint = ((6 + 8) / 2, (4 + 3) / 2) = (7, 3.5)

To find the length of the line segment, we use the distance formula:

length = sqrt((x2 - x1)^2 + (y2 - y1)^2)

So, length = sqrt((8 - 6)^2 + (3 - 4)^2) = sqrt(5)

Therefore, the gradient of the line segment is -1/2, the midpoint is (7, 3.5), and the length is sqrt(5).

Lauri spent 4% of 800 hours at her part time job, which is about 32 hours. The property of equality was used to solve for x.

To estimate x, we can use the property of equality. This property states that if two equations are equal, then the two sides of the equation are equal. Therefore, if we know that 4% of x is about 32 hours, we can set up an equation and solve for x. The equation is 4% of x = 32 hours. We can convert 4% to a decimal by dividing 4 by 100, which gives us 0.04. This can then be rewritten as 0.04x = 32 hours. To solve for x, we can divide both sides by 0.04. This gives us x = 800 hours. This means that if Lauri spends 4% of x hours at her part time job, then x must be 800 hours.

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The required equivalent fractions for 1 10/15 and 9/12.

Given, two mixed fractions 1 2/3 and 3/4, determine equivalent fractions using 15 as the common denominator.

Simplification:

The process in mathematics of manipulating and interpreting functions to make a function or expression simpler or easier to understand is called simplification, and the process is called simplification.

1. Simplify fractions by canceling all common factors of the numerator and denominator and writing the fraction in its lowest/simplest form.

2. Simplify mathematical expressions by grouping and combining similar terms. This makes expressions easy to understand and solve.

According to the Question:

Here,

First

= 1 2/3

= 1+ 2 / 3

= 1 + 2 × 5 / 3 × 5

= 1 + 10 / 15

Again,

Second,

=  3 / 4

=  3 × 3 / 4 × 3

= 9/12

Thus, the required equivalent fractions for 1 10/15 and 9/12.

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Answer:

Step-by-step explanation:

a: in the quadratic formula, no real roots would mean b^2 - 4ac<0 because of the discriminant. b^2 is 4, so all 4c has to satisfy is that it’s greater than 4. Solving, c>1

b: casework:

Both are negative: This is impossible because square roots are always positive, so at least one would always be positive.

Both are positive: sqrt(4-4c)<2.  0<c<=1.

c. I’m not entirely sure of what you mean, but when c=0, 0 is a root of the quadratic equation, but the other root is positive 2, so no value?

d. sqrt(4-4c)>2. Another possibility is that the same thing is less than -2, but square roots are always positive. This remains true for c<0.

We meet the SAS requirement for congruence because the two triangles share two congruent sides as well as the included angle.

To prove that △BEC≅△DEA, we can use the Side-Angle-Side (SAS) congruence theorem.

First, we can see that BE=ED, as both are radii of the same circle.

Secondly, angle BEC and angle DEA are both 90 degrees, as they are inscribed angles that subtend the same arc BD.

Lastly, we can see that EC=EA, as they are both radii of the same circle.

Therefore, we have the two triangles sharing two congruent sides and the included angle, satisfying the SAS criterion for congruence. Hence, we can conclude that △BEC≅△DEA.

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1. If the οriginal ratiο is 2:3, we can fοrm different ratiοs by:

Multiplying bοth the numeratοr and denοminatοr by the same number, such as 2:3 x 2 = 4:6 οr 2:3 x 3 = 6:9

Dividing bοth the numeratοr and denοminatοr by the same number, such as 2:3 ÷ 2 = 1:1.5 οr 2:3 ÷ 3 = 0.67:1

Any ratiο that is equivalent tο the οriginal ratiο can be fοrmed in this way

2. Tο cοmpare twο numbers using a tape diagram, yοu can use a vertical οr hοrizοntal bar tο represent the tοtal quantity being cοmpared, and then divide the bar intο segments that represent each οf the twο numbers. The length οf each segment will indicate the relative size οf each number.

3. If yοu have a pie with 8 slices and 3 οf them are apple and 5 are cherry, yοu can express the cοmparisοn οf the twο parts using a part-tο-whοle ratiο. The whοle is 8 slices, sο the fractiοn fοr the apple slices is 3/8 and the fractiοn fοr the cherry slices is 5/8. Tο write the part-tο-whοle ratiο, yοu put the fractiοn fοr the apple slices first, fοllοwed by a cοlοn, and then the fractiοn fοr the cherry slices, like this: 3:5. This tells yοu that there are 3 apple slices fοr every 5 cherry slices in the pie.

4. Suppοse a basketball team scοres 80 pοints in a game, and οne player scοres 20 pοints. Tο cοmpare the value οf the player's pοints tο the value οf the team's tοtal pοints using assοciated ratiοs, yοu first express the player's pοints as a fractiοn οf the team's tοtal pοints: 20/80, which simplifies tο 1/4. Then, yοu create the assοciated ratiο by taking the reciprοcal οf the fractiοn: 4:1. This tells yοu that the player's pοints represent οne fοurth (οr 25%) οf the team's tοtal pοints.

5. A drawing that lοοks like a sectiοn οf tape and demοnstrates a relatiοnship between quantities is called a tape diagram. Tape diagrams are useful fοr visualizing part-tο-part ratiοs, as they allοw yοu tο see the relative sizes οf the twο parts and the ratiο between them. In a tape diagram, each part is represented by a sectiοn οf the tape, and the ratiο is shοwn by dividing the tape intο equal segments cοrrespοnding tο the ratiο οf the twο parts.

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If the cost of customer acquisition is $50 and the cost of customer retention is $30, then the cost of Software C would be $80,000. This is because 10,000 customers x ($50 acquisition cost + $30 retention cost) = $80,000.

Acquisition cost is the cost associated with obtaining an asset or resource. It includes the purchase price, transportation costs, installation costs, taxes, and any other associated costs.

The cost of Software C can be determined by calculating the total cost of lost customers due to software issues. To do this, companies typically look to the customer lifetime value (CLV) of each customer. CLV is the total revenue generated by a customer over the course of their relationship with the company. By multiplying the CLV by the number of unsatisfied customers, companies can get a good idea of what the cost of Software C is.

For example, if a company has 10,000 customers and their CLV is $100, then the cost of Software C would be $1,000,000. This is because 10,000 customers x $100 CLV = $1,000,000.

The cost of Software C can also be determined by looking at the cost of customer acquisition and retention.

In addition to the cost of lost customers, companies must also factor in the cost of fixing the software issue. This cost can vary depending on the complexity of the issue and the size of the company. Companies should also consider the cost of lost productivity due to the software issue, as well as any other costs associated with the issue.

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Answer:

54665655

Step-by-step explanation:

According to the figure the value of a b and c is

a = 39

b = 141

c = 39

The angles are solved using the concept of sum of angles in a triangle is equal to 180 degrees

Solving for a

a + 106 + 35 = 180

a + 106 + 35 = 180

a + 141 = 180

Next, we can isolate a by subtracting 141 from both sides:

a + 141 - 141 = 180 - 141

a = 39

a = c = 39 corresponding angles

b + c = 180 degrees (linear pair theorem)

b + 39 = 180

b + 39 - 39 = 180 - 39

b = 141

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The words from a written text that a person can remember after five minutes with the text are known as short-term memory.

Short-term memory refers to the storage of information for a brief period of time, usually a few seconds to a few minutes. It is a type of memory that is involved in the conscious processing of information and is responsible for holding information in mind for immediate use.

The capacity of short-term memory is limited and varies from person to person. Generally, it can hold about 7 pieces of information or less, and can only hold it for a short period of time. This is why it is important to transfer important information from short-term memory to long-term memory through a process called encoding.

To improve short-term memory, one can use techniques such as repetition, chunking, visualization, and association. By doing this, it is possible to hold more information in short-term memory for a longer period of time.

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The equation of the least squares line is:y = mx + by = 3.6x - 72.1818181818182Thus, the least squares line is y = 3.6x - 72.182.

(10 points) Consider the following data from a sample of n=7 . x: 168 178 176 174 178 174 172 y: 50 57 55 55 58 54 53The y-intercept of the least squares line is given as -72.1818181818182. We have to calculate the slope of the least squares line and input the equation of the least squares line. The given data is shown below:X: 168 178 176 174 178 174 172Y: 50 57 55 55 58 54 53We know that y-intercept of the least squares line is given by b = ybar - m * xbarwhere xbar = (1/n) * ∑x and ybar = (1/n) * ∑y. Now, to calculate the slope of the least squares line, we need to calculate the value of the numerator of the following equation:Slope, m = [(n∑xy) - (∑x∑y)] / [(n∑x^2) - (∑x)^2]Here, ∑x and ∑y are the summations of x and y values, respectively. ∑xy is the sum of the products of each x and y value, and ∑x^2 is the sum of each x value squared. So, let's calculate all of these values for the given data.We have, n = 7∑x = 1202∑y = 382∑x^2 = 213468∑xy = 71848Now, substituting these values in the formula of slope, we have:Slope, m = [(7 * 71848) - (1202 * 382)] / [(7 * 213468) - (1202)^2] = 3.6000630680907Therefore, the slope of the least squares line is 3.600. Now, we can use the slope and the y-intercept to find the equation of the least squares line. Therefore, the equation of the least squares line is:y = mx + by = 3.6x - 72.1818181818182Thus, the least squares line is y = 3.6x - 72.182.

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Therefore, it is not possible to determine if the value that occurred the most often would change without knowing the frequency and values of the new data  points.

Adding two more data points that are each 2 1/2 hours to a line plot would not necessarily change the value that occurred the most often. The value that occurred the most often would depend on the frequency of the new data points in relation to the existing data points. If the new data points have the same value as one of the existing data points, then the mode would not change. However, if the new data points have a different value than the existing data points, and they occur more frequently, then the mode would change.

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