A function f is said to have a removable discontinuity at a if:
1. f is either not defined or not continuous at a.
2. f(a) could either be defined or redefined so that the new function is continuous at a.
Let f(x)=2x²+4x-6/x-1
Show that f has a removable discontinuity at 1 and determine the value for f(1) that would make f continuous at 1.Need to redefine f(1)=

120 is the number divisible by 6, 8, and 10.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

The common multiples to 6, 8, and 10.

6 x 20 =  120

8 x 15 = 120

10 x 12 = 120

So,

120 is divisible by 6, 8, and 10.

Thus,

120 is the number.

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The hypothesis tested are given as follows:

[tex]H_0: \mu = 3.2, H_a: \mu \neq 3.2[/tex]

The claim for this problem is given as follows:

"The mean salary for the baseball players on the East Coast is different from $3.2 million".

At the null hypothesis, we test if the claim is false, that is, if the mean salary is equals to 3.2 million, hence:

[tex]H_0: \mu = 3.2[/tex]

At the alternative hypothesis, we test if the claim is true, that is, if the mean salary is different of 3.2 million, hence:

[tex]H_a: \mu \neq 3.2[/tex]

The [tex]\mu[/tex] symbol, without the bar, is used, as we are testing for the population mean, not sample mean, hence the first option is the correct option.

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The quantities 6 and 2 are called proportions

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

In the ratio of yellow marbles to blue marbles, 6:2,

This means that

Yellow : Blue = 6 : 2

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

For every 6 yellow marbles, there are 2 blue marbles

This means that 6 and 2 are the proportions

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The value of the evaluated function f(x) = -3x² + 2x  at  

(i) f(-2) is -16   ;

(ii) f(a) is -3a² + 2a .

The Function is represented as : f(x) = -3x² + 2x  ;

(i) We have to evaluate the above function at f(-2),

So, we substitute x = -2 into the function:

we get ;

⇒ f(-2) = -3(-2)² + 2(-2)

⇒ f(-2) = -12 - 4 = -16  .

So ,  f(-2) = -16  .

(ii) Next we have to evaluate f(a),

So , we substitute x = a into the function:

⇒ f(a) = -3a² + 2a

So , f(a) = -3a² + 2a   .

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The given question is incomplete , the complete question is

For the following exercises, evaluate the function f(x) = -3x² + 2x ; at the given input: (i) f(-2) (ii) f(a)  .

a) The number of ways to deal the cards without getting one of the designated cards are equals to the 2250829575120.

b) The number of ways to deal each player 7 cards, regardless of whether the designated cards come out are equals to the 21945588357420.

c) The probability of a successful hand that will go all the way till everyone gets 7 cards is 0.1026.

Six friends group is playing poker one night. They have a standard 52-card deck. So, here, total number of possible outcomes of game = 52

Now, the designated cards are , Queen of Clubs, 10 of Hearts. So,

a) Number of cards are in the deck that are not one of the designated cards

= 52 - 2 = 50

Number of cards that need to be dealt in order for each player to have 7 cards

= 5× 7 = 35

Thus total possible number of ways

= ⁵⁰C₃₅ = 2250829575120, which are ways to deal the cards without getting one of the designated cards.

b) Number of cards are in the deck = 52

Number of cards that need to be dealt in order for each player to have 7 cards = 5× 7 = 35

Thus total possible number of ways

= ⁵²C₃₅ = 21945588357420

Which are ways to deal each player 7 cards, regardless of whether the designated cards come out.

c) The probability of a successful hand that will go all the way till everyone gets 7 cards is = Number of ways to deal the cards without getting one of the designated cards/Total number of ays to deal the cards

= 2250829575120/21945588357420

= 0.10256410256

Hence, required probability is 0.1026.

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The total area of both triangles is the product of the height and base of the flag.

The connecting of three noncolinear points results in a triangle, which is a three-sided closed-plane object. Triangles can be classified into three categories based on their side properties: equilateral, scalene, and isosceles.

Given, Anthony painted 2triangles of the same size on the top corners of his house flag for sports day.

We are aware of A parallelogram can be divided into two comparable triangles by dividing it along its diagonal.

A planar figure with opposite sides that are parallel and of equal length is called a parallelogram.

Since the area of a parallelogram is equal to its base times its height, the combined area of the two triangles will be the same.

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Answer:

To find y'(3), we need to use implicit differentiation to differentiate both sides of the equation with respect to x and then solve for y'.

Differentiating both sides with respect to x, we get:

(2x/25) + (2y/64) * (dy/dx) = 0

Now we can solve for dy/dx:

(2y/64) * (dy/dx) = -(2x/25)

dy/dx = -(2x/25) / (2y/64)

dy/dx = -32x/25y

To find y'(3), we need to substitute x=3 and y=6.4 into the expression for dy/dx:

y'(3) = -32(3)/(25)(6.4)

y'(3) = -0.3

Therefore, the value of y'(3) is -0.3

The value of y'(3) in (2x/25) + (2y/64) = 1, is  - 0.3

Finding the derivative of an implicit function is the process of implicit differentiation.

In other words, this method is utilized to discover the implicit derivative.

To find y'(3), After differentiating both sides of the equation with respect to x using implicit differentiation, we must next solve for y'.

Differentiating both sides with respect to x we get,

(2x/25) + (2y/64)×(dy/dx) = 0

Solving for dy/dx

(2y/64)×(dy/dx) = -(2x/25)

dy/dx = -(2x/25) / (2y/64)

dy/dx = -32x/25y

To find y'(3), Replacing x=3 and y=6.4 into the expression for dy/dx:

y'(3) = -32(3)/(25)(6.4)

y'(3) = -0.3

Therefore, the value of y'(3) is - 0.3

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As per the information provided, option B) The errors e1,e2, e; have the same variance is the assumptions for linear regression.

Regression analysis is a linear technique used to model the relationship between a scalar response and/or one or more explanatory variables, also known as the dependent and independent variables here.

Simple linear regression and multiple linear regression are two terms used to describe the process when there is only one explanatory variable present. This statement is different from multivariate linear regression, which thus predicts multiple correlated dependent variables as opposed to a single scalar variable present.

The first regression analysis technique that attracted a lot of research attention and was frequently applied in practical situations was linear regression. This is because models with linear rather than non-linear dependence on their unknown parameters are easier to fit, and it is also easier to determine the statistical properties of the resulting estimators.

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Answer:

7/3>x

Step-by-step explanation:

-5<9-6x

subtract 9 from both sides

-14<-6x

divide by 6

14/6<x

simplified its 7/3<x

but since we divided by a negative we switch the sign

final answer is 7/3>x

The product of 4.000329 × 1000 is the second option 4,000.329.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

We have to find the product of 4.000329 × 1000.

When a number is being multiplied by (10)ⁿ, 'n' number of zeroes will be added to the right of the number.

If the number is decimal number, decimal point is being shifted n digits to the right.

The question here is 4.000329 × 1000.

4.000329 × 1000 = 4.000329 × (10)³

Decimal point is shifted three digits to the right.

4.000329 × (10)³ = 4,000.329

Hence the correct option is B.  4,000.329.

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Answer:

Step-by-step explanation:

56

The slope of line q is equal to 3.

The slope of line q is equal to -1/3.

An equation for line p in point-slope form is y + 5 = -1/3(x - 6).

An equation for line p in slope-intercept form is y = -1/3x - 3.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c   ....equation 1.

Where:

From the information provided, we have the following linear equation in slope-intercept form for line q:

y = 3x + 5  ....equation 2.

By comparing equation 1 and equation 2, we can logically deduce the following:

Slope (m) = 3

Since line p is perpendicular to line q, the slope of line p is the negative reciprocal of the slope of line q;

m₁ × m₂ = -1

3 × m₂ = -1

Slope, m₂ of line p = -1/3.

At data point (6, -5), a linear equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-5) = -1/3(x - 6)

y + 5 = -1/3(x - 6)

By simplifying further, the slope-intercept form is given by;

y + 5 = -1/3(x - 6)

3y + 15 = -x + 6

3y = -x - 9

y = -1/3x - 3

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Complete Question:

Line p contains point (6, -5) and is perpendicular to line q. The equation for line q is y = 3x + 5. Write an equation for line p.

Find the slope of line q.

Find the slope of line p. (Write the negative reciprocal of the slope you found in Part I.)

Use the point given for line p and the slope you found in Part II to write an equation for line p in point-slope form: y - y1 = m (x - x1)

Use your equation from Part III to write an equation for line p in slope-intercept form: y = mx + b.

Rounded to the nearest tenth, the area of the region that receives the radio signal is approximately 6,366.2 square miles.

Consider a plane region described by a xy-plane graph. The signed area of the region is defined as the area of the graph on or above the x-axis. The negative area of the graph is defined as the area below the x-axis.

The formula A = πr² gives the area of a circle with radius r. In this case, the radio station broadcasts over a 45-mile radius, so the region that receives the radio signal is:

A = π(45)²

A ≈ 6,366.2 square miles

The area of the region that receives the radio signal is approximately 6,366.2 square miles when rounded to the nearest tenth.

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The value of x for the system of equations will be x=6.7.

What is a system of equations?

A set of simultaneous equations is a finite set of equations for which common solutions are sought in mathematics. It is also known as a system of equations or an equation system.

Given that the two equations are 2x + 2y = 17 and 4x - y = 25. The value of x will be calculated by eliminating the variable y from the equation.

Multiply the second equation by 2 and subtract from the first equation,

2x+2y=17.

8x-2y=50.

10x=67.

x= 67/10

x = 6.7.

Therefore, the value of x for the system of equations will be x=6.7.

\

The expression "D(50) - (D(15) ∪ D(20))" refers to the set difference between the set D(50) and the union of sets D(15) and D(20).

The set difference is the operation that gives you the elements that are in the first set (D(50)) but not in the second set (D(15) ∪ D(20)). Note that this prompt draws on Set Theory.

Set Theory is a branch of mathematics concerned with the study of sets, their properties, and their relationships.

In set theory, a set is a collection of distinct objects, and the set difference operation, represented by the minus sign (-), returns the elements that are in the first set but not in the second set.

The union of sets, represented by the symbol ∪, is the operation that gives you the set of all elements that are in at least one of the sets being considered.

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The height of the triangle is 20 and base of the triangle is 12.

"Information available from the question"

The base of a triangle is 8 ft. less than its height.

If the area is 120 [tex]ft^2.[/tex]

We have to find the base and the height of this triangle.

Now, According to the question:

Let the height be x then if the base is 8 ft. less, then the base is x - 8.

We know that:

Area of the triangle is :  (b × h)/2

Area of the triangle is : (x (x - 8)) /2

120 [tex]ft^2[/tex] = ([tex]x^{2} -8x[/tex])/2

240 = [tex]x^{2} -8x[/tex]

[tex]= > x^{2} -8x-240=0[/tex]

For solving equation, Use the quadratic formula :

x = (-b ± [tex]\sqrt{b^2-4ac}[/tex]) / 2a

a = 1

b = -8

c = -240

x = (-(-8) ± [tex]\sqrt{(-8)^2-4.1(-240)})/2.1[/tex]

By solving, we get

x = (8 ± 32)/2

We get the values :

x = 20 and x = -12

We know x = −12 can't be a solution as length can't be negative.

Base = x - 8

Base = 20 - 8

Base = 12

Hence, The height of the triangle is 20 and base of the triangle is 12.

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a) The determination of the dividends per share for the cumulative preferred and common stock for each year is as follows:

           Dividends per share

2011           $3.00

2012           $1.20

2013          $4.80

            Dividends per share

2011              $1.50

2012             $0

2013             $2.10

b) The determination of the amount of current dividends that preferred stock should receive per year is $75,000.

Cumulative preferred stock is a special class of preferred stock that enjoys cumulative dividends.

Cumulative dividends imply that any year when sufficient dividends are not declared, the arrears are carried forward to subsequent years.

It is the opposite of non-cumulative preferred stock.

On the other hand, the common stockholders can only receive dividends after the preferred stockholders have been paid, including their cumulative dividends.

Number of shares = 25,000

Dividend rate = 2%

Par value = $150

Total cumulative preferred stock = $3,750,000 (25,000 x $150)

Annual dividend = $75,000 ($3,750,000 x 2%)

Number of shares = 50,000

Par value = $15

Total common stock = $750,000 (50,000 x $15)

                  Dividends Due   (Dividends per share)

2011             $75,000             $3 ($75,000/25,000)

2012            $30,000             $1.2 ($30,000/25,000)

2013           $120,000             $4.8 ($120,000/25,000)

                  Dividends Available                      (Dividends per share)

2011           $75,000 ($150,000 - $75,000)    $1.50 ($75,000/50,000)

2012          $0 ($30,000 - $30,000)               $0

2013         $105,000 ($225,000 - 120,000)   $2.10 ($105,000/50,000)

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The probability she pulls out a purple piece of candy would be 0.22.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is Sam's fathers collection.

We can write the equations for upstream and downstream as -

x - y = 7/2

x + y = 21/10

Solving the equations graphically -

{x} = 2.8

{y} = 0.7
In still water, the speed would be -

S = 3 - 0.7

S = 2.3 Km/h

Distance peddled upstream -

D = 2.8 x 3.5 = 9.8 Km

Therefore, the speed in still water would be 2.3 Km/h and the distance peddled upstream would be 9.8 Km.

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Point of  y-intercept is (0,1)

In a graph, the point where the line or curve crosses the axis is called the intercept. If a point crosses the x-axis it is x-intercepts. If a point crosses y-axis it is y-intercepts.

Given the function is [tex]y=2.5^{x}[/tex]

y-intercept is the point where the graph of the function crosses the y-axis.

To find the point of y-intercept put x=0 in the given function, we get

if x=0  then [tex]y=2.5^{0}[/tex] ⇒ y=1.

The function crosses at the point 1 in the  y-axis.

Hence, point of  y-intercept is (0,1)

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The system of equations has infinitely many solutions.

What is a system of equations?

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

Here, we have

Given:

-2x - 3y + z = 7

-x - y + 3z = -10

-2x - y - z = 13

We have to how many solutions the system of equations has.

Arranging the above equations in form of a matrix and finding the determinant, we get,

Δ = [tex]\left|\begin{array}{ccc}-2&-3&1\\-1&-1&3\\-2&-1&-1\end{array}\right|[/tex]

= -2(1+3) +3(1+6) +1(1-2)

= - 4 + 21 -1 = 16

Δ₁ = [tex]\left|\begin{array}{ccc}7&-3&1\\-10&-1&3\\13&-1&-1\end{array}\right|[/tex]

= 7(1+4) +3(10-39) +1(10+13)

= 35 - 87 + 23

= -29

Hence, the system of equations has infinitely many solutions.

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The area of the figure is 596.625 in².

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

We will consider the figure to have a rectangle and a circle.

Rectangle:

Length = 28 in

Breadth = 15 in

Area = 28 x 15 = 420 in²

Semicircle:

Diameter = 15 in

Radius = 7.5 in

Area = 1/2 πr²

= 1/2 x 3.14 x 7.5²

Area = 176.625/2

Area = 88.3125

There are two semicircles so,

= 2 x 88.3125

= 176.625 in²

Now,

Area of the figure.

= 420 + 176.625

= 596.625 in²

Thus,

596.625 in² is the area of the figure.

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The height of flagpole c is given as follows:

66 ft.

Similar triangles are triangles that share these two features presented as follows:

For each flagpole, the parameters are given as follow:

The triangles are similar, hence the proportional relationship to obtain the height of flagpole's c is given as follows:

2/10 = 13.2/h

Applying cross multiplication, the height is obtained as follows:

2h = 10 x 13.2.

h = 132/2

h = 66 ft.

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Answer: all angles are equal

Step-by-step explanation:

in a equilateral triangle all angles will be 60°

Answer:

-x + 9

Step-by-step explanation:

a)  

 8x + 2 + (-9x + 7) = 8x + 2 - 9x + 7

                             = 8x - 9x + 2 + 7

                             = -x + 9

b) We can combine like terms. Like terms have same variable with same power. Here 8x and (-9x) have same variable 'x'. so, combine the coefficients of the like terms which give (-1).

8x - 9x = -1

Combine the constants. 2 + 7= 9

Answer:

2 vases of lilacs

3 vases of irises

Step-by-step explanation:

7( lilacs ) × 2( vases) = 14 flowers

5( irises ) × 3( vases) = 15 flowers

14 + 15 = 29 flowers

The value of the probabilities are

a. P(x ≥ 12.5) is 6.68%

b. P(x ≤ 9) is 2.28%

c. P(10.88 ≤ x ≤ 15.3) is 61.38%

d. P(4.72 ≤ x ≤ 12.46) is 99.45%

Probability is the measure of the likelihood of an event occurring. It is a way of quantifying uncertainty and predicting the likelihood of an outcome. In this question, we will use the normal distribution to calculate probabilities.

The mean is the center of the distribution, and the standard deviation measures the spread of the distribution.

a. P(x ≥ 12.5):

Using a standard normal distribution table, we find that the area to the right of 12.5 is 0.0668. This means that the probability of x being greater than or equal to 12.5 is 0.0668 or 6.68%.

b. P(x ≤ 9):

Using a standard normal distribution table, we find that the area to the left of 9 is 0.0228. This means that the probability of x being less than or equal to 9 is 0.0228 or 2.28%.

c. P(10.88 ≤ x ≤ 15.3):

Using a standard normal distribution table, we find that the area to the left of 15.3 is 0.9987 and the area to the left of 10.88 is 0.3849. Therefore, the area between 10.88 and 15.3 is

=> 0.9987 - 0.3849 = 0.6138.

This means that the probability of x being between 10.88 and 15.3 is 0.6138 or 61.38%.

d. P(4.72 ≤ x ≤ 12.46):

Using a standard normal distribution table, we find that the area to the left of 12.46 is 0.9946 and the area to the left of 4.72 is 0.0001. Therefore, the area between 4.72 and 12.46 is

=> 0.9946 - 0.0001 = 0.9945.

This the probability of x being between 4.72 and 12.46 is 0.9945 or 99.45%.

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a) The unit rate of Kate's sewing productivity can be found by dividing the number of dresses by the number of days:

Kate sews 100 dresses in 20 days.

The unit rate is 100 dresses / 20 days = 5 dresses per day.

b) The unit rate of Kim's running speed can be found by dividing the distance by the time:

Kim runs 5 km in 30 minutes.

The unit rate is 5 km / 0.5 hour = 10 km/hour.

Therefore, the unit rate for Kate's sewing productivity is 5 dresses per day, and the unit rate for Kim's running speed is 10 km/hour.