Find the following limit or state that it does not exist. x² -81 lim X-9 X-9 Simplify the given limit. x² -81 lim X-9 = lim X-9 (Simplify your answer.) Evaluate the limit, if possible. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. lim -81 X-9 (Type an exact answer.) OB. The limit does not exist.

The outer surface area of the building is 356 m².

The total area of a three-dimensional object's base, top, and any lateral or exterior surfaces is measured as surface area. A cone, cube, cuboid, or cylinder's surface area is the area it covers on the outside. The formula for a cube's total surface area is 6 (side)2. A cuboid's lateral surface area is equal to 2(length + width) height. Similar to this, a cube with side "a" has lateral surface area equal to 4 (side)2.

Given that,

radius of building = 7m

and its saint height = 14m

Outer surface area = πrl + 2πrh

                                  = πr( L + 2h )

                                 = 22/7 × 7 ( 14 + (2×6))

                                  = 22 × (14 + 12)

                                  = 22 × 26

                                  = 356 m².

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Answer:

Amount originally invested = $700

Step-by-step explanation:

[This answer assumes that the interest is simple interest.]

We are told that upon investing a certain amount of money for 4 years at a rate of 6%, we get $168 in interest. We are then asked to calculate the amount originally invested.

To solve this problem, we have to use the formula for simple interest:

[tex]\boxed{I = PRT}[/tex],

where:

• I ⇒ interest = $168

• P ⇒ principal (original) amount = $?

• R ⇒ interest rate = 6% = 0.06

• T ⇒ time for which the money is invested = 4 years.

Using the above formula and rearranging it to make P the subject of the equation, we can calculate the principal amount:

[tex]I = PRT[/tex]

⇒  [tex]P = \frac {I}{RT}[/tex]

⇒ [tex]P = \frac{168}{0.06 \times 4}[/tex]

⇒ P = 700

Therefore, the amount originally invested was $700.

False, t < 0 expresses that t is negative in symbols.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, t < 0 this explains that the symbolic value of the t will be less than zero in the number line.

Since A horizontal line with evenly spaced numerical increments is called a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

Therefore, We can say t < 0 expresses that t is negative in symbols.

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The solution to the inequality equation -3p > -6 or 4p + 1 > 13 is p < 2 or p > 3

-3p > -6

p < -6/-3

p < 2

or

4p + 1 > 13

Subtract 1 from both sides

4p > 13 - 1

4p > 12

divide both sides by 4

p > 12/4

p > 3

Hence, the solution to the given inequality 3p > -6 or 4p + 1 > 13 is p < 2 or p > 3

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The length, in units, of the rectangle is 7 units

The formula for calculating the area of a rectangle is expressed with the equation

A = lw

Given that the parameters are given as;

Now, we have that;

Length = l

width = 3 - l

Area = 28

Substitute the values, we get;

28 = l(3-l)

expand the bracket

28 = l² - 3l

Solve the quadratic equation

l² - 7l + 4l - 28 = 0

l - 7 = 0

l = 7 or l = -4

Hence, the value is 7 units

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a.) M(t) = 2500 + 40t is a representation of the savings account amount after t years. The $2500 starting sum is added to a $40 annual increase using this function.

b.) The total balance of the two accounts at the end of t years may be written as B(t) = m(t) + 500. In this function, the constant $500 checking account amount is added to the savings account balance, m(t).

Investment is the act of allocating funds or capital to buy securities or other assets with the hope of making a profit or seeing their value rise.

Investments come in a variety of shapes and sizes, including stocks, bonds, mutual funds, and other types of real estate and commodities. Choosing the appropriate mix of investments is a crucial component of a smart investing plan since each form of investment has unique risks and possible returns.

Investments are mostly made with the intention of increasing wealth over time. By investing, people can build wealth for long-term financial stability or save for future costs like retirement. Due to the fact that investment returns frequently outperform inflation rates, investing can also act as a hedge against inflation. The type of assets a person chooses and the amount of risk they are ready to take depend on their investment objectives and time horizon.

According to the question

A linear function, m(t) = 2500 + 40t, may be used to describe the savings account balance, where t is the number of years that have elapsed. The $2500 starting sum is taken into consideration, and for each year that has gone, an additional $40 is added. This gain might be compared to an annual interest rate or investment growth.

Then, B(t) = m(t) + 500 may be used to represent the combined balance of both accounts. This function transfers the fixed balance of $500 in the checking account to the savings account balance, m(t). We may simply fill in the value of t to get the total financial condition at any given year by merging both accounts.

Making decisions about spending, saving, and investing may be done using this kind of depiction, which is helpful for tracking financial development over time. It may also be used to define financial objectives and monitor progress toward them. One may change their spending patterns and investing strategies to get to the desired financial position by keeping an eye on the trend in the growth of the overall balance.

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a.) M(t) = 2500 + 40t is a representation of the savings account amount after t years. The $2500 starting sum is added to a $40 annual increase using this function.

b.) The total balance of the two accounts at the end of t years may be written as B(t) = m(t) + 500. In this function, the constant $500 checking account amount is added to the savings account balance, m(t).

Investment

Allocating money or capital to purchase securities or other assets in the hopes of turning a profit or seeing their value increase is known as investing.

Stocks, bonds, mutual funds, and other forms of real estate and commodities are just a few examples of the many shapes and sizes that investments can take. As each type of investment carries specific risks and potential rewards, selecting the right balance of investments is essential to a sensible investing strategy.

Most investments are made with the hope of accumulating money over time. By investing, people can increase their wealth and secure their long-term financial well-being or save for future expenses like retirement. Investing can also serve as an inflation hedge because it frequently outperforms inflation rates in terms of returns. The kind of assets a person selects and the level of risk they are willing to accept are determined by their investment goals and time horizon.

According to the question,

A linear function, m(t) = 2500 + 40t, may be used to describe the savings account balance, where t is the number of years that have elapsed. The $2500 starting sum is taken into consideration, and for each year that has gone, an additional $40 is added. This gain might be compared to an annual interest rate or investment growth.

Then, B(t) = m(t) + 500 may be used to represent the combined balance of both accounts. This function moves the fixed $500 check account balance to the savings account balance m(t). To obtain the complete financial situation for any given year by merging both accounts, we can simply enter in the value of t.

This form of depiction can be used to make decisions regarding spending, saving, and investing and is useful for following the evolution of your finances over time. Setting financial goals and tracking progress toward them are other uses for it. By keeping an eye on the trend in the growth of the overall balance, one can adjust their spending habits and investment methods to reach the desired financial position.

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Northern Dancer will take 2 2/5 minutes to run the Belmont stakes

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

2 minutes / (1 1/4 miles) = x / (1 1/2 miles)

We transform the mixed fractions into improper fractions and we have:

1 1/4 =

[(4*1)+1])/ 4=

(4+1) / 4 =

5/4

1 1/2 =

[(2*1)+1] / 2 =

(2+1) / 2 =

3/2

Substituting and clearing the value we get:

2 minutes /5/4 miles = x / 3/2 miles

8/5 = 2x/3

2x = 8/5 * 3

2x = 24/5

x = 24/5 / 2

x = 24/10

x = 12/5 = 2 2/5 minutes

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Correctly written question:

A Horse named Northern dancer won the Kentucky derby with a time of exactly 2 minutes. At this rate, how long would it take Northern dancer to run the Belmont stakes? The Kentucky Derby is  1 1/4 miles in the Belmont stakes is 1 1/2 miles.

The parametrization of the line of intersection of the two planes is <12, -6, 12>

A parametrization is a way of representing a line or a curve using a set of parameters.

First, we can find the normal vectors of the two planes.

For the first plane, the normal vector is given by <3, -6, -2>, and for the second plane, the normal vector is given by <2, 1, -2>.

The line of intersection will be parallel to the cross product of these two normal vectors, which is <12, -6, 12>.

Plugging in the values from the first plane, we get:

3x - 6y - 2z = 3

3x = 6y + 2z + 3

x = 2y + z + 1

Now that we have a point on the line, we can use this to parametrize the line.

We can use the direction vector <12, -6, 12> and the point <1, 0, 0> to find the parametrization of the line:

x = 1 + t * 12

y = 0 - t * 6

z = 0 + t * 12

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The mathematical operation is as follow:

12/ 3 + 7 x 1 - 11 = 0

BODMAS rule is an acronym that is used to remember the order of operations to be followed while solving expressions in mathematics. It stands for B - Brackets, O - Order of powers or roots, (in some cases, 'of'), D - Division, M - Multiplication A - Addition, and S - Subtraction.

Given:

12___3___7___1___11 = 0

We have to put the sign such that the resultant value 0.

First take division operation then addition then multiplication  and then subtraction.

12 / 3 = 4

and, 4 + 7 = 11

and, 11 x 1= 11  

and, 11 - 11 = 0

So, 12/ 3 + 7 x 1 - 11 = 0

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The cumulative percent frequency for students working less than 20 hours per week is 25%.

In statistics, the frequency of the first-class interval is added to the frequency of the second class, and this sum is added to the third class and so on then, frequencies that are obtained this way are known as cumulative frequency (c.f.). A table that displays the cumulative frequencies that are distributed over various classes is called a cumulative frequency distribution or cumulative frequency table. There are two types of cumulative frequency - lesser than type and greater than type. Cumulative frequency is used to know the number of observations that lie above (or below) a particular frequency in a given data set. Cumulative frequency is the total frequencies showcased in the form of a table distributed in class intervals. There are two types of cumulative frequency i.e. lesser than and greater than, let us learn more about both types.

The number of hours frequency is given as follows:

Number of hours   Frequency  Cumulative frequency

0 - 9                          20                20

10 - 19                       80                100

20 - 29                     200               300

30 - 39                     100                400

So, the cumulative percent frequency  for students working less than 20 hours per week is

= (No. of students working less than 20 hours/ total number of students)* 100

= (100/400)*100

= 25%

Thus, the cumulative percent frequency for students working less than 20 hours per week is 25%.

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Team A will need to sell at least 256 bags of popcorn to avoid losing money.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given total amount to be raised by each team is $100,

Team A wants to sell popcorn,

rent of popcorn machine = $15

total cost to be earned for team B = $100 + $15 = $115

let the number of candies sold be x

cost used in popcorn bag = $0.05 per stick

cost used in x popcorn bag  = $0.05x

the selling price of each popcorn bag  = $0.50

the selling price of x popcorn bag  = $0.50x

total gain = $0.50x - $0.05x

total gain = $0.45x

minimum number of popcorn bags to be sold for no loss

$0.45x = $115

x = 115/0.45

x = 255.55

x = 256

Hence for no loss, at least 256 popcorn bags are to be sold.

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The solution to the equation f(x) - g(x)=0 is the x-intercept of the two lines, which is the point at which the two lines intersect.

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Answer:

36 is 18% of 200

So you will just want to divide 36 by 200, and multiply by 100.

36/200 = 0.18

When multiplying a decimal by 100, you can just move the decimal point 2 digits to the right.

0.18 * 100 = 18

18%

Step-by-step explanation:

Hope it helps! =D

The order of steps will be :

Step 1 : p V (q ⇒ r)

Step 2 : p V ¬ q V r

Step 3 : ¬ q V p V r

Step 4 : q ⇒ (p V r)

Given,

¬p → (q → r)  and q → (p ∨ r) are logically equivalent.

Now to prove the equivalence,

¬p → (q → r) to q → (p ∨ r)

The order of steps is given below:

Step 1 : p V (q ⇒ r)

Step 2 : p V ¬ q V r

Step 3 : ¬ q V p V r

Step 4 : q ⇒ (p V r)

Hence the equivalence can be shown.

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By adding and subtracting 9, we will be able to complete squares and rewrite the expression as:

x^2 + 6x = (x + 3)^2 - 9

Remembert that the perfect square trinomial is:

(a + b)^2 = a^2 + 2ab + b^2

Here we have the quadratic expression:

x^2 + 6x

We can rewrite the second term as:

x^2 + 2*3*x

Then, comparing with the variables on the first equation, we can use:

x = a

3 = b

Then what we need to add to complete squares is 3^2 = 9

To not change the expression, we will add and subtract that number (which is equivalent to adding 0).

x^2 + 2*3*x + 9 - 9

(x^2 + 3*3x + 9) - 9

(x + 3)^2 - 9

That is the expression after we complete squares.

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(D) Statistical significance is achieved when the result is very unlikely to occur by chance. Practical significance is related to whether common sense suggests that the treatment makes enough of a difference to justify its use. It is possible for a treatment to have statistical significance, but not practical significance is correct.

Statistical significance is achieved when the result is very unlikely to occur by chance, and is usually determined by a p-value. Practical significance is related to whether common sense suggests that the treatment makes enough of a difference to justify its use, and is determined by the magnitude of the effect, such as the size of the difference between the treatment and control groups.

It is possible for a treatment to have statistical significance, but not practical significance. This means that the result is unlikely to occur by chance, but the magnitude of the effect may be small and not clinically meaningful. Conversely, a treatment can also have practical significance, but not be statistically significant, meaning that the magnitude of the effect is large enough to be considered important, but the result may not be statistically significant due to a large sample size, for example.

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Carbon is released back into the atmosphere when organisms die, volcanoes erupt, fires blaze, fossil fuels are burned, and through a variety of other mechanisms.

The atmosphere is the layer of gas that surrounds a planet, including Earth. Atmosphere is taken from the Greek words "atmos" and "sphaira". Atmos means water vapor or gas and sphaira means blanket.

As mentioned above, the atmosphere also surrounds the planets other than Earth. Generally the thickness of the atmosphere is approximately 1,000 kilometers. On Earth alone, the atmosphere is 560 kilometers thick from the ground to space.

The mass of Earth's atmosphere is known to be 59 x 1014 tonnes. The gas content of each planet's atmosphere is usually different, depending on the most abundant gas elements or compounds on that planet.

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Answer:

It would be a undefined slope. This is because the x value of a straight vertical line can go infinite in both ways without ever changing its y value.

The ladder makes a 60° angle with the wall.

What makes a right triangle?

A right triangle consists of two legs and a hypotenuse. The two legs meet at a 90° angle and the hypotenuse is the longest side of the right triangle and is the side opposite the right angle.

In this case, we can draw a diagram. What we get is a right triangle with one leg as 8 and the hypotenuse as 16.

This is a 30-60-90 triangle (because the leg is half the hypotenuse).

They want the angle the ladder makes with the wall, so the angle between hypotenuse and leg, which is 60 degrees.

cos (angle) = adjacent / hypotenuse = 8/16

arcos(8/16) = 60°

x = 60°

Hence, The ladder makes a 60° angle with the wall.

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The ladder makes an angle of 60° with the wall . The angle made between the ladder and the wall is 60°.

Here, these values are given,

Height  of ladder = 16 foot

Height of wall = 8 foot

So, We have to find the angle made between the ladder and the brick wall.

Let, the angle made between the ladder and the wall be x °.

So, According to question ,

We use trigonometry for finding the value of angle between the ladder and the wall.

cos∅ °= base/height ( b/h)

Because, base = height of wall and hypotenuse = height of ladder.

Then, cos x° = 1/2

 cos x ° = cos 60°

 So, x° = 60°

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Answer:

Step-by-step explanation:

PLACEHOLDER

Answer:

h = -12

Step-by-step explanation:

Here's a step-by-step explanation to solve the equation:

h/6 - 1 = -3

Start by adding 1 to both sides of the equation to isolate h/6 on one side.

h/6 - 1 + 1 = -3 + 1

h/6 = -2

Next, multiply both sides of the equation by 6 to isolate h on one side.

6 * (h/6) = 6 * (-2)

h = -12

So the solution is: h = -12.

a. Region is below both lines.

b. Region is above both lines

c. No solution

d. Region between both lines

Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Given inequalities,

a. y < 8+2x and 3 + 2x >y

by the graph

Region is below both lines

b. 5 + x < y and y > 7 + x

by the graph

Region is above both lines

c. y > 12 - 3x and 10 - 3x > y

by the graph,

No solution.

d. 6 - x < y and y < 9 - x

by the graph

Region is between both lines.

Hence,

a. Region for the inequalities is below both lines

b. Region for the inequalities is above both lines

c. Region for the inequalities has no solution

d. Region for the inequalities is between both lines

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The value represents the content of the current iteration, while the position represents the index or iteration number of that value.

In a for loop, the "value" refers to the current iteration value assigned to a variable, while the "position" refers to the iteration number or index.

For example, in a for loop that iterates over a list of numbers, the value could be each individual number in the list, while the position could be the index of that number in the list.

For example, consider the following code:

numbers = [1, 2, 3, 4, 5]

for i, value in enumerate(numbers):

   print("Position:", i, "Value:", value)

The output of this code would be:

Position: 0 Value: 1

Position: 1 Value: 2

Position: 2 Value: 3

Position: 3 Value: 4

Position: 4 Value: 5

Here, i represents the position, starting from 0 and increasing by 1 for each iteration, and value represents the value assigned to each number in the numbers list.

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The equation that represents the number of fourth-grade students in the group will be 4 x 8 - 27 = f.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The capacity of four vans is given as,

⇒ 4 x 8

There are 27 third-grade students in the group. Then the number of fourth-grade students in the group will be given as,

4 x 8 - 27 = f

The equation that represents the number of fourth-grade students in the group will be 4 x 8 - 27 = f.

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The domains of the relation are (-3, -2, -1, 2, 4)

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The independent variables are the domain of the relation.

Now,

The coordinates from the graph are:

(2, 0), (4, -1), (-1, 1), (-3, 4), and (-2, 0)

Now,

2, 4, -1, and -3 are the independent variables.

The domains are (-3, -2, -1, 2, 4)

Thus,

The domains are (-3, -2, -1, 2, 4)

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Jessie and Bob's balloon payment will be $529,229.56.

A balloon mortgage is a type of mortgage in which the borrower makes smaller monthly payments over the term of the loan, with a large balloon payment due at the end.

To calculate the balloon payment, we need to know the amount of the loan, the interest rate, and the term of the loan.

Given that Jessie and Bob are financing $425,500 to purchase a house, the interest rate is 6.55%, and the term of the loan is 30/8 (or 3.75) years, we can use the below formula to calculate the balloon payment:

Balloon payment = Loan amount * (1 + Interest rate * Loan term)

Balloon payment = $425,500 * (1 + 6.55% * 3.75)

Balloon payment = $425,500 * 1.249625

Balloon payment = $529,229.56

Therefore, Jessie and Bob's balloon payment will be $529,229.56.

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Answer:

Answer: 1/6

Step-by-step explanation:

Total number of numbers = 12Total number of 4  or 6 = 2P( 4 or 6) = 2/12 = 1/6Answer: 1/6

If the p-value is less than α in a two-tailed test then the null hypothesis should be rejected.

Hypothesis testing uses sample data from the population to draw useful conclusions regarding the population probability distribution.

A method for drawing statistical conclusions from population data is hypothesis testing. It is a technique for analysis that evaluates presumptions and establishes the likelihood of something based on a predetermined level of accuracy. Testing hypotheses offers a technique to determine whether the outcomes of an experiment are reliable.

Before doing the hypothesis testing, a null hypothesis and an alternative hypothesis are established.

Thus, If the p-value is less than α in a two-tailed test then the null hypothesis should be rejected.

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Multiplying by 0.05 is the same as decreasing by 95%.

Multiplying a number by 0.05 is equivalent to decreasing that number by a certain percentage. To determine this percentage, we can use the formula: 100 - (100 * 0.05) = 100 - 5 = 95. This means that multiplying a number by 0.05 is the same as decreasing it by 95%. For example, if a person has $100 and multiplies it by 0.05, the result will be $5, which is a decrease of 95% from the original amount.

In other words, 0.05 is equivalent to 95% of a number, and multiplying by 0.05 is the same as decreasing the number by 95%. This relationship between multiplication by 0.05 and decreasing by a certain percentage is important in various mathematical and real-world applications.

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Distinct prime factors does the product of these numbers have 2,3 , and 5 are the three distinct prime factors

Prime factorization is a process of factoring a number in terms of prime numbers i.e. the factors will be prime numbers.

Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors.

As we know, a composite number has more than two factors, therefore, this method is applicable only for composite numbers and not for prime numbers.

The numbers must be 4,5 , and 6 .

4+5+6=15 and

4*5*6=120

=2^3*3*5

Distinct prime factors does the product of these numbers have 2,3 , and 5 are the three distinct prime factors.

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Distinct prime factors do the product of these numbers have 2,3, and 5 are the three distinct prime factors

Prime factorization is a process of factoring a number in terms of prime numbers i.e. the factors will be prime numbers.

Prime factorization is defined as a way of finding the prime factors of a number, such that the original number is evenly divisible by these factors.

As we know, a composite number has more than two factors, therefore, this method is applicable only to composite numbers and not to prime numbers.

The numbers must be 4,5, and 6.

4+5+6=15 and

4*5*6=120

=2^3*3*5

Distinct prime factors the product of these numbers have 2,3, and 5 are the three distinct prime factors.

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