how to solve for the below problems

The rational function f(x) = (x² + 1)/(x² + 2x + 2) has no vertical asymptotes and no holes.

We have,

A rational function is a function that can be expressed as the ratio of two polynomials.

It can have vertical asymptotes and/or holes in its graph, depending on the behavior of the denominator polynomial.

To construct a rational function with no vertical asymptotes and no holes, we need to ensure that the denominator polynomial does not have any real roots.

This means that the denominator polynomial should either have no roots or only complex roots.

One way to achieve this is to use a quadratic polynomial in the denominator that has no real roots.

For example, consider the function:

f(x) = (x² + 1)/(x² + 2x + 2)

The denominator polynomial x² + 2x + 2 has no real roots because its discriminant, 2² - 4(1)(2) = -4, is negative.

This means that the function f(x) has no vertical asymptotes.

To check if the function has any holes, we need to simplify the function by canceling out any common factors between the numerator and denominator.

However, since the numerator x² + 1 has no common factors with the denominator, there are no terms to cancel out.

Therefore, the function f(x) has no holes either.

Thus,

The rational function f(x) = (x² + 1)/(x² + 2x + 2) has no vertical asymptotes and no holes.

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Answer:

a. The present value of these receivables is $42,123.64

b. The total value at the end of 10 years is $69,257.02

c. The present value of these payments is $10,059.37

Step-by-step explanation:

Step-by-step explanation:

If radius is 8cm    then diameter =  16 cm

circumference of a circle = pi * d = pi * 16 cm = ~ 50.27 cm

Answer:

C

Step-by-step explanation:

8 x 10^4 = 80,000

3 x 10^3 =   3,000

1  x  10 ^2 =    100

2 x 10^1 =         20

add it up

83,120

C is correct

Answer:7.02

Step-by-step explanation: cause im right

Answer:7 units

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

To find the average of a set of numbers, you add up all the numbers in the set and then divide by the total number of numbers in the set.

So, to find the average of the set of numbers 7, 6, 12, 5, 7, 6, 13, you would first add up all the numbers:

7 + 6 + 12 + 5 + 7 + 6 + 13 = 56

Then you would divide the sum by the total number of numbers in the set, which is 7:

56 / 7 = 8

Therefore, the average of the set of numbers 7, 6, 12, 5, 7, 6, 13 is 8.

Answer:

the answer you are looking for would be 8

The number of lateral faces of a pyramid with a six-sided base depends on the type of pyramid.

We have,

The number of lateral faces of a pyramid with a six-sided base depends on the type of pyramid.

If it is a regular pyramid, meaning that the base is a regular hexagon and the apex is directly above the center of the base, then it will have six lateral faces, each of which is a triangle.

If the pyramid is not regular, then it will have more than six lateral faces, but the exact number will depend on the specific shape of the base and the position of the apex.

If the base of a pyramid has ten sides, again, the number of lateral faces depends on the type of pyramid.

If it is a regular pyramid, meaning that the base is a regular decagon and the apex is directly above the center of the base, then it will have ten lateral faces, each of which is a triangle.

If the pyramid is not regular, then it will have more than ten lateral faces, but the exact number will depend on the specific shape of the base and the position of the apex.

Thus,

The number of lateral faces of a pyramid with a six-sided base depends on the type of pyramid.

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The complete question:

How many lateral faces does a pyramid whose base is a six-sided figure have? What if its base had ten sides?

Answer:

Step-by-step explanation:

no higher than 4

The correct sentences in the passage are option A, option B, and option E.

Let's check all the options, then we have

Any two squares are either similar or congruent. The statement is true.

If two lines are parallel, they never intersect. The statement is true.

If all the angles of a polygon are congruent, then it is a square. The statement is false because a regular polygon has an equal angle but it may be a pentagon, hexagon, etc.

The intersection of two lines always forms 4 congruent angles. The statement is false because opposite angles are the same. But if adjacent angles become the same, then the statement will be true.

A line can be drawn through any two distinct points. The statement is true.

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The line a and line d are perpendicular to each other.

Perpendicular lines and intersecting lines are the same because they both describe 2 lines that cross one another.

Perpendicular lines cross one another in a specific way.  The intersection of perpendicular lines forms 90 degree angles.

Constructing lines a and d:

After constructing the two lines; line a and line intersect or meet each other at 90 degrees to the horizontal.

Thus, we can conclude that the line a and line d are perpendicular to each other.

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Answer:line a and line d are perpendicular

saw the answers

1) Using the Law of Syllogism, we can combine statement 1 and statement 3 to conclude that Sally weighs more than Jill's car:

If something weighs more than 2000 pounds, then it weighs more than Jill’s car.

Sally weighs more than 2000 pounds.

Therefore, Sally weighs more than Jill's car.

2) Using the Law of Detachment, we can apply statement 2 to our conclusion from the Law of Syllogism to conclude that Sally is too heavy for the bridge:

If something weighs more than Jill’s car, then it is too heavy for the bridge.

Sally weighs more than Jill's car.

Therefore, Sally is too heavy for the bridge.

The Law of Syllogism opines that if two conditional statements have the same terms, then we can combine them to form a conclusion.

The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then its conclusion is also true.

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The fraction 9/10 is more than 78/100.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, and exponentiation) that are combined in a meaningful way.

To compare these two fractions, we can convert them to have a common denominator. In this case, the common denominator is 1000.

9/10 = (9/10) x (100/100) = 900/1000

78/100 = (78/100) x (10/10) = 780/1000

Now we can see that 900/1000 (which is equivalent to 9/10) is greater than 780/1000 (which is equivalent to 78/100).

Therefore, 9/10 is more than 78/100.

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Answer:

the missing value is y = 48.

Step-by-step explanation:

In a direct variation, the ratio of the two variables remains constant. We can use this fact to find the missing value y:

y / 18 = 8 / 3

To solve for y, we can cross-multiply:

y = 18 * 8 / 3

y = 48

Therefore, the missing value is y = 48.

When x = 7, what is the second coordinate in a scatter plot is: D. 112.8.

The approximate value x=4 to the nearest whole number is; C. 1,168.

In this scenario, the x-values would be plotted on the x-axis (x-coordinate) of the scatter plot while the y-values would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an exponential equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the x-values and y-values, an exponential equation for the line of best fit is given by

[tex]y = 31.86e^{0.18x}[/tex]

when x = 7, the second coordinate in this scatter plot is given by;

[tex]y = 31.86e^{0.18(7)}[/tex]

y = 112.8

logy = 0.75821x+0.03442

logy = 0.75821(4) +0.03442

logy = 3.03284 +0.03442

logy = 3.06726

y = log⁻¹(3.06726)

y = 1167.5084 ≈ 1,168

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Answer:

28(17) + π(7^2)

= 476 + 49π square meters

= 629.94 square meters

The requreid smallest whole number that rounds to 2,560 to the nearest ten is 2,565. When we round 2,565 to the nearest ten, we get 2,570, which is the desired result.

When rounding a number to the nearest ten, look at the digit in the tens place. If that digit is 5 or greater, we round up by adding 1 to the digit in the hundreds place. If that digit is less than 5, round down by keeping the digit in the hundreds place the same.

In the given question, 2,560 rounded to the nearest ten would be,

2,560 rounded up to 2,560 + 10 = 2,570.

Therefore, the smallest whole number that rounds to 2,560 to the nearest ten is 2,565. When we round 2,565 to the nearest ten, we get 2,570, which is the desired result.

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The calculated value of the length of segment DF is 51.96 units

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

The right triangle

The length of segment DF is then calculated as

sin(60) = DE/DF

Substitute the known values in the above equation, so, we have the following representation

sin(60) = 45/DF

So, we have

DF = 45/sin(60)

Evaluate the quotient

DF = 51.96

Hence, the segment DF is 51.96 units

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Answer:

Step-by-step explanation:

110

Answer:

(1/2)(4)(3)(2) = 12 cubic yards

The correct answer is A.

The standard error of the mean δ  for a sample of size n is calculated as:

δ = σ / √(n)

where σ is the population standard deviation and n is the sample size.

For a sample of size 8 taken from a normally-distributed population with a mean of 32 and a standard deviation of 7, the δ is:

δ  = 7 / √(8) ≈ 2.475

The 99.7% confidence interval for the sample mean is given by:

x ± 3 Substituting the values, we get:

32 ± 3(2.475)

where x is the sample mean.

Substituting the values, we get:

32 ± 3(2.475)

which simplifies to:

[24.575, 39.425]

Therefore, about 99.7% of the sample means taken from this population will fall within the interval [24.575, 39.425].

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well, we know the number of bacteria is decreasing, so we can use a Decay equation for that, with a 75% rate of decay.

[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &200000\\ r=rate\to 75\%\to \frac{75}{100}\dotfill &0.75\\ t=hours \end{cases} \\\\\\ A = 200000(1 - 0.75)^{t} \implies A = 200000(0.25)^t[/tex]

The linear function y = 2x + 5 shows that Sarah charges $5 as fixed amount before she begins selling newspapers.

The table representing amount of money which Sarah charges her customers to sell newspapers.

Let us consider 'x' represents the time per hour charges taken by Sarah from customers.

In the table,

For zero hours charges are $5.

It means Fixed charges taken by Sarah to sell newspaper.

Difference between the rate per hour is,

$7 - $5 = $2

$9 - $7 = $2

It represents for Sarah charges $2 per hour.

let us consider 'y' that represents total amount charges by Sarah.

Required linear function for selling news paper and charging amount is

y = $5 + 2x

⇒ y = 2x  + 5

Therefore, the linear function y = 2x + 5 represents option 1. Sarah charges $5 before she begins selling newspapers.

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The distribution that is positively skewed would be the Box plot in Option C.

When discussing distributions, a positive skew refers to the tail being lengthier on the right side as opposed to the left. As such, more extreme values are located on the right-hand portion of said distribution.

To put it another way, there is a predominance of data clustering toward the left with only a handful of instances where extreme values are found further along the right-hand scale. This scenario would prompt an observer to note how the mean outstrips the median.

The box plot in option C has most of the data towards the left side which is the positive side so this is positively skewed.

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1. The area of the smaller rectangle is approximately 96 in².

2. The length of the hypotenuse of the smaller triangle is 32 units.

If the scale factor of two similar rectangles is 4/7, then the ratio of their areas is (4/7)^2 = 16/49. This means that the area of the smaller rectangle is (16/49) times the area of the larger rectangle.

Let A be the area of the smaller rectangle. Then we have:

A = (16/49) * 294 in²

A = 96 in² (rounded to the nearest whole number)

Therefore, the area of the smaller rectangle is approximately 96 in².

2.  4/9, which simplifies to 2/3.

This means that the length of the hypotenuse of the smaller triangle is (2/3) times the length of the hypotenuse of the larger triangle.

Let x be the length of the hypotenuse of the smaller triangle. Then we have:

(2/3) * 48 = x

x = 32 units

Therefore, the length of the hypotenuse of the smaller triangle is 32 units.

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Darrion ran a total distance of 38 3/4 miles in 10 days.

We have,

To find the total distance Darrion ran in 10 days, we need to add up the distance he ran in the first five days and the distance he ran in the next five days.

Distance ran in the first five days

= 3 1/2 miles per day x 5 days

= 17 1/2 miles

Distance ran in the next five days

= 4 1/4 miles per day x 5 days

= 21(1/4) miles

Total distance Darrion ran in 10 days

= Distance ran in the first five days + Distance ran in the next five days

= 17 1/2 miles + 21 1/4 miles

= 38 3/4 miles

Therefore,

Darrion ran a total distance of 38 3/4 miles in 10 days.

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The probability that the Jones family had at least 4 girls is 0.5625 and the probability that the Jones family had at most 3 girls is 0.65625.

We can use the binomial probability formula to solve this problem. Let X be the number of girls in the Jones family, then X follows a binomial distribution with parameters n = 6 and p = 0.5.

The probability of having k girls in a family of 6 children is given by:

P(X = k) = (6 choose k) * [tex]0.5^{k}[/tex] * [tex]0.5^{6-k}[/tex]

where (6 choose k) is the binomial coefficient.

To find the probability of having at least 4 girls, we need to calculate the probability of having 4, 5, or 6 girls and add them up:

P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6)

= (6 choose 4) * [tex]0.5^{4}[/tex] * [tex]0.5^{2}[/tex] + (6 choose 5) * [tex]0.5^{0.5}[/tex] * [tex]0.5^{1}[/tex] + (6 choose 6) * [tex]0.5^{6}[/tex] * [tex]0.5^{0}[/tex]

= 0.234375 + 0.3125 + 0.015625

= 0.5625

Therefore, the probability that the Jones family had at least 4 girls is 0.5625 or 56.25%.

To find the probability of having at most 3 girls, we need to calculate the probability of having 0, 1, 2, or 3 girls and add them up:

P(X <= 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= (6 choose 0) * [tex]0.5^{0}[/tex] * [tex]0.5^{6}[/tex] + (6 choose 1) * [tex]0.5^{1}[/tex] * [tex]0.5^{5}[/tex] + (6 choose 2) * [tex]0.5^{2}[/tex] * [tex]0.5^{4}[/tex] + (6 choose 3) * [tex]0.5^{3}[/tex] * [tex]0.5^{3}[/tex]

= 0.015625 + 0.09375 + 0.234375 + 0.3125

= 0.65625

Therefore, the probability that the Jones family had at most 3 girls is 0.65625 or 65.625%.

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The linear equations and the values of the variables of the equations are;

A linear equation is an equation that can be presented as; y = mx + c, where m is the slope and c is the y-intercept.

1. Please find attached, the graph of the equations y = 2x and y = 3x + 2, created with MS Excel, showing the solution point (-2, 4)

The solution is x = -2, y = 4

2. Please find attached, the graph of the equations y = 2x and y = 3x + 2, created with MS Excel, showing the solution point (0, 3)

The solution is x = 0, y = 3

3. The equations are solved using substitution as follows;

y = 2 - 6·x

9·x + 2·y = 3

Therefore;

9·x + 2×(2 - 6·x) = 3

4 - 3·x = 3

3·x = 4 - 3 = 1

x = 1/3

y = 2 - 6·x

y = 2 - 6 × 1/3 = 0

y = 0

4. 8·x + 7·y = 43

2·x + y = 7

Therefore;

y = 7 - 2·x

8·x + 7·y = 43

8·x + 7 × (7 - 2·x) = 43

49 - 6·x = 43

6·x = 49 - 43 = 6

x = 6/6 = 1

x = 1

y = 7 - 2·x

y = 7 - 2 × 1 = 5

y = 5

5. y = 8 + 5·x

Therefore where 7·x + 9·y = -32, we get;

7·x + 9 × ( 8 + 5·x) = -32

52·x + 72 = -32

52·x = -32 - 72 = -104

x = -104/52 = -2

x = -2

y =  8 + 5·x

y =  8 + 5 × (-2) = -2

y = -2

6. x = 4 - 2·y

x = 1 - 3·y

Therefore; 4 - 2·y = 1 - 3·y

3·y - 2·y = 1 - 4 = -3

y = -3

x = 1 - 3·y

x = 1 - 3 × (-3) = 10

x = 10

7. The cost for Company is C = 5·x + 48

The cost for Company 2 is C = 11·x

Therefore; 5·x + 48 = 11·x

11·x - 5·x = 48

6·x = 48

x = 48/6 = 8

The amount of data in GB at which the cost of both options are the same is 8 GB

y = 11 × 8 = 88

B. The amount of data at which the cost of both options are the same indicates that when using a small data amount, the cost of Company 2 is much more affordable, however, after 8 GB, the cost of using Company 1 becomes more affordable, hence going with Company 2 is not a good idea

8. Let x represent the number of students who can ride in a van and let y represent the number of students who can right in a bus, we get;

5·x + 3·y = 196

x + 6·y = 266

x = 266 - 6·y

Therefore;

5·x + 3·y = 196

5 × (266 - 6·y) + 3·y = 196

1330 - 27·y = 196

1330 -196 = 27·y

1134

y = 1134/27 = 42

y = 42

x = 266 - 6·y

x = 266 - 6 × 42 = 14

x = 14

9. Let x represent the number of bottles the shampoo and let y represent the number of bottles of the conditioner bought, therefore;

x + y = 19

Let a represent the cost of a shampoo and let b represent the cost of a conditioner

a·x + b·y = 147

The cost of a shampoo, a = (147 - b·y )/x

Cost of a conditioner, b = (147 - a·x )/y

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The probability that event A or B takes place is P ( A ∪ B ) = 4/13

Given data ,

Let the probability of event A happening P ( A ) = 1/13

Let the probability of event B happening P ( B ) = 3/13

And , the probability of event A and B happening P ( A ∩ B ) = 0

So , from the probability rule ,

The probability that event A or B takes place is P ( A ∪ B ) and

P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ∩ B )

On simplifying , we get

P ( A ∪ B ) = 1/13 + 3/13 - 0

P ( A ∪ B ) = 4/13

Hence , the probability is 4/13

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Answer:

There are no boxes bro so how can I answer you . I gonna get better to see your boxes but I can't see i think there is a attachment you forget to take with quest .Because this quest is not looking like Mathematics it's like English Grammar.If you didn't like my answer you will say anything you want . But in my decision you my bestfriend. I help others to give answers so I am trying my best.

-Thank You By MrIshaan