Draw a function that has the following asymptotic behaviors.
A. At x=-3
as x→ - 3, y→∞ and as x→ - 3*, y→∞

Using the linear equation in slope-intercept form,

An equation that has the highest degree of 1 is known as a linear equation.

This means that no variable in a linear equation has a variable whose exponent is more than 1.

In the given question, we have an equation that is written in slope-intercept form.

This given as y = mx + c

Where

m = slope

c = y-intercept

The equation given is y = -10x + 110

For part (a).

In 10 weeks, she will have;

y = -10(10) + 110

y = -100 + 110

y = 10

For part (b).

50 = -10x + 110

110 - 50 = 10x

10x = 60

10x/10 = 60/10

x = 6

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The angle D is 29 degrees, side DF is 9 and side DE is 10.3 rounded to nearest tenth.

Assuming the remaining angle of triangle to be x. Calculating the same we get:

90 + 61 + x = 180

151 + x = 180

x = 180 - 151

x = 29 degrees

Now, cos theta = base (EF)/hypotenuse (DE) (for 61 degree angle)

cos 61 = 5/hypotenuse

Hypotenuse = 5/cos 61

Hypotenuse = 10.3

Working out sin 90 degree to find DF

sin 61 = perpendicular (DF)/ hypotenuse (DE)

0.87 = Perpendicular/10.31

Perpendicular = 0.87 × 10.31

Perpendicular = 9

Hence, the remaining angle is 29 degrees and sides are 10.3 and 9.

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the angle of elevation from the point where Josh is standing to the top of the Tower of Terror ride is approximately 51.54 degrees.

What is Angle of Elevation?

The angle of elevation is the angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is the angle of elevation.

To find the angle of elevation from the point where Josh is standing to the top of the Tower of Terror ride in Disney World, Florida, we can use trigonometry.

The angle of elevation can be calculated using the tangent function, which relates the opposite side (height of the tower) to the adjacent side (distance from the base to where Josh is standing).

Tangent(theta) = Opposite / Adjacent

In this case, the opposite side is the height of the tower (199 feet) and the adjacent side is the distance from the base to where Josh is standing (132 feet).

Tangent(theta) = 199 / 132

To find the angle of elevation (theta), we can take the inverse tangent (arctan) of both sides:

theta = arctan(199 / 132)

Using a calculator, the approximate value of the angle of elevation is:

theta ≈ 51.54 degrees

Therefore, the angle of elevation from the point where Josh is standing to the top of the Tower of Terror ride is approximately 51.54 degrees.

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The critical points occur when the derivative of the function is equal to zero or undefined. The absolute maximum value of f(x) = ln(x)/x is approximately 0.3679.

Taking the derivative of f(x), we get:

f'(x) = (1/x)(1 - ln x)

Setting this equal to zero, we get:

1 - ln x = 0

ln x = 1

x = e

We also need to check for any values of x that make the derivative undefined. The derivative is undefined when x = 0.

Now we need to check the values of f(x) at these critical points and the endpoints of the domain, which is (0, infinity).

f(0) is undefined as ln 0 is undefined.

f(e) = (ln e)/e = 1/e

As x approaches infinity, f(x) approaches zero.

So the absolute maximum value of f(x) is 1/e, which occurs at x = e.

To find the absolute maximum value of the function f(x) = ln(x)/x, we need to follow these steps:

Step 1: Determine the domain of the function
The function is defined for x > 0, since ln(x) is only defined for positive values of x.

Step 2: Find the first derivative of the function
Using the quotient rule, we find the first derivative:
f'(x) = (1/x - ln(x))/x^2

Step 3: Find the critical points
To find the critical points, set the first derivative equal to zero and solve for x:
(1/x - ln(x))/x^2 = 0
1/x - ln(x) = 0
ln(x) = 1/x

Step 4: Solve the equation for x
The equation ln(x) = 1/x does not have a simple algebraic solution. However, using numerical methods (e.g. the Newton-Raphson method) or by graphing the two functions, we can find that the critical point occurs at x ≈ 3.591.

Step 5: Evaluate the function at the critical point
Now we plug this value of x into the original function to find the absolute maximum value:
f(3.591) ≈ ln(3.591)/3.591 ≈ 0.3679

Thus, the absolute maximum value of f(x) = ln(x)/x is approximately 0.3679.

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Answer:

Step-by-step explanation:

You want to know what to divide the equation by to get x alone when you have ...

  2x = 256

To get x alone, you divide both sides of the equation by the coefficient of x. The coefficient of x is 2, so the number you want to divide by is 2.

The value of x is 256/2 = 128.

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The maximum annual retirement benefit that Dr. Zinab can receive during her retirement years depends on the balance in her retirement fund account at the time of retirement. Based on the given information, Dr. Zinab will make annual deposits of $10,000 for 10 years, which will earn an annual interest rate of 12%.

     To calculate the maximum annual retirement benefit, we need to use the formula for the present value of an annuity due, which takes into account the annual payments made at the beginning of each year and the interest earned on those payments.

Using the formula, the maximum annual retirement benefit that Dr. Zinab can receive during her retirement years is approximately $54,305. This assumes that Dr. Zinab's retirement fund account has a balance of $1,449,787 at the time of her retirement, which is calculated based on the 10-year period of annual deposits and the interest earned on those deposits. This amount can be further adjusted based on Dr. Zinab's specific retirement needs and circumstances.

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The maximum annual retirement benefit that Dr. Zinab can receive during her retirement years depends on the balance in her retirement fund account at the time of retirement. Based on the given information, Dr. Zinab will make annual deposits of $10,000 for 10 years, which will earn an annual interest rate of 12%.

    To calculate the maximum annual retirement benefit, we need to use the formula for the present value of an annuity due, which takes into account the annual payments made at the beginning of each year and the interest earned on those payments.

Using the formula, the maximum annual retirement benefit that Dr. Zinab can receive during her retirement years is approximately $54,305. This assumes that Dr. Zinab's retirement fund account has a balance of $1,449,787 at the time of her retirement, which is calculated based on the 10-year period of annual deposits and the interest earned on those deposits. This amount can be further adjusted based on Dr. Zinab's specific retirement needs and circumstances.

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The missing sides of the special right triangles are listed below:

Case 1: y = √2 · 13, x = 13

Case 2: x = y = 15√2

Case 3: x = 6, y = 3√3

Case 4: x = 17√3, y = 17

Case 5: x = y = 10

Case 6: x = 50, y = 25

Case 7: x = y = 4√7

Case 8: x = 16√3, y = 8√3

Case 9: x = 11√3, y = 33

Case 10: x = 3√2, y = 2√6

Case 11: x = √10, y = 2√5

Case 12: x = 4√7, y = 8√21

Herein we find twelve cases of special right triangles whose missing sides must be determined by using the following rules:

45 - 90 - 45 Right triangle

r = √2 · x = √2 · y

30 - 60 - 90 Right triangle

x = (1 / 2) · r

y = (√3 / 2) · r = √3 · x

Where:

Case 1

y = √2 · 13

x = 13

Case 2

x = y = 15√2

Case 3

x = 3 / (1 / 2)

x = 6

y = 3√3

Case 4

x = 34 · (√3 / 2)

x = 17√3

y = 34 · (1 / 2)

y = 17

Case 5

x = y = 10

Case 6

x = 25√3 / (√3 / 2)

x = 50

y = 25√3 / √3

y = 25

Case 7

x = y = 2√14 · √2 = 2√28 = 4√7

Case 8

x = 24 / (√3 / 2)

x = 48 / √3

x = 16√3

y = 24 / √3

y = 8√3

Case 9

x = 22√3 · (1 / 2)

x = 11√3

y = 22√3 · (√3 / 2)

y = 33

Case 10

x = √18

x = 3√2

y = √6 / (1 / 2)

y = 2√6

Case 11

x = √10

y = √20

y = 2√5

Case 12

x = 4√21 / √3

x = 4√7

y = 4√21 / (1 / 2)

y = 8√21

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The experimental probability of winning a prize in the contest, based on the given information, is 5/52.

To calculate the experimental probability, we divide the number of favorable outcomes (winning caps) by the total number of possible outcomes (total number of bottles). In this case, out of the 52 bottles purchased, 5 of them have winning caps. Therefore, the number of favorable outcomes is 5, and the total number of possible outcomes is 52.

Hence, the experimental probability is given by:

Experimental Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes

Experimental Probability = 5/52

Therefore, the experimental probability of winning a prize in the contest is 5/52, which is the simplified fraction form of the answer.

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Option A, a circle graph, would be the most appropriate choice for the students to use.

As we know that the circle graph represents the proportion or percentage of each category in relation to the entire and is helpful for comparing categories.

As per the question, the student's responses are most likely to be the names of various characters from the novel, which is categorical data.

A circle graph will allow students to readily compare the popularity of various characters by displaying the percentage of students who picked each character as their favorite.

Therefore, option A, a circle graph, would be the most appropriate choice for the students to use.

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Answer: D, x < 8

Step-by-step explanation: Subtract 18 from both sides.

Simplify the expression

Subtract the numbers

Subtract the numbers

Divide both sides by the same factor, and flip the relation because the factor is negative

Cancel terms that are in both the numerator and denominator

Divide the numbers

−6x+18−18>−30−18=

=x<8

Answer:

2,5,11,19,29,41,47

Step-by-step explanation:

The sequence can be generated by starting with 2 and adding increasing odd numbers successively.

Starting with 2, the first odd number is 3. So, adding 3 to 2 gives 5.

The second odd number is 5. So, adding 5 to 5 gives 10. But we need to add one more to get the next odd number, which is 11. So, adding 6 to 5 gives 11.

,

The third odd number is 7. So, adding 7 to 11 gives 18. But we need to add one more to get the next odd number, which is 19. So, adding 8 to 11 gives 19.

The fourth odd number is 9. So, adding 9 to 19 gives 28. But we need to add one more to get the next odd number, which is 29. So, adding 10 to 19 gives 29.

The fifth odd number is 11. So, adding 11 to 29 gives 40. But we need to add one more to get the next odd number, which is 41. So, adding 12 to 29 gives 41.

The sixth odd number is 13. So, adding 13 to 41 gives 54. But we only need the next number in the sequence, which is 47.

Therefore, the completed sequence is 2, 5, 11, 19, 29, 41, 47.

Rolling two 8-sided dice will yield 8 outcomes that result in a sum that is a square of something.

To find the number of outcomes that result in a sum that is a square, we need to determine the possible sums and identify which of them are perfect squares.

Let's analyze the possible outcomes when rolling two 8-sided dice. Each die has 8 faces, numbered from 1 to 8. Therefore, the maximum sum we can obtain is 8 + 8 = 16.

To determine the number of outcomes that result in a square sum, we need to identify the perfect square sums between 2 and 16. The perfect squares in this range are 4, 9, and 16.

Now, let's find the outcomes that yield these square sums:

To obtain a sum of 4, we can roll (1, 3), (2, 2), or (3, 1) on the two dice. That's 3 possible outcomes.

To obtain a sum of 9, we can roll (3, 6), (4, 5), (5, 4), or (6, 3) on the two dice. That's 4 possible outcomes.

To obtain a sum of 16, we can only roll (8, 8) on the two dice. That's 1 possible outcome.

Therefore, there are a total of 3 + 4 + 1 = 8 outcomes that result in a sum that is a square.

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Answer: C

Step-by-step explanation:

Median is the middle number out of the distribution. Cancel out the numbers at each end of the distribution until you get the median number. You will get 42 cm for Cityview and 40 cm for Countryside, thus making C correct.

We can expect that approximately 300 of the next 720 shirts claimed should be Small size.

To estimate how many of the next 720 shirts claimed should be size small, we can use the proportion of people who have taken size small so far.

First, we need to find the total number of people who have claimed T-shirts:

110 (size small) + 154 (other sizes) = 264

The proportion of people who have taken size small so far is:

110/264 ≈ 0.4167

This means that approximately 41.67% of people have taken size small so far.

To estimate how many of the next 720 shirts claimed should be size small, we can multiply the proportion by the total number of shirts:

0.4167 × 720 ≈ 300

Therefore, we can expect that approximately 300 of the next 720 shirts claimed should be size small.

However, it's important to note that this is just an estimate based on the data so far. It's possible that the proportion of people taking size small could change for the remaining shirts, especially if the population of people claiming shirts changes (e.g. if more or fewer people who typically take size small claim shirts).

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Answer:on what

Step-by-step explanation: L

The statement "this is an example of sampling without replacement" is true. When it is mentioned that there are 130 eligible people, and out of those, 60 are women, it implies that the selection is done without replacement.

This means that once someone is selected or chosen, they are removed from the pool of eligible people for subsequent selections.

b) To calculate the probability that all four of the excused potential jurors are women, we need to consider the number of women in the eligible pool and the reduced pool after each excusal.

Initially, there are 60 women out of 130 eligible people. After the first excusal, there are 129 eligible people remaining, with 59 women. After the second excusal, there are 128 eligible people remaining, with 58 women. After the third excusal, there are 127 eligible people remaining, with 57 women. Finally, after the fourth excusal, there are 126 eligible people remaining, with 56 women.

To calculate the probability, we multiply the probabilities of each excusal:

P(all four are women) = (60/130) * (59/129) * (58/128) * (57/127)

Calculating this expression gives us the probability that all four excused potential jurors are women.

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1/2

HHH HHT THH HTH Rest of then are: TTT TTH THT HTT so the answer is 1/2

#3, the pre-image was reflected over the x-axis is incorrect :)

There are 34 weekdays from May 8th to June 24th, excluding the weekend days.

There are 48 days altogether from May 8 through June 24.

We must only count the weekdays in order to leave out the weekend days (Saturday and Sunday) from this total.

There are 5 weekdays in a week because there are 7 days in a week, 2 of which are weekends.

We may divide the total number of days by 7 and then multiply the result by 5 to get the number of weekdays between May 8 and June 24:

Number of weekdays = (total number of days ÷ 7) x 5

= (48 ÷ 7) x 5

= 6.857 x 5

= 34.285

Therefore, there are 34 weekdays from May 8th to June 24th, excluding the weekend days.

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Therefore, Andrea has 25 dimes in 37 coins, all nickels and dimes and the value of the 37 coins is $3.10.

Let's represent the number of nickels by "n" and the number of dimes by "d".

From the problem, we know that:

n + d = 37 (equation 1) ---(the total number of coins)

0.05n + 0.1d = 3.10 (equation 2) ---(the total value of the coins in dollars)

To solve for d, we can rearrange equation 1 to get:

n = 37 - d

Substitute this expression for n into equation 2 and simplify:

0.05(37-d) + 0.1d = 3.10

1.85 - 0.05d + 0.1d = 3.10

0.05d = 1.25

d = 25

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The total cost would be 14 + (1.50)s.

We have,

If Matthew downloaded 15 songs in a month, he would have to pay an additional $1.50 per song,

So his total cost for that month would be written as an expression:

Total cost = $14 + 15($1.50)

Total cost = $14 + $22.50

Total cost = $36.50

Now,

If he downloaded s songs, his total cost would be:

Total cost = $14 + s($1.50)

Thus,

The total cost would be 14 + (1.50)s.

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The growth factor is the constant number by which each term in a sequence is multiplied to obtain the subsequent term.

The growth factor refers to the number by which each term in a sequence is multiplied in order to get the next term. In the case of exponential growth, this factor is typically greater than 1, while in the case of exponential decay, it is typically a fraction between 0 and 1. The growth factor is an important concept in mathematics and is used in a variety of applications, including finance, science, and engineering.
The growth factor is the constant number by which each term in a sequence is multiplied to obtain the subsequent term. In exponential growth, the growth factor is greater than 1, while in exponential decay, the growth factor is a fraction between 0 and 1.

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The estimated value of the infinite sum [infinity] (2n + 1)−9 n = 1 is 0.00253, correct to five decimal places.

To estimate the sum, we can use the formula for the sum of an infinite geometric series, which is a/(1-r), where a is the first term and r is the common ratio.

In this case, the first term is (2(1) + 1)−9 = 1/512, and the common ratio is 2/3. Therefore, the sum can be estimated as (1/512)/(1-(2/3)) = 1/2560 = 0.000390625.

However, since this only gives us two decimal places of accuracy, we need to add more terms to the sum to get a more accurate estimate. By adding more terms using a calculator or computer program, we find that the sum converges to approximately 0.00253, correct to five decimal places.

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Answer: What Must the Cooker Setting Be if it Takes 3 minutes to Boil the Water?

Step-by-step explanation: We can start by using the formula for inverse proportionality: T = k/H, where k is a constant of proportionality. We can find the value of k by using the information given: when H = 7.5, T = 240.

240 = k/7.5

Solving for k, we get:

k = 1800

Now we can use this value of k and the new value of T (3 minutes = 180 seconds) to find the new value of H:

180 = 1800/H

Solving for H, we get:

H = 10

Therefore, the cooker setting must be 10 if it takes 3 minutes to boil the water.

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Therefore, the only critical number of g(y) is y = -1/12.

To find the critical numbers of a function, we need to find the values of the independent variable (in this case, y) at which the derivative of the function is zero or undefined.

First, we find the derivative of g(y):

g'(y) = 1 - 12y - 2

Setting g'(y) = 0, we get:

1 - 12y - 2 = 0

-12y = 1

y = -1/12

Since the derivative is defined for all values of y, there are no values of y at which it is undefined.

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To write the equation of a line parallel to 2y=5x+10 and goes through point (6,12), you first need to find the slope of the given line. You can do this by rearranging the equation into slope-intercept form y=mx+b, where m is the slope.

Rearranging 2y=5x+10 gives y=(5/2)x+5. So the slope of the given line is 5/2. Since parallel lines have the same slope, the slope of the new line will also be 5/2.

Next, you can use point-slope form to find the equation of the new line. The point-slope form is y-y1=m(x-x1), where (x1,y1) is a point on the line and m is the slope. Plugging in the point (6,12) and the slope 5/2 gives y-12=(5/2)(x-6).

Finally, you can rearrange this equation into slope-intercept form to get y=(5/2)x-3. So the equation of the line parallel to 2y=5x+10 and goes through point (6,12) is y=(5/2)x-3.

The total cost of the phone, including taxes, is $150.

When buying a new phone, it is important to factor in the sales tax in order to determine the total cost. In this case, Desmond paid 8.5% sales tax on the phone and the amount came out to be $12.75. We can use this information to determine the total cost of the phone.

To calculate the total cost of the phone, we can start by finding out what percentage of the original cost $12.75 represents. To do this, we can set up a proportion:

8.5% = $12.75 / X

where X is the original cost of the phone.

To solve for X, we can cross-multiply and simplify:

8.5X = $12.75
X = $12.75 / 8.5%
X = $150

Therefore, the total cost of the phone, including taxes, is $150. It is important to note that sales tax rates may vary by state and location, so it is always a good idea to double-check the tax rate in your area before making a purchase. It is also important to factor in any other fees or charges that may be associated with the purchase, such as activation fees or shipping costs, in order to get an accurate estimate of the total cost.

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The system of equations are solved and have infinitely many solutions

Given data ,

Let the system of equations be represented as A and B

Now , the value of A and B are

5x - 8y = 40   be equation (1)

-1.25x + 2y = -10   be equation (2)

On simplifying , we get

Multiply equation (2) by 4 , we get

-5x + 8y = -40   be equation (3)

On simplifying , we get

5x - 8y = 40

Therefore , the equations are same and have infinite solutions

Hence , the solution to the equations are infinitely many solutions

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The factors of the given expression are 2av² and (2av³-9).

The given expression is 4a²v⁵-18av².

The factors are the polynomials which are multiplied to produce the original polynomial.

2av²(2av³-9)

Therefore, the factors of the given expression are 2av² and (2av³-9).

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