what sample size is necessary for a 95% confidence interval about the mean height of a shrub if we want a margin of error of 0.5 inches and the population standard deviation is known as 1.3 inches.

Answer: If Amanda runs two miles the first week and then adds two miles each subsequent week, we can create a sequence using arithmetic progression. The common difference between each term in the sequence is two, and the first term is two.

Using the formula for the nth term of an arithmetic progression, we can find the number of miles Amanda would run in the first 10 weeks of her training:

an = a1 + (n-1)d

where:

an = the nth term of the sequence

a1 = the first term of the sequence (2 miles in the first week)

n = the number of terms (up to 10 weeks)

d = the common difference between each term (2 miles per week)

So for n = 1 to 10, we have:

a1 = 2

d = 2

n = 1: a1 + (n-1)d = 2 + (1-1)2 = 2

n = 2: a1 + (n-1)d = 2 + (2-1)2 = 4

n = 3: a1 + (n-1)d = 2 + (3-1)2 = 6

n = 4: a1 + (n-1)d = 2 + (4-1)2 = 8

n = 5: a1 + (n-1)d = 2 + (5-1)2 = 10

n = 6: a1 + (n-1)d = 2 + (6-1)2 = 12

n = 7: a1 + (n-1)d = 2 + (7-1)2 = 14

n = 8: a1 + (n-1)d = 2 + (8-1)2 = 16

n = 9: a1 + (n-1)d = 2 + (9-1)2 = 18

n = 10: a1 + (n-1)d = 2 + (10-1)2 = 20

Therefore, Amanda would run 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20 miles in the first 10 weeks of her training if she followed the new regimen.

Step-by-step explanation:

List orders the times from shortest to longest

5 1/3 seconds

5 1/2 seconds

5 5/9 seconds

A decimal is a way of representing numbers using a base-10 positional notation system, where each digit represents a power of 10. It is written as a whole number followed by a decimal point and a series of digits representing fractions of 1.

According to the given information:

To order the times from shortest to longest, we need to convert them into a common format, such as a decimal or a common denominator.

First, let's convert the times to a common denominator of 9:

5 1/3 seconds = 16/3 seconds = 48/9 seconds

5 5/9 seconds = 50/9 seconds

5 1/2 seconds = 9/2 seconds = 45/9 seconds

Now we can order the times from shortest to longest:

48/9 seconds = 5 1/3 seconds

45/9 seconds = 5 1/2 seconds

50/9 seconds = 5 5/9 seconds

Therefore, the correct list in order from shortest to longest is:

5 1/3 seconds

5 1/2 seconds

5 5/9 seconds

So Bernard's first attempt was the shortest, his third attempt was the second longest, and his second attempt was the longest.

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The system of equation has no solution (option b).

Let's start by writing the equations in standard form, which is y = mx + b, where m is the slope of the line and b is the y-intercept. We have:

y = -5x - 1

y = -5x + 7

Both equations have the same slope of -5, which means they are parallel lines. However, the y-intercepts are different (-1 and 7), which means the lines are shifted up or down relative to each other.

We can also confirm this algebraically by subtracting one equation from the other:

y = -5x + 7 - (-5x - 1)

y = -5x + 5

We have simplified the system to a single equation in one variable, which has no solution. This confirms that the original system has no solution as well.

Hence the correct option is (b).

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As per the data mentioned in the table, Jade's mom is 0.7 ft or 1 ft taller than jade.

Mixed numbers represent whole numbers and proper fractions together. Usually represents a number between any two integers. Hybrid numbers are made by combining three parts:

An integer, a numerator, and a denominator. The numerator and denominator are part of the correct fraction giving the mixed number.

Height of jade's mom = 5⁵/₈ ft

Jade's height = 4⁵/₆

The difference in their heights is:

= (45/8) - (29/6)

= (270 - 232)/48

= 38/48

= 0.7 ft

0.7 ft ≈ 1 ft

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Therefore, the three consecutive odd integers are 17, 19, and 21.

An equation is a statement that shows the equality of two expressions, typically separated by an equal sign. An equation can contain variables, constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. The goal of solving an equation is to find the value(s) of the variable(s) that satisfy the equality.

Here,

Let x be the first odd integer, then the second and third odd integers are x+2 and x+4, respectively, since the difference between consecutive odd integers is 2.

The sum of the three consecutive odd integers is 57, so we can write:

x + (x+2) + (x+4) = 57

Simplifying and solving for x, we get:

3x + 6 = 57

3x = 51

x = 17

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A sample size of 87 is required to obtain a 98% confidence interval with a margin of error of 50.

To calculate the sample size required for a 98% confidence interval with a margin of error of 50, we need to use the following formula:

n = [Z*(σ/ME)]^2

where:

n = the sample size needed

Z = the Z-score for the desired confidence level (98% or 2.33)

σ = the standard deviation of apartments for rent in the area ($200)

ME = the margin of error ($50)

Plugging in the given values, we get:

n = [2.33*(200/50)]^2

n = [9.32]^2

n ≈ 86.7

Since we cannot have a fractional sample size, we round up to the nearest whole number to get the final answer.

Therefore, a sample size of 87 is required to obtain a 98% confidence interval with a margin of error of 50, given that the standard deviation of apartments for rent in the area is $200.

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The expression that represents the discounted price of the jacket is 0.7x. This means that the discounted price is 70% of the original price, or equivalently, that the discount reduces the price of the jacket by 30%.

What is original price?

In order to determine the sales price, the value of the discount would be subtracted from the original price.

When an item is offered at a discount, the discounted price is usually calculated by subtracting the discount from the original price. In this case, since the discount is 30%, we can find the amount of the discount by multiplying the original price x by 0.3. This gives us 0.3x, which is the amount of money that is being discounted from the original price. To find the discounted price, we subtract this amount from the original price, which gives us:

x - 0.3x = 0.7x

So, the expression that represents the discounted price of the jacket is 0.7x. This means that the discounted price is 70% of the original price, or equivalently, that the discount reduces the price of the jacket by 30%.

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Approximately 68.3% of passenger vehicles travel slower than 80 miles/hour.

The average rate of change of the car's position on the interval is ∆P/∆t.

To find the average rate of change of the car's position on the interval, follow these steps:

Identify the interval: First, determine the specific interval for which you need to find the average rate of change (e.g.,

between times t1 and t2).

Calculate the change in position:

Determine the car's position at both the beginning and end of the interval (e.g., positions P1 and P2).

Then, subtract the initial position (P1) from the final position (P2) to find the change in position (∆P).

Calculate the change in time: Subtract the initial time (t1) from the final time (t2) to find the change in time (∆t).

Calculate the average rate of change: Divide the change in position (∆P) by the change in time (∆t) to find the average

rate of change.

The average rate of change of the car's position on the interval is ∆P/∆t. Include units in your answer (e.g., meters per

second or miles per hour) to indicate the car's rate of change in position.

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The relationship between the functions are indicated in the attached graph. see further explanation below.

a. Elena's graph is obtained by shifting the original function f up by 50 units, so her function is g(d) = f(d) + 50 = 75 - (1.19)ª.

Han's graph is obtained by shifting the original function f up by 60 units and then to the right by 1 unit, so his function is h(d) = f(d - 1) + 60 = 85 - (1.19)^(a-1).

b. Using graphing technology, we can graph the three functions f, g, and h to compare how well they fit the given data. Here's an example graph:

graph of f, g, and h

c. From the graph, it appears that Han's function h fits the data better than Elena's function g. The graph of h seems to align more closely with the plotted data points than the other two functions. Moreover, the shift to the right and up of the graph of f seems to better capture the overall trend of the data, as it appears that the population increased and shifted slightly to the right over time.

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The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere.

We are given the diameter of the sphere, which is 8 cm. The radius, r, is half the diameter, so:

r = 8/2 = 4 cm

Substituting this value of r into the formula for the volume of a sphere, we get:

V = (4/3)π(4³) ≈ 268.08

Rounding this to the nearest whole number, we get:

V ≈ 268

Therefore, the volume of the sphere to the nearest whole number is 268 cm³, which is option D.

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The sum of fractions 6 13/28 and 8 3/32 when estimated  has a value of 14 1/2

To estimate the sum of fractions 6 13/28 and 8 3/32, we can round the fractions to the nearest whole number and then add them together.

Adding 6.5 and 8, we get:

6.5 + 8 = 14.5

Convert to fraction, we have

6.5 + 8 = 14 1/2

Therefore, the estimated sum of fractions 6 13/28 and 8 3/32 is 14 1/2

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The equations that are equivalent are: 2 + x = 5, x + 1 = 4, x + (-4) = 7

These equations can be solved to find x = 3 and x = 11, respectively.

An equation is a mathematical statement that uses an equal sign (=) to show that two expressions are equal.

Equations are equivalent if they have the same solution or solutions. In other words, if we substitute the same values for the variables in each equation, we will get the same result or results.

In the given options, the equations that are equivalent are:

2 + x = 5 and x + 3 = 5, since they both simplify to x = 3.

x + 1 = 4 and x = 3, since they both simplify to x = 3.

x + (-4) = 7 and x = 11, since they both simplify to x = 11.

The equation 9 + x = 6 has a different solution from the others, so it is not equivalent to any of them.

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Answer:

x + 4

Step-by-step explanation:

2(–x + 2) + 3x

-2x + 4 + 3x

x + 4

The length of the lake in miles for the given situation of travelling motor boat is equal to 9 miles.

Let us consider the length of the lake be d in miles.

Number of miles motor boat travelled per hour = 18 miles

When the motor boat travels at 18 miles per hour,

The time it takes to travel the length of the lake is,

t₁ = d/18

When the motor boat travels at 12 miles per hour,

The time it takes to travel the length of the lake is,

t₂ = d/12

Time it takes to travel the length of the lake at 18 miles per hour

=  one-quarter of an hour less than the time it takes at 12 miles per hour,

⇒ t₁ = t₂ - 1/4

Substituting the expressions for t₁ and t₂ from above, we get,

⇒ d/18 = d/12 - 1/4

Simplify this equation by multiplying both sides by the least common multiple of the denominators,

least common multiple = 36

⇒ 2d = 3d - 9

Solving for d, we get,

⇒ d = 9

Therefore, the length in miles of the lake is 9 miles.

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Answer:

  A (top)

Step-by-step explanation:

You want to know which box plot represents the data in the given list.

The difference between the box plots is the location of the median.

When the data is sorted into order, it is ...

  {2500, 2712, 3500, 3876, 4247, 4753, 4983, 5000, 6214, 7500}

There are an even number of elements in this list, so the median is the average of the middle two:

  median = (4247 +4753)/2 = 9000/2 = 4500

The median is represented by the line inside the box of the box plot. The plot with its median at 4500 is the top one (shown in the attachment).

The top box plot represents the data.

<95141404393>

Answer:

1. With the height and base of a triangle given, we can use the Pythagorean Theorem to find the length of the hypotenuse (the third side) of the right triangle.

Given:

Height (a) = 6

Base (b) = 8

We can plug these values into the Pythagorean Theorem formula:

a^2 + b^2 = c^2

Substituting the values:

6^2 + 8^2 = c^2

Simplifying:

36 + 64 = c^2

100 = c^2

Now, we can take the square root of both sides to solve for c:

√100 = √c^2

10 = c

So, the length of the hypotenuse (c) of the right triangle is 10 units.


2.
Given:

Base (b) = 8

One side (a or c) = 12

We can use the Pythagorean Theorem to find the length of the remaining side (either a or c) of the right triangle.

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Using the formula:

a^2 + b^2 = c^2

Substituting the values:

a^2 + 8^2 = 12^2

Simplifying:

a^2 + 64 = 144

Next, we can isolate a^2 by subtracting 64 from both sides of the equation:

a^2 = 144 - 64

a^2 = 80

Finally, we can take the square root of both sides to solve for a:

√(a^2) = √80

a ≈ 8.94 (rounded to two decimal places)

So, the length of the remaining side (either a or c) of the right triangle is approximately 8.94 units. Please note that depending on the context of the problem, you may need to use the positive square root value for a or c, depending on which side is relevant in the specific scenario.

Answer:

X = 10^2

Y = /80

Step-by-step explanation:

Pythagorean theorem = A^2 +B^2= C^2

Fist triangle

6^2+8^2

36 + 64= 100

/100 = 10^2

X= 10^2

Second triangle

Pythagorean theorem = C^2 - A^2= B^2

12^2 - 8^2

144 - 64= 80

/80 = /80

X = /80

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so for this inverse, since finding the inverse of the inverse, will give us the original function :)

[tex]f^{-1}(x)=-3x+2\implies y~~ = ~~-3x+2\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~-3y+2} \\\\\\ x-2=-3y\implies \cfrac{x-2}{-3}=y\implies \cfrac{2-x}{3}=y=f(x)[/tex]

The probability of trapping a coyote that is 17kg or larger, given an average weight of 14.5kg and a standard deviation of 4kg is approximately 0.2743 or 27.43%.

To solve the problem, we first need to standardize the weight of the coyote using the formula:

z = (x - μ) / σ

Where:

x = the weight of the coyote we want to find the probability for (17kg in this case)

μ = the population mean (14.5kg in this case)

σ = the population standard deviation (4kg in this case)

z = the standardized score

Substituting the given values in the formula, we get:

z = (17 - 14.5) / 4

z = 0.625

Next, we need to find the probability of getting a coyote weighing 17kg or more, which is equivalent to finding the area under the normal distribution curve to the right of z = 0.625. We can use a standard normal distribution table or a calculator to find this probability.

Using a calculator, we can use the cumulative distribution function (CDF) of the standard normal distribution. The CDF gives the area under the curve to the left of a specified z-score. Since we want the area to the right of z = 0.625, we can subtract the CDF from 1 to get the area to the right.

Using a standard normal distribution table or calculator, we find that the CDF for z = 0.625 is approximately 0.734. Therefore, the area to the right of z = 0.625 is 1 - 0.734 = 0.266 or 26.6%.

Thus, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.

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Using a standard normal distribution table or a calculator, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.

The standard normal distribution is a probability distribution that is used to calculate probabilities associated with a random variable that has a normal distribution with mean 0 and standard deviation 1. Any normally distributed random variable can be standardized by subtracting its mean and dividing by its standard deviation to obtain a new variable with mean 0 and standard deviation 1.

In this case, we are given that the weight of coyotes has a normal distribution with a mean of 14.5kg and a standard deviation of 4kg. We want to find the probability of trapping a coyote that is 17kg or larger.

To calculate this probability, we need to standardize the weight of a 17kg coyote using the formula:

z = (× - μ) / σ

where:

x is the value we want to standardize (in this case, 17kg),

μ is the mean of the distribution (14.5kg),

σ is the standard deviation of the distribution (4kg).

Substituting the values we have:

[tex]z =\frac{(17 - 14.5)}{4} = 0.625[/tex]

This value of 0.625 is the z-score for a coyote weighing 17kg. The z-score represents the number of standard deviations that a particular value is above or below the mean.

Next, we need to find the probability of a randomly selected coyote weighing 17kg or larger, which can be calculated using the standard normal distribution table or a calculator.

The standard normal distribution table gives the probability associated with a given z-score. However, since the table only gives probabilities for z-scores less than 0, we need to use the fact that the standard normal distribution is symmetric about the mean (0) to find the probability of a z-score greater than 0.625.

Specifically, we can use the property that:

P(Z > z) = 1 - P(Z < z)

where Z is a standard normal random variable and z is a z-score. This formula tells us that the probability of a z-score greater than a certain value is equal to 1 minus the probability of a z-score less than that value.

Using this formula, we can calculate:

P(Z > 0.625) = 1 - P(Z < 0.625)

We can look up the value of P(Z < 0.625) in a standard normal distribution table or calculate it using a calculator. For example, using a standard normal distribution table, we can find that P(Z < 0.625) = 0.734.

Substituting this value into the formula, we get:

P(Z > 0.625) = 1 - 0.734 = 0.266

Therefore, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.

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Median, because Sunny Town is skewed.

Descriptive statistics is a branch of statistics that deals with the collection, organization, analysis, and interpretation of numerical data. It involves using various statistical measures to describe and summarize the characteristics of a set of data. Descriptive statistics helps to make sense of large amounts of data by presenting it in a more meaningful and understandable way. Commonly used measures of central tendency in descriptive statistics include mean, median, and mode, while measures of dispersion include range, variance, and standard deviation. Descriptive statistics is widely used in various fields, such as business, medicine, economics, psychology, and social sciences, to name a few.

Median, because Sunny Town is skewed.

The skewness of the histogram for Sunny Town indicates that the data is not symmetrically distributed, and therefore the median would be a better measure of central tendency to compare the locations. The mean can be affected by extreme values or outliers, which might be present in the skewed distribution of Sunny Town, making it less reliable in this case.

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Answer:

To make a true equation, check your math to make sure that the values on each side of the equals sign are the same. Ensure that the numerical values on both sides of the "=" sign are the same to make a true equation. For example, 9 = 9 is a true equation. 5 + 4 = 9 is a true equation.

The probability that all four chosen balls are red is 14/6075.

Probability is a way to gauge how likely or unlikely something is to happen. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes an inevitable one.

Let's first find the probability of choosing two red balls from each of the two urns separately and then multiply the results.

The probability of choosing two red balls from urn 1 is:

P(2 red balls from urn 1) = (7/10) * (6/9) = 7/15

Similarly, the probability of choosing two red balls from urn 2 is:

P(2 red balls from urn 2) = (2/10) * (1/9) = 1/45

And the probability of choosing two red balls from urn 3 is:

P(2 red balls from urn 3) = (5/10) * (4/9) = 2/9

Now, we need to find the probability of choosing two urns out of three, and since the order in which we choose the urns does not matter, we can use combinations:

Number of ways to choose two urns out of three = C(3, 2) = 3

Therefore, the probability of choosing two urns out of three is 3/3 = 1.

Finally, we need to multiply the probability of choosing two red balls from each of the two urns and the probability of choosing two urns out of three:

P(all four balls are red) = P(2 red balls from urn 1) * P(2 red balls from urn 2) * P(2 red balls from urn 3) * P(choose two urns out of three)

= (7/15) * (1/45) * (2/9) * 1

= 14/6075

Therefore, the probability that all four chosen balls are red is 14/6075.

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Magada's loan factor is approximately 0.006367. This means that for every $1 borrowed, Magada will have to pay approximately $0.006367 per month for the next 25 years to repay the loan with an interest rate of 10.75%.

To calculate the loan factor, we first need to calculate the monthly interest rate and the total number of monthly payments.

Monthly interest rate = Annual interest rate / 12

= 10.75% / 12

= 0.8958%

Monthly payments = Number of years * 12

= 25 * 12

= 300

Now, we can use loan factor formula, which is:

Loan factor = [monthly interest rate * (1 + monthly interest rate)^n] / [(1 + monthly interest rate)^n - 1]

Substituting the values, we get:

Loan factor = [0.008958 * (1 + 0.008958)^300] / [(1 + 0.008958)^300 - 1]

= 0.006367

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Answer:

Step-by-step explanation:

a is 150 and b is 150 they are both the same answer unless you add 645+375 wich will be 1020.

The choice of measures of center and variability depends on the shape and characteristics of the distribution. If the distribution is skewed or has outliers, then the median and IQR would be more appropriate measures of center and variability, respectively.

The median is a measure of central tendency that represents the middle value in a dataset when the data is arranged in order of magnitude. Specifically, it is the value that separates the data set into two equal halves. In other words, half of the values in the dataset are greater than the median, and the other half are less than the median.

To calculate the median, you first need to arrange the data in order from lowest to highest (or highest to lowest).

The value that divides the data set into two equal portions is called the median. It is a robust measure of center, meaning that it is not affected by extreme values or outliers. The IQR is the range of values that contains the middle 50% of the data, and it is also a robust measure of variability.

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A. we can plot another point at (1, 112.5), and continue this pattern to draw the line. Linear equation graph

B. It will take 11 months to save a total of $237.50.

What is a graph?

In computer science and mathematics, a graph is a collection of vertices (also known as nodes or points) connected by edges (also known as links or lines).

a. To graph the linear equation y = 12.5x+100, we can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

Comparing y = 12.5x+100 to y = mx + b, we can see that the slope is 12.5 and the y-intercept is 100.

To graph the equation, we can plot the y-intercept at (0, 100), and then use the slope to find other points. The slope of 12.5 means that for every increase of 1 in x (i.e. for every month), y increases by 12.5. So, we can plot another point at (1, 112.5), and continue this pattern to draw the line.

linear equation graph

b. We want to find the value of x (the number of months) that corresponds to a value of y (the amount of money in savings) of $237.50.

We can set y = 237.50 in the equation y = 12.5x+100, and solve for x:

237.50 = 12.5x+100

Subtracting 100 from both sides, we get:

137.50 = 12.5x

Dividing both sides by 12.5, we get:

x = 11

So, it will take 11 months to save a total of $237.50.

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Answer:

1. x=34

2.x=10

3. x=22

4. x=81

5.x=1

6.x=-8

7.x=-6

8. x=61

9. x=0.8

10. x= 2

11. x=25.2

12.x=-4

13.x=64

14.x=29

15. x=19

Step-by-step explanation:

Part A: The sample space is {A, E, R, S, T}. Part B: The favorable outcomes is 1/5 that is every card can appear. Part C: The probability of choosing two consonants is 6/20.

The likelihood of an event occurring can be expressed using odds or probability. The ratio of favourable events to all conceivable outcomes is known as the probability. A number between 0 and 1 or a percentage between 0% and 100% are both acceptable ways to express it. The ratio of favourable events to unfavourable outcomes is known as the odds, on the other hand. "Odds in favour" or "odds against" are two ways to express odds.

Given that two cards are randomly selected without replacement from a pile of five cards labeled with the letters A, E, R, S, and T.  

The probability of both cards being consonants are = 3 *2 = 6

Part A: The sample space is {A, E, R, S, T}.

Part B: The favorable outcomes is 1/5 that is every card can appear.

Part C: The consonants are R, S, T:

Thus, choosing 2 consonants the probability is:

3 x 2 = 6.

The total outcomes are: 5 * 4 = 20 ways

The probability of choosing two consonants is 6/20.

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Using additional ink that is not necessary to convey information reduces the data-ink ratio, which should be maximized in order to effectively convey essential information in a table or chart.

Using additional ink that is not necessary to convey information reduces the data-ink ratio. The goal of maximizing the data-ink ratio is to ensure that the ink used in the visual representation of data is used only to convey the necessary information, without cluttering or distracting from the main message.

When unnecessary ink is used, it increases the amount of ink used overall, reducing the proportion of ink used for conveying information, and thus reducing the data-ink ratio. Therefore, to maximize the effectiveness of a table or chart, it's important to minimize the use of non-data ink and focus on the essential information.

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Nothing can be said about the curve, for the parametric equations where the range of is [-1, 9] and the range of is [-1, 9]. Option B is the correct answer.

The parametric equations define the curve in terms of the parameter t. The given ranges for t and u indicate the domain of the curve. Without additional information, it is difficult to say much about the curve.

Option A is incorrect because there is no reason to assume that the curve lies inside a circle with a center (-1, -1) and radius of 0.5.

Option C is incorrect because the range of u is greater than 3.

Option D is incorrect because the given range of t is not sufficient to define a line segment between (-1, 1) and (7, 3). Option E is incorrect because there is no reason to assume that the curve lies outside the rectangle [-1, 7] by [1, 3].

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The question is -

Suppose a curve is given by the parametric equations where the range of is [-1, 9] and the range of is [-1, 9]. what can you say about the curve? you must select all correct choices to get full credit on this problem.

A. The curve must lie inside a circle with a center (-1, -1) and radius of 0.5.

B. Nothing can be said about the curve.

C. The curve is completely contained in the rectangle [-1, 1] by [1, 3].

D. The curve is the line with endpoints (-1, 1) and (7, 3).

E. The curve must lie outside the rectangle [-1, 7] by [1, 3].

D. The curve is a circle with a center (-1, -1) and a radius of 3.