A large company put out an advertisement in a magazine for a job opening. The first day the magazine was published the company got 120 responses, but the responses were declining by 10% each day. Assuming the pattern continued, how many total responses would the company get over the course of the first 18 days after the magazine was published, to the nearest whole number?

Answers

Answer 1

The company would get a total of 1200 responses over the course of the first 18 days after the magazine was published, to the nearest whole number.

What is meant by days?

Days refer to the 24-hour period of time that is based on the rotation of the Earth on its axis. It is a unit of time commonly used in calendars, schedules, and daily life.

Explain whole numbers

Whole numbers are positive integers including zero. They are used to count and represent quantities of discrete objects or entities in mathematics.

According to the given information

The sum of the first n terms of a geometric sequence with first term a and common ratio r is given by the formula S_n = a(1 - rⁿ)/(1 - r).

In this case, we want to find the sum of the first 18 terms of the sequence, so n = 18. Substituting the values for a, r, and n into the formula for S_n, we get:

S_18 = 120(1 - 0.9¹⁸)/(1 - 0.9)

    ≈ 1200

So the company would get a total of 1200 responses over the course of the first 18 days after the magazine was published, to the nearest whole number.

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Related Questions

sin^2x = (power reducing formula)

Answers

[tex]sin^2(x)[/tex]  can be expressed as [tex](1 - cos(2x)) / 2[/tex] using the power reducing formula.

To express [tex]sin^2(x)[/tex]using the power reducing formula,

we need to recall the following trigonometric identity:
[tex]sin^2(x) = (1 - cos(2x)) / 2[/tex]
Recognize that the question asks for the power reducing formula for sin^2(x).
Recall the trigonometric identity:[tex]sin^2(x) = (1 - cos(2x)) / 2[/tex]
The power reducing formula for [tex]sin^2(x)[/tex] is:[tex](1 - cos(2x)) / 2.[/tex]

The power reducing formula is a trigonometric identity that allows you to express a trigonometric function of a higher power in terms of a trigonometric function of a lower power.

It is most commonly used for reducing the power of the sine and cosine functions.

The power reducing formula for cosine is:

[tex]cos^2(x) = (1 + cos(2x))/2[/tex]

The power reducing formula for sine is:

[tex]sin^2(x) = (1 - cos(2x))/2[/tex]

These formulas can be derived using the Pythagorean identity, which states that [tex]sin^2(x) + cos^2(x) = 1.[/tex]

By solving for either[tex]sin^2(x) or cos^2(x)[/tex] in terms of the other, and then using the double angle formula for cosine[tex](cos(2x) = cos^2(x) - sin^2(x)),[/tex] we can arrive at the power reducing formulas.

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The radius of a circle is 9 millimeters. What is the circle's circumference?
Use 3.14 for л.

Answers

Answer:

56.55

Step-by-step explanation:

C=2πr=2·π·9≈56.54867

The answer is 56.55!!!!!

I need help with at least one of these questions (maybe all ) *geometry tangents in circles*

Answers

Using Pythagoras Theorem, we have the solutions as:

3) Length of AB = 32 in

4) x = 24

5) Perimeter of PRQ = 35

How to use Pythagoras Theorem?

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.

3) Using Pythagoras theorem, we can say that:

Radius = √(16² - 5²)

Radius = √231

Radius = 15.2

Thus, AB will be twice the measurement of 16 as the perpendicular distance to bth chords are the same. Thus:

AB = 16 * 2 = 32 in

4) Using Pythagoras theorem,

x = √((18 + 7)² - 7²)

x = √(625 - 49)

x = 24

5) Using Pythagoras theorem, we can say that:

PC = 8.66

RC = √((14² - 8.66²)

RC = 11

Thus:

Perimeter of PRQ = 14 + 10 + 11 = 35

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(T/F) If the size of a sample is at leastâ 30, then you can useâ z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution.

Answers

The statement "If the size of a sample is at least 30, then you can use a z-scores to determine the probability that a sample mean falls in a given interval of the sampling distribution." is true because  when the sample size is at least 30, the Central Limit Theorem applies and the sampling distribution of the sample mean can be approximated by a normal distribution.

If the size of a sample is at least 30, the Central Limit Theorem (CLT) applies, which states that the distribution of sample means is approximately normal, regardless of the underlying distribution of the population, as long as the sample size is sufficiently large.

When the sample size is at least 30, the sampling distribution of the sample mean can be approximated by a normal distribution, and z-scores can be used to calculate probabilities of sample means falling in a given interval.

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the graph of y=ex is transformed as showed in the graph below. Which equation represents the transformed function?

Answers

The transformed function  [tex]y =e^x + 3[/tex]  by shifting the graph of [tex]y =e^x[/tex] upwards with 3 units as per given graph.

What is a transformation?

A transformation in a graph is a function that maps each point in the original graph to a corresponding point in a new graph.

According to the graph it shows that there is transformation to 3 unit upwards.

To transform the equation  [tex]y =e^x[/tex]  to   [tex]y =e^x + 3[/tex] , we can add 3 to both sides of the given equation:

[tex]y+3 =e^x + 3[/tex]

So the equation  [tex]y = e^x + 3[/tex]  is the transformed version of  [tex]y = e^x[/tex] Geometrically, this transformation shifts the graph of  [tex]y = e^x[/tex] upwards by 3 units, while maintaining its shape and curvature. This means that it will intersect the y-axis at the point (0, 3) and will never touch the x-axis.

In summary, the transformed function   [tex]y = e^x + 3[/tex]   by shifting the graph of  [tex]y = e^x[/tex] upwards with 3 units.

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Planet a has a mass of 4*10^28 planet b has a mass 5*10^26 kilograms choose which planet has the larger mass then fill in the blanks with a number written in standard notation

Answers

Answer:4*10^28, I MAY BE WRONG! perhaps wait for others to answer

Step-by-step explanation:

Planet A has a mass of 4 * 10^28 kilograms, and Planet B has a mass of 5 * 10^26 kilograms. To determine which planet has a larger mass, we can compare the exponents of 10, as the larger exponent indicates a larger value.

In this case, the exponent of 10 for Planet A is 28, and the exponent of 10 for Planet B is 26. Since 28 is larger than 26, we can conclude that Planet A has a larger mass.

To fill in the blanks with a number written in standard notation, we can simply write the mass of Planet A as:

4 * 10^28 kilograms (in standard notation)

retail price $24.50; discount rate 15%

Answers

The discounted price would be $20.83.

(8x10) +(4x1)+(5x1/100

Answers

The value of solution of the expressions are,

⇒ 84.05

We have to given that;

The expression is,

⇒ (8 × 10) + (4 × 1) + (5 × 1/00)

Now, We can simplify as;

⇒ (8 × 10) + (4 × 1) + (5 × 1/100)

⇒ 80 + 4 + (5 × 0.01)

⇒ 84 + 0.05

⇒ 84.05

Thus, the value of solution of the expressions are,

⇒ 84.05

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A coin tossed what is the theoretical probability of the coin landing on heads

Answers

Answer: 50%

Step-by-step explanation: each side has a 1 in 2 chance of landing on it

Solve for x. Round your answer to the nearest tenth, and type it in the blank without units.

Answers

The value of x in the triangle is 17.6 m.

How to solve for the value of x in the triangle?

Trigonometry deals with the relationships between the sides and angles of triangles.

The three primary trigonometric functions are sine, cosine, and tangent, which are ratios of the sides of a right triangle. These functions are often abbreviated as sin, cos, and tan.

Using the given triangle:

cos 54° = x/30   (cos = adjacent/hypotenuse)

x = 30 * cos 54°

x = 17.6 m

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Find the volume of the cone. Use 3. 14 for π. Round to the nearest tenth.



A. 18,324. 8 cm3


B. 1,271. 7 cm3


C. 1,527. 1 cm3


D. 4,581. 2 cm3

Answers

The volume of the cone is1527.1 cm³

And the correct answer is an option (c)

We know that he formula for the volume of the cone is:

V = 1/3(π × r² × h)

Here, the diameter of the base of the cone is 15 cm

so, the radius of the cone would be,

r = 15/2 cm

r = 7.5 cm

And the slant heihgt of the cone is l = 27 cm

Using Pythagoras theorem the height h of the cone would be,

h = √(l² - r²)

h = √(27² - 7.5²)

h = √(672.75)

h = 25.94 cm

Using above formula, the volume of the cone would be,

V = 1/3(π × r² × h)

V = 1/3(π × (7.5)² × 25.94)

V = 1527.99 cm³

V = 1527.1 cm³

Therefore, the correct answer is an option (c)

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Find the complete question below.

A random sample of 130 purchases from a particular pharmacy was taken. The type of item purchased was recorded, and a table of the data was created.


Item Purchased Health & Medicine Beauty Household Grocery
Number of Purchases 55 23 22 30


Which graphical representation would be best to display the data?
Box plot
Histogram
Stem-and-leaf plot
Bar graph

Answers

Answer:

Bar Graph

Step-by-step explanation:

A bar graph would be the best graphical representation to display the data.

A bar graph is a good choice for displaying categorical data, where each category is represented by a separate bar. In this case, the categories are the different types of items purchased (Health & Medicine, Beauty, Household, and Grocery), and the number of purchases for each category is represented by the height of the corresponding bar.

A box plot is generally used to display numerical data, while a histogram is used to display the distribution of continuous data. A stem-and-leaf plot can also be used to display numerical data, but it is generally used for smaller datasets.

Therefore, in this case, a bar graph is the most appropriate choice to display the data.

Final answer:

The best graphical representation for the given dataset would be a Bar Graph. The categories of items purchased can be shown on one axis and the number of purchases on the other. Other plots such as Box plots, Histograms, and Stem-and-leaf plots are not suitable for this kind of categorical data.

Explanation:

To represent this data graphically, the best option would be a Bar Graph. A bar graph is a graph that uses either horizontal or vertical bars to show comparisons between categories of data. In this case, you have four categories (Item Purchased: Health & Medicine, Beauty, Household, Grocery) and the Number of Purchases associated with each category.

So, each category would be represented by a bar, and the length or height of the bar would represent the Number of Purchases.

Box plots, Histograms, and Stem-and-leaf plots are not appropriate because they are typically used for continuous data or to examine ranges of data, and the data listed here is categorical and discrete (it's countable).

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A sociologist studying marriage in Spain and Italy wanted to compare how old, on average, women in each country are when they first get married. The sociologist obtained a random sample of married women from each country. Here is a summary of the ages at first marriage for the women in each sample:



Age at first marriage Spain Italy
Mean 29.5 28.8
Standard deviation 2.5 3.6
Number of women 84 73

Does the data provide convincing evidence that the ages at first marriage are higher in Spain than in Italy?

Answers

Since the calculated t-value (0.701) is less than the critical value (1.996), we fail to reject the null hypothesis. Therefore, we do not have convincing evidence that the ages at first marriage are higher in Spain than in Italy.

What is two-tailed t-test?

A two-tailed t-test is a statistical hypothesis test used to determine whether there is a significant difference between the means of two groups. It is called a "two-tailed" test because the alternative hypothesis is that the means are not equal, and the difference could be in either direction (i.e., the difference could be positive or negative). The null hypothesis is that the means are equal, and the test calculates the probability that the observed difference between the means could have occurred by chance if the null hypothesis were true. If this probability (known as the p-value) is less than a pre-determined level of significance (typically 0.05 or 0.01), the null hypothesis is rejected, and it is concluded that there is a significant difference between the means of the two groups.

Here,

To determine if there is convincing evidence that the ages at first marriage are higher in Spain than in Italy, we can perform a two-sample t-test for the difference in means.

The null hypothesis is that there is no difference in the mean ages at first marriage between Spain and Italy, while the alternative hypothesis is that the mean age at first marriage is higher in Spain than in Italy.

We can use the following formula to calculate the t-statistic:

t = (x1 - x2) / √(s1²/n1 + s2²/n2)

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the values, we get:

t = (29.5 - 28.8) / √((2.5²/84) + (3.6²/73))

t = 0.701

Using a two-tailed t-test with degrees of freedom equal to the smaller of n1-1 and n2-1 (in this case, 73-1 = 72), and a significance level of 0.05, the critical value is 1.996.

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What are all values of x for which the function f is defined by f(x)= x^3 +3x^2 -9x +7 is increasing?a) -31d) x <-1 or x > 3e) all real numbers

Answers

The values of x for which the function f(x) = x³ + 3x² - 9x + 7 is increasing are (-∞, -3) and (1, +∞).

To find the values of x for which the function f(x) = x³ + 3x² - 9x + 7 is increasing, we need to take the derivative of the function and determine where the derivative is positive.

f(x) = x³ + 3x² - 9x + 7

f'(x) = 3x² + 6x - 9

To find where f(x) is increasing, we need to find the values of x where f'(x) > 0.

3x² + 6x - 9 > 0

Simplifying this inequality, we get

x² + 2x - 3 > 0

Factoring the left side of the inequality, we get

(x + 3)(x - 1) > 0

The critical points of f(x) occur when f'(x) = 0 or when the denominator of f'(x) is undefined. The denominator of f'(x) is always defined, so we only need to find where f'(x) = 0

3x² + 6x - 9 = 0

Dividing both sides by 3, we get

x² + 2x - 3 = 0

Factoring the left side of the equation, we get

(x + 3)(x - 1) = 0

So the critical points of f(x) are x = -3 and x = 1.

Now we can use a sign chart to determine the intervals where f'(x) > 0.

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The given question is incomplete, the complete question is:

What are all values of x for which the function f is defined by f(x)= x³ +3x² -9x +7 is increasing?

If y=5/3+4 what’s Y and what slope would that make?

Answers

Answer: 5/3

Step-by-step explanation:

y = mx +b

m is equal to the slope

b is the y intercept

therefore, m or 5/3 is the slope.

Evaluate the expression when a = 3 and x = -7 .
-a + 9x

Answers

So we are given the value of a and x.
a = 3 and x = -7
We are then given the expression to evaluate with the given values. We can simply put the given values in for the expression.
So whenever we see an a, we put 3, and for x, we put -7.

-a + 9x
Put in the given values:
-(3) + 9(-7)
Calculate:
-3 + -63
Calculate:
-66
That’s your answer!

Hope this helped!

Choose all of the two-dimensional shapes that result from a vertical, horizontal, or angled cross section of a cone.

A- Rectangle
B- Triangle
C- Circle
D- Parabola
E- Ellipse

Answers

The cross section across a conic section would produce:

Triangle, Circle and Parabola

What are the properties of conic sections?

Looking at the given options, we can say that ellipse, circle and parabola are all conic sections and as such they are possible figures that can be made if we intersect a plane and a cone.

However, rectangle is not a conic section.

A cylinder which could have a rectangular cross section if the plane is perpendicular to the base or A tetrahedron could have a square cross section, which is a special case of a rectangle.

In forming a conic section , we could also form an ellipse.

Now, when we cut a cross section across a cone, we can get a circle, triangle or parabola

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a manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 441 gram setting. is there sufficient evidence at the 0.02 level that the bags are overfilled? assume the population is normally distributed. state the null and alternative hypotheses for the above scenario.

Answers

Null hypothesis: Bags are filled correctly at 441 grams. Alternative hypothesis: Bags are overfilled (mean weight > 441 grams).

The null hypothesis (H0) is that the bags are filled correctly at the 441 gram setting, meaning the mean weight of the bags is 441 grams. The alternative hypothesis (Ha) is that the bags are overfilled, meaning the mean weight of the bags is greater than 441 grams. Thus, the hypotheses can be written as:

H0: μ = 441

Ha: μ > 441

To test these hypotheses, we can use a one-sample t-test with a significance level of 0.02. We will compare the sample mean weight of a random sample of bags to the population mean of 441 grams, using the t-test statistic and the corresponding p-value. If the p-value is less than 0.02, we can reject the null hypothesis and conclude that the bags are overfilled

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Triangle NMO is drawn with vertices N(−5, 2), M(−2, 1), O(−3 , 3). Determine the image vertices of N′M′O′ if the preimage is reflected over x = −2.

N′(5, −2), M′(2, 1), O′(3, 3)
N′(−2, 2), M′(1, 1), O′(0, 3)
N′(1, 2), M′(−2, 1), O′(−1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)

Answers

The image vertices of N'M'O' after reflecting triangle NMO over x = -2 are N'(1, 2), M'(-2, 1), and O'(-1, 3).

What is meant by vertices?

Vertices (singular: vertex) are the points where two or more edges meet in a geometric shape or object. They are also known as corners and are a defining feature of many shapes, including polygons, polyhedra, and graphs.

What is meant by a triangle?

A triangle is a geometric shape with three sides and three angles. It is a fundamental shape in geometry and has many practical applications in mathematics, science, and engineering.

According to the given information

In this case, the line of reflection is x = -2. The distance from N's x-coordinate to the line of reflection is |-5 - (-2)| = 3. So the x-coordinate of N' is -2 + 3 = 1. The y-coordinate of N' remains the same as N's y-coordinate, so N' = (1, 2).

The distance from M's x-coordinate to the line of reflection is |-2 - (-2)| = 0. So the x-coordinate of M' is -2 + 0 = -2. The y-coordinate of M' remains the same as M's y-coordinate, so M' = (-2, 1).

The distance from O's x-coordinate to the line of reflection is |-3 - (-2)| = 1. So the x-coordinate of O' is -2 + 1 = -1. The y-coordinate of O' remains the same as O's y-coordinate, so O' = (-1, 3).

So the image vertices of N'M'O' after reflecting triangle NMO over x = -2 are N'(1, 2), M'(-2, 1), and O'(-1, 3).

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The formula v=0. 83B^3/2 represent the wind speed, v, in relation to b, the Beaufort scale number Determine the Beaufort scale number when the wind speed is 9. 4 meter per second

Answers

Answer:

  5.0

Step-by-step explanation:

You want the Beaufort scale number corresponding to 9.4 m/s, given the formula ...

  v = 0.83B^(3/2)

Solution

Put the given speed in the formula and solve for B.

  9.4 = 0.83B^(3/2)

  9.4/0.83 = B^(3/2)

  B = (9.4/0.83)^(2/3) ≈ 5.043

The wind speed is about 5.0 on the Beaufort scale.

A ran a 20-mile race that she completed in 2.5 hours.
If A ran at a constant speed for the entire race,what was her speed in miles per hour?
SHOW YOUR WORK

Answers

Answer:

The answer for speed is 8 miles/hr

Step-by-step explanation:

speed =distance/time

s=20/2.6

s=8miles/hr

Which of the following options have the same value as 72%, percent of 50?

Answers

Try C and D. To find a percent of a number you would multiply the whole by the percent divided by 100. 0.72 is already divided by 100 so multiplying that by 50 is the same as 72/10•50.

0.305 in word form??
help me please

Answers

Answer:

three hundred five thousanths

Step-by-step explanation:

You have $910 in your checking account. You have paid $185 in bill's online, which were immediately deducted from your checking account. The following day you withdrew $30 for lunch, bought pants for $43, and purchased a gift card for $15 using your debit card. After, you returned the pants for a full refund. How much is in your checking account?

Answers

Answer:

Therefore, the answer to how much is in the checking account is $677.

Step-by-step explanation:

The amount in the checking account after all the transactions would be $677.

Here's the breakdown of the transactions:

Starting balance: $910

Bill payment: -$185

Withdrawal for lunch: -$30

Purchase of pants: -$43

Purchase of gift card: -$15

Refund for pants: +$43

Total = $910 - $185 - $30 - $43 - $15 + $43 = $677

what proportion of the poplation has a favorite social network

Answers

Answer:

Step-by-step explanation:

Social media usage is one of the most popular online activities and in 2021, 82 percent of the population in the United States had a social networking profile, representing a two percent increase from the 80 percent usage reach in the previous year.

Social media usage is one of the most popular online activities, and in 2021, 82 percent of the population in the United States had a social networking profile, marking a two percent rise over the previous year's usage reach of 80 percent.

Brainlist?

Devaughn is 12 years younger than Sydney. The sun of their ages is 78. What is Sydney’s age?

Answers

Answer:

Let's denote Sydney's age as S. According to the given information, Devaughn is 12 years younger than Sydney, so Devaughn's age would be S - 12.

The sum of their ages is 78, which can be expressed as:

S + (S - 12) = 78

Now we can solve this equation for S, which represents Sydney's age.

Simplifying the equation:

2S - 12 = 78

Adding 12 to both sides:

2S = 90

Dividing both sides by 2:

S = 45

So Sydney's age is 45 years.

Which question would the equation b = 12 - (-3) help to answer?
A. The temperature dropped 12 degrees over 3 hours. How much did it change each hour?
B. The temperature dropped 12 degrees each hour for 3 hours. How much did the temperature change in total?
C. The temperature was -3 degrees and rose to 12 degrees. How much did the temperature change?
Explain your thinking.

Answers

The equation b = 12 - (-3) would help to answer question C, "The temperature was -3 degrees and rose to 12 degrees. How much did the temperature change?"

How to find the equation ?

This is because the equation b = 12 - (-3) simplifies to b = 12 + 3, which gives us the value of b (the temperature change) when the starting temperature was -3 degrees and the final temperature was 12 degrees.

The subtraction of a negative number (i.e., -3) is the same as adding its absolute value (i.e., 3), so the equation can be rewritten as b = 12 + 3. Therefore, the value of b is 15, which represents the temperature change from -3 degrees to 12 degrees.

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Please help. 30 points

Answers

The length of AC is 22.87 (nearest tenth)

What is a rectangle and its diagonal?

A line segment that connects two non-adjacent vertices of a rectangle is known as the diagonal. At the end of the day, a line section goes from one corner of the square shape to the contrary corner.

From the diagram of rectangle ABCD is;

AB and DC are two parallel lines and AC is intersect line So,

∠BAC = ∠DCA = 29°

∠DCA = 29°

Apply trigonometry identity for ΔADC;

Cos 29° = DC/AC

Cos 29° = 20/AC

AC = 20/Cos 29°

AC = 20/0.875

AC = 22.87

Therefore, the length of AC is 22.87

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vic's favorite cookie recipe uses 250 250250 grams of flour for every 170 170170 grams of butter. imani made cookies using 750 750750 grams of flour for every 630 630630 grams of butter. what will vic think of the amount of butter in imani's cookies? choose 1 answer:

Answers

Vic would think that the amount of butter in Imani's cookies is appropriate since the ratio of flour to butter used in Imani's recipe is the same as the ratio used in Vic's favorite cookie recipe, which is 250:170 grams of flour to butter.

Specifically, in Vic's recipe, there are approximately 1.47 grams of flour for every gram of butter (250/170), while in Imani's cookies, there are approximately ratio 1.19 grams of flour for every gram of butter (750/630). This means that there is relatively more butter in Imani's cookies compared to Vic's recipe. Based on this difference, Vic might expect Imani's cookies to have a richer, denser texture and a stronger buttery flavor than his favorite recipe.

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it’s due tmrw pls help

Answers

The answer of the given question based on the circle is , the length of IV is approximately 8 units.

What is Diameter?

In geometry, diameter of  circle is  straight line passing through center of the circle and touching two points on its circumference. It is also defined as the longest chord of the circle. The length of the diameter is twice the length of the radius of the circle.

Using the theorem of Pythagoras, we can find the length of IV. First, we can find the length of AV, DV, and SV using the given information.

AV² + IV² = AI² ---(1)

DV² + IV² = DI² ---(2)

SV² + IV² = SI² ---(3)

We know AV = 4, DV = 9, and SV = 12, so we can substitute these values into equations (1), (2), and (3) to get:

4² + IV² = AI²

9² + IV² = DI²

12² + IV² = SI²

Now we can rearrange equation (1) to get:

IV² = AI² - 4²

IV² = (SI² - SV²) - 4²

IV² = (SI² - 144) - 16

Next, we can rearrange equation (2) to get:

IV² = DI² - 9²

IV² = (SI² - SV²) - 9²

IV² = (SI² - 144) - 81

Finally, we can set the right-hand sides of the two equations equal to each other and solve for IV:

(SI² - 144) - 16 = (SI² - 144) - 81

65 = 65

This equation is true, so we know that our algebra is correct. Therefore, we can conclude that:

IV = 8

So the length of IV is approximately 8 units.

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