Verify the identity so that the left side looks like the right side.
[tex]\frac{1-cos(x)}{sin(x)}=\frac{sin(x)}{1+cos(x)}[/tex]

The two missing points on the line are:

(0, -1)

(-5, 0)

And the slope, using these points, is a = -1/5

Remember that a general linear equation is:

y = ax + b

Where a is the slope and b is the y-intercept.

If that line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Here we can look at line e and find the two missing y-values, for the first point we have:

(0, -1)

For the second point we have:

(-5, 0)

Using these two, we will get the slope:

a = (0 + 1)/(-5 - 0) = -1/5

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Rectangle ABCD was translated 8 units left and then 7 units down.

We can see vertex A(2,4) of rectangle ABCD moves to A"(-6,-3), in a way that A translated 8 units left (-8)and 7 units down(-7) to A".

A plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square.

Vertex is a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet. The plural of a vertex is vertices.

A line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between its endpoints.

that is (2-8,4-7)=(-6,-3)

Similarly the other vertices of rectangle ABCD moves to form rectangle A"B"C"D"

B (2,2) → B" (-6,-5)

C (6,2) → C" (-2,-5)

D(6,4) → D" (-2,-3)

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The measure of IJ is 29, when IJ is dilated by a scale factor of 2 to form I' J', and I' J' measures 58. Geometric figures in two or three dimensions can be expanded and contracted using dilation mathematics.

Dilation refers to the change in size without a change in shape of an object. The scale factor may also cause the object's size to either increase or decrease.

Dilation is hence the process of resizing or altering an object. It is a transformation that makes the objects smaller or larger by applying the provided scale factor. It is a transformation that makes the objects smaller or larger by applying the provided scale factor. The pre-image is the original figure, while the image is the new figure created as a result of dilation. Dilation comes in two varieties:

As an object experiences expansion, its size expands.

Contraction is the process of a thing getting smaller.

Given:

I'J' is IJ with the scale factor of 2.

so (IJ) × 2= (I'J)

(IJ) × 2 = 58

58 ÷ 2 = 29

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1) A function to model the cost of C after t years since 2000 is [tex]C = 4,291(1 + 0.0315)^t[/tex]

2)If the trend continues,  a student expect to pay for room and board in 2017 is $7862.35 .

What is exponential function?

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

Here we need to use exponential function formula to find the cost function . Then,

=> [tex]f(x)=a(1+r)^t[/tex]

Where a is cost for room in 2000 and r is rate of change.

Then model the cost of room and board C after t years since 2000, we can use the formula:

=> [tex]C = 4,291(1 + 0.0315)^t[/tex]

where 0.0315 represents the annual increase of 3.15% expressed as a decimal.

Now we have to find the cost of room and board in 2017, we need to substitute t = 17 (since 2017 is 17 years after 2000) into the function and round the result to the nearest hundredth.

So,[tex]C = 4,291\times(1 + 0.0315)^{17}[/tex]

=>C = 7,862.35

Therefore, a student would expect to pay approximately $7862.35 for room and board in 2017 if the trend continued.

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Solving the given inequality, we get the value of x to be,

x ≥ 16.

In a mathematical equation with an inequality, both sides must be equal. In inequality, we don't use equations but rather compare two values. The signs greater than (or greater than or equal to), less than (or less than or equal to), or not equal to are used in place of the equal sign.

Here in the question, we have the inequality:

x - 4 ≥ 12

Now to simplify this we will add 4 on both sides,

⇒ x - 4 + 4 ≥ 12 + 4

⇒ x ≥ 16

So, this implies that the value of x is greater than or equal to 16.

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The total volume of the mixture obtained by Rico when he mixes 20 liters of milk with water in a ratio of 20:1 is 21 liters.

When a ratio of 20:1 is given for milk and water, it means that for every 20 parts of milk, there is 1 part of water. Therefore, the total number of parts in the mixture is 20 + 1 = 21.

We know that Rico mixed 20 liters of milk, which represents 20 parts of the mixture. To find the corresponding volume of water, we can use the ratio given.

The ratio of milk to water is 20:1, which means that for every 20 parts of milk, there is 1 part of water. Thus, the volume of water in the mixture is [tex]\frac{1}{20}[/tex] of the total volume of the mixture.

Volume of water = [tex]\frac{1}{20}[/tex] x Total volume of the mixture

Since we know that the volume of milk is 20 liters, we can substitute that value in the equation to solve for the total volume of the mixture:

20 = ([tex]\frac{20}{21}[/tex]) x Total volume of the mixture

Total volume of the mixture = (20 × 21) ÷ 20

= 420 ÷ 20

= 21 liters

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The complete question is:

What is the total volume of the mixture obtained by Rico when he mixes 20 liters of milk with water in a ratio of 20:1?

The density of the lobster population in the area labeled NBHK is C) 9.02 lobsters/mi^2.

Population density refers to the number of people living in a given area, usually expressed as the number of individuals per square mile or kilometer.

To calculate population density, you can divide the total population of a given area by its land area. For example, if a city has a population of 1 million people and an area of 100 square miles, its population density would be 10,000 people per square mile.

The figure has two trapezoid and the areas are 306 and 756. Total area will be 1062 miles².

Lobster population will be:

= 6817 / 756

= 9

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Answer:Sin and cosine of the acute angle are complementary trigonometric functions. This means that between these trigonometric functions, the rule of complementary acute angles applies: sin64° = cos(90°-64°) = cos26°

So, if we have given cos64° = cosx  and we want to determine the value of the acute angle x, given the complementarity of the angles to 90 degrees, the required value of the angle x is 26°.

The answer is: x = 26°

Step-by-step explanation:

A forecast is defined as a(n) prediction of future values of a time series which is option B.

Using past data as inputs, forecasting is a process that produces accurate predictions of the future course of trends. Companies use forecasting to decide how to spend their budgets and make plans for forthcoming costs. Often, this is based on the anticipated demand for the provided goods and services.

Forecasting is a tool used by investors to predict if certain events, such sales projections, would raise or lower the price of a company's stock. For businesses that require a long-term view on operations, forecasting also offers an essential benchmark.

To predict how trends, like as the GDP or unemployment, will change in the upcoming quarter or year, equity analysts utilise forecasting. Lastly, statisticians may examine the probable effects of a change in business operations via forecasting. Data may be gathered, for example, on how altering company hours affects consumer happiness or how changing particular work conditions affects staff productivity.

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By answering the presented question, we may conclude that As a result, the slope-intercept equation to represent the total amount of points on the test is y = (-1/2)x + 10.

In mathematics, the slope-intercept form of a linear equation is an that the equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point on the line where it intersects the y-axis. Since it allows you to easily view the line and identify its slope and y-intercept, the slope-intercept form is a useful way to describe a line's equation. The slope of the line denotes its steepness, while the y-intercept indicates where the line crosses the y-axis.

Let x denote the number of spelling and y the number of vocabulary questions. Because there are a total of 18 questions, we know:

x + y = 18

5x + 10y = 15 points

We must solve for y 5x + 10y = 100 to put this equation in slope-intercept form.

10y = -5x + 100

y = (-1/2)x + 10

As a result, the slope-intercept equation to represent the total amount of points on the test is y = (-1/2)x + 10.

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Answer:

The first box is 4 and the second box is 4

The solution is
([tex]\frac{3}{2}[/tex],1)

Step-by-step explanation:

y = 2x -2  Subtract 2x from both sides

-2x + y = -2  Multiply all the way through by - 2

4x - 2y = 4  You are doing this so that you can add it to the first equation 4x + 2y = 8

     4x + 2y = 8

(+) 4x - 2y = 4

       8x       = 12  Divide both sides by 8

x = [tex]\frac{12}{8}[/tex] = [tex]\frac{3}{2}[/tex]

To find y substitute [tex]\frac{3}{2}[/tex] for x and solve for y

y = 2x - 2

y = [tex]\frac{2}{1}[/tex] x [tex]\frac{3}{2}[/tex] - 2

y = 3 - 2

y = 1

Helping in the name of Jesus.

Answer:

Part A = 4x - 2y = 4

Part B = (1.5, 1)

Step-by-step explanation:

Part A:

y = 2x - 2

2y = 4x -4

4x - 4 = 2y

4x - 2y = 4

Part B:

4x + 2y = 8

2y = 8 - 4x

y = (8 - 4x)/2

y = 2x -2

(8 - 4x)/2 = 2x -2

8 - 4x = 4x - 4

8x = 12

x = 1.5

4x + 2y = 8

4(1.5) + 2y = 8

6 + 2y = 8

2y = 2

y = 1

(1.5, 1)

Flow rate =[tex]V_{new} / time = (3.5 * V_{old}) / time = (3.5 * 576,000) / 84 = 23,333[/tex] gallons per hour (rounded to the nearest gallon) will be circulated.

What is meant by rate?

In general, a rate is a measure of how quickly something changes over time or with respect to some other quantity. It is typically expressed as a ratio of two quantities, where the numerator represents the amount of change and the denominator represents the time or other quantity over which the change occurs.

If the new exhibit is 3 1/2 times larger than the old one, then its volume is:

[tex]V_{new} = 3.5 * V_{old[/tex]

We know that in the old exhibit, 576,000 gallons of water circulated over 24 hours. Therefore, the flow rate of water in gallons per hour is:

576,000 gallons / 24 hours = 24,000 gallons per hour

To find the flow rate in the new exhibit, we need to divide the total volume of water by the number of hours. Since we want the flow rate in gallons per hour, we can write:

Flow rate = [tex]V_{new[/tex] / time

Plugging in the values we have:

Flow rate = (3.5 * [tex]V_{old[/tex]) / time

We don't know the time yet, but we do know that the flow rate should be the same as in the old exhibit, which was 24,000 gallons per hour. So we can set up an equation:

24,000 = (3.5 * [tex]V_{old[/tex]) / time

To solve for time, we can multiply both sides by time:

24,000 * time = 3.5 * [tex]V_{old[/tex]

Then we can divide both sides by 24,000:

time = (3.5 * [tex]V_{old[/tex]) / 24,000

Plugging in [tex]V_{old[/tex] = 576,000, we get:

time = (3.5 * 576,000) / 24,000 = 84 hours

Therefore, in the new exhibit, 3.5 times larger than the old one, the flow rate of water in gallons per hour will be:

[tex]Flow rate = V_{new} / time = (3.5 * V_{old}) / time = (3.5 * 576,000) / 84 = 23,333[/tex]gallons per hour (rounded to the nearest gallon).

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Answer:

To find out how many gallons per hour will be circulated in the new exhibit, we need to first determine the volume of the old exhibit. Given that 576,000 gallons of water circulated through the old tank over 24 hours, we can calculate the amount of water circulated per hour.

To do this, we divide the total gallons by the number of hours:

576,000 gallons / 24 hours = 24,000 gallons per hour

Now, we know that the new exhibit is 3 1/2 times larger than the old one. To find the volume of the new exhibit, we multiply the volume of the old exhibit by 3 1/2.

Let's assume the volume of the old exhibit is x gallons.

The volume of the new exhibit is 3 1/2 times larger than the old one, so the volume of the new exhibit is 3 1/2 * x.

To calculate the new volume, we need to convert the mixed fraction 3 1/2 into an improper fraction. It equals 7/2.

So, the volume of the new exhibit is 7/2 * x.

Now, we can determine the amount of water circulated per hour in the new exhibit.

To find this, we multiply the volume of the new exhibit by the rate of circulation per hour in the old exhibit (24,000 gallons/hour):

(7/2 * x) * 24,000 gallons/hour = (7 * 24,000 * x) / 2 gallons/hour = 168,000x gallons/hour

Therefore, the number of gallons per hour that will be circulated in the new exhibit is 168,000x, where x represents the volume of the old exhibit.

Please note that the actual value of x (the volume of the old exhibit) is not given in the question, so we can't determine the exact number of gallons per hour. However, we can express it as a multiple of the volume of the old exhibit.

Step-by-step explanation:

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The probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds is 94%.

To solve this problem, we can use the Central Limit Theorem, which states that the distribution of sample means is approximately normal for large sample sizes.

First, we need to calculate the standard error of the mean (SEM) using the formula

SEM = standard deviation / sqrt(sample size)

SEM = 29.5 / sqrt(45) = 4.4

Next, we can standardize the sample mean using the formula

z = (x - μ) / SEM

where x is the sample mean, μ is the population mean, and SEM is the standard error of the mean.

For the lower limit, we have

z = (185.7 - 193.2) / 4.4 = -1.70

For the upper limit, we have

z = (206.5 - 193.2) / 4.4 = 3.02

We can use a standard normal distribution table or calculator to find the probabilities associated with these z-scores.

The probability of z being between -1.70 and 3.02 is approximately 0.9429 or 94%. Therefore, the probability that for a random sample of 45 wait times, the mean is between 185.7 and 206.5 seconds is 94%.

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The final balance of the checking account after these transactions would be $375 - 2x. Note that we do not have information about the actual values of x, so we cannot determine the final balance precisely.

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

The initial balance of the checking account is $350.

If the customer makes two withdrawals, one $50 more than the other, let's assume the smaller withdrawal amount is x. Then, the larger withdrawal amount will be x + $50.

So, the new balance of the checking account after these two withdrawals would be:

$350 - x - (x + $50) = $350 - 2x - $50 = $300 - 2x

After this, the customer makes a deposit of $75, which would increase the balance of the checking account to:

$300 - 2x + $75 = $375 - 2x

Therefore, the final balance of the checking account after these transactions would be $375 - 2x. Note that we do not have information about the actual values of x, so we cannot determine the final balance precisely.

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Complete question:

Write an expression for the new balance using as few terms as possible. A checking account has a balance of $350. A customer makes two withdrawals, one $50 more than the other. Then he makes a deposit of $75.

The probability that a student chosen at random plays the drums is approximately 34%.

What is probability?

The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place. A certain event has a chance of 1, while an impossible event has a probability of 0.

The total number of students in the middle school who play the drums is 14 + 10 = 24.

The total number of students in the middle school is:

5 + 12 + 14 + 4 + 12 + 5 + 10 + 8 = 70

The probability of selecting a student who plays the drums at random is:

24/70 = 0.34285714285714286

To express this probability as a percentage, we multiply by 100 and round to the nearest whole number:

0.34285714285714286 * 100 ≈ 34

Therefore, the probability that a student chosen at random plays the drums is approximately 34%.

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The volume of the solid generated when the trapezoid is rotated about side DA is approximately 1586.6 cubic units (rounded to the nearest tenth).

A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.

Given:

DC = 7

DA = 6

DE = 6

AB = 14

Height of the trapezoid:

ED = (DC/AB) * EA = (7/14) * EA = 0.5 * EA

Height = EA - ED = EA - 0.5 * EA = 0.5 * EA

Circumference of the cylindrical shell:

Circumference = 2 * π * AB = 2 * π * 14

Thickness of the cylindrical shell:

Since the trapezoid is being rotated about side DA, the thickness (Δx) will vary along DA. We'll integrate with respect to x from 0 to 6 (the length of DA).

Volume of the solid generated:

Volume = ∫(0 to 6) [2 * π * 14 * 0.5 * EA * Δx]

Substituting EA = DE + DA = 6 + 6 = 12Volume = ∫(0 to 6) [2 * π * 14 * 0.5 * 12 * Δx]

Integrating:

Volume = 2 * π * 14 * 0.5 * 12 * [x] from 0 to 6

Volume = 2 * π * 14 * 0.5 * 12 * (6 - 0)

Volume = 504 * π

Approximating to the nearest tenth:

Volume ≈ 504 * 3.14 ≈ 1586.6 cubic units (rounded to the nearest tenth)

Therefore, the volume of the solid generated when the trapezoid is rotated about side DA is approximately 1586.6 cubic units (rounded to the nearest tenth).

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Answer: Let's say the total number of students surveyed is "x".

We know that 65% of the students surveyed said their favorite color was red, which means that 325 students said their favorite color was red.

We can set up a proportion to solve for "x":

65/100 = 325/x

To solve for "x", we can cross-multiply:

65x = 32500

Dividing both sides by 65, we get:

x = 500

Therefore, Hakeem surveyed 500 students in total.

Step-by-step explanation:

The null hypothesis is (typically) rejected, when (b) the p-value is less than or equal to .05.

In hypothesis testing, the Null-Hypothesis represents the default assumption,

whereas the alternative hypothesis represents the claim made by the researcher.

The "p-value" is defined as a probability metric which indicates the likelihood of observing the data, given that the null hypothesis is true.

If the p-value is small (less than or equal to .05), it means that it is unlikely to observe the data, assuming the null hypothesis is true.

Therefore, a p-value less than or equal to .05 is considered statistically significant, and the null hypothesis is typically rejected, the correct option is (b).

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The given question is incomplete, the complete question is

The null hypothesis is (typically) rejected, when select one:

(a) the p-value is less than or equal to .5

(b) the p-value is less than or equal to .05

(c) the p-value exceeds .05

(d) the p-value exceeds .5

263 more story artists are there than ​interns.

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

From the pie chart we see that the story artists constitute 20% of the total employee strength of 1540 employees and the interns constitute only 5% of that number

In actual values

Number of story artists = 1620 x 20% = 1620 x 20/100 = 324

Number of interns = 1620 x 5% = 1620 x 5/100 = 81

Difference = 324 - 81 = 263

Hence, 263 more story artists are there than ​interns.

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Complete question:

The circle graph represents the jobs at a digital animation company with 1,620 employees. How many more story artists are there than interns​?

See the image attached.

For the logarithm to be positive, the argument of the logarithm (i.e., 2x+c) must be greater than zero.

Solve the inequality 2x+c > 0 for x:

2x > -c

x > -c/2

Therefore, for x > -c/2, the logarithm Y=log(2x+c) will be positive.

a. The probability that the top-selling Red and Voss tire wears out before 60,000 miles can be found by calculating the Z-score and using a standard normal distribution table. The Z-score formula is: Z = (X - μ) / σ, where X is the distance (60,000 miles), μ is the mean (71,000 miles), and σ is the standard deviation (5,000 miles).

Z = (60,000 - 71,000) / 5,000 = -11,000 / 5,000 = -2.2. Using a standard normal distribution table, the probability is approximately 0.0139 or 1.39%.

b. To find the probability that a tire lasts more than 81,000 miles, calculate the Z-score: Z = (81,000 - 71,000) / 5,000 = 10,000 / 5,000 = 2. Using the standard normal distribution table, the probability of a Z-score less than 2 is approximately 0.9772. Since we want the probability of the tire lasting more than 81,000 miles, we need to find the complement: 1 - 0.9772 = 0.0228 or 2.28%.

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The prοbability οf drawing twο A cards is [tex]$1/8$[/tex] .

The prοbability fοrmula establishes the likelihοοd that an event will οccur. It is the prοpοrtiοn οf favοurite websites tο all favοurite websites. P (B) is the prοbability οf an event "B" is hοw the prοbability fοrmula can be stated. The number "n" (B) represents the favοurite mοments οf an event "B."

There are three cards, each labelled with the letter A οr D. Since there are twο A cards, there are a tοtal οf [tex]$2^3 = 8$[/tex] pοssible equally likely οutcοmes when twο cards are drawn with replacement frοm the set.

The pοssible οutcοmes are: AA, AD, DA, DD, AA, AD, DA, DD.

Out οf these eight pοssible οutcοmes, there is οnly οne οutcοme that cοrrespοnds tο drawing twο A cards: AA. Therefοre, the prοbability οf drawing twο A cards is  [tex]$1/8$[/tex] .

In οther wοrds,

[tex]$P(A,A) = \boxed{\frac{1}{8}}$[/tex].

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Answer:

m = 5

n = 2

c = 7

Step-by-step explanation:

Use the property of degrees (when dividing two same based numbers with different degree indicators, the degree indicators are subtracted)

[tex] \frac{ {9}^{ - 3} }{ {9}^{2} } = \frac{1}{ {9}^{m} } [/tex]

[tex] {9}^{ - 3 - 2} = {9}^{ - 5} [/tex]

[tex] {9}^{ - 5} = \frac{1}{ {9}^{m} } [/tex]

If the degree indicator is negative, the number is written as a fraction (1 in the numerator) and the degree indicator is raised to the denominator with a positive sign:

m = 5

.

[tex] \frac{ {x}^{ - 4} }{ {x}^{ - 6} } = {x}^{n} [/tex]

[tex] {x}^{ - 4 - ( - 6) } = {x}^{ - 4 + 6} = {x}^{2} [/tex]

n = 2

.

[tex] \frac{ ({ - 11})^{7} }{ ( { - 11})^{0} } = ( { - 11})^{c} [/tex]

Raising any number to the zero power makes it one

[tex] \frac{ ({ - 11})^{7} }{1} = ({ - 11})^{c} [/tex]

When dividing by 1, the number does not change

[tex]( { - 11})^{7} = ({ - 11})^{c} [/tex]

c = 7

Based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75, thus the correct option is (d). The question is related to hypothesis testing in statistics.

If the p-value is 0.03 and the level of significance is 0.10, we reject the null hypothesis if the p-value is less than 0.10.

Since the null hypothesis is not specified in the question, we assume that it is that the average rating of the fruit drink is no more than 4.75.

Therefore, if the p-value is less than 0.10, we would reject the null hypothesis and conclude that there is sufficient evidence to support the alternative hypothesis that the average rating of the fruit drink is more than 4.75.

Since the p-value, in this case, is 0.03, which is less than the level of significance of 0.10, we would reject the null hypothesis and conclude that based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75.

Therefore, the correct answer is (d) based on the sample data, there is sufficient evidence to conclude that the average rating is more than 4.75.

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The function to model the value of p of the car after t years can be expressed as:

p(t) = 28,175 * (1 - 0.085)^t

where 0.085 represents the percentage of depreciation per year, and t represents the number of years.

To find the value of the car after 6 years, we substitute t = 6 into the function:

p(6) = 28,175 * (1 - 0.085)^6

p(6) = 28,175 * 0.5386

p(6) ≈ 15,199.35

Therefore, the value of Jeff's car after 6 years will be approximately $15,199.35.

The minimum score that a student must obtain to be in the top 30% of students taking the national standardized examination for college admission is approximately 658.4.

To find the minimum score that a student must obtain to be in the top 30% of students taking the test, we need to find the score that corresponds to the 70th percentile of the distribution.

Using a standard normal distribution table or a calculator, we can find that the z-score corresponding to the 70th percentile is approximately 0.52.

We can use the formula for transforming a score from a normal distribution to a standard normal distribution to find the corresponding score in the original distribution:

z = (x - mu) / sigma

where z is the z-score, x is the score in the original distribution, mu is the mean of the distribution, and sigma is the standard deviation of the distribution.

Rearranging this formula, we get:

x = mu + z * sigma

Substituting the values we have, we get:

x = 510 + 0.52 * 270

x = 658.4

Therefore, to be among the top 30% of test-takers and be eligible for admission to the college, a student must score at least 658.4 on the exam.

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A) Quartile 1 (Q1): 2, Quartile 2 (Q2): 6, Quartile 3 (Q3): 7, Decile 1 (D1): 1, Decile 2 (D2): 2, Decile 3 (D3): 3, Decile 4 (D4): 7

B) Quartile 1 (Q1): 11, Quartile 2 (Q2): 14, Quartile 3 (Q3): 16, Decile 1 (D1): 11, Decile 2 (D2): 12, Decile 3 (D3): 14, Decile 4 (D4): 17

C) Quartile 1 (Q1): 77, Quartile 2 (Q2): 85, Quartile 3 (Q3): 94, Decile 1 (D1): 71, Decile 2 (D2): 81, Decile 3 (D3): 87, Decile 4 (D4): 98

D) Quartile 1 (Q1): 42, Quartile 2 (Q2): 66, Quartile 3 (Q3): 86, Decile 1 (D1): 28, Decile 2 (D2): 42, Decile 3 (D3): 57, Decile 4 (D4): 98

E) Quartile 1 (Q1): 100, Quartile 2 (Q2): 117, Quartile 3 (Q3): 133, Decile 1 (D1): 33, Decile 2 (D2): 100, Decile 3 (D3): 111, Decile 4 (D4): 147

F) Quartile 1 (Q1): 113, Quartile 2 (Q2): 126, Quartile 3 (Q3): 146, Decile 1 (D1): 110, Decile 2 (D2): 113, Decile 3 (D3): 121, Decile 4 (D4): 848

Number is an important part of mathematics, and it is used in virtually every aspect of life.

A) First, we need to arrange the data in order:

[1,1,2,2,2,2,2,3,3,3,3,4,5,6,6,7,7,7,7,9,9]

The median is the middle value of the data set. Since there are 21 values, the median is the average of the [tex]$10^{th}$[/tex] and [tex]$11^{th}$[/tex] values, which is 6.

The first quartile [tex]$Q_1$[/tex] is the median of the lower half of the data set. The lower half of the data set is [1,1,2,2,2,2,2,3,3,3], which has 10 values. The median of this set is the average of the [tex]$5^{th}$[/tex]and [tex]$6^{th}$[/tex] values, which is 2.

The third quartile[tex]$Q_3$[/tex]is the median of the upper half of the data set. The upper half of the data set is [4,5,6,6,7,7,7,7,9,9], which also has 10 values. The median of this set is the average of the[tex]$5^{th}$[/tex] and[tex]$6^{th}$[/tex]values, which is 7.

The interquartile range (IQR) is the difference between the third and first quartiles: IQR =[tex]Q_3[/tex] - [tex]Q_1[/tex]= 7 - 2 = 5.

To find the deciles, we need to divide the data into $10$ equal parts. Since we have 21 data points, we need to find the values that divide the data into groups of $2$. The [tex]$k^{th}$[/tex] decile[tex]$D_k$[/tex] is the[tex]$k \cdot n/10$-th[/tex] value, where $n$ is the number of data points. The deciles are:

$D_1 = 1, D_2 = 2, D_3 = 2, D_4 = 2, D_5 = 3,$

$D_6 = 6, D_7 = 7, D_8 = 7, D_9 = 9$

B) Again, we need to arrange the data in order:

$10,11,12,12,14,14,14,15,15,15,15,16,16,16,17,17,14,14$

The median is the average of the[tex]$9^{th}$[/tex] and[tex]$10^{th}$[/tex] values, which is $15$.

The first quartile $Q_1$ is the average of the[tex]$4^{th}$[/tex] and [tex]$5^{th}$[/tex]values, which is $14$.

The third quartile $Q_3$ is the average of the [tex]$14^{th}$[/tex] and [tex]$15^{th}$[/tex]values, which is $16$.

The interquartile range (IQR) is [[tex]Q_3[/tex] - [tex]Q_1[/tex]= 16 - 14 = 2].

To find the deciles, we need to divide the data into [10] equal parts. Since we have 18 data points, we need to find the values that divide the data into groups of 2. The deciles are:

[[tex]D_1[/tex]= 10, D_2 = 12, D_3 = 14, D_4 = 14, D_5 = 14,]

[[tex]D_6[/tex]= 15, D_7 = 15, D_8 = 16, D_9 = 17]

From the above calculation, it can be seen that the quartiles and deciles of each set of data differ.

This is due to the different values of the data sets and the number of data points in each set.

The quartiles and deciles show different ranges and values which indicate the spread of the data and also help to identify any skewness in the data.

Summarizing, the quartiles and deciles provide an important measure of the spread of the data, helping to identify any outliers or skewness.

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Note that given the perimeter of the Rhombus above, KN will be 35.03 inches

Since JKLM is a rhombus, all sides have the same length. Let's call this length "x".

Also, since JL and KM are diagonals of the rhombus, they bisect each other at point N. This means that JN = NL and KN = NM.

We know that JN = 16 inches, and we need to find KN. To do this, we need to first find x, the length of the sides.

The perimeter of the rhombus is 72 inches, so we can write:

4x = 72

Dividing both sides by 4, we get:

x = 18

Now we can use the Pythagorean theorem to find NM (which is equal to KN):

(NM)² = (JN)² + (JM)²

We know that JN = 16, and we can find JM using the fact that JL and KM are perpendicular bisectors of each other:

JM = √[(2x)² - x²] = sqrt(3x²) = x √(3)

Substituting x = 18 and simplifying, we get:

(NM)² = 16² + (18 √(3))²

(NM)² = 256 + 972

(NM)² = 1228

NM = √(1228) = 35.03

Therefore, KN is approximately 35.0 inches (to the nearest tenth).

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Answer:

Los dos números naturales son 12 y 58.

Step-by-step explanation:

Llamemos al número más pequeño "x" y al número más grande "y".

Del problema sabemos que:

x + y = 70 (ya que la suma de los dos números naturales es 70)

Cuando el número mayor se divide por el número menor, el cociente es 4 con un resto de 10. Esto se puede escribir como:

y = 4x + 10 (ya que 4 es el cociente y 10 es el resto)

Ahora podemos sustituir la segunda ecuación en la primera ecuación:

x + (4x + 10) = 70

Simplificando esta ecuación, obtenemos:

5x + 10 = 70

Restando 10 de ambos lados, obtenemos:

5x = 60

Dividiendo ambos lados por 5, obtenemos:

x = 12

Ahora que conocemos x, podemos volver a sustituirlo en una de las ecuaciones anteriores para encontrar y:

y = 4x + 10 = 4(12) + 10 = 58

Por lo tanto, los dos números naturales son 12 y 58.