1 County fair admission costs $5. Each game ticket costs $2. Arianna has $21 to
spend at the fair. She writes the inequality 5 + 2g ≤ 21 to represent how many
game tickets, g, she can purchase at the fair. Which values in the set {3, 8, 10, 13)
are solutions of the inequality? Show your work.

The best center of the speed of the last 10 pitches thrown by a pitcher is the mean

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

{90, 92, 85, 88, 94, 86, 93, 90, 88, 95}

The possible measure of centers are

In this case, we use the mean

This is because the data values do not have any outlier present in them

Hence, the center is the mean

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The model have 4 degrees of freedom if a regression model has a sample of 30 observations using a dependent variable, 3 independent variables, and a constant.

In a linear regression model, the degrees of freedom for the model are calculated as the number of independent variables plus one (for the constant or intercept term). Therefore, in this case, since the model has 3 independent variables and a constant, the degrees of freedom for the model would be 3 + 1 = 4.

The degrees of freedom for the model represent the number of parameters estimated from the data to build the model. These parameters are the coefficients or weights of the independent variables and the constant term.

The degrees of freedom for the model are used to calculate the F-statistic, which is a measure of the overall significance of the regression model. The F-statistic is calculated as the ratio of the explained variance to the unexplained variance of the model, and it is compared to the F-distribution with degrees of freedom (k, n-k-1), where k is the number of independent variables and n is the sample size.

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The size and nature of the dataset, the choice of independent variables, and the assumptions underlying the model, should also be considered when interpreting [tex]R^2[/tex] values.

The percent of the total variance that can be explained by the regression equation is known as the coefficient of determination, denoted as[tex]R^2.[/tex]

It represents the proportion of the total variation in the dependent variable (Y) that is accounted for by the independent variable(s) (X) included in the regression model.
To calculate[tex]R^2[/tex], you can follow these steps:
Obtain the sum of the squared differences between the actual and predicted values of the dependent variable (also known as the residual sum of squares, or RSS).
Obtain the sum of the squared differences between the actual values of the dependent variable and their mean (also known as the total sum of squares, or TSS).
Divide the RSS by the TSS: [tex]R^2 = 1 - (RSS/TSS).[/tex]
[tex]R^2[/tex] ranges between 0 and 1, with higher values indicating a better fit of the regression model.

An[tex]R^2[/tex] of 1 indicates that the regression equation perfectly explains the total variance, while an [tex]R^2[/tex] of 0 indicates that the regression equation does not explain any of the total variance.
Keep in mind that while[tex]R^2[/tex] is a useful measure of model fit, it should not be the only criterion used to evaluate the quality of a regression model.

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Answer:  the answer is A. 14.

Step-by-step explanation: In each trial of the reenactment, Scott chooses one card from the stack and records its digit. Based on the given data, a digit of or 1 speaks to a objective scored, and a digit of 2 through 9 speaks to a missed endeavor.

Out of the 5 endeavors per amusement, on the off chance that Scott scores precisely 2 objectives, it implies he missed 3 endeavors. Subsequently, the likelihood of this occasion can be calculated as:

P(exactly 2 objectives) = (0.2)²(0.8)³ = 0.008192

This likelihood can be utilized to discover the anticipated number of diversions in which Scott scores precisely 2 objectives, by duplicating it by the overall number of diversions reenacted:

Anticipated number of recreations = P(exactly 2 objectives) × Add up to number of recreations = 0.008192 × 84 ≈ 0.68

Adjusting to the closest entire number, we get that Scott is anticipated to score precisely 2 objectives in 1 diversion out of the 84 recreated diversions.

Sampled 200 delinquent credit card accounts instead of 100, the margin of error would decrease.

Sampled 200 delinquent credit card accounts, the margin of error for the sample mean at a 95% confidence level would be $80.164.

Smaller than the margin of error we found earlier for a sample size of 100.

The margin of error for the sample means at a 95% confidence level, we need to use the formula:
[tex]Margin of error = z\times (standard deviation / square root of sample size)[/tex]
[tex]z\times[/tex] is the z-score for the 95% confidence level, which is 1.96.
So, plugging in the given values, we get:
[tex]Margin of error = 1.96 \times  (578 / \sqrt 100)[/tex]
[tex]Margin of error = 1.96 \times 57.8[/tex]
Margin of error = 113.008
Therefore, the margin of error for the sample mean at a 95% confidence level is $113.008.
Repeated samples of 100 delinquent credit card accounts and computed the sample mean each time, we would expect the true population mean to be within $113.008 of our sample mean about 95% of the time.
The margin of error is inversely proportional to the square root of the sample size. So, as the sample size increases, the margin of error decreases.
To see this, let's plug in the new sample size into the margin of error formula:
[tex]Margin of error = 1.96 \times (578 / \sqrt 200)[/tex]
[tex]Margin of error = 1.96 \times 40.9[/tex]
Margin of error = 80.164

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Given statement: The rule of thumb for estimating the time of completion is 1.5 times what you originally think it will be.

Given statement is True.

The reason for this rule of thumb is that tasks often take longer than initially estimated due to unforeseen challenges, dependencies, and other factors that can cause delays.

By estimating the time of completion as 1.5 times the original estimate, you are accounting for these potential delays and allowing for a more realistic timeline.

This rule of thumb is not a hard and fast rule, and there will be cases where tasks take less or more time than 1.5 times the original estimate. However, it can be a helpful guideline for project planning and resource allocation, as it helps to ensure that sufficient time and resources are allocated to complete tasks within a realistic timeframe.

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Answer:

4. Mean: 89

5. Median: 90

6. Mode: None.

Step-by-step explanation:

To find the mean, add all of the numbers, then divide by the total.

There are 7 numbers in this set.

First, add all of the numbers. Then, divide the sum by 7.

[tex]85+95+88+93+94+78+90= 623\\623/7 =89[/tex]

The mean of this data set is 89!

------------------------------------------------

Now, let's find the median.

The median is the "middle number" of the data set.

First, put all of the numbers in order from least to greatest.

85, 95, 88, 93, 94, 78, 90

↓

78, 85, 88, 90, 93, 94, 95,

The number in the middle of the data set is 90!

Therefore, the median is 90.

------------------------------------------------

Now, let's find the mode.

The mode is the number that appears most frequently.

85, 95, 88, 93, 94, 78, 90

Since each number appears once, then there is no mode.

Let me know if you have any questions.

When the width of the rectangle is 4 in, the length is 6 in.

Let's call the length of the rectangle "L" and the width "W". The problem states that the area of the rectangle is constant, so we can write:

LW = A

where A is some constant. We are also told that the length varies inversely with the width, which means that if the width increases, the length must decrease proportionally to keep the area constant. Mathematically, this means

L ∝ 1/W

or

L = k/W

where k is some constant of proportionality. We can find k by using the information given in the problem. We are told that when the width is 3 in, the length is 8 in

8 = k/3

Multiplying both sides by 3 gives:

24 = k

Now we can use this value of k to find the length when the width is 4 in:

L = k/W = 24/4 = 6 inches

When the width of the rectangle is 4 in, the length is 6 in, where the length and width of the rectangle are related by the inverse proportion L = k/W, with k = 24.

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The second derivative is negative, the point (x, y) = (3, 7) corresponds to a local maximum on the curve.

To find the leftmost point on the curve defined by the parametric equations x = t² + 2t and y = t² - 2t + 3, we need to find the value of t that corresponds to this point. We can do this by analyzing the derivative of the curve with respect to t.

The leftmost point on the curve corresponds to the point where the slope of the curve is zero or undefined. This occurs when the derivative of y with respect to x is zero or undefined.

We can express y as a function of x by eliminating t from the given parametric equations. Solving for t in terms of x, we get:

t = -1 ± √(x + 1)

Substituting this value of t in the equation for y, we get:

y = (x + 1) ± 4√(x + 1) + 3

y = ±4√(x + 1) + x + 4

To find the leftmost point on the curve, we need to find the value of x that corresponds to this point. We can do this by finding the minimum value of x for which y is defined.

Differentiating y with respect to x, we get:

dy/dx = 1 + 2/√(x + 1)

Setting dy/dx = 0, we get:

1 + 2/√(x + 1) = 0

2/√(x + 1) = -1

Solving for x, we get:

x = 3

Note that this value of x is within the given range of -2 ≤ t ≤ 3. Therefore, the leftmost point on the curve is the point corresponding to t = 1.

To justify that we have found the requested point, we can analyze the second derivative of y with respect to x. The second derivative will tell us whether the point corresponds to a local minimum, local maximum, or inflection point.

Differentiating dy/dx with respect to x, we get:

d²y/dx² = -2/[tex](x + 1)^{(3/2)}[/tex]

Substituting x = 3, we get:

d²y/dx² = -2/64

Since the second derivative is negative, the point (x, y) = (3, 7) corresponds to a local maximum on the curve. Therefore, we have found the leftmost point on the curve as requested.

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The question is -

Identify the requested point and justify that you have found the requested point by analyzing an appropriate derivative. x = t² + 2t, y = t² - 2t + 3, - 2 ≤ t ≤ 3 Leftmost point

Answer:

6x² + 19x + 15

Step-by-step explanation:

(2x+3)(3x + 5)

= 6x² + 10x + 9x + 15

= 6x² + 19x + 15

So, the answer is 6x² + 19x + 15

Therefore, the solution is equation (x, y) = (52/7, -10/7).

To solve the system of equations by elimination, we need to eliminate one of the variables. We can do this by multiplying one or both equations by a constant to create opposite coefficients for one of the variables. Then, we can add or subtract the equations to eliminate that variable and solve for the other variable. Here's how to solve the given system of equations:

Multiply the first equation by 3 and the second equation by 2 to create opposite coefficients for y:

[tex]3(x - 2y = 12) - > 3x - 6y = 36[/tex]

[tex]2(-5x + 3y = -44) - > -10x + 6y = -88[/tex]

Add the equations to eliminate y:

[tex]3x - 6y + (-10x + 6y) = 36 + (-88)[/tex]

[tex]-7x = -52[/tex]

Solve for x by dividing both sides by -7:

[tex]x = 52/7[/tex]

Substitute x = 52/7 into either equation to solve for y. Using the first equation:

[tex]52/7 - 2y = 12[/tex]

[tex]-2y = 12 - 52/7[/tex]

[tex]-2y = 72/7 - 52/7[/tex]

[tex]-2y = 20/7[/tex]

[tex]y = -(10/7)[/tex]

Check the solution by substituting the values of x and y into both equations:

[tex]x - 2y = 12 - > 52/7 - 2(-10/7) = 12 (true)[/tex]

[tex]-5x + 3y = -44 - > -5(52/7) + 3(-10/7) = -44 (true)[/tex]

Therefore, the solution is (x, y) = (52/7, -10/7).

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(a) The probability that the sum of the numbers is 8 is 0.1.

(b) The probability that the sum of the number is 6 or less is 0.5.

(c) The probability that the first number is 2 or the sum is 5 is 0.35.

A probability is the number of desired outcomes divided by the number of total outcomes.

The possible outcomes are:

(1,2), (1,3), (1,4), (1,5).

(2,1), (2,3), (2,4), (2,5).

(3,1), (3,2), (3,4), (3,5).

(4,1), (4,2), (4,3), (4,5).

(5,1), (5,2), (5,3), (5,4).

Total outcomes = 20

(a) The sum of the numbers is 8.

There are only two ways to get a sum of 8: (3, 5), (5,3). So the probability of getting a sum of 8 is:

P(sum of 8) = 2/20

= 0.1

Therefore, the required probability is 0.1.

(b) The sum of the number is 6 or less.

To get a sum of 6 or less, we can have the following combinations:(1, 2), (1, 3), (1, 4), (1, 5), (2,1), (2, 3), (2,4), (3,1), (3,2), (4,1), (4,2), (5,1).So the probability of getting a sum of 6 or less is:

Total outcomes = 20

P(sum of 6 or less) = 10/20

=0.5

Therefore, the required probability is 0.5.

(c) The first number is 2 or the sum is 5

There are three ways to satisfy this condition:(2,1), (2, 3), (2,4), (2, 5), (1,4), (3, 2), (4,1). So the probability of getting a number that satisfies this condition is:

Total outcomes = 20

P(first number is 2 or sum is 5) = 7/20

= 0.35.

Therefore, the required probability is 0.35.

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Yes, 2 is a zero of the polynomial  [tex]Xe3-8xe2+18x-12[/tex]

To determine if 2 is a zero of the polynomial [tex]Xe3-8xe2+18x-12[/tex], we can plug in 2 for x and see if the result is 0.

So, if we substitute x=2, we get:

[tex](2)^3 - 8(2)^2 + 18(2) - 12 = 0[/tex]

Simplifying this equation, we get:

8 - 32 + 36 - 12 = 0

This equation is true, which means that 2 is indeed a zero of the polynomial [tex]Xe3-8xe2+18x-12.[/tex]

Therefore, we can conclude that the polynomial can be factored as:

[tex](X-2)(X^2-6X+6)[/tex]

This means that the other two zeros of the polynomial are the solutions of the quadratic equation [tex]X^2-6X+6=0[/tex] which can be found using the quadratic formula.

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Answer:

Angles 6 and 8 are vertical angles.

The slope of the linear regression prediction equation is 1,600, which means that for each additional year of

schooling, the expected increase in salary is 1,600.

The slope of the linear regression prediction equation can be calculated by using the formula:

slope = (y2 - y1) / (x2 - x1)

where y2 is the second data point (in this case, 28,600),

y1 is the first data point (in this case, 27,000),

x2 is the second value of the independent variable (in this case, 13 years of schooling), and

x1 is the first value of the independent variable (in this case, 12 years of schooling).

Plugging in the values, we get:

slope = (28,600 - 27,000) / (13 - 12)

slope = 1,600 / 1

slope = 1,600

Therefore, the slope of the linear regression prediction equation is 1,600, which means that for each additional year of

schooling, the expected increase in salary is 1,600.

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The estimated regression equation for the given data is y = -30.7 + 3.409x

To develop an estimated regression equation for the given data, we need to use the method of least squares.

The formula for the slope of the regression line is given by:

b = ∑(xi - x)(yi - y) / ∑(xi - x)²

where xi and yi are the individual values of the two variables, x and y are their respective means.

The formula for the intercept of the regression line is given by:

a = y - b × x

where a is the intercept and b is the slope.

Using the given data, we can calculate the values of x, y, b, and a as follows

x = (6 + 11 + 15 + 18 + 20) / 5 = 14

y = (7 + 9 + 12 + 21 + 30) / 5 = 15.8

∑(xi - x)(yi - y) = (6 - 14)(7 - 15.8) + (11 - 14)(9 - 15.8) + (15 - 14)(12 - 15.8) + (18 - 14)(21 - 15.8) + (20 - 14)(30 - 15.8) = 306.8

∑(xi - x)² = (6 - 14)² + (11 - 14)² + (15 - 14)² + (18 - 14)² + (20 - 14)² = 90

b = ∑(xi - x)(yi - y) / ∑(xi - x)² = 306.8 / 90 = 3.409

a = y - b × x = 15.8 - 3.409 × 14 = -30.7

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The given question is incomplete, the complete question is:

Given are data for two variables, x and y. Develop an estimated regression equation for these data.

The coin makes approximately 16.53 turns when rolled on its edge for 1.34 m.

The circumference of the coin can be calculated as follows to determine the number of turns it makes:

C = πd

where C is the circumference, d is the diameter, and π is the mathematical constant pi (approximately equal to 3.14159).

So, for the given $2 coin with a diameter of 25.75 mm, the circumference is:

C = πd = 3.14159 x 25.75 mm ≈ 80.926 mm

Divide the distance traveled by the coin's circumference to determine the number of turns it makes when rolled on its edge for 1.34 meter:

Number of turns = distance traveled / circumference of the coin

Number of turns = 1.34 m / 0.080926 m

Number of turns ≈ 16.53

Therefore, the coin makes approximately 16.53 turns when rolled on its edge for 1.34 m.

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Answer:

To determine which ratio is proportional to 80:60, we need to simplify the ratio by dividing both terms by their greatest common factor. In this case, the greatest common factor of 80 and 60 is 20, so:

80/20 = 4

60/20 = 3

Therefore, the simplified ratio is 4:3.

Now we can compare this ratio to the given options to see which one is proportional to 4:3:

16:15 is not proportional

16:12 is proportional (since 16/4 = 4 and 12/3 = 4)

18:15 is not proportional

18:12 is proportional (since 18/3 = 6 and 12/2 = 6)

Therefore, the ratio that is proportional to 80:60 is 16:12.

Answer:

11 1/2

Step-by-step explanation:

A. The number of 7-card stud poker hands is 133,784,560 and the number of 7-card stud poker hands is 674,274,182,400.

B. The number of hands of 7-draw poker that contain the ace of hearts is 18,009,460.

C. The probability that a 7-card draw hand contains the ace of hearts is 0.135.

a) The number of 7-card draw poker hands can be calculated using the combination formula, which is:

[tex]^{n} C_{r}[/tex] = n! / (r! * (n - r)!)

where n is the total number of cards in the deck (52) and r is the number of cards in each hand (7).

So, the number of 7-card draw poker hands is:

[tex]^{52} C_{7}[/tex] = 52! / (7! * (52 - 7)!)

= 133,784,560.

The number of 7-card stud poker hands can be calculated using the permutation formula, which is:

[tex]^{n} P_{r}[/tex] = n! / (n - r)!

where n is the total number of cards in the deck (52) and r is the number of cards in each hand (7).

So, the number of 7-card stud poker hands is:

[tex]^{52} P_{7}[/tex] = 52! / (52 - 7)!

= 674,274,182,400.

b) To count the number of hands of 7-draw poker that contain the ace of hearts, we can treat the ace of hearts as a special card that must be included in each hand. Then, we need to choose the remaining 6 cards from the 51 cards that are not the ace of hearts.

So, the number of hands of 7-draw poker that contain the ace of hearts is:

[tex]^{51} C_{6}[/tex] = 51! / (6! * (51 - 6)!)

= 18,009,460.

c) To calculate the probability that a 7-card draw hand contains the ace of hearts, we can use the formula:

P(event) = number of favourable outcomes / total number of possible outcomes

The total number of possible 7-card draw hands is 133,784,560, which we calculated in part (a).

The number of favourable outcomes is the number of hands of 7-draw poker that contain the ace of hearts, which we calculated in part (b).

So, the probability that a 7-card draw hand contains the ace of hearts is:

P(ace of hearts) = 18,009,460 / 133,784,560 ≈ 0.135

The required probability is 0.135.

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Answer:

f(x) is the blue graph, g(x) is the red graph.

x^2 - 3x + 17 - (2x^2 - 3x + 1) = 16 - x^2

16 - x^2 = 0 when x = -4, 4

So the area between these two graphs is (using the TI-83 graphing calculator):

fnInt (16 - x^2, x, -4, 4) = 85 1/3

The percentage of the original area of wetlands currently left in the United States is approximately 50%. So, the correct

option is 50% (option 3).

Percentages are a way of expressing a proportion or a fraction as a part of 100. It is denoted by the symbol "%".

According to the United States Environmental Protection Agency (EPA), it is estimated that about 50% of the original

wetlands in the contiguous United States have been lost since the 1600s due to human activities such as agriculture,

development, and urbanization. Therefore, the correct answer to the question is 50%.

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The percentage of the original area of wetlands currently left in the United States is approximately 50%.

Wetlands are regions of land where the soil is continually or intermittently soaked with water. Wetlands have a particular hydrology, soil, and vegetation mix that results in specialised ecosystems that offer a variety of ecological functions.

There are many different types of habitats where wetlands can be found, such as coastal locations, interior regions, and high-altitude mountain regions. They come in a variety of shapes, such as marshes, swamps, bogs, fens, and estuaries, and can be freshwater, brackish, or saline.

Wetlands are significant for several reasons. For species, such as migrating birds, amphibians, and fish, they offer crucial habitats. They also aid in removing contaminants from water, lessen the effects of flooding, and give people access to recreational activities. Wetlands are crucial for carbon sequestration as well.
Based on the information provided, the question is asking for the approximate percentage of the original area of wetlands currently left in the United States. The answer is approximately 50%.

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The expression that gives the area as a function of the width is 4w²+3w.( option B)

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

The area of a rectangle is expressed as ;

A = l×w, where l is the length and w is the width.

Since the length is 3 inches more than four times the width, then;

l = 3+4w

Representing 3+w for l in the area formula, then we have;

A = (3+4w)(w)

A = 4w²+3w

therefore the expression that represents the area is 4w²+3w

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Hong rode the scooter for approximately 86 minutes.

Let's start by using algebra to solve for the number of minutes Hong rode the scooter.

Let's say the number of minutes Hong rode the scooter is "m". Then, we can set up the following equation:

Total cost = $5 fee + 9 cents per minute x m minutes

$12.74 = $5 + $0.09m

Next, we'll solve for "m" by isolating it on one side of the equation:

$12.74 - $5 = $0.09m

$7.74 = $0.09m

m = $7.74 ÷ $0.09

m ≈ 86

Therefore, Hong rode the scooter for approximately 86 minutes.

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Answer:

x> - 15

Step-by-step explanation:

I guess this will help

The monthly interest rate is the annual interest rate divided by 12

To calculate the monthly interest rate, we need to divide the annual interest rate by 12 (since there are 12 months in a year).

So if the annual interest rate is 8%, the monthly interest rate can be calculated as:

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 8% / 12

Monthly interest rate = 0.6667%

Therefore, the monthly interest rate would be 0.6667%.

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The distance between the two points can be found to be, and the number that goes beneath the radical symbol is 80.

To find the distance between two points in a plane, you can use the distance formula derived from the Pythagorean theorem. The distance formula is:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

In this case, the coordinates of the two points are (-4, 1) and (4, 5). So, x₁ = -4, y₁ = 1, x₂ = 4, and y₂ = 5.

Now, apply the distance formula:

d = √[(4 - (-4))² + (5 - 1)²]

d = √[(8)² + (4)²]

d = √(64 + 16)

d = √80

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[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{ \textit{we'll use this one} }{a^{log_a (x)}=x} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2(16x)=4\implies 2^{\log_2(16x)}=2^4\implies 16x=2^4\implies x=\cfrac{2^4}{16}\implies x=1[/tex]

Step-by-step explanation:

rotate the triangle in your mind (or as actual picture on your phone or computer), so that the right angle is the bottom right or bottom left, and C being the opposite bottom angle.

then we see

28 = cos(C) × 35

21 = sin(C) × 35

and so,

sin(C) = 21/35 = 3/5

cos(C) = 28/35 = 4/5

tan(C) = sin(C)/cos(C) = 3/5 / 4/5 = 3/4