an endangered species has a population of 5000. scientists estimate that the stock is decreasing at 3% per year. at this rate, approximately how many years will it be before 60% of the species remains?

The answer is: 1 triangle is possible  given the following side maesurment: 3 feet , 5 feet, 4 feet.

To determine how many triangles are possible with these side measurements, we can use the triangle inequality theorem, which states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

What is inequality theorem?

In this case, we have three side measurements: 3 feet, 5 feet, and 4 feet. Let's call these sides a, b, and c, respectively. Using the triangle inequality theorem, we can see that:

a + b > c

a + c > b

b + c > a

Substituting in the values of a, b, and c, we get:

3 + 5 > 4

3 + 4 > 5

4 + 5 > 3

All three of these inequalities are true, so it is possible to form a triangle with these side measurements.

To determine how many distinct triangles are possible, we can use the fact that any two triangles are distinct if and only if they have at least one side with a different length. In this case, all three sides have different lengths, so there is only one distinct triangle that can be formed with these side measurements.

Therefore, the answer is: 1 triangle.

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Complete question is: 1 triangle is possible given the following side maesurment: 3 feet , 5 feet, 4 feet.

The third quartile is $10.6575, which means that 75% of all days the stock is below this value.

The range of the stock price is from $8.82 to $16.17, and the distribution is uniform, which means that the probability of the stock price being any value between the minimum and maximum is the same.

To find the third quartile, we need to find the value x such that 75% of the observations are less than or equal to x, and 25% of the observations are greater than or equal to x.

Since the distribution is uniform, we can find x by finding the value that separates the bottom 25% of the distribution from the top 75% of the distribution.

The bottom 25% of the distribution spans from $8.82 to some value x. Since the distribution is uniform, we can find x by setting the probability of the stock price being less than or equal to x to 0.25, which gives:

(x - 8.82) / (16.17 - 8.82) = 0.25

Solving for x, we get:

x - 8.82 = 0.25 * (16.17 - 8.82)

x - 8.82 = 1.8375

x = 10.6575

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Answer:

(5,2)

Step-by-step explanation:

Let's solve your system by substitution.

[tex]x+y=7{\text{ ; }}x=y+3[/tex]

Step 2: let Solve [tex]$x+y=7$[/tex] for[tex]$x$[/tex]

[tex]x+y=7[/tex]

[tex]x+y +(-x)=7+(-x)[/tex] (Add (-x) on both sides)

[tex]y=-x+7[/tex]

0+(x)=7-x-y+(x)   (Add (x) on both sides)

x = -y + 7

x/1 = -y+7/1  (divide through by 1)

x = -y + 7

Substitute -y+7 for x in x = y + 3, then solve for u

(-y + 7) = y + 3

-y + 7 = y + 3 (simplify)

-y+7+(-7) = y + 3 + (-7)    (Add (-7) on both sides)

-y=y-4

-y = y-4 (simplify)

-y+(-y)=y-4+(-y)  (Add (-y) on both sides)

-2y-=-4

-2y/-2 = -4/-2  (Divide through by -2)

y = 2

Substitute in 2 for y in x = -y + 7

x =  -y+7

x = -2+7

x = 5

Answer:

x = 5 and y = 2

Answer:

Step-by-step explanation:

The circumference of the bicycle wheel can be determined by the formula:

Circumference = π x diameter

where π (pi) is a mathematical constant equal to approximately 3.14.

Substituting the given diameter of 1.25 ft, we get:

Circumference = 3.14 x 1.25 ft

Circumference = 3.925 ft (rounded to three decimal places)

Each revolution of the wheel covers a distance equal to the circumference of the wheel. Therefore, if the odometer recorded 254 revolutions, the distance covered by the bicycle is:

Distance = 254 x Circumference

Distance = 254 x 3.925 ft

Distance = 996.95 ft (rounded to two decimal places)

Therefore, the bicycle traveled approximately 996.95 feet.

The evaluation of the algebraic expression 8a-1+0.5b when a=1/4 and b=10 is 6.

We are given an expression 8a−1+0.5b8, and we are asked to evaluate it when a = 1/4 and b = 10. Substituting these values, we get:

8(1/4) - 1 + 0.5(10) = 2 - 1 + 5

Simplifying the expression on the right-hand side, we get:

8a−1+0.5b8 = 6

Therefore, when a = 1/4 and b = 10, the value of the expression 8a−1+0.5b8 is 6.

This means that if we substitute the given values for a and b, the resulting expression will have a value of 6. It is important to correctly substitute the values before evaluating the expression to obtain the correct answer.

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____The given question is incomplete, the complete question is given below:

Evaluate 8 a − 1 + 0.5 b 8a−1+0.5b8, a, minus, 1, plus, 0, point, 5, b when a = 1 4 a= 4 1 a, equals, start fraction, 1, divided by, 4, end fraction and b = 10 b=10b, equals, 10.

The probability of obtaining 10 or fewer families earning less than $35,000 per year in a simple random sample of 30 families from a large city with 45% of families in that income bracket is approximately 0.041 or 4.1%.

We can use the binomial distribution formula to calculate the probability of obtaining 10 or fewer families earning less than $35,000 per year in a simple random sample of 30 families from a large city where 45% of families earn less than $35,000 per year.

Let's denote the probability of a family earning less than $35,000 per year as "p", which is 0.45 in this case, and the number of trials or families sampled as "n", which is 30 in this case.

The probability of obtaining k families earning less than $35,000 per year in a simple random sample of 30 families can be calculated using the binomial distribution formula:

P(X ≤ 10) = Σ(i=0 to 10) [n choose i] * p^i * (1-p)^(n-i)

where n = 30, p = 0.45, and X is the random variable representing the number of families earning less than $35,000 per year in the sample.

Using a binomial calculator or software, we can calculate:

P(X ≤ 10) ≈ 0.041

Therefore, the probability that a simple random sample of 30 families will have 10 or fewer families earning less than $35,000 per year is approximately 0.041 or 4.1%.

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The fractions a. 5/7 b. 30/42 e. 45/84 are equivalent to 15/21.

       When it comes to fractions, equivalent means that both fractions show the same part of a whole. The numerator and denominator of equivalent fractions may be multiplied or divided by the same number or the number multiplied by the numerator and denominator should be the same.

 The following are steps to simplify fractions:

 First, find the greatest common factor (GCF) of both numbers.

And then divide both numbers by the GCF. The result is the simplified fraction.

            The greatest common factor of 15 and 21 is 3. By dividing both 15 and 21 by 3, the simplified fraction will be found.

                   15/21 = 5/7

 By dividing both 30 and 42 by 6, the simplified fraction will be found.

                     30/42 = 5/7

 By dividing both 45 and 84 by 3, the simplified fraction will be found.

       45/84 = (5/12)21/15 and 25/31 are not equivalent to 15/21.

     Therefore, the correct options are a. 5/7 b. 30/42 e. 45/84

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Answer:

200 times as large.

Step-by-step explanation:

To find out how many times 8 x 10^6 is as large as 4 x 10^4, we need to divide 8 x 10^6 by 4 x 10^4:

(8 x 10^6)/(4 x 10^4) = (8/4) x (10^6/10^4) = 2 x 10^2

Therefore, 8 x 10^6 is 200 times as large as 4 x 10^4.

Answer:

3x as large

Step-by-step explanation:

8 x 10^6 = 4800

4 x 10^4 = 1600

4800/3 = 1600

The volume for each cylinder, given the dimensions, is as follows:

1. r = 4 units, h = 6 units, V = 96π units².

2. r = 8 units , h = 3 units , V = 192π units².

3. r = 1 unit(half of the diameter), h = 5 units, V = 5 units².

4. r = 5 units, h = 7 units, V = 175π units².

The volume of a cylinder of radius r and height h is given by the equation presented as follows, in which the square of the radius is multiplied by π and the height, hence:

V = πr²h.

Then the equation is applied to each option in this problem with the given dimensions to obtain the volumes.

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As a result, during its flight, the football will strike the ground twice: once when it is kicked off and once more 3 seconds later.

A mathematical equation, including such 6 x 4 = 12 x 2, states that two quantities and values are equivalent. a meaningful noun. Equations are employed when two or more variables need to be added up and the results need to be computed in order to comprehend or explain the entire issue. As a result, the football will hit the ground twice during its flight: once after the game has kicked off and again three seconds later.

h =

0 = -16x² + 48x

0 = 16x(3 - x)

Either 16x or (3 - x) equals 0, which makes this equation equal to zero.

Hence, the answers to x are:

x = 0, when 16x = 0

when 3 - x = 0, x equals 3.

The football will therefore strike the ground twice during its flight—once when it is kicked off and once more 3 seconds later.

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The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

We are given that the line passes through the point (-8, 7) and has a slope of -5/4. So we can substitute these values into the slope-intercept form and solve for b:

y = mx + b

7 = (-5/4)(-8) + b

7 = 10 + b

b = -3

Therefore, the equation of the line in slope-intercept form is:

y = (-5/4)x - 3

The woman at the dinner party consumed 24 fluid ounces of wine containing approximately 4.8 standard drinks assuming the wine had an alcohol content of 12%. She exceeded the recommended limit for moderate drinking on that day.

Assuming each glass of wine contained 8 fluid ounces, the woman consumed a total of 24 fluid ounces of wine throughout the evening.

To determine the number of standard drinks ingested, we need to know the alcohol content of the wine. In the United States, a standard drink is defined as containing 0.6 fluid ounces or 14 grams of pure alcohol.

Assuming the wine had an alcohol content of 12% (which is a typical percentage for table wine), we can calculate the number of standard drinks ingested by using the following formula:

Number of standard drinks = (Volume of alcohol consumed in ounces x % alcohol by volume) / (0.6 ounces of alcohol per standard drink)

Number of standard drinks = (24 fl oz x 0.12) / 0.6 fl oz

Number of standard drinks = 4.8

Therefore, the woman consumed approximately 4.8 standard drinks.

To determine if she drank alcohol in moderation, we need to consider the recommended limits for moderate drinking. According to the National Institute on Alcohol Abuse and Alcoholism, moderate drinking is defined as up to one drink per day for women.

Since the woman consumed 4.8 standard drinks in one evening, she exceeded the recommended limit for moderate drinking for that day.

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Answer:

-0.2

Step-by-step explanation:

[tex]\frac{y2-y1}{x2-x1}[/tex]

^This here is how I calculated the slope^

Y2=4

Y1= 2

4-2= 2

X2=-7

x1=3

-7-3=-10

2/-10

or -2/10

Answer: 10 feet > 3 yards

Step-by-step explanation:

if 1 yard = 3 feet

then 3 yards = 9 feet

so 10 feet > 3yards

Answer:The equation of a line that passes through a point is an algebraic equation. It can also be referred to as the Slope-Intercept Equation.The equation of the line that passes through the point (4, 4) and has a slope of 0 is written as: y = 4 The equation of the line through a point (x1, y1) can be represented by the algebraic equation:y = mx + cwhere:m = slopec = y - interceptFrom the question,(x1, y1) = (4, 4)m = slope = 0Substituting these values into the algebraic equation,4 = (0 x 4) + c Hence, y = 4The equation of the line that passes through the point (4, 4) and has a slope of zero is y = 4

Answer:

y=4

Step-by-step explanation:

If a line has a slope of 0, then it is a horizontal line, and all points on the line have the same y-coordinate. We are given that the line passes through the point (4, 4). Therefore, the equation of the line in slope-intercept form is:

y = b

where b is the y-coordinate of the point through which the line passes. In this case, b = 4, so the equation of the line is:

y = 4

Therefore, the equation of the line in slope-intercept form is y = 4.

(Please could you kindly mark my answer as brainliest)

The following question is incomplete.

Please complete the question so it can be answered.

Without the actual Production possibility frontier table or chart we cannot determine the exact quantities.

However, based on the information provided, we can determine that the production combo of 9 pies and 8 tarts is a point on Daisy's PPF.

This means that Daisy can produce 9 pies and 8 tarts per week using her available resources of 5 lbs of flour.

To fully analyze production possibilities of Daisy, we would need to see her complete PPF, which would show all possible combinations of pies and tarts that she could produce with her resources.

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the function represents exponential decay with a rate of decrease of 5.9% per unit increase in x.

In the exponential function y = [tex]620(0.941)^x:[/tex]

The base of the exponent is 0.941, which is between 0 and 1.

As x increases, the value of [tex](0.941)^x[/tex]gets smaller and smaller, approaching 0 but never reaching it.

Therefore, the function represents exponential decay.

To determine the percentage rate of decrease, we can use the formula:

rate of decrease = (1 - base) x 100%

In this case, the base is 0.941, so the rate of decrease is:

rate of decrease = (1 - 0.941) x 100% = 5.9%

The exponential function is y = 620(0.941)^x.
To determine whether the function represents growth or decay, we need to look at the base of the exponential function, which is 0.941. Since this base is less than 1, the function represents decay.
To determine the percentage rate of decrease, we can use the formula:

r = (1 - b) x 100%
where r is the percentage rate of decrease, and b is the base of the exponential function.
In this case, b = 0.941, so we have:

r = (1 - 0.941) x 100%
= 0.059 x 100%
= 5.9%

Therefore, the exponential function y = 620(0.941)^x represents decay with a rate of 5.9% per unit of x.

A sort of mathematical function called exponential decay can be used to explain a quantity's decline across time or space. The quantity at any given time will change at a pace that is proportionate to the quantity itself, which is characterised by a decreasing rate of change. In other words, the amount of reduction decreases as time or space grows, but it never decreases to zero.

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y=620(0.941)^x y=620(0.941) x

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To make 2 gallons of a 20% salt solution, combine 0.86 gallons of the 12% salt solution and 1.14 gallons of the 26% salt solution.

Let x be the amount of the 12% salt solution needed in gallons, and y be the amount of the 26% salt solution needed in gallons to make 2 gallons of a 20% salt solution.

Based on the provided data, we can construct the following system of two equations:

X + y = 2 (total volume of the mixture is 2 gallons)

0.12x + 0.26y = 0.2(2) (total salt content of the mixture is 20% of 2 gallons)

Simplifying the second equation, we get:

0.12x + 0.26y = 0.4

Multiplying the first equation by 0.12 and subtracting it from the second equation, we get:

0.14y = 0.16

Y = 1.14

Substituting y = 1.14 into the first equation, we get:

X + 1.14 = 2

X = 0.86

In order to create 2 gallons of a 20% salt solution, 0.86 gallons of the 12% salt solution and 1.14 gallons of the 26% salt solution must be combined.

The complete question is:-

How much of a 12% salt solution must combined with a 26% salt solution to make 2 gallons of a 20% salt solution?

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We need to calculate the z-test score. It is a statistical test for inference that tests the null hypothesis that the mean of a sample from a normal population equals a specified value, and it is a test of statistical significance. Z-score: Z = (x - μ) / (σ / √n)μ = 3000, x = (2176 + 2784) / 2 = 2480, σ is the standard error of the mean, and n is the number of data points.

Z = (2480 - 3000) / (3000 / √n). The standard error of the mean (SEM) is calculated as follows: SEM = σ / √nσ = (2784 - 2176) / (2 × 1.96) = 303.64. Therefore, SEM = σ / √n=303.64 / √n(303.64 / √n) = (3000 - 2176) / 1.96n = 141.56n = 142Z = (2480 - 3000) / (303.64 / √142)Z = -12.95.

Since Z is less than -1.96, the test is significant at the 5% level of significance. Therefore, we can refuse the null hypothesis, and the alternative hypothesis is accepted. Therefore, the data support the alternate hypothesis that the number of burglaries per month is not equal to 3000.

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However, sin⁻¹ is defined to return an angle between -90° and 90°, so it returns the angle that is closest to 30° (which is 30° in this case).

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems related to geometry, physics, engineering, and many other fields. Trigonometry is based on the study of the six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions describe the ratios of the lengths of the sides of a right triangle, and can be used to calculate the unknown side lengths or angles of a triangle.

Here,

If sin 30° = 0.5, then sin⁻¹(0.5) is the angle whose sine is 0.5. In other words, we are looking for the angle whose sine is 0.5. Since sin 30° = 0.5, we know that one possible answer is 30 degrees. However, there are other angles that also have a sine of 0.5. One way to find the other angles is to use the inverse sine function, denoted as sin⁻¹. This function takes a value between -1 and 1 as its input and returns an angle between -90° and 90° as its output. So, if we want to find sin⁻¹(0.5), we are asking: what angle has a sine of 0.5?

The answer is: sin⁻¹(0.5) = 30°.

Note that there are other angles that also have a sine of 0.5, such as 150°, 390°, etc.

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Complete question:

Using the equality above, copy and complete the following:

The value of sin⁻¹ (0.5)​ when sin 30° = 0.5.

The area of the composite figure is 80ft².

Composite shapes may have overlaps between their perimeter and area.

Although we frequently define any shape's area through its perimeter, these two ideas are distinct. The area determines how much room the shape can store, while the perimeter merely draws the object's exterior border. Hence, the space that a shape encloses within its perimeter or boundary is its area.

Calculating the areas of various fundamental shapes is necessary to determine the area of a composite shape.

Breaking the form down is the easiest method:

Separate the composite shape into its constituent parts.

Each fundamental shape's area should be determined separately.

Add these areas together to determine the composite shape's area.

Here, first the area of the triangle:

1/2 × b × h

=1/2 ×(18-7-7) × 4

= 1/2 × 4 × 4

= 8ft².

Now, area of the rectangle:

b × l

= 4× 18

= 74ft².

Area of the whole figure = 8 + 72 = 80ft².

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Answer:

11/7: +9.42

Step-by-step explanation:

The remainder when a 90-digit number 9999 is divided by 89 is 0, as the result of applying the divisibility rule of 89, which involves reversing the digits of the number and subtracting the smaller from the larger.

To find the remainder when a 90-digit number 9999 is divided by 89, we can use the divisibility rule of 89. The rule states that for any integer n, the number obtained by reversing the digits of n and subtracting the smaller from the larger is divisible by 89.

In this case, we reverse the digits of 9999 to get 9999 again, and subtract the smaller from the larger to get 0. Since 0 is divisible by any number, including 89, the remainder when 9999 is divided by 89 is 0.

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Step-by-step explanation:

Which of the following shows an example of two irrational numbers being multiplied to get a rational number?

Responses

option c

The equation of the line of reflection that reflects shape P into shape Q is y = −2x + 12.

To find the equation of the line of reflection that reflects shape P into shape Q, we need to follow some steps:

Step 1: Draw the mirror line. To reflect a point or shape, we must have a mirror line. The mirror line is the line that passes through the reflection and is perpendicular to the reflecting surface. It serves as a reference for reflecting points or shapes.

Step 2: Find the midpoint of PQ. The midpoint of PQ is the point that lies exactly halfway between P and Q.

Step 3: Find the slope of PQ. The slope of PQ is the rise over run or the difference of the y-coordinates over the difference of the x-coordinates.

The slope formula is given by m = (y2 − y1) / (x2 − x1).

Step 4: Find the perpendicular slope of PQ. The perpendicular slope of PQ is the negative reciprocal of the slope of PQ. It is given by m⊥ = −1/m.

Step 5: Write the equation of the line of reflection. The equation of the line of reflection is given by y − y1 = m⊥(x − x1) or y = m⊥x + b, where m⊥ is the perpendicular slope of PQ and b is the y-intercept of the line. To find b, we substitute the coordinates of the midpoint of PQ into the equation and solve for b. Then we substitute m⊥ and b into the equation to get the final answer.

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Number of ways that  can we choose the officers, if individual members are allowed to hold 2 but not all 3 offices is 49,825

One member holds all three offices: There are 25 options for choosing the member who will hold all three offices.

Two members hold two offices each: There are 25 options for choosing the first member, and 24 options for choosing the second member (since one member cannot hold all three offices). Then, for the first member, there are 3 options for which offices they will hold, and for the second member, there are 2 options for which offices they will hold. Here we have to use the permutation. So the total number of ways is

25 × 24 × 3 × 2 = 36,000

Three members hold one office each: There are 25 options for choosing the first member, 24 options for choosing the second member, and 23 options for choosing the third member. So the total number of ways is

25 × 24 × 23 = 13,800

Therefore, the total number of ways to choose the officers is

25 + 36,000 + 13,800 = 49,825

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Arabella drive 17. 8 miles a day, Yaya drives 1. 6 times as far for each day. Therefore, 598.08 miles Yaya drive in three weeks.

Miles:

The mile, sometimes the international mile or the regulation mile, to distinguish it from other miles, is an imperial unit of the United Kingdom and a customary unit of distance in the United States; both are based on the old imperial unit of length, 5,280 imperial feet or 1,760 meters. The statute mile was standardized by an international agreement between the Commonwealth of Nations and the United States in 1959, when it was officially redefined as 1,609,344 meters in terms of SI units.

According to the Question:

We know that:

In a week there are 07 days

Therefore,

In 03 weeks there are = 7×3

                                     = 21 days

Given that :

Arabella drive 17.8 miles daily

and Yaya drives 1.6 times far from 17.8 miles daily.

Therefore,

Yaya drives = 17.8 × 1.6 miles

                    = 28.48 miles

Now,

for three weeks = 28.48 × 21

                           = 598.08 miles.

Therefore, 598.08 miles Yaya drive in three weeks.

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If we see the scatter plot we can conclude that the possible relation between x and y is linear and with a positive correlation since when the values of x increase the values for y increases as well.

[tex]Cov(x,y) =\frac{\sum_1^n(x_i-X')(y_i-Y')}{n-1}[/tex]

 [tex]\sum_1^5(6-16)(6-10)+(11-16)(9-10)....(27-16)(12-10)=106\\\\and\\Cov(x,y)=\frac{106}{4}=26.5\\\\r=0.693[/tex]

For this part we use excel in order to create the scatterplot and we got the result on the figure attached

If we see the scatter plot we can conclude that the possible relation between x and y is linear and with a positive correlation since when the values of x increase the values of y increase as well

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this

[tex]Cov(x,y) =\frac{\sum_1^n(x_i-X')(y_i-Y')}{n-1}[/tex]

:  

[tex]Cov(x,y) =\frac{\sum_1^n(x_i-X')(y_i-Y')}{n-1}[/tex]

 [tex]\sum_1^5(6-16)(6-10)+(11-16)(9-10)....(27-16)(12-10)=106\\\\and\\Cov(x,y)=\frac{106}{4}=26.5\\\\r=0.693[/tex]

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Answer:29160

Step-by-step explanation:

The value of x in the right triangle when calculated is approximately 13.8 units

Given the right-angled triangle

The side length x can be calculated using the following sine ratio

So, we have

sin(39) = x/22

To find x, we can use the fact that sin(39 degrees) = x/22 and solve for x.

First, we can use a calculator to find the value of sin(39 degrees), which is approximately 0.6293.

Then, we can set up the equation:

0.6293 = x/22

To solve for x, we can multiply both sides by 22:

0.6293 * 22 = x

13.8446 = x

Rewrite as

x = 13.8446

Approximate the value of x

x = 13.8

Therefore, x is approximately 13.8 in the triangle

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