Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36

The probability that a student is a science major, given they are a graduate student is given as follows:

P(science|graduate) = 0.7203 = 72.03%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes for this problem are given as follows:

Hence the probability that a student is a science major, given they are a graduate student is obtained as follows:

P(science|graduate) = 188/261

P(science|graduate) = 0.7203 = 72.03%.

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Answer:

0.72

Step-by-step explanation:

The approximate area of the park is given as follows:

450 blocks squared.

To obtain the area of a rectangle, you need to multiply the dimensions of the rectangle, which are the length and the width.

Hence the formula for the area of the rectangle is given as follows:

Area = Length x Width.

According to the map on the left, Central Park is about 50 blocks long by 9 blocks wide, hence the length and the width are given as follows:

Hence the area of Central Park is calculated as follows:

Area = 50 x 9

Area = 450 blocks squared.

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1 hot dog costs amount $8.00 and 1 hamburger costs $10.80.

Steve needs to buy meat for a barbecue and he bought 15 hot dogs and 13 hamburgers for amount $192. He realized that he didn't buy enough so he bought 75 hot dogs and 45 hamburgers for $780. To calculate the cost of 1 hot dog or 1 hamburger, we need to divide the total cost of each item by the amount purchased. For the hot dogs, we divide $780 by 75, which gives us $8.00. For the hamburgers, we divide $780 by 45, which gives us $10.80. Therefore, the cost of 1 hot dog or 1 hamburger is $8.00 and $10.80 respectively.

Hot Dogs :  ($192 + $780) / (15 + 75) = $8.00

Hamburgers : ($192 + $780) / (13 + 45) = $10.80

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The number of guests at a theme park can be modeled by the function p(t), where t is measured in hours and p is the number of guests. The function p(t) is a solution to the logistic differential equation.

The formula for logistic differential equation is dp/dt = p/3 - p^2/60000. This equation models the rate of change of the number of guests at the theme park over time.

To find the solution to this equation, we can use separation of variables. First, we can rearrange the equation to get:

dp/(p/3 - p^2/60000) = dt

Next, we can integrate both sides of the equation to get:

∫dp/(p/3 - p^2/60000) = ∫dt

Using partial fraction decomposition, we can rewrite the integral on the left-hand side of the equation as:

∫(3/60000)/(1 - 3p/60000)dp = ∫dt

Integrating both sides of the equation gives us:

-20000ln|1 - 3p/60000| = t + C

Solving for p gives us:

1 - 3p/60000 = Ce^(-t/20000)

3p/60000 = 1 - Ce^(-t/20000)

p(t) = 20000 - (20000C)e^(-t/20000)

To find the value of C, we can use the initial condition p(0) = p0:

p0 = 20000 - 20000C

C = (20000 - p0)/20000

Substituting this value of C back into the equation for p(t) gives us the solution:

p(t) = 20000 - (20000 - p0)e^(-t/20000)

This is the solution to the logistic differential equation that models the number of guests at a theme park over time.

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On the arranged survey, the statistical margin of error is supposed to be 14.73 SEK.

In a large consumer survey, 610 randomly selected customers are interviewed in a large grocery store. They are asked, among other things, how much they have shopped for. On average, they have shopped for 412 SEK with a standard deviation of 181 SEK .

Estimate with a 95% confidence interval the average purchase amount in the entire population. The formula for finding the margin of error is given as;

Margin of Error = z * (σ/√n)

Where:

σ is the standard deviation

n is the sample size

z is the Z-score for the desired confidence level, which is 95%.

Z-score corresponding to 95% confidence level is 1.96

Margin of Error = 1.96 * (181/√610) = 14.73

The statistical margin of error is 14.73 SEK.

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Finding the following percentiles for the standard normal distribution

a) P₁(61st percentile)

b) P₂(39th percentile)

c) P₃(75th percentile)

d) P₄(25th percentile)

e) P₅(15th percentile)

First of all, let's find the Z score of these percentiles with the help of the table below:

Z tableimage0.265 / 0.04 = 6.625.

This is greater than the maximum value in the table; hence we can consider it as 6.55.

P₁: When percentile is 61, z value is 0.42.

The formula to calculate percentile is as follows:

Percentile = Area to the left of Z score * 1000.42

= Area to the left of Z score * 1000.42 / 100

= Area to the left of Z score0.1664 (area to the left of Z score) + 0.5 = 0.6664 (area to the left of Z score)

P₁ = 66.64% P₂: When percentile is 39, z value is -0.26.

The formula to calculate percentile is as follows:

Percentile = Area to the left of Z score * 100-0.26

= Area to the left of Z score * 100-0.26 / 100

= Area to the left of Z score0.3950 (area to the left of Z score) + 0.5 = 0.8950 (area to the left of Z score)

P₂ = 89.50% P₃: When percentile is 75, z value is 0.68.

The formula to calculate percentile is as follows:

Percentile = Area to the left of Z score * 1000.68

= Area to the left of Z score * 1000.68 / 100

= Area to the left of Z score0.2486 (area to the left of Z score) + 0.5 = 0.7486 (area to the left of Z score)

P₃ = 74.86% P₄: When percentile is 25, z value is -0.68.

The formula to calculate percentile is as follows:

Percentile = Area to the left of Z score * 100-0.68

= Area to the left of Z score * 100-0.68 / 100

= Area to the left of Z score0.2486 (area to the left of Z score) + 0.5 = 0.7486 (area to the left of Z score)

P₄ = 25.14% P₅: When percentile is 15, z value is -1.04.

The formula to calculate percentile is as follows:

Percentile = Area to the left of Z score * 100-1.04

= Area to the left of Z score * 100-1.04 / 100

= Area to the left of Z score0.1492 (area to the left of Z score) + 0.5 = 0.6492 (area to the left of Z score)

P₅ = 64.92%.

Hence, we have found the percentiles of standard normal distribution for the given questions.

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It would cost approximately $45.14 to drive 225 miles in a rental car that gets 29 miles per gallon.

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

First, we convert the gas price from liters to gallons. One liter is equal to 0.264172 gallons, so:

$1.54 per liter = $1.54 / 0.264172 gallons = $5.82 per gallon

Next, we need to calculate how many gallons of gas are needed to drive 225 miles. If the car gets 29 miles per gallon, we can calculate the gallons of gas needed as:

225 miles / 29 miles per gallon = 7.7586 gallons

Finally, we can calculate the total cost of gas as:

Total cost = gallons of gas needed x gas price per gallon

Total cost = 7.7586 gallons x $5.82 per gallon

Total cost = $45.14

Therefore, it would cost approximately $45.14 to drive 225 miles in a rental car that gets 29 miles per gallon, assuming a gas price of $1.54 per liter in France.

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The converted height of Pat’s pen pal in feet and inches when it is 1.27 meters tall is given by 4  feet 2 inches.

Height of Pat’s pen pal  = 1.27 meters

Convert the height from meters to centimeters,

1 meter = 100 centimeters

Multiply by 100 to convert meters to centimeters we get,

1.27 meters

= 1.27 x 100

= 127 centimeters

Convert the height from centimeters to inches

1 inch = 2.54 centimeters

Divide by 2.54 to convert centimeters to inches we get,

127 centimeters

= 127 centimeters ÷ 2.54

= 50 inches

Convert the total number of inches to feet and inches,

1 feet = 12 inches

Divide by 12 to convert inches to feet and inches we have,

50 inches

= 50 ÷ 12

= with 4 quotient and 2 remainder

= 4  feet 2 inches tall

Therefore, Pat's pen pal is 4 feet and 2 inches tall.

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Answer:

Step-by-step explanation:

[tex]-13-23=-13+(-23)[/tex]    (add -23 instead of subtracting +23)

          [tex]=-36[/tex]

[tex]-13-(-23)=-13+(23)[/tex]   (add +23 instead of subtracting -23)

          [tex]=10[/tex]          

The equations that are equivalent to 5 - (6 - 2x) = (3x+4)/2 are  -1 + 2x = (3x+4)/2; and 30 - 10x = (3x+4)/2 .

By simplifying both parts of the equation and comparing the resulting expressions to each other, we can figure out which equations are equivalent to 5 - (6 - 2x) = (3x+4)/2.

5 - (6 - 2x) = (3x+4)/2

5 - 6 + 2x = 3x/2 + 2

2x - 1 = 3x/2 + 2

To get rid of the fraction, multiply both parts by two.

4x - 2 = 3x + 4

Adding 2 to both ends and subtracting 3 times:

x = 6

Let's verify which of the provided equations is equal to x = 6 now.

-1 + 2x = (3x+4)/2, where x = 6 results in:

-1 + 2(6) = (3(6) + 4)/2 \s11 = 11

The initial equation and this one are equivalent, and both are correct.

When we change x to 6, we obtain the following equation: 30 - 10(6) = (3(6) + 4)/2 -30 = -30.

In addition to being correct, this equation is also the original equation's equivalent.

If we substitute 6 for x, we obtain the following equation: 5-(6 - 2(6)) = 3/2(6)+2 1 = 8

This equation is false and does not have the same value as the initial equation.

When we replace x with 6, we obtain the formula 5- (6 - 2(6)) = 3(6)+4

3 = 22

Additionally, this equation is false and is not equal to the initial equation.

2 + 4x = 3x + 4:

When x = 6 is substituted, the result is: -2 + 4(6) = 3(6) + 4 (20) = 22.

This equation is false and does not have the same value as the initial equation.

As a result, the formulae corresponding to 5 - (6 - 2x) = (3x+4)/2 are: -1 + 2x = (3x+4)/2 30 - 10x = (3x+4)/2

A) -1 + 2x = (3x+4)/2; and C) 30 - 10x = (3x+4)/2 are the solutions.

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Answer:

to find x u will do : 61+132+x=1290

x=1290-193

x=1097

The total amount of water Carlos drank throughout the day is 2.65 liters.

In order to calculate the total amount of water Carlos drank throughout the day, we must add all the amounts that he drank. The total amount of water Carlos drank during the day is equal to:

1/5 liters + 3/4 liters + 7/20 liters

This can be expressed in fraction form as:

[tex]\frac{19}{20} + \frac{27}{20} + \frac{7}{20} = \frac{53}{20}[/tex]

= 2.65 liters

Therefore, Carlos drank a total of 2.65 liters of water throughout the day.

To calculate this, we can use the addition of fractions formula. This formula states that to add two fractions, we must find the least common denominator of the two fractions, and then add the numerators of the two fractions.

In this case, the least common denominator of the three fractions is 20. This is because all three fractions have a denominator of 20, and 20 is the smallest number that can be divided by both 5 and 4.

Once we have the least common denominator, we can add the numerators of the fractions. For the first fraction, 1/5, the numerator would be 1, for the second fraction, 3/4, the numerator would be 3, and for the third fraction, 7/20, the numerator would be 7.

Therefore, the addition of fractions formula would look like this:

[tex]\frac{1 + 3 + 7}{20}\\\\ = \frac{11}{20}\\\\ = 2.65 liters[/tex]

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The tοtal area οf the shape cοmprising the rectangle and semicircle is apprοximately 2153.43 square feet.

Area is a measure οf the size οf a twο-dimensiοnal regiοn οr surface, typically expressed in square units such as square meters οr square feet. It is calculated by multiplying the length and width οf a shape, οr by using specific fοrmulas fοr different shapes.

The area οf a rectangle with sides 30' and 60' is given by multiplying the length and width, sο:

Area οf rectangle = length × width

Area οf rectangle = 30' × 60'

Area οf rectangle = 1800 square feet

The area οf a semicircle with radius 15' can be fοund by first calculating the area οf a full circle with radius 15' and then dividing by 2, since a semicircle is half οf a circle. The fοrmula fοr the area οf a circle is:

Area οf circle = π × radius²

Substituting the value οf the radius intο the fοrmula, we get:

Area οf circle = π × 15²

Area οf circle = π × 225

Area οf circle ≈ 706.86 square feet

Therefοre, the area οf the semicircle is apprοximately:

Area οf semicircle = (1/2) × Area οf circle

Area οf semicircle ≈ (1/2) × 706.86

Area οf semicircle ≈ 353.43 square feet

The tοtal area οf the shape cοmprising the rectangle and semicircle is the sum οf the areas οf the twο shapes, sο:

Tοtal area = Area οf rectangle + Area οf semicircle

Tοtal area = 1800 + 353.43

Tοtal area ≈ 2153.43 square feet

Therefοre, the tοtal area οf the shape cοmprising the rectangle and semicircle is apprοximately 2153.43 square feet.

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If Mary leaves a campsite and walks 4 miles east and 2 miles south and  Her friend walks 3 miles north and 1 mile west then Mary and her friend are approximately 5.83 miles apart.

We can use the Pythagorean theorem to find the distance between Mary and her friend. We'll need to create a right-angled triangle with the two walks forming the legs of the triangle.

Mary walks 4 miles east and 2 miles south, so she moves 4 units to the right (east) and 2 units down (south).

Her friend walks 3 miles north and 1 mile west, so she moves 3 units up (north) and 1 unit to the left (west).

We can see that the two walks form a right-angled triangle. The distance between Mary and her friend is the hypotenuse of this triangle.

Let's calculate the length of each leg of the triangle:

The length of the horizontal leg is 4 - 1 = 3 miles (Mary moves 4 miles to the right and her friend moves 1 mile to the left).

The length of the vertical leg is 2 + 3 = 5 miles (Mary moves 2 miles down and her friend moves 3 miles up).

Now, we can use the Pythagorean theorem:

distance² = 3² + 5²

distance² = 9 + 25

distance² = 34

distance = √(34)

≈ 5.83 miles

Therefore, Mary and her friend are approximately 5.83 miles apart.

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The complement of the given event is that 29% of the person's credit card purchases are less than seventy dollars.

To describe the complement of the given event, we need to first understand what complement means in probability theory. The complement of an event is the set of outcomes that are not included in the event.

So, the given event is that 71% of a person's credit card purchases are seventy dollars or more. This means that 100% - 71% = 29% of the person's credit card purchases are less than seventy dollars. This is the complement of the given event.

Hence, the complement of the given event is that 29% of the person's credit card purchases are less than seventy dollars.

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The equation that is true when x is equal to 3 is (x/3) = 1. By substituting the given x value and simplifying the equation we can solve.

Division is a mathematical operation that is used to split a quantity or value into equal parts or groups. It is one of the four basic arithmetic operations, along with addition, subtraction, and multiplication.

The equation that is true when x = 3 is:

x/3 = 1

Substituting x = 3, we get:

3/3 = 1

Which is true, since 3 divided by 3 is equal to 1.

The other equations:

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Round to the nearest whole number A company sold 200 devices in 2007.

Number is a mathematical concept that can be used to represent an amount, value, or quantity. It is an abstract concept that can be used to count, measure, and compare. Numbers can be represented in many different forms such as words or symbols. Numbers are also used in algebra and other mathematical operations, as well as in everyday life.

The company sold 180 devices in 2008. The number of devices that the compnay sales is decreasing exponentially. If this trend continues, How many devices will the company sell in 2012?
Round to the nearest whole number. Based on the trend of the company's sales, it is estimated that the company will sell approximately 140 devices in 2012. This is a decrease of 40 devices from the sales in 2008. This trend is expected to continue into future years due to the exponential decrease in the number of devices sold.

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Rounding to the nearest whole number, the company will sell 75 devices in 2012.

Number is a mathematical concept that can be used to represent an amount, value, or quantity. It is an abstract concept that can be used to count, measure, and compare. Numbers can be represented in many different forms such as words or symbols. Numbers are also used in algebra and other mathematical operations, as well as in everyday life.

To calculate the number of devices that the company will sell in 2012 using an exponential model, we can use the following equation:

y = 200e(-0.08x)

where y is the number of devices sold, 200 is the number of devices sold in 2007, and 0.08 is the rate of decay per year.

Plugging in x=5 (for 2012), we get:

y = 200e(-0.08×5) = 200e(-0.4) = 74.7

Rounding to the nearest whole number, the company will sell 75 devices in 2012.

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Step-by-step explanation:

To find the minimum height of the satellite during the given time period, we need to find the vertex of the parabolic function f(x) = 2x^2 - 16x + 800.

The vertex of a parabola with equation f(x) = ax^2 + bx + c is given by the formula:

x = -b / 2a and f(x) = -b^2 / 4a + c

In this case, a = 2, b = -16, and c = 800. Substituting these values into the formula, we get:

x = -(-16) / 2(2) = 4

f(x) = -(-16)^2 / 4(2) + 800 = 848

Therefore, the minimum height of the satellite during the given time period is 848 kilometers, and it occurs after 4 hours of flight time.

Answer:A. y = 0.6^x - 2

Step-by-step explanation:

This was something I put in and It worked fine. Hope this helps. If you want more help, check out Khan Academy.

From the graph, the equation that's is represented is A. 0.6x - 2.

From the equation, on the coordinate plane, the curve opens up and to the right. It crosses the x-axis at (negative 1.5, 0) and then crosses the y-axis at (0, negative 1).

Here, based on the family the graph below belongs to, the equation represented is the first equation which is 0.6x - 2.

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Answer:

Javier has $5. He sells a video game on an online auction site for $100. He must pay a $16 fee to the auction site. Javier then splits the.   Not sure

Step-by-step explanation:

The expressiοn 2(x-1)(x+1)/(-x-20) can be written as 2(x+1)/(x-5).

Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.

Tο simplify the expressiοn 2(x-1)(x+1)/(-x-20), yοu can fοllοw these steps,

Factοr the denοminatοr, (-x-20), tο get (x-5)(x+4).

Rewrite the numeratοr as 2(-1).

Substitute the factοred denοminatοr frοm step 1 intο the expressiοn, giving 2(-1)/[(x-5)(x+4)].

Factοr the numeratοr, 2(x-1)(x+1), and cancel οut the cοmmοn factοr οf (x-1) frοm the numeratοr and denοminatοr.

sο we get as, The final simplified expressiοn is 2(x+1)/(x-5).

Therefοre, The final simplified expressiοn is 2(x+1)/(x-5).

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After solving the inequalities, the values of x are [x<3/4] and [x>-1] respectively.

We can learn about the relative size of values via inequality.

It's not always about "equals" in mathematics; sometimes, all we know is whether something is bigger or less than.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made.

So, solve for x as follows:

3-4x<0

-4x< -3

x = -3/-4

x < 3/4

Similarly,

2x-4>-2

2x>-2+4

2x>2

x>-2/2

x>-1

Therefore, after solving the inequalities, the values of x are [x<3/4] and [x>-1] respectively.

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Answer: (-6,-4)

Step-by-step explanation:

Midpoint formula

(x,y) midpoint= ((x1+x2)/2, (y1+y2)/2)

X: (0-12)/2=-6

Y: (0-8)/2=-4

(-6,-4)

Answer:

A

Step-by-step explanation:

lucky for u, finding the midpoint is really easy to learn and master

alright so first you take a look at both points. we got:

-       (0,0)

-       (12,8)

we need to add the x coordinates

0+12 = 12

then divide by 2

12/2 = 6

6 the x coordinate for our segment midpoint

now we need to add the y coordinates

0+8 = 8  

divide by 2

8/2 = 4

4 is the y coordinate for our segment midpoint

How now we combine the x value and y value to create a coordinate:

(6,4)

That matches choice A

Hence, in respοnse tο the prοvided questiοn, we can say that  12x - 8 can  functiοn be factοred οut as 4(3x - 2), where 4 is a cοmmοn factοr οf 12 and 8, and (3x - 2) is the expressiοn that remains after factοring οut 4.

Mathematicians research numbers and their variants, equatiοn and related structures, οbjects and their lοcatiοns, and prοspective lοcatiοns fοr these things. The term "mοdule" is used tο describe the cοnnectiοn that exists in between set οf inputs, each οf which has a cοrrespοnding οutput. A functiοn is an input-οutput cοnnectiοn in which each inputs results in sοmething like a single, distinct return. A dοmain, cοdοmain, οr scοpe is assigned tο each functiοn. Functiοns are usually denοted by the letter f. (x). An x is used fοr entry. On capabilities, οne-tο-οne capabilities, multiple prοwess, in capabilities, and οn capabilities are the fοur majοr types οf accessible functiοns.

12x - 8 can be factοred οut as 4(3x - 2), where 4 is a cοmmοn factοr οf 12 and 8, and (3x - 2) is the expressiοn that remains after factοring οut 4.

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Complete question:

We can describe 12x-8 as an expression.

It can also be written as 4(3x-2)

4(3x-2) is a ___ of 12x-8.

What is the blank?

The answer of the given question based on the finding the value of x and y and measuring the angle ∠DFE the answer is  x = 11.8 and y = -8 and angle ∠DFE is 88° degrees.

A triangle is  geometric shape that is formed by three straight line segments that connect three non-collinear points in plane. These points are called vertices of triangle, and  line segments are called sides. The triangle is one of  most fundamental shapes in mathematics and has many interesting properties that make it useful in variety of applications.

Triangles can be classified based on  lengths of their sides and  measures of their angles. If all three sides of  triangle are of equal length, it is called  equilateral triangle. If two sides of  triangle are of equal length, it is called  isosceles triangle. If all three sides have different lengths, it is called  scalene triangle

In triangle DEF, we know that the sum of the angles is 180° degrees, so:

∠DEF + ∠DFE + ∠EFD = 180°

Substituting the given values, we have:

92° + (5x - 7) + 36° = 180°

Simplifying the equation, we get:

5x + 121 = 180

5x = 59

x = 11.8

Now we know x, then we can find y:

y = 180 - 92 - 36 - (5x - 7) = 45 - 5x

y = 45 - 5(11.8) = -8

Therefore, x = 11.8 and y = -8.

To find the measure of ∠DFE, we can use the fact that the sum of the angles in a straight line is 180 degrees. ∠DFE is opposite to angle D, which is 92°, so:

∠DFE = 180° - 92° = 88°

Thus, the measure of ∠DFE is 88° degrees.

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4 + 7×6 = 4 + 42 = 46

12 + 9×3 - 1 = 12 + 27 - 1 =39 - 1 = 38

The required length of the arc is 5.75 units.

A circular represents 360 degrees. A circular can be split up into smaller sections. An arc is a segment of a circle, and arcs are designated based on their angles. The three types of arcs are semicircles (v = 180°), major arcs (180° v 360°), and minor arcs (0° v 180°).

We have;

∠EFG =30° = π/6

and EF =11 units

To find; length of arc EG.

So, we know that;

∅(Radian) = arc/ radius

π/6 = arc/11

arc = 11π/6

Arc = 5.75 units.

Thus, required length of the arc is 5.75 units.

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Complete question:

Answer:

3.7

Step-by-step explanation:

Hypotenuse is 5

Adjacent is unknown x

Cos 42 = adjacent / hypotenuse

Co's 42 = x/ 5

0.74 = x/5

Multiply both sides by 5

3.7 = x