A system of linear equations and a reduced matrix for the system are given. 1 0 Nm 1 x - y + z = 3 3x + 2z = 7 (x - 4y + 2z = 5 0 1 0 1 Use the reduced matrix to find the general solution of the system, if one exists. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answers in terms of z as in Example 3.) (x, y, z) = ( (x, y, z) = *) (b) If multiple solutions exist, find two specific solutions. (Enter your answers as a comma-separated list of ordered triples. If there is no solution, enter NO SOLUTION.) (x, y, z) =

Diameter = 16 mm

Radius = Diameter/2

= 16/2

= 8 mm

Total height of figure = 32 mm

Height of cylinder = 19 mm

Height of cone = 32 - 19

= 13 mm

Volume of cylinder = πr²h

Substituting the values of r and h in above formula,,

[tex] \longrightarrow \sf \pi \times {(8)}^{2} \times 19 \\ \\ \longrightarrow \sf \pi \times 64 \times 19 \\ \\ \longrightarrow \sf 1216 \pi \\ \\ \longrightarrow \sf 3820.17 \: mm^{3}\\ \\ [/tex]

Hence, Volume of cylinder is 3820.17 mm³

Now,

Volume of cone = 1/3 πr²h

[tex] \longrightarrow \sf \dfrac{1}{3} \times \pi \times {(8)}^{2}\times 13 \\ \\ \longrightarrow \sf \dfrac{1}{3} \times \pi \times 64 \times 13 \\ \\ \longrightarrow \sf 871.26~ mm^3 \\ \\ [/tex]

Hence, Volume of the cone is 871.26 mm³

Volume of composite figure = Volume of cylinder + Volume of cone.

= 3820.17 + 871.26

= 4691.43 mm³

Therefore, Volume of the composite figure is 4691.43 mm³.

The five-number summary for this data set is 36, 38.5, 50.5, 53, and 57, and the interquartile range is 14.5.

Measures of statistical dispersion, or the spread of the data, include the interquartile range. In addition to the IQR, other names for it include the midspread, middle 50%, fourth spread, and H-spread.

To find the five-number summary and interquartile range for this data set, we first need to find the quartiles.

Step 1: Find the median (Q2)

When a data collection is sorted from least to largest, the median is the midway value. Since there are 12 values in this data set, the median is the average of the sixth and seventh values:

Median (Q2) = (50 + 51)/2 = 50.5

Step 2: Find the lower quartile (Q1)

The lower quartile is the median of the lower half of the data set. Since there are 6 values below the median, we take the median of those values:

Q1 = (38 + 39)/2 = 38.5

Step 3: Find the upper quartile (Q3)

The upper quartile is the median of the upper half of the data set. Since there are 6 values above the median, we take the median of those values:

Q3 = (53 + 53)/2 = 53

Now we have all the information we need to construct the five-number summary and interquartile range:

Minimum: 36

Lower quartile (Q1): 38.5

Median (Q2): 50.5

Upper quartile (Q3): 53

Maximum: 57

Interquartile range (IQR) = Q3 - Q1 = 53 - 38.5 = 14.5

the five-number summary for this data set is 36, 38.5, 50.5, 53, and 57, and the interquartile range is 14.5.

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Answer:

4th degree

Step-by-step explanation:

When you are looking for the degree of an expression or equation, you just look for the biggest exponent.

Here, there is an

"x to the 4th power",

a "minus3 to the second power" and

a "9x" (which is a power of 1)

So the biggest exponent is 4...4th degree. That's it!

A total of 5 glove prices meet the condition of having an absolute deviation from the mean of $8 or less.

To find the mean price, we need to sum up all the glove prices and divide by the total number of gloves.

Sum of glove prices = $55 + $42 + $28 + $39 + $82 + $25 + $40 + $32 + $45 + $38 + $52 + $34 = $512

Total number of gloves = 12

Mean price = Sum of glove prices / Total number of gloves = $512 / 12 = $42.67

To find the absolute deviation of each glove price from the mean, we subtract the mean from each price and take the absolute value.

Absolute deviation from mean for each glove = |Price - Mean price|

For example, for the first glove price of $55, the absolute deviation from the mean is |$55 - $42.67| = $12.33

We want the absolute deviation to be at most $8, so we need to find how many glove prices have an absolute deviation from the mean of $8 or less.

We can calculate the absolute deviation for each glove price and count how many are less than or equal to $8.

First row:

|$55 - $42.67| = $12.33

|$42 - $42.67| = $0.67

|$28 - $42.67| = $14.67

|$39 - $42.67| = $3.67

|$82 - $42.67| = $39.33

|$25 - $42.67| = $17.67

Out of the 6 glove prices in the first row, 2 have an absolute deviation from the mean of $8 or less.

Second row:

|$40 - $42.67| = $2.67

|$32 - $42.67| = $10.67

|$45 - $42.67| = $2.33

|$38 - $42.67| = $4.67

|$52 - $42.67| = $9.33

|$34 - $42.67| = $8.67

Out of the 6 glove prices in the second row, 3 have an absolute deviation from the mean of $8 or less.

Therefore, a total of 5 glove prices meet the condition

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The given condition is incomplete, the complete question is:

a baseball player wants to buy a new glove. the table shows the prices of several gloves. the player is willing to pay the mean price with an absolute deviation of at most $8. how many of the glove prices meet this condition?

The function f(x) has a decreasing end behaviour on the right when its leading coefficient is negative and its degree is greater than or equal to 2.

This means that the terms in the function must be decreasing from left to right and the last term must be negative. To illustrate, an example of a function with a decreasing end behaviour on the right could be

f(x) = -2x2 + 3x + 4.

The leading coefficient is -2, which is negative, and the degree is 2, which is greater than or equal to 2. The terms decrease from left to right, and the last term is negative, which both fulfil the requirements for the function to have a decreasing end behaviour on the right.

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The factors that could be part of the function so that the function has a decreasing end behavior on the right are as follows: - A negative coefficient of the highest degree term.

- An odd degree of the highest degree term and a negative coefficient.
- An even degree of the highest degree term and a negative coefficient.
Explanation:
A function's end behavior refers to what happens to the function's values as x approaches positive or negative infinity. A function's end behavior is said to be decreasing if the values of the function decrease as x approaches infinity, and increasing if the values of the function increase as x approaches infinity.
There are three cases when the function has a decreasing end behavior on the right:

1. If the highest degree term has a negative coefficient, the function will have a decreasing end behavior on the right. For example, the function f(x) = -2x³ - 4x² + 3x + 6 will have a decreasing end behavior on the right.
2. If the highest degree term is odd and has a negative coefficient, the function will have a decreasing end behavior on the right.

For example, the function f(x) = -x⁵ + 2x³ - x will have a decreasing end behavior on the right.
3. If the highest degree term is even and has a negative coefficient, the function will have a decreasing end behavior on the right. For example, the function f(x) = -4x⁶ + 3x⁴ - 2x² + 1 will have a decreasing end behavior on the right.

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The value of 50.7 / 7 is approximately equal to 7.24285714.

The given expression is 50.7 / 7.

Creating equal groupings or determining how many individuals are in each group after a fair distribution is the basic objective of division.

To simplify the expression, we need to perform the division operation.

In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

To solve this, we can perform the following steps:

First, we can write the given expression as:

50.7 ÷ 7

Then, we can perform the division operation as shown below:

50.7 ÷ 7

= 7.24285714 (rounded to 8 decimal places)

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Answer:

6y

Step-by-step explanation:

because if u divde

Answer:

 (2,0). First use a graphing calculator called demos. graph the y=5x-10

Once you graph the equation. Look for the cooordinates of the graph. One the coordinates are 2,0

Step-by-step explanation: Hope this helps!! Mark me brainliest!! Have a great spring break!! :))

The density of the textbook which is in the rectangular prism with dimensions is 0.0738 grams per cubic centimeter.

Define density.

Density is the mass of a component per unit volume.

       →d = M/V,

where d is density, M is mass, and V is volume, is the expression for density. Grams per cubic centimeter are a standard unit of measurement for density.

 The volume of a component = length*breadth*height

Given:

length = 16cm; breadth = 10cm; height = 5cm; Mass = 59grams

The volume of the book = 16 * 10 * 5

                                         = 800 cm³

The density of the textbook = Mass/volume

                                               = 59/800

                                  Density = 0.07375 g/cm³

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The percentage of fat in a 200 calorie peanut butter sandwich is 40%.

To find the percentage of fat in a 200 calorie peanut butter sandwich if the total amount of calories of fat are 80 calories, we need to use the formula:

Percentage of fat = (Calories of fat / Total calories) x 100

Let's substitute the given values in the above formula:

Calories of fat = 80

Total calories = 200

Percentage of fat = (80/200) x 100 = 40%

Therefore, the percentage of fat in a 200 calorie peanut butter sandwich is 40%.

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The probability that at least three students seek assistance in 10 days is approximately 0.117.

We can use the Poisson distribution to model the number of students who seek assistance in 10 days. Let X be the number of students who seek assistance in 10 days.

Then X follows a Poisson distribution with parameter λ=2.4, where λ is the mean number of students who seek assistance per day multiplied by 10 (the number of days).

Using the Poisson probability formula, we can calculate the probability of at least three students seeking assistance:

P(X ≥ 3) = 1 - P(X < 3) = 1 - [P(X=0) + P(X=1) + P(X=2)]

We can find that:

P(X ≥ 3) = 0.117

Therefore, the probability that at least three students seek assistance in 10 days is approximately 0.117.

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Therefore, the correct answer is option D: "The wire is on the cylinder axis and carries current i in the direction opposite to that of the current in the shell. "Option E, "the wire does not carry any current," is not correct because the wire is in a region with a magnetic field, and therefore will have an induced current.

we are asked to determine the position and direction of the wire that is parallel to the cylinder axis in the hollow region. The long straight cylindrical shell has an inner radius R and an outer radius Ro, and carries a current i that is uniformly distributed over its cross section. The wire is located in the hollow region, which is defined as r > R and r < Ro.

Based on this information, we can determine the position and direction of the wire.To begin, we know that the wire must be on the cylinder axis since it is parallel to the axis. This eliminates options A, B, and C. Additionally, we know that the current in the wire must be in the opposite direction to the current in the shell. This is because the magnetic field created by the current in the shell will induce a current in the wire that is opposite in direction in order to create a repulsive force.

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The elements of the sequence that are divisible by 5 occur every third term, while the elements divisible by 13 occur every fourth term. There are no elements of the sequence that are divisible by 65, since there are no elements that are divisible by both 5 and 13.

To find which elements of the sequence are divisible by 5, we need to find the remainder of each element when divided by 5. Using the first few terms of the sequence, we get:

a₁ = -1, a₂ = 0, a₃ = 5, a₄ = 13, a₅ = 29, a₆ = 61, a₇ = 125, a₈ = 253, ...

To check if an element is divisible by 5, we only need to look at the units digit of the number, since any multiple of 5 ends in 5 or 0. From the sequence, we can see that the units digit of a₃ is 5, so a₃ is divisible by 5. To find any other elements that are divisible by 5, we can look for a pattern in the units digits of the terms. We can see that the units digits of the terms cycle through 5, 3, 1, and 9. Since 5 appears in the cycle, every third term of the sequence will be divisible by 5. Therefore, the only elements of the sequence that are divisible by 5 are a₃, a₆, a₉, a₁₂, and so on.

To find which elements of the sequence are divisible by 13, we can use a similar approach. We need to find the remainder of each element when divided by 13. From the sequence, we can see that the units digit of a₄ is 3, so a₄ is not divisible by 13. To find any other elements that are divisible by 13, we can look for a pattern in the remainders of the terms. We can see that the remainders cycle through 3, 8, 6, and 10. Since 10 appears in the cycle, every fourth term of the sequence will be divisible by 13. Therefore, the only elements of the sequence that are divisible by 13 are a₄, a₈, a₁₂, a₁₆, and so on.

To find if any elements of the sequence are divisible by 65=5.13, we need to find elements that are divisible by both 5 and 13. From our analysis above, we can see that a₃ is the only element of the sequence that is divisible by 5, and a₄ is the only element that is divisible by 13. Therefore, there are no elements of the sequence that are divisible by 65, since the only way a number can be divisible by 65 is if it is divisible by both 5 and 13.

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Complete question:

Consider the sequence a₁ = = 2¹-3=-1₁ -2²-3=1, 0₂= 03 =2³-3=5, 04-2¹-3=13, ⠀ a₁ = 2" - 3, defined for positive integers n. Which elements of this sequence are divisible by 5? What about 13? Are any elements of this sequence divisible by 65= 5. 13? Why or why not?​

If a triangular pyramid has a base shaped like an equilateral triangle. its surface area is: 120.41 square feet.

To solve this problem, we can use the formula for the surface area of a pyramid:

Surface area = base area + (1/2) x perimeter of base x slant height

First, we need to find the area of the base, which is an equilateral triangle. The formula for the area of an equilateral triangle is:

Area = (square root of 3) / 4 x (side length)^2

Substituting the given values, we get:

Area = (square root of 3) / 4 x 9^2

Area = (square root of 3) x 20.25

Area = 11.06 (rounded to two decimal places)

Next, we need to find the perimeter of the base, which is simply 3 times the side length:

Perimeter = 3 x 9

Perimeter = 27

Finally, we can use the given slant height to find the surface area:

Surface area = 11.06 + (1/2) x 27 x 8.1

Surface area = 11.06 + 109.35

Surface area = 120.41 square feet (rounded to two decimal places)

Therefore, the surface area of the triangular pyramid is approximately 120.41 square feet.

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log5 x∧4 + log5 2x - log5 3x - correct. The property of logarithms to be used a log b = log a∧b.

A logarithm is a mathematical function that represents the relationship between the logarithm of a number and its actual value. In simpler terms, a logarithm is the exponent to which a base must be raised to get a certain value.

4 log5 x + log5 2x - log5 3x

Marta incorrectly applied a property of logarithms at step 1:

log5 4x + log5 2x - log5 3x - incorrect

log5 x∧4 + log5 2x - log5 3x - correct

The property of logarithms to be used:

a log b = log a∧b.

Therefore at step 1 she incorrectly applied.

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The percentage of people aged 55-64 who answered “yes” was slightly lower (50%), followed by people aged 65-74 (45%) and people over 75 (43%).

Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol “%” and is used to compare values or express change. It can be used to compare two or more numbers, to show how much one number is a percentage of another, or to indicate the rate of change. In mathematics, percentages are often used to compare the size of one number to the size of another number.

The bar chart shows that the percentage of people who responded “yes” to listening to audiobooks increases with age. Only 18% of people aged 18-24 said they listen to audiobooks, while 30% of people aged 25-34 and 44% of people aged 35-44 responded positively. The percentage continues to increase with age, with the highest percentage of people aged 45-54 saying they listen to audiobooks (54%).
The percentage of people aged 55-64 who answered “yes” was slightly lower (50%), followed by people aged 65-74 (45%) and people over 75 (43%).

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No, since the ratios do not constitute a whole. Option(a) is the required response to the posed query.

A collection of categorical data can be summarised using a bar chart, and continuous data can be made categorical using auto-binning. The bar chart uses several bars to show data, with each bar denoting a distinct category.

A pie chart, also known as a circle chart, is a visual representation of the various values of a given variable or a way to summarise a collection of nominal data. This kind of chart consists of a circle with numerous parts. A specific group is represented by each segment. A pie chart is useful for organising and displaying data by proportion of the total.

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The rest of the question is,

Would it be appropriate to display the data with a pie chart?

a). No, because the proportions are not parts of a whole.

b). No, because the data categories are too broad.

c). Yes, because the data are grouped into categories.

d). Yes, because the data can be represented by a relative frequency compared to the whole.

Therefore , the solution of the given problem of arithmetic mean comes out to be A(n) = 130 + (n - 1)13  = 286 inches.

The usual values of a list are determined by adding up every single integer one of the items on the list, which are frequently referred to as the organization's objectives. The number of list items with the highest abundance is then used to adjust these average values. Mathematical growth trends are similar. The number 21 turns into seven by adding three to the true means of the digits 5, 7, and 9, which is 4.

Here,

We can use the explicit formula for an arithmetic sequence to symbolize the height of the bamboo plant after "n" days:

=> A(n) = a + (n - 1)d

Therefore, the following explicit method can be used to determine the height of the bamboo plant after "n" days:

=> A(n) = 130 + (n - 1)13

Adding "n = 13" to the calculation will yield the height of the bamboo plant after 13 days:

=> A(13) = 130 + (13 - 1)13

=> A(13) = 130 + 12(13)

=> A(13) = 286

As a result, the bamboo growth will reach a height of 286 inches after 13 days.

The right response is thus:

=> A(n) = 130 + (n - 1)13 , or 286 inches.

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Answer:

11.52 feet

Step-by-step explanation:

The formula for the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius.

We can rearrange the formula to solve for the radius:

r = (3V/4π)^(1/3)

Substituting the given volume V = 7,234.56 ft³, we get:

r = (3(7,234.56)/(4π))^(1/3) ≈ 11.52 ft

Therefore, the radius of the sphere is approximately 11.52 feet.

Answer:

10 + 2x

also,

2x + 10

Step-by-step explanation:

"a number value" is the unknown, so use a variable (letter) I used x, but could be almost any letter (avoid e and i, they have other math meanings)

"10 more than" means to add on 10. You can do that up front or at the end. Order is way more important for subtracting, so no worries here.

"product" means multiplying. So the "product of 2 and a number" is 2x.

So to translate this word phrase into an algebraic expression, you get:

10 + 2x

but also 2x + 10 is the same thing.

Answer:

In a circle, an exterior angle is formed when a side of a triangle is extended. The measure of the exterior angle is equal to the sum of the measures of the two intercepted arcs.

Let x be the measure of the exterior angle. Then we have:

x = 84° + 108°

x = 192°

Therefore, the measure of the exterior angle is 192°.

The number which is absent in the first 31 digits of the pi is 9

The digit that is absent in the first 31 digits of pi is the digit 9. Pi is an irrational number with an infinite number of decimal places, and it is believed to be a random sequence of digits. However, the absence of the digit 9 in the first 31 digits of pi is just a coincidence and has no special mathematical significance.

It is important to note that the digits of pi are not random in the strict sense of the word, but they appear to be so, and they follow a pattern that has yet to be fully understood by mathematicians. The quest to discover the properties of pi has been ongoing for centuries, and it continues to be a fascinating and important area of research in mathematics.

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The given question is incomplete, the complete question is:

Which number is absent in the first 31 digits of pi

The values of x is [tex]x < 39.5[/tex].

Given that the shopkeeper spends on rent and electricity is [tex]= 5x+14[/tex]

Spending of shopkeeper on rent [tex]= 3x-7[/tex]

So shopkeeper spends on electricity [tex]= (5x+14) - (3x-7) = 2x+21[/tex]

Given that amount the shopkeeper spends on electricity less than 100.

So suitable inequality,

[tex]2x+21 < 100[/tex]

[tex]2x < 100-21[/tex]

[tex]2x < 79[/tex]

[tex]x < 39.5[/tex]

All the values of [tex]x < 39.5[/tex].

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Answer:

To calculate the future value of an investment earning compound interest, we can use the formula:

FV = P(1 + r/n)^(nt)

where:

FV is the future value

P is the principal (starting amount)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

In this case, we have:

P = 6000

r = 0.18 (18% annual interest rate)

n = 12 (compounded monthly)

t = 8

Substituting these values into the formula, we get:

FV = 6000(1 + 0.18/12)^(12*8)

FV = 6000(1.015)^96

FV = 6000(3.045)

FV = 18270

Therefore, the future value of $6000 earning 18% interest, compounded monthly for 8 years, is $18,270.

Answer:

The line y = 2 - 5/20 can be simplified to y = 2 - 1/4 = 7/4.

Substituting y = 7/4 into the equation of the circle, we get:

(x - 5)² + (7/4 + 1)² = 25

(x - 5)² + (15/4)² = 25

(x - 5)² = 25 - (15/4)²

x - 5 = ±√(25 - (15/4)²)

x = 5 ± √(25 - (15/4)²)

Simplifying, we get:

x = 5 ± √(400/16 - 225/16)

x = 5 ± √(175/16)

x = 5 ± (√175)/4

Therefore, the two intersection points are:

Left point: (5 - (√175)/4, 7/4)

Right point: (5 + (√175)/4, 7/4)

Answer:

-3x

Step-by-step explanation:

FIrst you subract 2 from both sides then eliminate the x's

The score located at -3sx (standard deviation) from the mean in a normal distribution is 75. This is because in a normal distribution, the mean is the center and -3sx is three standard deviations away from the mean. Therefore, the score located at -3sx would be the mean minus three standard deviations, which is 120-45=75.

To further explain, a normal distribution is a probability distribution characterized by a symmetrical bell-shaped graph, and it's determined by the mean and standard deviation of the dataset. In this case, the mean is 120 and the standard deviation is 15. Therefore, the data would have an average score of 120 and an average range of 30 (15 plus and minus from the mean). If the score is located at -3sx, it would be three standard deviations away from the mean and the score would be 75.

Therefore, the score located at -3sx would be the mean minus three standard deviations, which is 120-45=75.

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Answer:50

Step-by-step

Answer:

Answer is D

Step-by-step explanation:

The absolute value is the distance between a number and zero. The distance between −50 and 0 is 50

The result is the t-statistic, which is used to compare the two samples.

The t-test is used to compare the means of two independent samples. The formula for the t-test is:

[tex]t = (x1 - x2) / √[s2/n1 + s2/n2][/tex],

where x1 is the mean of the first sample, x2 is the mean of the second sample, s2 is the variance of the two samples, and n1 and n2 are the sizes of each sample.

To calculate the t-test, first you need to calculate the mean for each sample. If the sample size is small (less than 30), then you should use the sample standard deviation.

Next, calculate the variance for each sample by taking the sum of the squared differences from the mean, and dividing by n-1 (where n is the sample size).

Finally, calculate the t-test statistic by substituting the means and variances into the formula above. The result is the t-statistic, which is used to compare the two samples.

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Answer:

x = 118.5°

Step-by-step explanation:

the measure of the chord- chord angle x is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is

x = [tex]\frac{1}{2}[/tex] (27 + 210)° = [tex]\frac{1}{2}[/tex] × 237° = 118.5°

The value of x in the given circle by secant lines is 118.5 degrees.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

A straight line that intersects a circle in two points is called a secant line

A chord is in a unique secant line and every secant line defines a unique chord.

The measure of the angle x is half the sum of the measures of the arcs intercepted by the angle and its vertical angle

x=1/2(210+27)

x=1/2(237)

Divide two hundred thirty seven by two

x=118.5

Hence, the value of x in the given circle by secant lines is 118.5 degrees.

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