.a semi-elliptical arch in a stone bridge has a span of 6 meters and a central height of 2 meters. find the height of the arch at a distance of 1.5 m from the center of the arch.

Answer:  The area of the smaller circle is [tex]65.6cm^{2}[/tex].

Step-by-step explanation:

A = [tex]\pi r^{2}[/tex], r is the radius.

1. Find out the diameter of the small circle.

[tex]\frac{1}{3}(27)= 9[/tex]

2) Find out the radius, r.

[tex]radius = \frac{diameter}{2} =\frac{9}{2} =4.5[/tex]

3) We plugin r = 4.5 into the formula to solve the area of the smaller circle.

[tex]A=\pi r^{2}=\pi (4.5)^{2} =65.6cm^{2}[/tex]

The circumference of Circle C is found as 53π.

In the given figure:

AD = 28 and DB = 45

∠ADB = 1/2 *∠ACB

∠ADB = 90

Applying Pythagorean theorem in ΔABD.

AB² = AD² + DB²

AB² = 28² + 45²

AB = √2809

AB = 53

Radius = 53/2

circumference of Circle C:

C = 2πr

C = 2*π* (53/2)

C =  53π

Thus, the circumference of Circle C is found as 53π.

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The solution of the match is

(1) Orthocenter          (C) The point at which the altitudes of a triangle                                                

                                              meet.

(2) Centroid                 (D) The point at which the medians of a triangle

                                             meet.

(3) Circumcenter         (A) The point of intersection of the perpendicular                  

                                             bisectors of the sides of a triangle.

(4) Incentre                 (B) The point at which the three angle bisectors      

                                             of a triangle meet.

The orthocenter of a triangle is the point where the altitudes of the triangle intersect. The orthocenter is not always inside the triangle, and in some cases, it may lie outside the triangle.

The centroid of a triangle is the point where the three medians of the triangle intersect. The centroid is always inside the triangle, and it is also the center of mass of the triangle.

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect.  The circumcenter is not always inside the triangle, and in some cases, it may lie outside the triangle.

The incentre of a triangle is the point where the three angle bisectors of the triangle intersect. The incentre is always inside the triangle, and it is also the center of the circle that is inscribed inside the triangle.

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Complete Question:

Match the following.

(1) Orthocenter         (A) The point of intersection of the perpendicular                  

                                             bisectors of the sides of a triangle.

(2) Centroid                 (B) The point at which the three angle bisectors of

                                             a triangle meet.

(3) Circumcenter         (C) The point at which the altitudes of a triangle

                                              meet.

(4) Incentre                 (D) The point at which the medians of a triangle

                                             meet.

Answer:

y=6x-8

Step-by-step explanation:

The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We are given the slope m = 6 and a point on the line (1,-2). We can use point-slope form to find the equation and then simplify it to slope-intercept form.

Point-slope form: y - y1 = m(x - x1)

Substitute the values of m, x1, and y1:

y - (-2) = 6(x - 1)

Simplify the right side:

y + 2 = 6x - 6

Subtract 2 from both sides:

y = 6x - 8

This is the equation of the line in slope-intercept form.

Answer:

Step-by-step explanation:

Let's call the length of the shorter leg of the isosceles trapezoid "a" and the length of the longer leg "b".

From the problem, we know that:

a = 0.1x - 0.5 (length of one leg is 0.1.x - 0.5 meters)

b = 0.3x - 2.1 (length of the other leg is 0.3.x-2.1 meters)

Since we know that the trapezoid is isosceles, we know that a = b. So we can set the two expressions equal to each other:

0.1x - 0.5 = 0.3x - 2.1

Now we can solve for x:

0.2x = 1.6

x = 8

Now that we know x, we can substitute it back into the expressions for a and b to find their lengths:

a = 0.1(8) - 0.5 = 0.3 meters

b = 0.3(8) - 2.1 = 0.3 meters

Therefore, each of the legs of the solar panel are 0.3 meters long.

The value of angle CI is equal to 40 for the triangle.

What is geometry?

Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that I is the incenter of the triangle AI = 3x+7, BI = 5x-11, and CI = 52-2x.

The value of BI will be calculated as,

AI = BI

3x + 7 = 5x - 11

2x = 18

x = 6

Now for the value of angle CI:

CI = 52 - 2x

CI = 52 - 2 x 6

CI = 52 - 12

CI = 40

Therefore, the value of angle CI is equal to 40 for the triangle.

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The percent error for Jason's measurement is 7.14%. This means that his measurement was off by 7.14% compared to the actual value.

Percent error is a measure of the difference between an actual value and an estimated or measured value, expressed as a percentage of the actual value. It is used to evaluate the accuracy of measurements or calculations.

To calculate the percent error for Jason's measurement, we first need to find the absolute error, which is the difference between his measurement and the actual value:

Actual value minus measured value equals absolute error.

Absolute error = |14 - 13|

Absolute error = 1 inch

Next, we can use the formula for percent error:

(Absolute error / Actual Value) x 100% equals the percent of error.

Percent error = (1 / 14) x 100%

Percent error = 0.0714 x 100%

Percent error = 7.14%

Therefore, the percent error for Jason's measurement is 7.14%. This means that his measurement was off by 7.14% compared to the actual value.

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Answer: 1287

Step-by-step explanation:

The model will be as follows: y = b0 + b1x1 + b2x2 + u

To write a model that allows the variance of u to differ between men and women, the best option is to use the heteroscedasticity model. This model will enable the variances to differ between the genders without depending on other factors.

The model will be as follows: y = b0 + b1x1 + b2x2 + u, Where y = dependent variable, b0 = constant or intercept, b1 and b2 are the coefficients for the independent variables x1 and x2, u = error term for the model. However, this model does not allow the variance of u to differ between men and women.

To achieve this, we need to modify the model to allow the variance of u to differ between men and women. This can be done by using the weighted regression model. The model will be as follows: y = b0 + b1x1 + b2x2 + u, where y = dependent variable, b0 = constant or intercept, b1 and b2 are the coefficients for the independent variables x1 and x2, u = error term for the model.

The weights can be represented as: wi = 1/σ^2i, where: wi = weight for observation, iσi = standard deviation of the ith observation. This model will allow the variance of u to differ between men and women without depending on other factors.

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The probability of selecting 46 students out of a college population where 65% still need to take another math class is 0.05433 or 5.433%.

The probability of selecting 46 students out of a college population of which 65% still need to take another math class can be calculated using the binomial probability formula. To calculate the probability, the following information is needed:

Using the binomial probability formula, we can calculate the probability of selecting 46 students out of a college population where 65% still need to take another math class as follows:

[tex]P(X=46) = (N!/((N-r)! * r!)) * (p^r) * (1-p)^(N-r)[/tex]

[tex]= (100!/((100-46)! * 46!)) * (0.65^46) * (1-0.65)^(100-46)[/tex]
[tex]= 0.05433[/tex]

Therefore, the probability of selecting 46 students out of a college population where 65% still need to take another math class is 0.05433 or 5.433%.

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The coordinates of point Q in the parallelogram is (2b + 2a,2c)

The coordinates are given as:

P(2b, 2c) Q(?, ?) S(0, 0) R(2a, 0)

The parallelogram form of the object indicates that the distances PQ and RS are equal.

The distance RS is calculated as:

RS = ( 2a - 0, 0)

This gives

RS = (2a, 0)

Coordinate Q is calculated as:

Q = P + RS

This gives

Q = (2b,2c) + (2a,0)

Evaluate the sum

Q = (2b + 2a,2c)

Hence, the coordinates of point Q is (2b + 2a,2c)

Midpoint of SQ=(b+ a ,c)

Midpoint of PR=(a+ b, c)

hence, SQ and PR bisect each other.

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0.4

The probability that an undergraduate business major intends to attend classes full-time in pursuit of an MBA degree depends on the individual student's preferences and situation. Generally speaking, studies have shown that about 40% of undergraduate business majors choose to pursue an MBA degree full-time after graduating. Therefore, the probability of an undergraduate business major pursuing an MBA degree full-time can be estimated at 0.4.

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The mean absolute deviation (MAD) of the given set of data is 3.875.

To calculate the mean absolute deviation, we first need to find the mean of the data set by adding up all the numbers and dividing by the total number of values:

Mean = (12 + 10 + 12 + 6 + 8 + 4 + 2 + 12) / 8

Mean = 8

Next, we find the absolute deviation of each number from the mean. To do this, we subtract the mean from each number and take the absolute value:

|12 - 8| = 4

|10 - 8| = 2

|12 - 8| = 4

|6 - 8| = 2

|8 - 8| = 0

|4 - 8| = 4

|2 - 8| = 6

|12 - 8| = 4

Then, we find the mean of the absolute deviations:

Mean absolute deviation = (4 + 2 + 4 + 2 + 0 + 4 + 6 + 4) / 8

Mean absolute deviation = 26 / 8

Mean absolute deviation = 3.875

Therefore, the mean absolute deviation of the given set of data is 3.875.

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Complete Question:

what is the mean absolute deviation of the following set of data 12 10 12 6 8 4 2 12.

Answer:

Step-by-step explanation:

Circle centre: (4,7)

Radius: 3

Equation is:

  [tex](x-h)^2+(y-k)^2=r^2[/tex]   (where (h,k) is center, r is radius)

  [tex](x-4)^2+(y-7)^2=3^2[/tex]

  [tex](x-4)^2+(y-7)^2=9[/tex]     (This is the general standard form )

in expanded form,

  [tex](x^2-8x+16)+(y^2-14y+49)=9[/tex]

  [tex]x^2+y^2-8x-14y+56=0[/tex]

Note: Unless stated either form is an acceptable answer.

The measure of the angle the cable car track makes with the valley floor is approximately 38.7 degrees.

The slope or inclination of a line or surface is sometimes referred to as the grade in mathematics. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on a line or surface is what is meant by this term. Usually, the grade is given as a percentage or a fraction. In engineering, building, and transportation, grades are frequently used to define the slope of roads, railroads, and other infrastructure. The grade, which refers to how steep the slope is when referring to a cable car, is a crucial element in determining the safety and effectiveness of the system.

To find the angle we use the trigonometric functions:

tan(θ) = grade = rise/run

Given that, the grade of the incline is 78%, then grade = 0.78.

θ = arctan(0.78) ≈ 38.7 degrees.

Hence, the measure of the angle the cable car track makes with the valley floor is approximately 38.7 degrees.

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When researching a population where it is impossible or impractical to compile a list of the elements, the sampling technique that is appropriate to use is known as the cluster sampling technique

Cluster sampling is a type of probability sampling that is frequently used when the population is too large to be measured as a whole. The population is divided into smaller, more manageable clusters that are less difficult to study than the entire population.Therefore, cluster sampling is an excellent alternative when the target population cannot be measured because it is too large, too vast, or too hard to reach. In this technique, clusters are chosen by a random process or some other procedure.The final sampling method is achieved by selecting samples from within the clusters, which are frequently chosen using simple random sampling or some other appropriate method. When it comes to cluster sampling, it's important to remember that the clusters chosen must be heterogeneous internally but homogeneous externally.

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Based on the given information, the scout should choose Player A if they are looking for consistency.

What are range and standard deviation?

Range is the difference between the highest and lowest scores in the set.

Standard deviation measures how spread out the scores are from the mean.

To determine which player is more consistent, we need to look at the variability in their scores. One way to measure variability is to calculate the range and the standard deviation of each player's scores.

The smaller the range, the more consistent the player's scores are.

A smaller standard deviation indicates that the scores are closer together, which means the player is more consistent.

Using the data provided, we can calculate the range and standard deviation for both players:

Player A:

Range = 21 - 0 = 21

Standard deviation = 5.70

Player B:

Range = 48 - 3 = 45

Standard deviation = 10.89

From these calculations, we can see that Player A has a smaller range and a smaller standard deviation, which means that their scores are more consistent than Player B's. Therefore, the scout should choose Player A if they are looking for consistency.

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The college instructor is most concerned with equity standards.

Equity standards are when an instructor adjusts grades to ensure fairness to all students regardless of their individual performances.

This means that if a class as a whole does not do as well as last year, the instructor will alter the distribution of grades so that the overall grades reflect the effort put in by the class.

For example, if the class average is a C, the instructor may raise some grades to a B or even A in order to ensure that the grades are fair to all students in the class.

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The probability of rolling a sum of 7 or less on two dice is 11/36. This can be expressed as a decimal number rounded to four decimal places as 0.3056.

We need to look at the possibilities when rolling two dice. Each die has six sides, which means the total number of outcomes when rolling two dice is 36. There are 11 combinations of two dice that produce a sum of 7 or less: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (3,1), (3,2). So, 11/36 can be simplified to 1/4, or 0.3056.

To understand this in a more visual way, you can draw a table and use colored dots to indicate the possible combinations. This will show you that out of 36 total possibilities, 11 of them produce a sum of 7 or less.

In summary, the probability of rolling a sum of 7 or less on two dice is 11/36, which can be expressed as a decimal number rounded to four decimal places as 0.3056.

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The 99% confidence interval on the true mean EMG activity for all seniors in the class is option (a) [34.7296, 36.8704]

To calculate the 99% confidence interval for the true mean EMG activity for all seniors in the class, we can use the formula

CI = X ± Zα/2 (σ/√n)

where

X = sample mean = 35.8

Zα/2 = the critical value for the 99% confidence interval, which can be found using a standard normal distribution table or calculator. For a two-tailed test, α/2 = 0.005, so Zα/2 = 2.576.

σ = sample standard deviation = 2.5

n = sample size = 40

Substituting these values into the formula, we get

CI = 35.8 ± 2.576 (2.5/√40) = [34.7296, 36.8704].

Therefore, the correct option is (a) [34.7296, 36.8704]

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The answer choice that is the most appropriate is B. A one-sample z-interval for estimating a population proportion

This is the most appropriate method because you are trying to estimate the proportion of all registered voters who have a favorable impression of Candidate A based on the sample data.

A one-sample z-interval is used when you want to estimate a population proportion using a sample proportion.

To calculate the one-sample z-interval for estimating a population proportion, you can use the following formula:

Confidence Interval = p ± Z * sqrt((p * (1 - p)) / n)

where:

Using this method, you will calculate a confidence interval that estimates the true proportion of registered voters who have a favorable impression of Candidate A, based on the sample data.

This is the most appropriate method because it focuses on estimating a single population proportion and incorporates the sample data and sample size into the calculation.

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The missing side length for the triangle is given as follows:

[tex]x = \frac{16\sqrt{3}}{3}[/tex]

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 60º on the triangle, we have that:

The tangent of 60º is equals to the square root of 3, hence the value of x is obtained as follows:

tan(60º) = 16/x

[tex]\sqrt{3} = \frac{16}{x}[/tex]

[tex]x = \frac{16}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}[/tex]

[tex]x = \frac{16\sqrt{3}}{3}[/tex]

The triangle is given by the image presented at the end of the answer.

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Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The expression 2(10+12) can be rewritten as 44 using the distributive property of multiplication over addition.

The distributive property is a fundamental property of arithmetic that relates multiplication to addition and subtraction. The distributive property of multiplication over addition states that for any numbers a, b, and c

a( b + c ) = ab + ac

Using this property, we can rewrite the expression 2(10+12) as

2( 10 + 12 ) = 2(10) + 2(12)

Here, we have distributed the factor of 2 over the terms inside the parentheses, using the distributive property. This gives us:

2(10+12) = 20 + 24

Simplifying further, we get

2(10+12) = 44

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Changing the value of "a" in the quadratic function affects the vertical stretch or compression and the direction of the opening of the parabola, compared to the graph of the quadratic parent function.

What is function?

A relationship or expression involving one or more variables

The function g(x) = 6x^2 is a quadratic parent function, which means it is the simplest form of a quadratic function.

When we change the value of "a" in the general form of a quadratic function:

f(x) = ax^2 + bx + c

we change the shape of the graph of the function. Specifically, changing the value of "a" stretches or compresses the graph vertically, and changes the direction of the opening of the parabola.

If "a" is positive, the parabola opens upwards, and if "a" is negative, the parabola opens downwards. The larger the absolute value of "a", the more stretched or compressed the parabola becomes.

In the case of g(x) = 6x^2, "a" is positive and equal to 6, which means the graph is stretched vertically by a factor of 6 compared to the parent function. The parabola opens upwards and is narrower than the parent function.

If we were to change the value of "a" to a different positive value, for example "a" = 3, the graph would still open upwards but would be less stretched than g(x) = 6x^2. On the other hand, if we were to make "a" negative, for example "a" = -6, the graph would open downwards, and be a reflection of the graph of g(x) = 6x^2 about the x-axis.

In summary, changing the value of "a" in the quadratic function affects the vertical stretch or compression and the direction of the opening of the parabola, compared to the graph of the quadratic parent function.

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Answer:

Interpolation and extrapolation are two methods used to estimate data points within or beyond a given set of values.Interpolation is the process of estimating a data point within the given range of values, based on the relationship between the known data points. For example, suppose we have the following data points: (1, 3), (2, 5), and (4, 9). If we want to estimate the value of y for x = 3, we can use interpolation to calculate it based on the trend of the data points within the given range. In this case, we can see that the slope of the line between (2, 5) and (4, 9) is the same as the slope of the line between (1, 3) and (2, 5). Therefore, we can estimate the value of y for x = 3 to be 7, using the trend of the known data points.Extrapolation, on the other hand, is the process of estimating a data point beyond the given range of values, based on the trend of the known data points. For example, suppose we have the same data points as before: (1, 3), (2, 5), and (4, 9). If we want to estimate the value of y for x = 5, we can use extrapolation to calculate it based on the trend of the known data points. In this case, we can see that the slope of the line between (2, 5) and (4, 9) is the same as the slope of the line between (1, 3) and (2, 5). Therefore, we can estimate the value of y for x = 5 to be 11, assuming that the trend of the known data points continues beyond the given range.Here is a graph that shows both interpolation and extrapolation:

{graph attached below}

In the graph, the blue dots represent the known data points. The red line represents the trend of the known data points, which can be used for interpolation and extrapolation. The green dot represents an interpolated data point, while the purple dot represents an extrapolated data point.In summary, interpolation and extrapolation are similar in that they both involve estimating data points based on the trend of the known data points. However, they differ in that interpolation estimates data points within the given range of values, while extrapolation estimates data points beyond the given range of values.

hope this helps!

Answer:

(2, 180)

Step-by-step explanation:

w(x)=-5x^2+20x+160

a=-5 b=20

x=-20/2x(-5)

x=2

w(2)=180

2, 180

The appropriate measure of variability for the data shown is the range, and its value is 48. The answer is: "The range is the best measure of variability, and it equals 48."

What is variability?

To determine the appropriate measure of variability for the data shown, we need to consider the characteristics of the data set. Since the data set is relatively small and discrete, the range would be an appropriate measure of variability.

To calculate the range, we subtract the smallest value from the largest value:

Largest value: 58

Smallest value: 10

Range = Largest value - Smallest value = 58 - 10 = 48

Therefore, the appropriate measure of variability for the data shown is the range, and its value is 48. The answer is: "The range is the best measure of variability, and it equals 48."

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a) There are three values of x, namely -3, -2, and -1, for which g(x) = 0.

b) The absolute minimum value of g on the interval -7 ≤ x ≤ 9 is 20, and the absolute maximum value of g is 90

a. To check if there is a value of x for -3 ≤ x ≤ 2 such that g(x) = 0, we can plug in each value in the interval and see if any of them make g(x) equal to 0:

g(-3) = -3² + 5(-3) + 6 = 0

g(-2) = -2² + 5(-2) + 6 = 0

g(-1) = -1² + 5(-1) + 6 = 0

g(0) = 0² + 5(0) + 6 = 6

g(1) = 1² + 5(1) + 6 = 12

g(2) = 2² + 5(2) + 6 = 20

So, we can see that there are three values of x, namely -3, -2, and -1, for which g(x) = 0.

b. To find the absolute minimum and maximum values of g on the interval -7 ≤ x ≤ 9, we can first find the critical points of g by taking its derivative:

g'(x) = -2x + 5

Setting g'(x) = 0, we get:

-2x + 5 = 0

-2x = -5

x = 5/2

So, the only critical point of g is x = 5/2.

We can now check the values of g at the endpoints of the interval and the critical point:

g(-7) = -7² + 5(-7) + 6 = 20

g(9) = 9² + 5(9) + 6 = 90

g(5/2) = (5/2)² + 5(5/2) + 6 = 43.25

Therefore, the absolute minimum value of g on the interval -7 ≤ x ≤ 9 is 20, which occurs at x = -7, and the absolute maximum value of g is 90, which occurs at x = 9.

We can justify this by noting that g is a quadratic function with a negative leading coefficient, which means that it opens downward and has a maximum value at its vertex (which occurs at x = 5/2). Since the vertex is within the given interval, and the function is decreasing on the left and increasing on the right of the vertex, the maximum and minimum values of g must occur at the endpoints of the interval.

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