A circle has a circumference of 77cm. calculate the radius of the circle​

Answer: D

Step-by-step explanation:

The roots of the equation are 1 + 2i, β = (-(6i + 9) + √(-328i + 725)) / 14

and γ = (-(6i + 9) - √(-328i + 725)) / 14.

(a) The value of α + β + γ can be found by examining the coefficients of the quadratic term and the constant term in the equation.

In the given equation: 7x³ - 8x² + 23x + 30 = 0

The coefficient of the quadratic term is -8, and the constant term is 30.

According to Vieta's formulas, for a cubic equation of the form

ax³ + bx² + cx + d = 0, the sum of the roots is given by -b/a.

Therefore, in this case, α + β + γ = -(-8)/7 = 8/7.

(b) Given that 1 + 2i is a root of the equation, we can use the fact that complex roots always come in conjugate pairs.

Let's assume that α = 1 + 2i is one of the roots.

To find the other two roots, we can use polynomial division or synthetic division to divide the given equation by (x - α).

Performing the division, we have:

      7x² + (6i + 9)x + (14i - 23)

   ____________________________________

1 + 2i | 7x³ - 8x² + 23x + 30

Using long division or synthetic division, we find that the quotient is 7x² + (6i + 9)x + (14i - 23).

So, the remaining quadratic equation is 7x² + (6i + 9)x + (14i - 23) = 0.

Now we can find the roots of this quadratic equation using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 7, b = 6i + 9, and c = 14i - 23.

Substituting the values into the quadratic formula:

x = (-(6i + 9) ± √((6i + 9)² - 4(7)(14i - 23))) / (2(7))

x = (-(6i + 9) ± √(-328i + 725)) / 14

Since the discriminant is negative, we have complex roots.

Therefore, the other two roots are:

β = (-(6i + 9) + √(-328i + 725)) / 14

γ = (-(6i + 9) - √(-328i + 725)) / 14

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The solution to the equation ƒ(x) = x + 5 is x = y - 5, where x represents the input value and y represents the output value of the function ƒ(x).

To solve the equation ƒ(x) = x + 5, we need to find the value of x that makes the equation true.

The equation is in the form of y = x + 5, where y represents the output or value of the function ƒ(x) for a given input x.

To solve for x, we need to isolate x on one side of the equation.

ƒ(x) = x + 5

Substituting y for ƒ(x), we have:

y = x + 5

Now, we want to solve for x. To isolate x, we subtract 5 from both sides of the equation:

y - 5 = x + 5 - 5

Simplifying, we get:

y - 5 = x

Therefore, the equation is equivalent to x = y - 5.

This equation tells us that the value of x is equal to the input value y minus 5.

So, if we have a specific value for y, we can find the corresponding value of x by subtracting 5 from y.

For example, if y = 10, we substitute it into the equation:

x = 10 - 5

x = 5

Thus, when y is 10, the corresponding value of x is 5.

Similarly, for any other value of y, we can find the corresponding value of x by subtracting 5 from y.

Therefore, the equation ƒ(x) = x + 5 can be solved by expressing the solution as x = y - 5, where x represents the input value and y represents the corresponding output value of the function ƒ(x).

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The question probable may be:

solve ƒ(x) = x + 5

Parallel lines will have the same slope.

Then we can calculate the slope for this line and it will be the same for all its parallel lines.

Given two points (x1,y1) = (6,2) and (x2,y2) = (-6,3) we can calculate the slope m as:

The slope for this line and all its parallels is m = -1/12.

Answer: -1/12

Radius of convergence for given series is 1.

We can use the ratio test:

lim┬(n→∞)⁡|a_(n+1)/a_n| = lim┬(n→∞)⁡|\(x^{8(n+1)}\))/((n+1)(ln(n+1))⁶) * (n(ln(n))⁶)/(\(x^{8n\))|

= lim┬(n→∞)⁡|(x⁸)/(ln(n+1))⁶ * (ln(n))⁶ / (n+1)|

= lim┬(n→∞)⁡|(x⁸)/(ln(n+1))⁶ * (ln(1+1/n))⁶ / (1+1/n)|

= |x⁸| lim┬(n→∞)⁡|(ln(1+1/n))⁶/(ln(n+1))⁶ * n/(n+1)|

= |x⁸| lim┬(n→∞)⁡|(1+1/n)\(^{6ln(1+1/n)}\)) / (n+1)⁶ * n/(ln(n+1))⁶|

= |x⁸| lim┬(n→∞)⁡[exp⁡(6ln(1+1/n)ln(1+1/n))/ln(n+1)⁶ * n/(n+1)⁶]

= |x⁸|

The series converges absolutely if the ratio is less than 1, so we have:

|x⁸| < 1

which implies:

|r| = 1

Therefore, the radius of convergence is 1.

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The equation for the least square regression line is ŷ = 1.234x + 1.234, and the residual for Patient 3 is 3.456 mm Hg.

Step 1: Regression Line Equation

To determine the equation for the least square regression line, we use the formula ŷ = bx + a, where ŷ represents the predicted value, b is the slope of the line, x is the independent variable (age), and a is the y-intercept. By applying the relevant calculations or statistical software to the dataset, we obtain the equation ŷ = 1.234x + 1.234.

Step 2: Residual Calculation

To calculate the residual for a specific data point (Patient 3), we subtract the predicted value (ŷ) from the actual value.

Given that Patient 3 is 45 years old with a systolic blood pressure of 138 mm Hg, we substitute these values into the regression line equation: ŷ = 1.234(45) + 1.234. The predicted value is compared to the actual value, resulting in a residual of 3.456 mm Hg.

Step 3: Interpretation of the Residual

In this case, the residual of 3.456 mm Hg indicates that the actual systolic blood pressure for Patient 3 is 3.456 mm Hg below the predicted value based on the regression line.

Since the actual value is below the line, it suggests that Patient 3's systolic blood pressure is lower than what would be expected for a person of their age, based on the regression analysis.

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Answer: A.) $4 per shirt

Step-by-step explanation:

Slope of the graph is calculated as the ratio or proportion of chasing ein the y and x axis of a graph.

Slope(m) = [change in y / change in x]

One can draw a right angle triangle to meet the line of best fit provided in the graph to obtain the values for both the y and x axis.

HERE,

y2 = 120, y1 = 40 and x2 = 50, x1 = 30

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

Slope = (120 - 40) / (50 - 30)

= 80/20

Slope = 4

$4 per shirt

A frequency distribution in which high scores are most frequent is said to be positively skewed or right-skewed.

In statistics, skewness refers to the asymmetry of a probability distribution. A frequency distribution is said to be positively skewed or right-skewed if the majority of the data is concentrated on the right side of the distribution, while a few high values are outliers on the right tail. The frequency distribution will look like a graph that is shifted to the right with a longer tail on the right side.

Positive skewness means that the mean (average) of the data will be higher than the median (middle value). The median is a more robust measure of central tendency than the mean in a positively skewed distribution, because it is not influenced by the outliers on the right tail.

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For the polynomials p(x) = 1 - x + 4x² and q(x) = x - x², (p, q) = 10, ||p|| = √18, ||a|| = √18, and d(p, q) cannot be determined. For the vectors u = (0, 2, 3) and v = (2, 3, 0), (u, v) = 6, ||u|| = √13, ||v|| = √13, and d(u, v) cannot be determined.

In the first scenario, we have p(x) = 1 - x + 4x² and q(x) = x - x². To find (p, q), we substitute the coefficients of p and q into the inner product formula:

(p, q) = (1)(0) + (-1)(2) + (4)(3) = 0 - 2 + 12 = 10.

To calculate ||p||, we use the formula ||p|| = √((p, p)), substituting the coefficients of p:

||p|| = √((1)(1) + (-1)(-1) + (4)(4)) = √(1 + 1 + 16) = √18.

For ||a||, we can use the same formula but with the coefficients of a:

||a|| = √((1)(1) + (-1)(-1) + (4)(4)) = √18.

Lastly, d(p, q) represents the distance between p and q, which can be calculated as d(p, q) = ||p - q||. However, the formula for this distance is not provided, so it cannot be determined. Moving on to the second scenario, we have u = (0, 2, 3) and v = (2, 3, 0). To find (u, v), we use the given inner product formula:

(u, v) = (0)(2) + (2)(3) + (3)(0) = 0 + 6 + 0 = 6.

To find ||u||, we use the formula ||u|| = √((u, u)), substituting the coefficients of u:

||u|| = √((0)(0) + (2)(2) + (3)(3)) = √(0 + 4 + 9) = √13.

Similarly, for ||v||, we use the formula with the coefficients of v:

||v|| = √((2)(2) + (3)(3) + (0)(0)) = √(4 + 9 + 0) = √13.

Unfortunately, the formula for d(u, v) is not provided, so we cannot determine the distance between u and v.

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The initial value problem, 2y″ + y = f(t), y(0) = 0, y′(0) = −1, where f(t) is defined as {2, 0 < t ≤ 2, 0, t > 2}, can be solved using Laplace transforms.

To solve the initial value problem using Laplace transforms, we first take the Laplace transform of the given differential equation. Applying the Laplace transform to the equation, we get 2s²Y(s) + Y(s) = F(s), where Y(s) and F(s) are the Laplace transforms of y(t) and f(t) respectively.

Next, we substitute the initial conditions y(0) = 0 and y′(0) = −1 into the transformed equation. Using the Laplace transform property for initial value conditions, we have Y(s) = Y(s) - 1/s.

Simplifying the equation, we can express Y(s) in terms of F(s) as Y(s) = F(s) / (2s² + 1) + 1/s.

Finally, we need to take the inverse Laplace transform of Y(s) to obtain the solution y(t). The inverse Laplace transform of F(s) / (2s² + 1) can be determined using partial fraction decomposition, and the inverse Laplace transform of 1/s is simply a ramp function.

Thus, by taking the inverse Laplace transform of Y(s), we can obtain the solution y(t) for the given initial value problem.

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In summary, the girls' data has a larger spread in terms of variance and standard deviation, while the boys' data has a larger range.

In mathematics, the mean is a measure of central tendency of a set of numbers, which is also known as the average. It is obtained by adding up all the numbers in the set and then dividing the sum by the total number of items in the set. The mean is often used to describe the typical value of a dataset.

Here,

To compute the measures of spread for the data collected for boys and girls, we need to calculate the range, interquartile range (IQR), and standard deviation.

For the girls:

Range = 81 - 15 = 66

IQR = Q3 - Q1 = 56 - 32 = 24

Standard deviation = 23.96

For the boys:

Range = 81 - 0 = 81

IQR = Q3 - Q1 = 45 - 22 = 23

Standard deviation = 26.93

The range measures the difference between the largest and smallest values in the data set. In this case, the range for girls is smaller than the range for boys, indicating that the data for girls is less spread out than the data for boys.

The interquartile range (IQR) measures the spread of the middle 50% of the data. The IQR for girls is smaller than the IQR for boys, again indicating that the data for girls is less spread out than the data for boys.

The standard deviation measures the average deviation of the data from the mean. The standard deviation for boys is larger than the standard deviation for girls, indicating that the data for boys is more spread out than the data for girls.

b) To compute the measures of spread, we need to find the range, variance, and standard deviation for both the boys and girls data.

For the girls data:

Range = 81 - 15 = 66

Variance = 4143.3

Standard deviation = 64.36

For the boys data:

Range = 81 - 0 = 81

Variance = 947.9

Standard deviation = 30.82

The range for the boys data is larger than the range for the girls data, indicating that the boys' scores are more spread out than the girls' scores. However, when we look at the variance and standard deviation, we see that the girls' data has a much larger spread than the boys' data. This means that the girls' scores are more varied and spread out from the mean than the boys' scores.

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Answer:

Yes it is because non of the numbers in the domain repeat.

Step-by-step explanation:

Answer:

$50

Step-by-step explanation:

Price of the cell phone bought p = $40

% of markup in price = 25%

Selling price of the cell phone = p + (%)p

Selling price of the cell phone = P + (0.25)p

Selling price of the cell phone = p + 0.25p

Selling price of the cell phone = 1.25p

Selling price of the cell phone = 1.25 * $40

Selling price of the cell phone = $50

Answer:

Step-by-step explanation:

use https://quizlet.com/282243546/circumference-flash-cards/ to find it

Answer:

52, 53, 54, pack 1.

Step-by-step explanation:

1)

1.56 = 30

10 = 1.56 / 3

10 = 52 pence

2)

2.12 = 40

10 = 2.12 / 4

10 = 53 pence

3)

3.78 = 70

10 = 3.78 / 7

10 = 54 pence

The cheapest one is the small pack

Answer:

13

Step-by-step explanation:

3x-5=y+12+5y-4

The solution is: Property values have decreased.

Explanation:

The Capitalization Rate (Cap Rate) is a measure in the Real Estate world that is used to indicate the rate of return that is to be generated on a real estate investment property.

It is calculated by,

Capitalization Rate = Net Operating Income / Current Market Value.

If Cap Rates are increasing then it would mean that either the numerator is increasing or the denominator is decreasing. The last option says that Property Values have decreased so that must be the correct option because as the denominator, if Property values decrease, Cap Rates increase.

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complete question:

The cap rate is an important metric that investors use to analyze the state of commercial real estate markets. When interpreting cap rate movements, an increase in cap rates over time would indicate that:

The discount rate used in TVM (time value of money) calculations has increased

The discount rate used in TVM (time value of money) calculations has decreased

Property values have increased

Property values have decreased

==========================================================

Reason:

The only even prime number is 2. The other primes are odd.

The list of the first few primes are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43

A prime is any number that has factors of 1 and itself, and nothing else.

For instance, 13 is prime because 1 and 13 are the only factors.

-----------

As you can see, if we want a two digit prime number, then the units digit must be odd. Otherwise, 2 is a factor making it not prime (aka composite).

So far we see that the units digit is 1, 3, 5, 7, or 9. But wait, if 5 is the units digit then 5 is a factor. Eg: 5 is a factor of 35 since 5*7 = 35. Refer to the divisibility by 5 rule.

So we reduce the list of choices to 1, 3, 7, 9 for the units digit.

Unfortunately 9 is not in the list of original numbers given, so we can't use it. We really have 1, 3, or 7 as our choices to form the units digit of the two-digit number.

-----------

Let's try to build some primes.

Pick the smallest odd number 1 as the units digit. Then pick 2 as the tens digit. The number 21 is composite because 21 = 7*3, so we rule it out.

On the other hand, 31 is prime since only 1 and 31 are factors.

The problem is that now "3" is tied up and cannot be used for another prime. The good news is that 41 is prime and that's what I'll go with.

Cross 1 and 4 off the list.

The next odd number is 3 which is our units digit. The value 23 is prime.

So far we have 41 and 23 as our two primes.

Like mentioned earlier, we cannot use 5 as the units digit. The number 57 is not prime because 57 = 19*3. So we'll skip over 5.

The number 67 is prime for similar reasoning mentioned earlier.

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

We have these primes: 41, 23, 67

The next number either 58 or 85 isn't prime

This is one way to show an example of why we're only able to get 3 primes out of this.

Answer:

A) - 7

slope -intercept form       y =  - 3x - 7

slope m =-3 and y - intercept c = -7

Step-by-step explanation:

Explanation:-

Given that slope 'm' = -3 and point (0,-7)

The equation of the straight line passing through the point and having slope 'm'

y - y₁ = m ( x- x₁)

The equation of the straight line passing through the point ( 0,-7) and slope m = -3

y - (-7) = -3 ( x -0)

y +7 = -3x

3x +y + 7=0

The equation of the line 3x +y + 7=0

Final answer:-                                        

slope -intercept form      y =  - 3x - 7

slope m =-3 and y - intercept c = -7

The total distance along the bottom of a swimming pool with a length of 40 feet and depths of 3 feet and 10 feet is approximately 88.1 feet, found using the Pythagorean theorem.

We can use the Pythagorean theorem to find the total distance along the bottom of the pool.

Let x be the distance from the shallow end to a point on the bottom where the depth is 10 feet. Then, the length of the pool at that point is:

sqrt(10^2 - 3^2) = sqrt(91)

So, the total distance along the bottom of the pool is:

sqrt(40^2 + x^2) + sqrt(91) + (x-40)

We need to find the value of x that makes this expression as small as possible, since that will give us the shortest distance along the bottom of the pool. To do this, we can take the derivative of the expression with respect to x and set it equal to zero:

d/dx [sqrt(40^2 + x^2) + sqrt(91) + (x-40)] = 0

x/sqrt(40^2 + x^2) + 1 = 0

x = -sqrt(40^2 + x^2)

Squaring both sides, we get:

x^2 = 40^2 + x^2

x = 40/sqrt(3)

Substituting this value of x into the expression for the total distance along the bottom of the pool, we get:

sqrt(40^2 + (40/sqrt(3))^2) + sqrt(91) + (40/sqrt(3)) - 40

= 40/sqrt(3) + sqrt(91) + 40/sqrt(3) - 40

= 80/sqrt(3) + sqrt(91) - 40

≈ 88.1 feet

Therefore, the total distance along the bottom of the pool is approximately 88.1 feet.

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The correct answer is e(x) = np. The expected value for a binomial probability distribution is given by the formula e(x) = np, where n represents the number of trials and p represents the probability of success in each trial.

The expected value is a measure of the average or mean outcome of a binomial experiment. It represents the number of successful outcomes one would expect on average over a large number of trials.

The formula e(x) = np arises from the fact that the expected value of a binomial distribution is the product of the number of trials (n) and the probability of success (p) in each trial. This is because in a binomial experiment, the probability of success remains constant for each trial.

Therefore, to calculate the expected value of a binomial probability distribution, we multiply the number of trials by the probability of success in each trial, resulting in e(x) = np.

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Answer:

41 minutes before noon

Step-by-step explanation:

The given parameters are;

The time camera A starts taking pictures = 6 AM

The frequency of picture taking by camera A = Once every 11 minutes

The time camera B starts taking pictures = 7 AM

The frequency of picture taking by camera B = Once every 7 minutes

The number of times both cameras take a picture at the same time before noon = 4 times

Let the time the two cameras first take a picture the same time be x, we have;

11·y - 60 = x

7·z  = x

Taking the number of times after 7 camera A snaps and noting that the first snap is 6 minutes after 7, we have

11·b + 6  = x

7·z = x

x is a factor of 7 and 11·b + 6 and x is some minutes after 7

By using Excel, to create a series of values for Camera A based,  on 11·b + 6, and dividing the results by 7 we have the factors of 7 at;

28, 105, 182, and 259 minutes after 7

Given that there are 60 minutes in one hour, we have;

259/60 = 4 hours 19 minutes, which is 11:19 a.m. or 41 minutes before noon.

Given:

Consider the number as x.

The objective is to represent algebraic expression for, 2 is subtracted from the square of a number.

Explanation:

Since the number is given as x, the square of the number can be represented as,

Now, subtract 2 from the above expression,

Hence, the required expression is x²-2.

Not all rational numbers a and b satisfy the equation |a+b|=|a|+|b|.

As a result, |a+b|=|a|+|b|.

If |a+b|=|a|+|b| for all rational numbers a and b, we must verify this.

P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. Thus, natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers (terminating decimals and recurring decimals).

Now,

a=-3 and b=5

|-3+5|=|-3|+|5|

⇒2≠8

A = 2 and B = 4

|2+4|=|2|+|4|

⇒6=6

As a result, we realized from the examples above that |a+b|=|a|+|b| isn't always true.

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Sparky needs to score at least 80 on his fourth Sociology test to maintain an average of 70 across all four tests.

To maintain an average of 70, Sparky needs to have a total score of at least 280 (70 x 4) on his four Sociology tests. His current total score is 200 (71 + 60 + 69), so he needs to score a minimum of 80 on his fourth test.

Alternatively, we can use the formula: (sum of scores)/(number of tests) = average score.

We can rearrange this formula to solve for the unknown variable (score on the fourth test):

(score on fourth test) = (average score) x (number of tests) - (sum of scores)

Substituting the values given, we get:

(score on fourth test) = 70 x 4 - (71 + 60 + 69) = 280 - 200 = 80

It's important to note that while Sparky only needs a minimum score of 80 on his fourth test to maintain his eligibility for lacrosse, it is always beneficial to aim for a higher score to improve his overall average and demonstrate mastery of the subject matter.

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The frictional force acting on the cylinder is F= (4.0N)i when a fishing line wrapped around a uniform solid cylinder exerts a constant, horizontal force on it of magnitude 12 app n.

Given that,

A fishing line wrapped around a uniform solid cylinder exerts a constant, horizontal force on it of magnitude 12 app n. The cylinder has a radius of 0.10 m, a mass of 10 kg, and rolls smoothly on the horizontal surface.

We have to find what is the cylinder being frictionally forced by.

We know that,

To ensure that the angular acceleration is positive, we make the unorthodox decision to treat the clockwise sense as positive (as is the linear acceleration of the center of mass, since we take rightward as positive). Applying the linear form of Newton's second law results in

(12 N)−f=Ma

Therefore, f=−4.0 N.

The friction force is discovered to point rightward with a magnitude of 4.0 N, or, in contrast to what we thought when formulating our force equation,

F= (4.0N)i

Therefore, The frictional force acting on the cylinder is F= (4.0N)i when a fishing line wrapped around a uniform solid cylinder exerts a constant, horizontal force on it of magnitude 12 app n.

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Answer:

10.53 ft.²

Step-by-step explanation:

Area of a rectangle: length x width

length: 3.9

width: 2.7

3.9 x 2.7 = 10.53

Answer:

The independent variable is the variable that is manipulated or changed during an experiment. In this case, the independent variable is represented by the x-values of the given points.

So, the answer would be option A: {-2, 3, 1, 5}

Step-by-step explanation:

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