Write a polynomial function of least degree that has real
coefficients, the given zeros, and a leading coefficient of
1, 1-2i, 1-sqrt(5)

In the given diagram of circle O, we need to find various measurements. Let's consider the following measurements:

Diameter (d): The diameter of a circle is the distance across it, passing through the center. To find the diameter, we can measure the distance between any two points on the circle that pass through the center. Let's say we measure it as 12 units.

Radius (r): The radius of a circle is the distance from the center to any point on the circumference. It is half the length of the diameter. In this case, the radius would be 6 units (12 divided by 2).

Circumference (C): The circumference of a circle is the distance around it. It can be found using the formula C = 2πr, where π is approximately 3.14 and r is the radius. Using the radius of 6 units, we can calculate the circumference as C = 2 * 3.14 * 6 = 37.68 units. Rounding to the nearest whole number, the circumference is approximately 38 units.

Area (A): The area of a circle is the measure of the surface enclosed by it. It can be calculated using the formula A = πr^2. Substituting the radius of 6 units, we can find the area as A = 3.14 * 6^2 = 113.04 square units. Rounding to the nearest whole number, the area is approximately 113 square units.

In summary, for circle O, the diameter is 12 units, the radius is 6 units, the circumference is approximately 38 units, and the area is approximately 113 square units.

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Answer: 1.8 L/h

Step-by-step explanation:

To convert the rate of water dripping from a tap from millilitres per second (ml/sec) to litres per hour (L/h), we need to use conversion factors.

Step 1:

First, let's convert the rate from millilitres per second to litres per second.

There are 1000 millilitres in a litre, so we can divide the rate in millilitres per second by 1000 to get the rate in litres per second:

\(\LARGE \boxed{\textsf{0.5 ml/sec $\div$ 1000 = 0.0005 L/sec}}\)

Step 2:

We can convert the rate from litres per second to litres per hour. There are 3600 seconds in an hour, so we can multiply the rate in litres per second by 3600 to get the rate in litres per hour:

\(\LARGE \boxed{\textsf{0.0005 L/sec $\times$ 3600 = 1.8 L/h}}\)

Therefore, the rate of water dripping from the tap is 1.8 L/h.

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Using the concepts of mean and standard deviation, and the central limit theorem, it is found that:

a. The mean is of: 3.3

b. The standard deviation is of: 1.23.

c. They would have a mean of 3.3 and a standard deviation of 0.55.

For this problem, the mean is given by:

M = (2 + 3 + 2 + 3 + 3 + 4 + 2 + 4 + 3 + 2 + 2 + 7 + 3 + 4 + 5 + 3 + 3 + 3 + 3 + 5)/20 = 3.3

The standard deviation is:

\(S = \sqrt{\frac{(2 - 3.3)^2 + (3 - 3.3)^2 + \cdots + (3 - 3.3)^2 + (5 - 3.3)^2}{20}} = 1.23\)

It states that for distribution of sample means of size n:

Hence, since 1.23/sqrt(5) = 0.55, the sample means would have a mean of 3.3 and a standard deviation of 0.55.

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The area of the region R bounded by the graph of f(x) = x^2(x-6) and the x-axis on the interval [-1, 7] is approximately 371.00 square units.

To find the area of the region R bounded by the graph of f(x) = x^2(x-6) and the x-axis on the interval [-1, 7], we need to integrate the function f(x) over that interval. The area can be calculated using the definite integral:

Area = ∫[a,b] f(x) dx

In this case, a = -1 and b = 7. Let's calculate the area using integration:

Area = ∫[-1,7] x^2(x-6) dx

To solve this integral, we expand the polynomial and simplify:

Area = ∫[-1,7] (x^3 - 6x^2) dx

Next, we integrate term by term:

Area = (1/4)x^4 - (2/3)x^3 | [-1,7]

Now, we substitute the upper and lower limits of integration:

Area = [(1/4)(7^4) - (2/3)(7^3)] - [(1/4)(-1^4) - (2/3)(-1^3)]

Simplifying further:

Area = (1/4)(2401) - (2/3)(343) - (1/4)(1) + (2/3)(-1)

Area = 600.25 - 228.33 - 0.25 - 0.67

Area ≈ 371.00 (rounded to the nearest hundredth)

Therefore, the area of the region R bounded by the graph of f(x) = x^2(x-6) and the x-axis on the interval [-1, 7] is approximately 371.00 square units.

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Answer:8

Step-by-step explanation:take off the negative symbol

The equation x^2 - 14x + 24 = 0 can be solved to find the roots. The roots of the equation are x1 = 2 and x2 = 12.

To find the roots of the equation x^2 - 14x + 24 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the roots can be calculated using the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -14, and c = 24. Plugging these values into the quadratic formula, we get:

x = (-(-14) ± √((-14)^2 - 4(1)(24))) / (2(1))

= (14 ± √(196 - 96)) / 2

= (14 ± √100) / 2

= (14 ± 10) / 2

This gives us two solutions:

x1 = (14 + 10) / 2 = 24 / 2 = 12

x2 = (14 - 10) / 2 = 4 / 2 = 2

Therefore, the roots of the equation x^2 - 14x + 24 = 0 are x1 = 2 and x2 = 12.

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Answer:

99

Step-by-step explanation:

We can set up and solve this equation:

X + X - 50 = X + 49

X = 99

True. It's because the capacitance between two plates depends on the electric field between them, which is naturally geometry-dependent; if you have charges in different places, you get a different electric field.

A capacitor's capacitance is affected by the area of the plates, the distance between the plates, and the dielectric's ability to support electrostatic forces.
The capacitance of a parallel plate capacitor (depending on its geometry) is given by the formula C=Ad C = A d, where C is the capacitance value, A is the area of each plate, d is the distance between the plates, and is the permittivity of the material between the parallel capacitor's plates.
The curvature of the plates indicates whether the plates are spherical or cylindrical. As a result, the only factor that has no effect on the capacitance of the capacitor is the type of material used to make the plates.

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Answer:

here is the ananswer

Step-by-step explanation:

red go to red and black to black

The probability of a lion living more than 10.1 years is approximately 1 - 0.1587 = 0.8413, or 84.13% (rounded to the nearest hundredth).

To use the empirical rule, we first need to convert the value of 10.1 years into a z-score:

z = (x - μ) / σ

where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

z = (10.1 - 12.5) / 2.4

z = -1.00

Using the empirical rule, we know that approximately:

68% of the data falls within one standard deviation of the mean

95% of the data falls within two standard deviations of the mean

99.7% of the data falls within three standard deviations of the mean

Since we want to estimate the probability of a lion living more than 10.1 years, we need to find the area under the normal curve to the right of this value. This is equivalent to finding the area to the left of the z-score of -1.00 (since the standard normal distribution is symmetric).

From a standard normal distribution table or calculator, we can find that the area to the left of z = -1.00 is approximately 0.1587.

Therefore, the probability of a lion living more than 10.1 years is approximately 1 - 0.1587 = 0.8413, or 84.13% (rounded to the nearest hundredth).

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Given the following functions:

f(x) = 4x² + 5x – 3

g(x) = 4x³ – 3x² + 5

Finding (f-g)(x) means f(x) - g(x).

We get,

Therefore, the answer is letter D. (f - g)(x) = -4x³ + 7x² + 5x – 8

Answer: x = 4

Step-by-step explanation:

2(x+1)=10

Distributive properties

a*(b+c)=(a*b)+(a*c)

Using distributive properties

Then

2*(x+1)=(2*x)+(2*1)

2*(x+1)=2x+2

Now, commutative properties

a*b=b*a

Addition is cumulative

a+(-b)=(-b)+a

Therefore applying to 2x+2

2x+2+(-2)=2x+(-2)+2

Then, applying to the equation

2x+2+(-2)=10+(-2), +×-=-

2x+2 -2=10-2

2x=8

Using division properties

ax=b

If a is none zero

Then ax/a=b/a

Therefore x=b/a

Applying that to 2x=8

2x=8. Divide both side by 2 which is none zero

2x/2= 8/2

x=4

Option B

Subtraction Property of equality

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Answer:

2x + 2 − 2 = 10 − 2; Subtraction Property of Equality

Mark me, It would be my very first!!

Part 1 of 2. To be 95% confident that the estimate is within 0.05 of the true proportion of women over age 55 who are widows, you need to take a sample size of 296.

Part2 of 2. If no estimate of the sample proportion is available, you should take a sample size of 385 to achieve a 95% confidence level and a margin of error of 0.05.

To determine the sample size required to estimate the true proportion of women over age 55 who are widows with a 95% confidence level and a margin of error of 0.05,

We can use the formula for sample size calculation for proportions.

n = (Z² × p × q) / E²

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (in this case, 95% confidence level corresponds to a Z-score of approximately 1.96)

p = estimated proportion of women over age 55 who are widows (given as 0.26)

q = 1 - p (the complement of p)

E = margin of error (0.05)

Plugging in the values:

n = (1.96² ×0.26 × (1 - 0.26)) / 0.05²

n=295.98

Part 2 of 2: If no estimate of the sample proportion is available, the worst-case scenario is when the proportion is 0.5 (maximum variability).

In this case, we can use the same formula but substitute p with 0.5.

n = (Z² × p × q) / E²

n = (1.96² ×0.5 × (1 - 0.5)) / 0.05²

n = 384.16

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The shaded area of the circles that are given will be 32π.

It should be noted that the area of a circle is calculated by using:

= πr²

where r = 4

In this case, we have two shaded circles. The area will be:

= 2(πr²)

= 2(π × 4²)

= 2(16π)

= 32π

In conclusion, the area is 32π.

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Yes, I'm familiar with those anatomical ratios. If my hand measures 17 cm, my height is around 170cm and my arm is around 34 cm.

They are often used to estimate a person's height or the length of their limbs based on easily measurable body parts.

Using those ratios, if your hand measures 17 cm, we can estimate that your height is around 170 cm (17 cm hand length x 10). However, it's important to note that this is just an estimation and may not be completely accurate.

As for the length of your arm, we can use the first ratio you mentioned - that the distance from the elbow to the end of the hand is one fifth of the height of a man. If we assume your height is 170 cm based on the hand measurement, then your arm length should be around 34 cm (1/5 of 170 cm).

It's important to keep in mind that these ratios were developed based on averages and may not be accurate for every individual. Additionally, there are many other factors that can influence a person's height and body proportions, such as genetics and environmental factors.

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The distance from Jim's house to the mall is given as follows:

11.25 miles.

Suppose that we have two points with coordinates given as follows:

\((x_1, y_1)\) and \((x_2, y_2)\)

Then the equation for the distance between these two points is given as follows:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The coordinates are given as follows:

Hence the distance is given as follows:

\(D = \sqrt{(17 - 8)^2+(13 - 1)^2}\)

D = 15 units.

Each unit represents 0.75 miles, hence the distance in miles is given as follows:

15 x 0.75 = 11.25 miles.

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

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Answer:

\(y = - 5x + 17\)

Step-by-step explanation:

\(i n \: slope \: intercept \: form \: y = mx + c \\ for \: the \: \: liear \: equaton = 5x + y = 17 \\ y = - 5x + 17\)

Answer:

ab is 68 units and midpoint is -24

Step-by-step explanation:

its just simple addition and subtraction

The minimum total weight that the anchor may have is 40 pounds (lb).

To reckon the minimum total weight that the anchor may have, we need to consider the evenness of forces acting on the wood. The pressure of the timber bear be balanced apiece upward force exerted apiece anchor. Let's assume the burden of the anchor is represented apiece changeable "A" in pounds (lb).

Given:

Weight of the timber (T) = 40 lb/ft³

Weight of the anchor (A) = mysterious (to be determined)

Density of concrete (ρ) = 150 lb/ft³

The capacity of the timber maybe calculated utilizing the weight and mass facts:

Volume of the timber = Weight of the wood / Density of the timber

Volume of the trees = 40 lb / 40 lb/ft³

Volume of the timber = 1 ft³

Now, because the timber is grasped horizontally, the pressure of the trees can be thought-out as a point load applied at the center of the wood. Thus, the upward force exerted for one anchor should be able the weight of the wood.

Weight of the timber (T) = Upward force exercised apiece anchor

40 lb = A

Therefore, the minimum total weight that the anchor grant permission have is 40 pounds (lb).

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The statement "Quadrilaterals A and B are both squares" does not provide enough information to determine whether A and B are scale copies of one another.

To determine if two quadrilaterals are scale copies of each other, we need to compare their corresponding sides and angles. If the corresponding sides of two quadrilaterals are proportional and their corresponding angles are congruent, then they are scale copies of each other.

In this case, since both A and B are squares, we know that all of their angles are right angles (90 degrees). However, we do not have any information about the lengths of their sides. Without knowing the lengths of the sides of A and B, we cannot determine if they are scale copies of each other.

Therefore, the statement cannot be determined as true or false based on the given information.

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The number of ways  5 puppies can be chosen from a litter of 8 puppies is 56 ways

Permutation has to do with arrangement while combination has to do with selection.

From the queston, since we are to select 5 puppies from a litter of 8 puppes, this can be done as shown:

8C5 = 8!/(8-5)!5!

8C5 = 8!/3!5!

8C5 = 8*7*6*5!/6*5!

8C5 = 8* 7

8C5 = 56ways

Hence the number of ways  5 puppies can be chosen from a litter of 8 puppies is 56 ways

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Answer:

 Slope = 0.667/2.000 = 0.333

 x-intercept = 6/1 = 6.00000

 y-intercept = 6/-3 = 2/-1 = -2.00000

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    4*x-12*y-(24)=0

Step 1: Pulling out like terms

Pull out like factors :

  4x - 12y - 24  =   4 • (x - 3y - 6)  

Equation at the end of step 1:

Step 2:

Equations which are never true:

Solve :    4   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Equation of a Straight Line

Solve   x-3y-6  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  x-3y-6  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 2/-1 so this line "cuts" the y axis at y=-2.00000

 y-intercept = 6/-3 = 2/-1  = -2.00000  

Calculate the X-Intercept :

When y = 0 the value of x is 6/1 Our line therefore "cuts" the x axis at x= 6.00000

 x-intercept = 6/1  =  6.00000  

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -2.000 and for x=2.000, the value of y is -1.333. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -1.333 - (-2.000) = 0.667 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  0.667/2.000 =  0.333  

Geometric figure: Straight Line

 Slope = 0.667/2.000 = 0.333

 x-intercept = 6/1 = 6.00000

 y-intercept = 6/-3 = 2/-1 = -2.00000

Answer: 3

Step-by-step explanation:

Subtract the cost of paperback books from Jonelle's total amount.

(22.50 - 4.50)

Then, you'll get ($18).

Divide (18) by the number of hardcover books.

(18/6)

Finally, you'll get $3 for the cost of each hardcover book.

Answer:

c²=√181=13.45, or 13.5

Step-by-step explanation:

The pythagorean theorem is a²+b²=c²

Given this, we will plug in our numbers like this: 9²+10²=c²

9²+10²=181, but we have to find the square root of that.

c²=√181=13.45, or 13.5

I hope this helps!! :)

Step-by-step explanation:

We have a right triangle which allows us to use the Pythagorean Theorem

Answer:

see explanation

Step-by-step explanation:

There is a common difference d between consecutive terms, that is

d = 7 - 2 = 12 - 7 = 17 - 12 = 5

This indicates the sequence is arithmetic with nth term

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = 5 , then

\(a_{n}\) = 2 + 5(n - 1) = 2 + 5n - 5 = 5n - 3

Then

a₂₄ = 5(24) - 3 = 120 - 3 = 117

Adjust the parameters as needed, such as the step size (h) and the final x-value (xn), and run the code to obtain the solution for y(x).

The resulting plot will show the solution curve.

To solve the given set of differential equations using the Runge-Kutta method in MATLAB, we need to convert the second-order differential equations into a system of first-order differential equations.

Let's define new variables:

y = y(x)

z = dz/dx

Now, we have the following system of first-order differential equations:

dy/dx = z (1)

dz/dx = -k/(2y) (2)

To apply the Runge-Kutta method, we need to discretize the domain of x. Let's assume a step size h for the discretization. We'll start at x = 0 and proceed until x = infinite.

The general formula for the fourth-order Runge-Kutta method is as follows:

k₁ = h f(xn, yn, zn)

k₂ = h f(xn + h/2, yn + k₁/2, zn + l₁/2)

k₃ = h f(xn + h/2, yn + k₂/2, zn + l₂/2)

k₄ = h f(xn + h, yn + k₃, zn + l₃)

yn+1 = yn + (k₁ + 2k₂ + 2k₃ + k₄)/6

zn+1 = zn + (l₁ + 2l₂ + 2l₃ + l₄)/6

where f(x, y, z) represents the right-hand side of equations (1) and (2).

We can now write the MATLAB code to solve the differential equations using the Runge-Kutta method:

function [x, y, z] = rungeKuttaMethod()

   % Parameters

   k = 1;              % Constant k

   h = 0.01;           % Step size

   x0 = 0;             % Initial x

   xn = 10;            % Final x (adjust as needed)

   n = (xn - x0) / h;  % Number of steps

   % Initialize arrays

   x = zeros(1, n+1);

   y = zeros(1, n+1);

   z = zeros(1, n+1);

   % Initial conditions

   x(1) = x0;

   y(1) = 0;

   z(1) = 0;

   % Runge-Kutta method

   for i = 1:n

       k1 = h * f(x(i), y(i), z(i));

       l1 = h * g(x(i), y(i));

       k2 = h * f(x(i) + h/2, y(i) + k1/2, z(i) + l1/2);

       l2 = h * g(x(i) + h/2, y(i) + k1/2);

       k3 = h * f(x(i) + h/2, y(i) + k2/2, z(i) + l2/2);

       l3 = h * g(x(i) + h/2, y(i) + k2/2);

       k4 = h * f(x(i) + h, y(i) + k3, z(i) + l3);

       l4 = h * g(x(i) + h, y(i) + k3);

       y(i+1) = y(i) + (k1 + 2*k2 + 2*k3 + k4) / 6;

       z(i+1) = z(i) + (l1 + 2*l2 + 2*l3 + l4) / 6;

       x(i+1) = x(i) + h;

   end

   % Plotting

   plot(x, y);

   xlabel('x');

   ylabel('y');

   title('Solution y(x)');

end

function dydx = f(x, y, z)

   dydx = z;

end

function dzdx = g(x, y)

   dzdx = -k / (2*y);

end

% Call the function to solve the differential equations

[x, y, z] = rungeKuttaMethod();

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Based on the information, the percentage increase for the area s greater as it is 600% greater

Here, we have a square of side length 3 cm

The area of the square is 3² = 9 cm²

Perimeter of the square = 4L = 4 * 3 = 12 cm

When we triple the length of the square, its new length becomes 3 ,× 3 = 9 cm

Area here will be 9 * 9 = 81 cm²

Perimeter = 4 L = 4 * 9 = 36cm

To calculate percentage change, we use the formula;

(new value - old value)/old value * 100%

For the perimeter;

(36-12)/12 * 100% = 24/12 * 100% = 2 * 100% = 200%

For the area;

(81-9)/9 * 100% = 72/9 * 100% = 8 * 100% = 800%

The percentage increase of the area is greater by: 800% - 200% = 600%

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The side length of the square shown is tripled.

3 cm

Which percent of increase is greater the percent of increase for the perimeter of the square or the percent of increase for the area

To calculate QPT, we need to multiply Q by P and then multiply the result by T.

Let's perform the calculations step by step:

Q * P:

[246 859 132] * [1 0 3;

8 6 4;

1 2 4]

= [2461 + 8598 + 1321 2460 + 8596 + 1322 2463 + 8594 + 132*4;

... ... ... ...

... ... ... ...]

= [7002 6100 5346;

... ... ...;

... ... ...]

Next, we multiply the result by T:

[7002 6100 5346] * [2 7 9;

3 4 2;

8 6 3]

= [70022 + 61003 + 53468 70027 + 61004 + 53466 70029 + 61002 + 5346*3;

... ... ... ...

... ... ... ...]

= [34842 71682 82584;

... ... ...;

... ... ...]

Therefore, QPT is equal to:

[34842 71682 82584;

... ... ...;

... ... ...]

Please note that the actual values of the calculations may differ depending on the specific numbers provided in the matrices P, Q, and T.

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Answer:

I think the answer is -7

because : 3(-5) + 4(2)

-15 + 8

= -7