Real life Applications of Polynomials?

The following are the area of the sectors:

6a). π square inches

6b). 24π square centimeters

7a). 9 square centimeters

7b). 16.7 square inches

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

For question 6:

a). (40/360) × π × 3 in × 3 in = π in²

b). (135/360) × π × 8 cm × 8 cm = 24π cm²

For question 7:

a). (90/360) × π × 6 cm × 6 cm = 9 cm²

b). (60/360) × π × 10 in × 10 in = 16.7π in²

Therefore, the following are the area of the sectors:

6a). π square inches

6b). 24π square centimeters

7a). 9 square centimeters

7b). 16.7 square inches

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Answer:

9pi

Or

28.278

Step-by-step explanation:

If you need the exact answer just type in 3.142x3 Squared then it will give you the exact answer but if not just find the pi button on the calculator and put in pi x 3 squared

Answer:

B,C,D

ONLY

Step-by-step explanation:

Answer:

(-2,-5)

(1,1)

(3,5)

for ed

Step-by-step explanation:

Answer:

67 degrees

Step-by-step explanation:

We have a right triangle with the following known values:

B = 90

A = 23 (46/2=23 since AD is the angle bisector)

D = ?

180 = 90 + 23 + D and we solve

67 = D

On a graph, the absolute value of a number is always non-negative.

The absolute value of a number is defined as the distance of that number from zero on the number line. Since the distance can never be negative, the absolute value of a number is always non-negative.

This is reflected in the graph of an absolute value function. The graph of an absolute value function, |x| is a V-shape that opens upward, with the vertex of the V being the point where the absolute value function equals zero. The two arms of the V extend out from this point, going in opposite directions along the number line. The coordinates of the vertex (0,0) and the graph is always non-negative.

It's important to note that although the absolute value is always non-negative on a graph, the input value (x) can be both positive and negative. The output of the absolute value function (|x|) will always be positive.

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Answer:

u +v = < 7,9 >

Step-by-step explanation:

You are given u = <9,4> and v = <-2,5>. You are asked to find u+v. all you need to do is to add them with their respective position. u+v = <9-2, 4+5>, u+v = <7,9>. This is the correct answer.

Use the formula:

Radio= r, Height= h

V= 3.14xrx2h

r =25, h=31

V= 3.14 x 25 x 2 (31) =. 4867

V= 4867 cubic inches

Step-by-step explanation:

Answer:

\(y \geq -4\)

Step-by-step explanation:

This is because the lowest the y-coordinate goes to is -4.

The total surface area of a circle with diameter 14cm would be 307.72 cm².

To calculate the total surface area of a circle with diameter 14cm, we first need to find the radius by dividing the diameter by 2.

So, the radius would be 7cm.

Next, we use the formula for the area of a circle, which is pi multiplied by the radius squared

So, the area of the circle would be 3.14 x 7 x 7, which is equal to 153.86 cm².

However, since we need to find the total surface area, we also need to consider the curved surface area of the circle, which is the circumference multiplied by the height.

As there is no height for a circle, the curved surface area would be equal to the area of the circle. Hence, the total surface area of a circle with diameter 14cm would be 2 x area of the circle, which is 307.72 cm².

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Answer:

In explanation below.

Step-by-step explanation:

Presumably, the proof you have in mind is to use a=b=2–√a=b=2 if 2–√2√22 is rational, and otherwise use a=2–√2√a=22 and b=2–√b=2. The non-constructivity here is that, unless you know some deeper number theory than just irrationality of 2–√2, you won't know which of the two cases in the proof actually occurs, so you won't be able to give aa explicitly, say by writing a decimal approximation.

Answer:

x=4

Step-by-step explanation:

18 = 3(3x − 6)

Divide each side by 3

18/3 = 3( 3x-6)/3

6 = 3x-6

Add 6 to each side

6+6 = 3x-6+6

12 = 3x

Divide by 3

12/3 = 3x/3

4 =x

Answer: 4 = x

Step-by-step explanation: To solve this equation, we start by

distributing the 3 through the parenthses on the right side.

3(3x) is 9x and 3(-6) is -18.

So our equation now reads 18 = 9x - 18.

Our next step is to get the x term by itself on the right side.

So we add 18 to both sides to get 36 = 9x.

Now divide both sides by 9 to get 4 = x.

The rate of change of height of oil when the oil is 15 inches high is 4/3π in/s.

Given that:

The height of the cone = 20 inches

Radius of the cone = 2 inches

The volume of oil in an inverted conical basin is increasing at a rate of 3 cubic inches per second

Formula used: The formula for volume of a cone is given as:

V = 1/3πr²h

Where V is the volume, r is the radius, and h is the height.

Now, differentiate both sides of the volume formula with respect to time t.

V = 1/3πr²h

Differentiate both sides with respect to time t.

dV/dt = d/dt (1/3πr²h)

Put values,

dV/dt = d/dt (1/3 x π x 2² x h)

dV/dt = 4/3 π x dh/dt x h

Volume of an inverted cone is given as:

V = 1/3πr²h

Now, radius, r = h / (20/2)

= h/10

So, we can write V in terms of h as

V = 1/3 π (h/10)² x h

= 1/300π h³

Now, differentiate both sides with respect to time t.

dV/dt = d/dt (1/300π h³)

dV/dt = 1/100 π h² x dh/dt

Now, we are given that the volume of oil in an inverted conical basin is increasing at a rate of 3 cubic inches per second. So,

dV/dt = 3 cubic inches per second

From the above equation,

1/100 π h² x dh/dt = 3

Divide both sides by 1/100 π h².

dh/dt = 3 x 100/ π h²

= 300/ π h²

Now, we are required to find the rate of change of height of oil when the oil is 15 inches high. Put h = 15 in above equation,

dh/dt = 300/ π (15)²

= 4/3 π in/s

Hence, the rate of change of height of oil when the oil is 15 inches high is 4/3π in/s.

Conclusion: Therefore, the correct option is 4/3π in/s.

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This value is approximately equal to 0.2356 inches per second, which can be approximated as 2/π inches per second.

To find the rate at which the height of the oil is changing when the oil is 15 inches high, we can use related rates and the volume formula for a cone.

The volume of a cone can be expressed as:

V = (1/3) * π * r^2 * h

where V is the volume, r is the radius, h is the height, and π is a constant.

Given that the volume of the oil is increasing at a rate of 3 cubic inches per second, we have:

dV/dt = 3 in^3/s

We need to find dh/dt, the rate at which the height of the oil is changing when the oil is 15 inches high.

We are given the following values:

r = 2 inches

h = 15 inches

To relate the rates, we can differentiate the volume equation with respect to time:

dV/dt = (1/3) * π * (2r * dr/dt * h + r^2 * dh/dt)

Substituting the given values and the known rate dV/dt, we get:

3 = (1/3) * π * (2 * 2 * dr/dt * 15 + 2^2 * dh/dt)

Simplifying the equation, we have:

1 = (4/3) * π * (2 * dr/dt * 15 + 4 * dh/dt)

Now, we need to solve for dh/dt:

4 * dh/dt = 3 / [(4/3) * π * (2 * 15)]

4 * dh/dt = 3 / [(8/3) * 15 * π]

dh/dt = (3 * 3 * π) / (8 * 15 * 4)

dh/dt = (9 * π) / (120)

Simplifying further:

dh/dt = (3 * π) / (40)

Therefore, the rate at which the height of the oil is changing when the oil is 15 inches high is (3 * π) / (40) inches per second.

This value is approximately equal to 0.2356 inches per second, which can be approximated as 2/π inches per second.

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Answer:

c > -22 1/2

Step-by-step explanation:

Step 1: Multiply both sides by -5/2 and flip the sign.

Therefore, the answer is c > -22 1/2.

Answer:

23

Step-by-step explanation:

Answer:

but much research has been done and more has learned about brain injuries in the last 5 years

Explanation:

because this shows they are telling more players about the injuries and informing them about the dangers of playing

Answer:

Step-by-step explanation:

The volume formula can be used to find the height and width of a box with volume 4368 in³ and height 1 in greater than width.

The volume formula is ...

  V = LWH

Substituting given information, using w for the width, we have ...

  4368 = (24)(w)(w+1)

We want to find the value of w.

  182 = w² +w . . . . . . . . divide by 24

  182.25 = w² +w +0.25 = (w +0.5)² . . . . . . add 0.25 to complete the square

  13.5 = w +0.5 . . . . . . . . take the positive square root

  w = 13 . . . . . . . . . . . . subtract 0.5

  h = w+1 = 14

The height of the box is 14 inches; the width is 13 inches.

__

Additional comment

By "completing the square", we can arrive at the exact dimensions of the box, as we did above. Note that we only added 0.25 to the equation to do this.

For numbers close together, the geometric mean (root of their product) is about the same as the arithmetic mean (half the sum):

  \(\sqrt{w(w+1)}\approx\dfrac{w+(w+1)}{2}=w+\dfrac{1}{2}\\\\w\approx\sqrt{182}-\dfrac{1}{2}\approx12.99\)

Using this approximation to arrive at the conclusion w=13 saves the steps of figuring the value necessary to complete the square, then adding that before taking the root.

There's a 95% chance that the true proportion is in the confidence interval.

When we want to estimate a property of a population (a population's parameter), without surveying the population, we use samples.

Then, with the information of the samples we can calculate the statistics and infere properties about a population. This inferences obviously came with some uncertainty, depending on the properties of the sample and specially the sample size.

When we talk about confidence intervals, we use the statistic of the sample (in this case, the mean) to estimate a range of values it is expected to find the true mean of the population. The width of this interval depends on the sample standard deviation and the sample size.

The value of the confidence interval (95%, 99%, etc.) represent the probability that the true mean is within this interval.

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Given statement solution is :- The correlation coefficient between weight and spending is approximately 0.5.

To calculate the correlation coefficient (also known as the Pearson correlation coefficient), you need to follow these steps:

Calculate the mean (average) of both the weight and spending data.

Calculate the difference between each weight measurement and the mean weight.

Calculate the difference between each spending measurement and the mean spending.

Multiply each weight difference by the corresponding spending difference.

Calculate the square of each weight difference and spending difference.

Sum up all the products from step 4 and divide it by the square root of the product of the sum of squares from step 5 for both weight and spending.

Round the correlation coefficient to an appropriate number of decimal places.

Here's an example using sample data:

Weight (in pounds): 150, 160, 170, 180, 190

Spending (in dollars): 50, 60, 70, 80, 90

Step 1: Calculate the mean

Mean weight = (150 + 160 + 170 + 180 + 190) / 5 = 170

Mean spending = (50 + 60 + 70 + 80 + 90) / 5 = 70

Step 2: Calculate the difference from the mean

Weight differences: -20, -10, 0, 10, 20

Spending differences: -20, -10, 0, 10, 20

Step 3: Multiply the weight differences by the spending differences

Products: (-20)(-20), (-10)(-10), (0)(0), (10)(10), (20)(20) = 400, 100, 0, 100, 400

Step 4: Calculate the sum of the products

Sum of products = 400 + 100 + 0 + 100 + 400 = 1000

Step 5: Calculate the sum of squares for both weight and spending differences

Weight sum of squares: (\(-20)^2 + (-10)^2 + 0^2 + 10^2 + 20^2\)= 2000

Spending sum of squares: \((-20)^2 + (-10)^2 + 0^2 + 10^2 + 20^2\) = 2000

Step 6: Calculate the correlation coefficient

Correlation coefficient = Sum of products / (sqrt(weight sum of squares) * sqrt(spending sum of squares))

Correlation coefficient = 1000 / (sqrt(2000) * sqrt(2000)) = 1000 / (44.721 * 44.721) ≈ 1000 / 2000 = 0.5

Therefore, the correlation coefficient between weight and spending in this example is approximately 0.5.

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Given the following equation:

You can solve for "x" by following these steps:

1. You must distribute the negative sign of the left side of the equation:

2. Now you need to add the like terms of the left side of the equation:

3. Apply the Subtraction property of equality by subtracting 7 from both sides of the equation:

4. Finally, you can apply the Division property of equality by dividing both sides of the equation by -2:

The answer is:

The risk of explosion in the process industry is 6.6594e-06 per year.

To calculate the risk of explosion, we need to consider the probability of a gas release, the probability of ignition, and the probability of fatal injury.

Step 1: Calculate the probability of an explosion.

The probability of a gas release per year is given as\(1.23 * 10^-^5\).

The probability of ignition is 0.54.

The probability of fatal injury is 0.32.

To calculate the risk of explosion, we multiply these probabilities:

Risk of explosion = Probability of gas release * Probability of ignition * Probability of fatal injury

Risk of explosion = 1.23 * \(10^-^5\) * 0.54 * 0.32

Risk of explosion = 6.6594 *\(10^-^6\) per year

Therefore, the risk of explosion in the process industry is approximately 6.6594 * 10^-6 per year.

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Answer:

Total marks = 468

Step-by-step explanation:

to find their total marks, you should simply find the sum of all the marks scored by Kiran and Surya in all subjects. That is done as follows:

99 + 69 + 91 + 92 + 33 + 84 =  468

Given a function of two variables, n and k, denoted as h(n, k), the function describes a mathematical relationship or operation that depends on the values of both n and k. Further details about the specific function, its definition, or purpose are required to provide a more comprehensive explanation.

A function of two variables, h(n, k), typically represents a mathematical relationship or operation that involves two independent variables, n and k. The specific form and purpose of the function can vary widely depending on the context or problem at hand.

To understand the behavior and properties of the function h(n, k), additional information is needed. This may include the mathematical expression defining the function, any constraints or conditions on the variables, and the intended interpretation or application of the function.

The function h(n, k) could represent various scenarios, such as a cost function in economics, a probability distribution in statistics, or a mathematical model in a scientific context. Without more details, it is challenging to provide a specific explanation or analysis of the function and its implications.

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To solve the vector equation using Gaussian elimination, let's set up an augmented matrix and perform row operations: the solution (4, -2) represents the weights or coefficients used to combine the given vectors to obtain the target vector [2, 4].

[−1 1 | 2]

[2  1 | 4]

Row 2 - 2 * Row 1:

[−1  1 | 2]

[0  -1 | 2]

Row 2 * -1:

[−1  1 | 2]

[0   1 | -2]

Row 1 + Row 2:

[−1  2 | 0]

[0   1 | -2]

Row 1 + 2 * Row 2:

[−1  0 | -4]

[0   1 | -2]

Now, we have the matrix in row-echelon form. Let's solve for the variables:

From the first row: -x1 = -4 => x1 = 4

From the second row: x2 = -2

Therefore, the unique solution to the vector equation is x1 = 4 and x2 = -2.

To illustrate this solution geometrically:

1) Intersection of two lines in a plane:

The vector equation represents two lines in a plane. The line formed by the first vector [-1, 1] passes through the point [2, 4], while the line formed by the second vector [2, 1] also passes through the point [2, 4]. The unique solution (4, -2) represents the intersection point of these two lines in the plane.

2) Weights in a linear combination of vectors:

The solution (4, -2) can be expressed as a linear combination of the given vectors. It means that we can multiply the first vector by 4 and the second vector by -2, then add them together to obtain the resulting vector [2, 4]. Mathematically:

4 * [-1, 1] + (-2) * [2, 1] = [2, 4]

This demonstrates that the solution (4, -2) represents the weights or coefficients used to combine the given vectors to obtain the target vector [2, 4].

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To determine whether the proportions of widows and widowers living different lengths of time after the death of their spouse are equal, you can conduct a chi-squared test of independence. This test compares the observed frequencies (the number of widows and widowers living different lengths of time) to the expected frequencies, which are the frequencies that you would expect to see if the two variables (widowhood and length of time survived) were independent.

To perform the chi-squared test, you will need to calculate the chi-squared statistic and the corresponding p-value. If the p-value is less than 0.05, you can conclude that there is a significant difference between the proportions of widows and widowers living different lengths of time after the death of their spouse. If the p-value is greater than 0.05, you cannot conclude that there is a significant difference between the proportions of widows and widowers.

To calculate the chi-squared statistic and p-value, you will need to follow these steps:

Calculate the expected frequencies for each group (widows and widowers) in each time period (less than 5 years, 5-10 years, more than 10 years). To do this, you will need to multiply the total number of widows (100) by the proportion of widows in each time period, and the total number of widowers (100) by the proportion of widowers in each time period.

Subtract the expected frequencies from the observed frequencies and square the result for each time period.

Divide each squared difference by the expected frequency and sum the results. This is the chi-squared statistic.

To calculate the p-value, you will need to consult a chi-squared table or use a statistical software program to determine the p-value corresponding to the chi-squared statistic and the degrees of freedom (which is equal to the number of time periods minus 1).

If the p-value is less than 0.05, you can conclude that there is a significant difference between the proportions of widows and widowers living different lengths of time after the death of their spouse. If the p-value is greater than 0.05, you cannot conclude that there is a significant difference between the proportions of widows and widowers

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Answer:

slope of 2 and y-intercept of 1

(3rd answer choice)

Step-by-step explanation:

Answer:

It's the last one doesn't matter which way you go they are both going to the negative way because they are going down and to the left so they are both negative. I hope this helps good luck.

Answer:

diamond or teeth or chromium

By this equation y = 1,716 - 112x he find that how much money he still owes after each month of the plan.

According to the statement

Jonathan bought a new computer for $1,716

He will pay $143 a month for 12 months.

Total amount he will for 12 months is 143(`12)

Now,

y = the money he still owes

x = the number of months (from x = 0 to x = 12)

y = 1,716 - 112x

So, By this equation y = 1,716 - 112x he find that how much money he still owes after each month of the plan.

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The standard normal distribution is a probability distribution over the entire real line with mean 0 and standard deviation 1. A random variable following this distribution is referred to as a standard normal random variable.

a) The statement “The random variable is continuous” is true for a standard normal random variable. A continuous random variable can take on any value in a given range, whereas a discrete random variable can only take on certain specific values. Since the standard normal distribution is a continuous distribution defined over the entire real line, a standard normal random variable is also continuous.

b) The statement “The mean of the variable is 0” is true for a standard normal random variable. The mean of a standard normal distribution is always 0 by definition.

c) The statement “The median of the variable is 0” is true for a standard normal random variable. The standard normal distribution is symmetric around its mean, so the median, which is the middle value of the distribution, is also at the mean, which is 0.

Therefore, all of the statements a, b, and c are true for a random variable with standard normal probability distribution, and the answer is d. None of the above.

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Answer:

Step-by-step explanation:

The equation that Dimitri and Jillian were trying to solve is expressed as

(x+1)(x+3) = 12. They are both solving this equation to get the value of x.

Based on the their suggestion, Jillian strategy would have been the best and the only one that will work for us in solving the equation but he didn't take cognizance of 12 when using the formula in his second step hence None of them are correct. The following steps should have been taken;

Step 1: Multiply out the expression (x+1)(x+3)

= (x+1)(x+3)

= x(x)+ 3x+x+1(3)

= x² + 3x + x + 3

= x² + 4x + 3

He got x² + 4x + 3 on expansion

Step 2: He should have rewrote the equation as shown;

x² + 4x + 3 = 12

x² + 4x + 3 -12 = 0

x² + 4x -9 = 0

Step 3: He used the quadratic formula to factorize the expression x² + 4x + 3 where a = 1, b = 4 anad c = -9

x = (-b±√b²-4ac)/2a

x = (-4±√(4)²-4(1)(-9))/2(1)

x = -4±√16+36/2

x = (-4±2√13)/2

x = (-4+2√13)/2 or  (-4-2√13)/2

x = -2+√13 or -2-√13

Hence Neither of them is correct. Jillian is almost correct but he should have equated the equation to zero by taking 12 into consideration before factorizing.

Answer:

15.4

Step-by-step explanation:

∠RSA =

95`

95-18=

77/5=

15.4

4 x 15.4=

61.6+7=

68.6