Define brittleness and strength​

Based on the given set of coordinates pairs, we can draw a diagram to show the domain and the range.

Once we defined the domain and range sets, we noticed that there are to domain values 13 and 1 assigned with one range value 54, that relation violates the function definition.

The statement "If a function is differentiable, then it is continuous" is generally true. In summary, if a function is differentiable at a point, it must also be continuous at that point.

Differentiability is a stronger condition than continuity. If a function is differentiable at a point, it means that it has a derivative at that point, indicating the existence of a well-defined tangent line.

A key property of differentiability is that it implies continuity. In other words, if a function is differentiable at a point, it must also be continuous at that point.

On the other hand, a function can be continuous without being differentiable. Continuous functions have no abrupt jumps, holes, or vertical asymptotes in their graphs. However, they may have corners, cusps, or vertical tangents, which prevent them from being differentiable at those points. Therefore, while differentiability guarantees continuity, continuity does not necessarily imply differentiability.

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Complete question - Write the conserve and contrapositive of the following statement- "If a function is differentiable then it is continuous."

For the quadratic equation -6x²+ 36x - 84 = 0, the values obtained are x1 = 3 - √(5)i and x2 = 3 + √(5)i.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The quadratic equation given is -  -6x²+ 36x - 84 = 0

To solve the equation first multiply -6x² × - 84 = 504x²

Now deduce the LCM of 504x².

504x² = 2 × 2 × 2 × 3 × 3 × 7 × x × x

Through the LCM add the number in such a way that the result should be  36x and multiplied the result should be 504x².

This is not possible since the equation has imaginary roots.

It will be represented in complex number form.

Apply the formula -

x = [(-b) ± √(b² - 4ac)] / 2a

Substitute the values into the equation -

x = [(-36) ± √{(36)² - 4(-6)(-84)} / 2(-6)

x = [(-36) ± 12√(5)i / 2(-6)

x1 = [(-36) + 12√(5)i / 2(-6)           x2 = [(-36) - 12√(5)i / 2(-6)

x1 = 3 - √(5)i                                 x2 = 3 + √(5)i

Therefore, the results are x1 = 3 - √(5)i and x2 = 3 + √(5)i.

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Answer:

n = -15         and          m = -3

Step-by-step explanation:

To solve the given system of equation, we will follow the steps below:

n = 5m ----------------------------------------------------------------------------(1)

n = \(\frac{2}{3} m -13\) ---------------------------------------------------------------------(2)

substitute for n= 5m in equation (2)

5m =  \(\frac{2}{3} m -13\)

subtract \(\frac{2}{3} m\) from both-side of the equation

5m -  \(\frac{2}{3} m\)  = \(\frac{2}{3} m\) -  \(\frac{2}{3} m -13\)

At the right-hand side of the equation  \(\frac{2}{3} m\)  will cancel-out leaving us with just -13

5m -  \(\frac{2}{3} m\)  = -13

\(\frac{15m - 2m }{3}\) = -13

\(\frac{13m}{3}\) = -13

multiply both-side of the equation by 3

3 ×  \(\frac{13m}{3}\) = -13 ×  3

At the left-hand side of the equation 3 will cancel-out 3 leaving is with just 13m

13m = -39

Divide both-side of the equation by 13

13m/13  = -39/13

m = -3

substitute m = -3 in  equation (1)

n = 5m

n = 5 (-3)

n = -15

Therefore, n = -15         and          m = -3

The equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is 3x + 2y + z = 8.

We need a point b and a vector v along the line in order to characterize it. We might alternatively begin with the two points a and b and use the formula v = ab.
A point Q and a vector n perpendicular to the plane are required in order to describe a plane. Later on, we'll look at how to get n from various types of information, such as the positions of three points on a plane.

A plane is a flat, endlessly long, two-dimensional surface. A plane is a point with zero dimensions, a line with one dimension, and space with three dimensions in two dimensions. The picture below that is attached shows the answer.

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Question correction:

Find the equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0

Answer:

3+1/2n

Step-by-step explanation:

3 more of technically means +3 and 1/2 of n would be 1/2n so just put them together

a) The range is 14.

b) The sample variance is 20.78.

c) The sample standard deviation is 4.56.

a) Range

The range of a given set of data values is the difference between the maximum and minimum values in the set. In this case, the maximum value is 15 and the minimum value is 1. So, the range is:

Range = maximum value - minimum value

Range = 15 - 1

Range = 14

b) Sample variance

To calculate the sample variance, follow these steps:

1. Calculate the sample mean (X). To do this, add up all of the data values and divide by the total number of values:

n = 9

∑x = 7 + 4 + 6 + 12 + 8 + 15 + 1 + 9 + 13 = 75

X = ∑x/n = 75/9 = 8.33

2. Subtract the sample mean from each data value, square the result, and add up all of the squares:

(7 - 8.33)² + (4 - 8.33)² + (6 - 8.33)² + (12 - 8.33)² + (8 - 8.33)² + (15 - 8.33)² + (1 - 8.33)² + (9 - 8.33)² + (13 - 8.33)² = 166.23

3. Divide the sum of squares by one less than the total number of values to get the sample variance:

s² = ∑(x - X)²/(n - 1) = 166.23/8 = 20.78

Therefore, the sample variance is 20.78 (rounded to two decimal places).

c) Sample standard deviation

To calculate the sample standard deviation, take the square root of the sample variance:

s = √s² = √20.78 = 4.56

Therefore, the sample standard deviation is 4.56 (rounded to two decimal places).

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To estimate the standard deviation of our  forecast, we'd  generally use cross-validation. Specifically, we'd divide the data into a training set and a  confirmation set.

We will fit the statistical  literacy  system on the training set and use it to make future forecasting on the  confirmation set. We'd calculate the mean squared error( MSE) of the forecast, which is the  normal of the squared differences between the future values and the  factual values.

Eventually, we'd take the square root of the MSE to  gain the estimated standard  divagation of our future prediction. This system allows us to assess the  delicacy of our model and estimate the  query of our  prediction.

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Answer:b

Step-by-step explanation:

Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

The solution in interval notation is [4, +∞).

To solve the compound inequality -3y <= -3 and 4y - 1 >= 15, we will solve each inequality separately and then combine the solutions.

First, let's solve -3y <= -3:

Divide both sides by -3, remembering to reverse the inequality symbol since we are dividing by a negative number:

-3y/(-3) >= -3/(-3)

y >= 1

Next, let's solve 4y - 1 >= 15:

Add 1 to both sides:

4y - 1 + 1 >= 15 + 1

4y >= 16

Divide both sides by 4:

y >= 4

Now, we have the solutions y >= 1 and y >= 4.

To combine these solutions, we take the intersection of the two intervals:

The solutions lie where both conditions are satisfied, which is when y is greater than or equal to 4.

Therefore, the solution in interval notation is [4, +∞).

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a.9v3-4v3+v5+2v5

=5v3+v3+2v5

=5v3+3v5

b.10v2+4v2+6v2

=4v2+4v7

Answer:

(3x-4)(2x+5)

Step-by-step explanation:

6x^2 + 7x + 24

= 6x^2 + (15-8)x + 24

= 6x^2 + 15x - 8x + 24

= 3x( 2x+5 ) - 4( 2x+5 )

= (3x-4)(2x+5)

To calculate the nominal interest rate in Excel, you can use the following formula:

nominal interest rate = (monthly payment * number of payments) / loan amount

For example, if your loan amount is $212,000, your monthly payment is $950, and the number of payments is 360, you can use the following formula:

nominal interest rate = (950 * 360) / 212000

This will give you the nominal interest rate as a decimal. To convert it to a percentage, you can multiply it by 100.

To calculate the effective interest rate, you can use the following formula:

effective interest rate = POWER((1 + nominal interest rate),(1/number of payments per year)) - 1

Note that the "number of payments per year" in this formula should be the number of times per year that you make a payment. So if you make monthly payments, the number of payments per year would be 12.

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The congruent segments, \( SC \cong HR \) and \( HR \cong AB\), according to the substitution property of equality, gives; \( SC \cong AB \)

The given parameters are;

Required;

To prove;

\( SC \cong AB\)

Solution;

From the given parameters, and the definition of congruency, we have;

According to the symmetric property of equality, we have;

SC = HR

Therefore;

According to the substitution property of equality, we have;

If a = b and a = c, therefore;

b = c

Which gives;

HR = SC

HR = AB

Therefore;

SC = AB

Which gives;

\( SC \cong AB \) (Inverse of the definition of congruency)

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The answer to this question is less coping strategies.

What are coping strategies?

Coping strategies are ways through which an individual gains some control over their emotions

Yes research has proved that the   Younger adults use more coping strategies than Older adults because now a days so methods for coping strategies like Cigerrate, alcohol, drugs etc things are easily being available to them and they use that to overcome their emotions

where as older adults have already seen most of their life so they are less likely to use these things to overcome their emotions

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As the result g(x,y) has a relative minimum at the critical point (3,3) and a saddle point at the critical point (-1,-1).

To find the critical points of the function g(x,y) = x² - 2xy + ⅓y³ - 3y, we need to compute the partial derivatives with respect to x and y, and then solve for the points where both partial derivatives are equal to zero.

(a) Find all the critical points of g:

∂g/∂x = 2x - 2y
∂g/∂y = -2x + y² - 3

Set both partial derivatives equal to zero and solve for x and y:

2x - 2y = 0  →  x = y
-2x + y² - 3 = 0

Substitute x = y into the second equation:

-2y + y² - 3 = 0

This is a quadratic equation in y. Solve for y:

y² - 2y - 3 = 0
(y - 3)(y + 1) = 0

So, y = 3 or y = -1. Then, corresponding x values are x = 3 and x = -1. Therefore, the critical points are (3,3) and (-1,-1).

(b) To determine the nature of each critical point, we need to find the second partial derivatives and compute the determinant of the Hessian matrix:

∂²g/∂x² = 2
∂²g/∂y² = 2y
∂²g/∂x∂y = ∂²g/∂y∂x = -2

The Hessian matrix is:

|  2  -2 |
| -2  2y |

The determinant of the Hessian matrix is:

D = (2)(2y) - (-2)(-2) = 4y - 4

For the critical point (3,3):

D(3,3) = 4(3) - 4 = 8 > 0 and ∂²g/∂x² > 0, which indicates a relative minimum.

For the critical point (-1,-1):

D(-1,-1) = 4(-1) - 4 = -8 < 0, which indicates a saddle point.

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Answer: about 2 times greater

Step-by-step explanation:

To determine if a line and plane are parallel, verify if the line's direction vector is orthogonal to the plane's normal vector. If parallel, the line lies on the plane, if perpendicular, and skews to the plane. If neither is true, the line is skew to the plane.

(a) To determine whether the given line and the given plane are parallel or not, we need to verify if the direction vector of the line is orthogonal to the normal vector of the plane. If the direction vector of the line is parallel to the plane,

then the line lies on the plane. If the direction vector of the line is orthogonal to the plane, then the line is perpendicular to the plane. If neither of these is true, then the line is skew to the plane.The direction vector of the given line is (1,-1,-2), and the normal vector of the plane x+2y+3z-9=0 is (1,2,3). To check whether the direction vector of the line is orthogonal to the normal vector of the plane, we compute their dot product.

So, we have: (1,-1,-2)·(1,2,3)=1-2-6=-7As the dot product of the direction vector of the line and the normal vector of the plane is not equal to 0, the line is not parallel to the plane.

Therefore, the line and plane are not parallel.(b) To determine whether the given line and the given plane are parallel or not, we need to verify if the direction vector of the line is orthogonal to the normal vector of the plane. If the direction vector of the line is parallel to the plane, then the line lies on the plane. If the direction vector of the line is orthogonal to the plane,

then the line is perpendicular to the plane. If neither of these is true, then the line is skew to the plane.The direction vector of the given line is (3,2,-1), and the normal vector of the plane 4x-y+2z+1=0 is (4,-1,2). To check whether the direction vector of the line is orthogonal to the normal vector of the plane, we compute their dot product. So, we have: (3,2,-1)·(4,-1,2)=12-2-2=8As the dot product of the direction vector of the line and the normal vector of the plane is not equal to 0, the line is not parallel to the plane. Therefore, the line and plane are not parallel.

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Answer:

Step-by-step explanation:

The correct statement is: d.  "The impact on the volume if the dimensions are multiplied by 14  the new volume will be 14 times the original volume.      

To determine the impact on the volume when the dimensions of the cone are multiplied by 14, we need to calculate the new volume and compare it to the original volume. Let's denote the original radius as r and the original height as h.

Given:

Original radius (r) = 12 ft

Original height (h) = 24 ft

New radius = 14 * r

New height = 14 * h

The formula for the volume of a cone is V = (1/3) * π * r^2 * h.

Original Volume (V_original) = (1/3) * π * (r^2) * h

= (1/3) * π * (12^2) * 24

≈ 10845.12 cubic feet

New Volume (V_new) = (1/3) * π * ((14 * r)^2) * (14 * h)

= (1/3) * π * (196 * r^2) * (14 * h)

= (1/3) * π * (196 * (12^2)) * (14 * 24)

= (1/3) * π * 196 * 144 * 336

≈ 1086615.36 cubic feet

Comparing the new volume to the original volume:

a. The volume will decrease by 116.

False. The new volume is significantly larger than the original volume, so it does not decrease by 116.

b. The original volume will be divided by 43.

False. Dividing the original volume by 43 does not yield the new volume.

c. The original volume is decreased by approximately 2111.15 units^3.

False. The difference between the new volume and the original volume is much larger than 2111.15 units^3.

d. The new volume will be 14 times the original volume.

True. The new volume is approximately 14 times the original volume.

e. The original volume will be multiplied by 164.

False. Multiplying the original volume by 164 does not yield the new volume.

Therefore, the correct statement is:

d. The new volume will be 14 times the original volume.

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9514 1404 393

Answer:

  3

Step-by-step explanation:

Vertical angles share a vertex point, and have opposite rays for sides. In short, they are across the point of intersection from each other. Vertical angles do not have a common side (they are not adjacent).

The first part of the problem is to identify angle NCA. That is shown in red in the attachment. The vertical angle is across the point of intersection. It is angle 3.

Answer  

1,863.5

Step-by-step explanation: add 165.85 +20.50 =186.35 the do 186.35 x 10 =1,863.5

Without the standard deviation, we cannot calculate the standard error or the 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B.

To calculate a 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B, we can use the least squares means estimates provided in the JMP output.

According to the JMP output, the estimate for the mean time required to stabilize emergency condition 4 using display panel B is 10.375000.

To calculate the confidence interval, we need to find the margin of error. The margin of error can be calculated using the formula:

Margin of Error = Critical Value * Standard Error

In this case, we need to find the critical value for a 95 percent confidence interval. Since we have a sample size of 24 (as mentioned in the question), we can use the t-distribution with (24-1) degrees of freedom to find the critical value.

Looking up the critical value in the t-distribution table, with (24-1) degrees of freedom and a confidence level of 95 percent, we find that the critical value is approximately 2.064.

The standard error can be calculated using the formula:

Standard Error = Standard Deviation / √(sample size)

The standard deviation is not provided in the given information. Therefore, we cannot calculate the standard error or the confidence interval without this information.

In summary, without the standard deviation, we cannot calculate the standard error or the 95 percent confidence interval for the mean time required to stabilize emergency condition 4 using display panel B.

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Step-by-step explanation:

the answer is in the above image

Answer: -3

Step-by-step explanation:

Given points (-1,6) and (2,-3), we can use the slope formula y2-y1/x2-x1 to find the slope

6-(-3)/-1-2 = 9/-3 = -3

Slope is -3

5 more than a number is greater or equal to 27

The "number" can be represented as x.

\(\boxed{x+5\geq 27}\)

The option that matches to the given equation is as follows:

a.) Option A

b.) Neither A nor B

C.) Option A

d.) Neither A nor B

e.) Option B

f.) Option B

g.) Option B

h.) Neither A nor B

Option A = 4+3 = 7 can also be written as 7-4 = 3

Option B = 3+3+3+3 =12

= 4(3) = 12

= 12/4 = 3

For question a.)

7 = 3+4 . This represents the diagram of option A.

For question b.)

4-3 = 7 . This doesn't have any representation.

For question C.)

7-4 = 3 . This represents the diagram of option A.

For question d.)

4-3 = 7. This doesn't have any representation.

For question e.)

3+3+3+3 = 12. This represents the diagram of option B.

For question f.)

12= 4÷3. This doesn't have any representation.

For question g.)

12÷4 = 3. This represents the diagram of option B.

For question h.)

3÷3÷3÷3 = 12. This doesn't have any representation.

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Answer:

19

Step-by-step explanation:

straight line=180°

180-123=57

57/3=19

19*3=57

Answer:

The simplified expression has four terms.

The simplified expression has a constant term.

The simplified expression is cubic.

The simplified expression is a trinomial.

The statements that are true about the result of simplifying this polynomial are:

b. The simplified expression is a polynomial.

c. The simplified expression has a constant term.

Sums of terms of the form k x xⁿ, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. A description of polynomials.

All other options are false. As it is not cubic because it is degree 4, and it does not have four terms as it has five terms. And it is not trinomial as it has five terms, not three.

The full solution is;

t³(8 + 9t) - (t² + 4)(2 - 3t)

8t³ + 9t⁴ - (2t² - 3t³ + 8 - 12t)

8t³ + 9t⁴ - 2t² + 3t³ - 8 + 12t

9t⁴ + 11t³ - 2t² + 12t - 8

Therefore, the correct options are a, and b.

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The product of the factors in the given expression comes to be \(7.35932 *10^{-3}\).

The given expression is:

\((1.466*10^{-8} )(5.02*10^5)\)

We can rewrite the given expression as

\((1.466*5.02)(10^{-8} *10^5)\)

If we have two numbers with the same base we can write the product of the numbers as a single base followed by the addition of exponents.

\(a^m*a^n = a^{m+n}\)

\(1.466*5.02=7.35932\)

\(10^{-8} *10^5 = 10^{-3}\)....from exponent addition rule

So, \((1.466*10^{-8} )(5.02*10^5)=7.35932 *10^{-3}\)

Therefore, the product of the factors in the given expression comes to be \(7.35932 *10^{-3}\).

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Answer:

7.3593 and -3

Step-by-step explanation:

Got it right on the assignment.