a is 15 A is the inverse ol matrix A,give the values of g and h below,showing all working and simplifying results as far as possible 3 (iv) Solve the system of simultaneous equations 2x+3y+z=4 x-2y+2z=4 4y-3x-3z=5 ing.matrixinversion:

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The length of AC is given as follows:

AC = 25.

Applying the secant-tangent theorem, we have that the following equation holds true:

CD² = BC(AC + BC).

Hence the value of x is obtained as follows:

15² = 9(9 + 3x + 1)

15² = 9(10 + 3x)

225 = 90 + 27x

x = (225 - 90)/27

x = 5.

Then the length of AC is of:

AC = 3(5) + 1 + 9

AC = 25.

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Answer:

25/4 or 6.25

Step-by-step explanation:

Given that the general equation of  a quadratic equation is given as

ax^2 + bx + c = 0, to complete the square, we subtract c from both sides of the equation and add the square of (b/2a) to both sides.

Hence given x^2-5x-19=0, to complete the square, we add

(-5/2)^2 to both sides following the illustration given.

This is 25/4 or 6.24

Answer:

# 1 the missing side is 11,  20+12+12= 44

Step-by-step explanation:

Answer:

1. 5

2. 4

3. 2

4. 10

Step-by-step explanation:

i did this already. so i knew the answers

Answer:

3x + 4y = 16  The rule is you can do any valid operation on both sides of an equation and it will still be equal. Subtract 4y.

3x = -4y + 16  Divide by 3.

x = -4y/3 + 16/3  Answer B.

The solution for the equation 3x + 4y = 16 for x is (16 - 4y)/3 or 16/3 - 4y/3. The correct option is D.

The slope-intercept form of the equation of a line is y = mx + b.

To solve for x, we need to isolate x on one side of the equation. To do this, we can follow these steps:

Move the term containing y to the other side of the equation by subtracting 4y from both sides:

3x + 4y - 4y = 16 - 4y

Simplifying the left-hand side gives:

3x = 16 - 4y

Divide both sides by 3 to isolate x:

3x/3 = (16 - 4y)/3

Simplifying the left-hand side gives:

x = (16 - 4y)/3

So the solution for x is:

x = (16 - 4y)/3

Thus, the correct option is D.

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The integral evaluates to zero, which does not match the given result. Thus, the statement is not verified.

To verify the given integrals using the method of residues, we need to evaluate the integrals using the complex variable approach and the concept of residues. Here are the evaluations for each integral:

To solve the integral \($\int_{0}^{2\pi} (2 + \sin \theta) \, d\theta$\) using the complex variable approach, we can rewrite the integrand as

\($2\left(\frac{1}{2}\right) + \sin \theta$\),

which is equivalent to \($ \rm {Re}(e^{i\theta})$\).

Using the complex variable \($z = e^{i\theta}$\) the differential dz becomes \($dz = i e^{i\theta} \, d\theta$\).

The integral can now be expressed as:

\($ \[\int_{0}^{2\pi} (2 + \sin \theta) \, d\theta = \int_{C} {Re}(z) \, dz,\]\)

where C represents the contour corresponding to the interval \($[0, 2\pi]$\).

By evaluating the integral along the contour C, we obtain the result \($\frac{3\pi}{2}$\).

In conclusion, the value of the integral \($\int_{0}^{2\pi} (2 + \sin \theta) \, d\theta$\) is \($\frac{3\pi}{2}$\) when using the complex variable approach.

where C is the unit circle in the complex plane.

Now, we need to find the residue of Re(z) at z = 0. Since Re(z) is an analytic function, the residue is zero.

By the residue theorem, the integral of an analytic function around a closed curve is zero if the curve does not enclose any poles.

As a result, the integral evaluates to zero, which does not correspond to the supplied result. As a result, the statement cannot be validated.

Similarly, we can apply the method of residues to the other integrals to check their validity. However, it's important to note that some of the given results do not match the actual evaluations obtained through the residue method. This suggests that there may be errors in the given results or a mistake in the formulation of the problem.

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Answer:

All students are correct.

Step-by-step explanation:

The volume of a cylinder is the area of the base multiplied by the height.

First student:

V = Bh,

where B = area of the base

and h = height

This is a correct calculation of the volume.

Second student:

area of a circular cross section multiplied by the cylinder's height

Since the base has the same area as a circular cross section, this is correct.

Third student:

V = πr²h

πr² is the area of the base

This is also correct.

All students are correct.

Answer:

C) SSA Similarity Theorem

Step-by-step explanation:

The SAS Similarity Theorem asserts that if two sides of one triangle are proportionate to two sides of another triangle, and both triangles' included angles are congruent, the two triangles are similar.

The implicit differentiation of the function x³cos(2y) - 3x⁴ + 2e^(3y) = 7 using Total Derivatives and Partial Derivatives is:

3x²cos(2y) - 6x³y' sin(2y) - 12x³ + 6ye^(3y) = 0

To find the implicit differentiation of the given function, we will use the method of Total Derivatives and Partial Derivatives. We differentiate both sides of the equation with respect to x using the Chain Rule as follows:

d/dx [x³cos(2y) - 3x⁴ + 2e^(3y)] = d/dx [7]

Using the Chain Rule, we get:

(3x²cos(2y) - 12x³) + (-12x³y' sin(2y) + 6ye^(3y) y')

Next, we isolate the derivative term y' by moving all other terms to the right-hand side of the equation:

-12x³y' sin(2y) + 6ye^(3y) y' = 12x³ - 3x²cos(2y)

Factor out y' from the left-hand side of the equation:

y'(-12x³ sin(2y) + 6ye^(3y)) = 12x³ - 3x²cos(2y)

Finally, we can solve for y' by dividing both sides by (-12x³ sin(2y) + 6ye^(3y)):

y' = (12x³ - 3x²cos(2y)) / (-12x³ sin(2y) + 6ye^(3y))

Therefore, the implicit differentiation of the given function using Total Derivatives and Partial Derivatives is:

3x²cos(2y) - 6x³y' sin(2y) - 12x³ + 6ye^(3y) = 0

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Answer:

(-5,1)

Step-by-step explanation:

The solution of the system is where the two lines intersect

The graphs cross at x=-5 y = 1

The  reverse of multiply by 44 is: 0.02272727.

Instead of multiplying by 44  we can  divide by the reciprocal of 44 reason been that division is the multiplicative reverse. Dividing by a digit is the same things as multiplying by the reciprocal of the digit.

Hence,

reverse of multiply by 44

Let the multiplicative reverse by x

44 (x)=1

x=1/44

x= 0.02272727

Prove:

0.02272727×44

=1

Therefore the  reverse of multiply by 44 is: 0.02272727.

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Answer:

=48

Step-by-step explanation:

Answer:

k/-8=-6

k=-6*-8

k=48

Step-by-step explanation:

Answer:

The answer is 127.6

Step-by-step explanation:

To find the volume of something, you multiply.

So:5.5 times 3.2 times 7.25 is equal to 127.6

HOPE THIS HELPS YOU!!!!    :)

Answer:

127.60 square inches

Step-by-step explanation:

Multiply the diameters all together to get your answers.

5.5 x 3.2 x 7.25

Multiply

5.5 x 3.2 = 17.6

Multiply some more

17.6 x 7.25 = 127.6

You can also just multiply like this:

5.5 x 3.2 x 7.25 = 127.6

Hope this helped :)

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Answer:

Step-by-step explanation:

35: 1, 5, 7, 35

125: 1, 5, 25, 125

GCF: 5

Check the picture below.

"Statistics: The Art and Science of Learning from Data" (4th edition) is a valuable resource for understanding and applying statistical principles, providing insights into data analysis and decision-making processes.

Statistics is the art and science of learning from data. It involves collecting, organizing, analyzing, interpreting, and presenting data to gain insights and make informed decisions. In the 4th edition of the book "Statistics: The Art and Science of Learning from Data," you can expect to find a comprehensive exploration of these topics.

This edition may cover important concepts such as descriptive statistics, which involve summarizing and displaying data using measures like mean, median, and standard deviation. It may also delve into inferential statistics, which involve making inferences and drawing conclusions about a population based on a sample.

Additionally, the book may discuss various statistical techniques such as hypothesis testing, regression analysis, and analysis of variance (ANOVA). It may also provide real-world examples and case studies to illustrate the application of statistical methods.

When using information from the book, it is important to properly cite and reference it to avoid plagiarism. Be sure to consult the specific edition and follow the guidelines provided by your instructor or institution.

In summary, "Statistics: The Art and Science of Learning from Data" (4th edition) is a valuable resource for understanding and applying statistical principles, providing insights into data analysis and decision-making processes.

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Answer: 3

Step-by-step explanation:

The correct definition of dependent events is two events are dependent if the outcome of the first event affects the outcome of the second event.

Two events are dependent if the outcome of one of the event depends on the outcome of the first event.  An example of a dependent event is if it rains, the floor would be wet.

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The ponderal index cannot be computed without the value of the constant "a" in the formula. Therefore, the ponderal index for a person who is 76 inches tall and weighs 192 pounds cannot be determined.

To compute the ponderal index, we need the formula and the value of the constant "a."

a) The formula for the ponderal index is given as I = a, where I represents the ponderal index and a is a constant. However, the value of the constant "a" is missing in the provided information. Without knowing the value of "a," we cannot compute the ponderal index for a person who is 76 inches tall and weighs 192 pounds.

b) Similarly, without knowing the value of the constant "a," we cannot determine the weight of a man who is 77 inches tall and has a ponderal index of 11.56.

To compute the ponderal index or determine the weight, we need the specific value of the constant "a" in the given formula.

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Answer:

2/16

Step-by-step explanation:

this is the 4th equivalent fraction to 1/8

The true statements are:

The area under the curve to the left of the pth percentile is equal to p

The area under the curve to the right of the pth percentile is equal to (1-P)

For the first set of statements regarding the standard normal distribution:

1. For z < 0; P(Z < 2) < 0

  - This statement is true. Since z < 0, the probability of Z being less than 2 (a positive value) is less than 0.

2. P(Z < 0) = 0.50

  - This statement is true. For the standard normal distribution, the probability of Z being less than 0 is 0.50 or 50%.

3. P(Z > 0) = 0.0

  - This statement is false. The probability of Z being greater than 0 is not 0.0 but rather 0.50 or 50%.

4. For z > 0, P(Z < 2) < 0.50

  - This statement is true. When z is positive, the probability of Z being less than 2 is less than 0.50.

5. For z > 0, P(Z < 2) > 0.50

  - This statement is false. When z is positive, the probability of Z being less than 2 is always less than 0.50.

6. P(Z > 0) = P(Z < 0) = 0

  - This statement is false. The probability of Z being greater than 0 and less than 0 is both 0.50 or 50%.

Therefore, the true statements are:

- For z < 0; P(Z < 2) < 0

- P(Z < 0) = 0.50

- For z > 0, P(Z < 2) < 0.50

For the second set of statements regarding the pth percentile of a continuous random variable:

1. The area under the curve to the left of the pth percentile is equal to p

  - This statement is true. The pth percentile represents the value below which a certain percentage (p) of the data falls.

2. The area under the curve to the left of the pth percentile is equal to (1-p)

  - This statement is false. The area to the left of the pth percentile is equal to p, not (1-p).

3. The area under the curve to the right of the pth percentile is equal to (1-P)

  - This statement is true. The area to the right of the pth percentile is equal to (1 - p).

4. The area under the curve to the right of the pth percentile is equal to p

  - This statement is false. The area to the right of the pth percentile is equal to (1 - p), not p.

5. The pth percentile is positive

  - This statement's validity depends on the specific distribution being considered. The pth percentile could be positive, negative, or zero, depending on the distribution.

Therefore, the true statements are:

- The area under the curve to the left of the pth percentile is equal to p

- The area under the curve to the right of the pth percentile is equal to (1-P)

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Investing οne pesο at a mοnthly cοmpοund interest rate οf 5% fοr 30 years results in apprοximately 30.1267 pesοs.

Tο calculate the tοtal amοunt οf mοney that sοmeοne wοuld have after 30 years οf investing οne pesο at a mοnthly cοmpοund interest rate οf 5%, we wοuld need tο use the fοllοwing fοrmula:

\(A = P(1 + r/n)^{(nt)\)

Where:

A = the tοtal amοunt οf mοney at the end οf the investment periοd

P = the principal amοunt invested (in this case, οne pesο)

r = the annual interest rate (in this case, 5%)

n = the number οf times the interest is cοmpοunded per year (since the interest is cοmpοunded mοnthly, n = 12)

t = the number οf years οf the investment periοd (in this case, 30)

Plugging in these values, we get:

\(A = 1(1 + 0.05/12)^{(12*30)\)

\(A = 1.05^{(360)\)

\(A = 30.1267\)

Therefοre, after 30 years οf investing οne pesο at a mοnthly cοmpοund interest rate οf 5%, the tοtal amοunt οf mοney that wοuld be οbtained is apprοximately 30.1267 pesοs.

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Complete Question:

The concept of compound interest may not be very familiar, but it is something relatively simple: each time a capital generates interest, it will be added, thus obtaining a larger amount, which will produce higher interest.

What capital would a person obtain in 30 years by investing a peso at a compound interest rate of 5% per month?

Answer:

up

Step-by-step explanation:

a is positive

Answer:

8.69>8.6

Step-by-step explanation:

Because 8.69 has .09 more than 8.6

Answer:

8.69 > 8.60

Step-by-step explanation:

You need to add a zero to the end to 8.6 so it's easier to compare. Since all the digits in the two numbers are the same except 9 and zero, those are what you need to compare. 9>0, so 8.69 > 8.6

hope this helped! :)

Given the standard deviation of 1, If Kayden were to run 37 practice trials, of the 400 meters dash, 84%  would be slower than 88 seconds.

The following information is given:

Kayden runs the 400-meter dash, his finishing times are normally distributed with a mean of 90 seconds and a standard deviation of 1 second;

Mean (μ) = 90

Standard deviation (σ) = 1

We are supposed to find Kayden were to 37 practice trials of the 400-meter dash, how many of those trials would be faster than 88 seconds, to the nearest whole number i.eP (x < 88)

z = (x - μ) /σ

z = 88 - 90/1

z = -2

We must refer to the z table for the value of P; where

p (x < 88) = 0.0228

Recall that Kayden was to run 37 practice trials. hence

P (x < 88) = 37 * 0.0228

= 0.8436

Therefore, to the nearest whole number, we can state that 84% would be faster than 88 seconds.

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• For every increase in height, the temperature is -5

• The temperature on the surface is when y = 23

Given the equation:

Where y represent the temperature (in degrees Celsius), and x represent the height above the surface (in kilometers).

For x = 1, we have:

23 - 5(1) = y

y = 23 - 5 = 18

For x = 2, we have:

23 - 5(2) = y

y = 23 - 10 = 13

For x = 3, we have:

23 - 5(3) = y

y = 23 - 15 = 8

For every increase in height, the temperature is -5

The temperature on the surface is when x = 0

23 - 5(0) = y

y = 23

Answer:

\(-\frac{1}{5} t^{15}\)

Step-by-step explanation:

sry if im wrong