A factorization A = PDP^-1 is not unique. For A = [9 -12 2 1], one factorization is P = [1 -2 1 -3], D= [5 0 0 3], and P^-1 = [3 -2 1 -1]. Use this information with D_1. = [3 0 0 5] to find a matrix P_1, such that A= P_1.D_1.P^-1_1.

Answer:

n=6

Step-by-step explanation:

The mean is lower than the mode which is lower than the median.

A skewed curve is a type of statistical distribution in which the data is unevenly distributed. It is often referred to as an asymmetric distribution, meaning that the two halves of the curve look different. Skewed curves can be either positively or negatively skewed, depending on which direction the data points are shifted. Positively skewed curves tend to have a long tail to the right, while negatively skewed curves have a long tail to the left. This type of distribution is commonly seen in real-world data, such as income or wealth distributions.

A negatively skewed curve is characterized by a tail on the negative side of the graph. This means that the data points have a higher probability of being lower than the mean. As such, the mean is lower than the mode, which is lower than the median. The mean is the arithmetic average of all of the data points, the mode is the most frequent value, and the median is the midpoint of the data points.

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Answer:

Gallons

Step-by-step explanation:

Since its a fish tank and in high diameter it would be used for a big measurement unit so the answer would be gallons.

Answer:

pounds

Step-by-step explanation:

she would need inches gallons and teapoons,in order to find the volume.

hope this helps.

Answer:

a = c * SinФ

Step-by-step explanation:

SinФ = opp / hyp

c = hyp

a = opp

SinФ = a / c

therefore

a = c * SinФ

Answer: 24 inches

Step-by-step explanation:

Let the radius be represented by x

Therefore, the height will be = 2×x = 2x

Volume of a cylinder = πr²h

where, Volume = 3500

π = 3.14

r = x

h = 2x

We then slot in the values into the formula

Volume = πr²h

3500 = 3.14 × x² × 2x

3500 = 3.14 × 2x²

2x² = 3500 / 3.14

2x² = 1114.65

Divide through by 2

x² = 1114.65 / 2

x² = 557

x = ✓557

x = 23.6 = 24 approximately

The radius is 24 inches

The random selection of a sample to represent the proportions of a population divided by sex and size of school attended is called stratified random sampling.

Stratified random sampling is a sampling method used when a population is divided into subgroups or strata based on certain characteristics, such as sex and size of school attended. In this method, a random sample is taken from each subgroup proportionate to its size in the population. This ensures that each subgroup is represented in the sample and reduces the chance of sampling bias.

For example, if the population of high school seniors is divided into two strata based on sex and two strata based on size of school attended, there would be four subgroups. A random sample would then be taken from each subgroup to create a representative sample of the entire population.

Stratified random sampling is commonly used in research studies and surveys to ensure that the sample accurately represents the population being studied. It allows for more precise estimates and statistical inferences to be made about the population as a whole.

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The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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Answer:

It's 18 days

Step-by-step explanation:

Answer:

Not a Function

Step-by-step explanation:

The equation x^2 + y^2 = 9 is not a function because it does not pass the vertical line test

x2 + y2 = 9 is that function or not an function

its a function

Answer:

A

Step-by-step explanation:

the answer is a because i did a review with my teacher and it was a

The missing reasons in Wong's argument will be:

Reason 1: an alternate exterior angle with one of the angles in the triangle

Reason 2: vertical angles with the other two interior angles in the triangle

Recall:

Angle a in the diagram attached below is an alternate exterior angle and it will be equal to the exterior angle formed by lines m, x, and y.

Angles b and c are both vertical angles, and they will be equal to each of the angles they are directly opposite to each of the interior opposite angles in the triangle.

If we add all three angles, they should give us 180°. This therefore means that:

m∠a + m∠b + m∠c = 180°

Therefore, the missing reasons in Wong's argument will be:

Reason 1: an alternate exterior angle with one of the angles in the triangle

Reason 2: vertical angles with the other two interior angles in the triangle

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The distance around a hockey rink, ignoring the corner rounding, is 570 feet. To find the distance around the hockey rink, we need to calculate the perimeter of the rectangle.

The perimeter of a rectangle is given by the formula: perimeter = 2 * (length + width).

In this case, the length of the rectangle is 200 feet and the width is 85 feet. Substituting these values into the formula, we have perimeter = 2 * (200 + 85) = 2 * 285 = 570 feet.

Therefore, the distance around a hockey rink, ignoring the corner rounding, is 570 feet, which corresponds to option A) 570 ft.

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Answer:

Slope: 1

__________

y-intercept: (0,0)

Step-by-step explanation:

When overlaying data sets with spatial joins, logical consistency is important because it ensures that the results are accurate and reliable. This is because spatial joins involve combining different data sets based on their geographic locations, and any inconsistencies in the data can lead to errors and inaccuracies.

Logical consistency helps to ensure that the data sets being combined are compatible and can be accurately joined together. For example, if one data set uses a different projection than another data set, the resulting spatial join may be inaccurate or even impossible. Similarly, if the data sets contain different attribute values for the same geographic features, the resulting spatial join may be inconsistent or incomplete.Problems with spatial joins can be reduced by ensuring that the data sets being combined are logically consistent. This can involve standardizing the projections, attribute values, and other data properties to ensure that they are compatible.

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Answer:

Scale factor = 7

Step-by-step explanation:

Dilation with scale factor to map HEFG to DABC will be,

Scale factor = \(\frac{\text{Dimension of Image DABC}}{\text{Dimension of preimage HEFG}}\)

                    = \(\frac{\text{Length of CD}}{\text{Length of GH}}\)

Length of CD = Distance between two points C(0, -7) and D(-7, 0)

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

                       = \(\sqrt{(-7-0)^2+(0+7)^2}\)

                       = \(\sqrt{98}\)

                       = \(7\sqrt{2}\)

Length of GH = Distance between G(0, -1) and H(-1, 0)

                       = \(\sqrt{(-1-0)^2+(0+1)^2}\)

                       = \(\sqrt{2}\)

Scale factor = \(\frac{7\sqrt{2} }{\sqrt{2} }\)

                    = 7

Answer:

C

Step-by-step explanation:

The length of arc AC (L) is calculated as

L = circumference of circle × fraction of circle

  = 2πr × \(\frac{150}{360}\)

  = 2π × 12 × \(\frac{5}{12}\)

 = 2π × 5

 = 10π ≈ 31.42 → C

As the cone has the same base area and height with those of  cylinder, the volume of the cone is 1/3 the volume of the cylinder of 18.33π cubic units.

The volume of a cylinder is given by:

V =  πr²h

Where:

r = radius of the base

h = height of the cylinder

The volume of a cone is given by:

V = 1/3  πr²h

Relation between the volume of a cylinder and a cone which have the same radius of their base and the same height is:

V_cone = 1/3 V_cylinder

In this problem, the volume of the cylinder is:

V(cylinder) = 55π cubic units.

Since the cone has the same base area and the same height as those of the cylinder, then,

V(cone) = 1/3 V(cylinder)

             = (1/3) 55π

             = 18.33 π cubic units.

There are some typos in your question. Most likely it was:

The following cylinder has a volume 55π  cubic units and a height of 5 units. The cone has the same base area and height, and it has a slant height of 6 units. What is the volume of the cone?

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The center of gravity (x¯, y¯) of the wire is approximately (2.546, 2.546).

To find the center of gravity (x¯, y¯) of the wire, we can use the concept of geometric centroids. For a quarter of a circle in the first quadrant, the center of gravity will coincide with the centroid of the quarter-circle.

The centroid coordinates (x¯, y¯) of a quarter-circle with radius R can be found using the following formulas:

x¯ = (4R)/(3π)

y¯ = (4R)/(3π)

In this case, the radius of the quarter-circle is 6. Plugging this value into the formulas, we get:

x¯ = (4 * 6) / (3 * π)

= 24 / (3 * 3.14159)

≈ 2.546

y¯ = (4 * 6) / (3 * π)

= 24 / (3 * 3.14159)

≈ 2.546

Therefore, the center of gravity (x¯, y¯) of the wire is approximately (2.546, 2.546).

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As a result, the area of the surface formed by rotating the given curve about the x-axis throughout the period [9, 20] is 864π.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.

Here,

The area of the surface generated when a curve is revolved about an axis is known as the surface area of revolution and can be calculated using the formula:

A = 2π ∫ y dx

where y is the equation of the curve being revolved and the integral is taken over the interval [a,b] in which the curve is being revolved.

In this case, the curve is given by y = 8√x on the interval [9, 20]. So, the surface area of revolution is:

A = 2π ∫_9^20 8√x dx

This integral can be evaluated using substitution. Let u = √x, so that du = dx / 2√x and x = u^2. Then:

A = 2π ∫_3^4 8u * 2u du

= 2π * 8 * ∫_3^4 u^2 du

= 2π * 8 * [u^3/3]_3^4

= 2π * 8 * (64/3 - 27/3)

= 2π * 8 * (37/3)

= 864π

So, the area of the surface generated when the given curve is revolved about the x-axis over the interval [9, 20] is 864π.

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Answer:

y = 8.34x + 35

Step-by-step explanation:

Ivy has an empty barrel having weight = 35 pounds

Having 10 gallons of water barrel weighs = 118.4 pounds

After collecting 20 gallons of water barrel weighs = 201.8 pounds

There is a common difference in the weight of the barrel as he collects the rain water = (201.8 - 118.4) = 83.4 pounds

Therefore, its a linear process and forms a straight line when we graph the function.

Let the equation of the line is,

y = mx + b

Where m = slope of the line

b = y-intercept

Two points lying on the line will be (0, 35) and (10, 118.4)

Slope of the line 'm' =  \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

                                 = \(\frac{118.4-35}{10-0}\)

                                 = 8.34

y-intercept of the line 'b' = 35

Therefore, equation of the line is,

y = 8.34x + 35

The difference in the account balances at the end of the loan terms is given as follows:

$1,686.87.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for the offer 2 are given as follows:

P = 75000, r = 0.035, n = 12, t = 62/12.

Hence the balance of the offer 2 is given as follows:

B = 75000 x (1 + 0.035/12)^(12 x 62/12)

B = $89,842.51.

The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:

91529.38 - 89842.51 = $1,686.87.

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Answer:

-20.2m - 11.8

Step-by-step explanation:

To solve the integral of 1/sqrt(x^2 - a^2) dx, we can use the substitution method. Let u = x^2 - a^2, then du/dx = 2x, and dx = du/2x.
Substituting into the integral, we get:

∫ 1/sqrt(x^2 - a^2) dx = ∫ 1/sqrt(u) * du/2x
= (1/2) ∫ 1/sqrt(u) du  

= (1/2) * 2sqrt(u) + C
= sqrt(x^2 - a^2) + C

Therefore, the answer to the integral of 1/sqrt(x^2 - a^2) dx is sqrt(x^2 - a^2) + C, where C is the constant of integration.

In summary, the integral of 1/sqrt(x^2 - a^2) dx can be solved using the substitution method, where u = x^2 - a^2. The final answer is sqrt(x^2 - a^2) + C, where C is the constant of integration.

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The integral of \(\frac{1}{\sqrt{x^2 - a^2}} dx\) is \(\ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\), where C is the constant of integration

What is intergration?

Integration is a fundamental concept in calculus that involves finding the antiderivative or integral of a function. It is the reverse process of differentiation, which is concerned with finding the derivative of a function.

To find the integral of \(1/\sqrt(x^2 - a^2) dx\), we can use a trigonometric substitution. Let's substitute \(x = a sec(\theta)\), where \(sec(\theta)\) is the reciprocal of the cosine function.

By making this substitution, we can express dx in terms of \(d(\theta)\) as follows:

\(dx = a sec(\theta) tan(\theta) d(\theta)\)

Now, let's substitute these values into the integral:

\(\int \frac{1}{\sqrt{x^2 - a^2}} dx\\\\= \int \frac{1}{\sqrt{(a \sec(theta))^2 - a^2}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{\sqrt{a^2(\sec^2(theta) - 1)}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{\sqrt{a^2(\tan^2(theta))}} (a \sec(\theta) \tan(\theta)) d(\theta)\\\\= \int \frac{1}{a \tan(theta)} (a \sec(\theta) \tan(\theta)) d(\theta)\)

Simplifying the expression, we have:

\(= \int \sec(\theta) d(\theta)\)

The integral of \(sec(\theta)\) can be evaluated as the natural logarithm of the absolute value of \(sec(\theta)\) plus the tangent\((\theta)\):

\(= \ln|\sec(\theta) + \tan(\theta)| + C\)

Finally, substituting back \(x = a sec(\theta)\), we get:

\(= \ln|\sec(\theta) + \tan(\theta)| + C\\\\= \ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\)

Therefore, the integral of \(\frac{1}{\sqrt{x^2 - a^2}} dx\) is \(\ln\left|\frac{\sqrt{x^2 - a^2}}{a} + \frac{x}{a}\right| + C\), where C is the constant of integration

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Answer:

m=4

p=3

so...

4+3³=31

its B

Answer:

hi this is my old account

Step-by-step explanation:

Answer:

ur mom

Step-by-step explanation:

genehrrddjdhxxhdhdi hope this didnt help

Answer:

point-slope form, standard form, and slope-intercept form

Step-by-step explanation:

The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.

Here is an image with each form

Answer:

p=0.60w

Step-by-step explanation:

Let

p ----> the price of a watermelon in dollars

w ---> the weight of a watermelon in pounds

In this problem we have a proportional relationship

Remember that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form  or  

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem

p=kw

The value of the constant of proportionality k is the same that the unit rate

Find out the unit rate

Divide the total cost by the total weight

k=4.38/7.3=0.60per lb

substitute in the equation

p=0.60w

Step-by-step explanation:

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