Prove the second part of Theorem 6: Let w be any solution of Ax = b, and define vh = w - p. Show that vh is a solution of Ax = 0. This shows that every solution of Ax = b has the form w = p + vh with p a particular solution of Ax = b and vh a solution of Ax = 0.

The solution is : 3500km is the actual length of appalachian trail.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

given that,

If 5cm represents 400km on the scale, and the map shows 43.75cm then,

Let ,

5cm .......400km

43.65cm......u

now, we get,

Hence by cross multiplication,

5cm* u=43.75cm × 400km

U =(43.75cm ×400km)/5cm

   =(17500/5)km

  =3500km

Hence, The solution is : 3500km is the actual length of appalachian trail.

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The area of the figure can be found to be 53 cm ²

The figure given is a composite shape so to find the area of the figure, you need to divide the shape into two other shapes.

The area of the first shape is :

= Length x Width

= 5 x 4

= 20 m ²

The area of the second shape would be :

= Length x Width

= ( 3 + 5 + 3 ) x 3

= 11 x 3

= 33 cm ²

The area of the shape is :

= 20 + 33

= 53 cm ²

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The capacity of the tank is 7234.56litres

Capacity refers to the amount of fluid a container can hold. It expressed in units like litres (l), millilitres (ml). Capacity is also known as volume of a substance.

The capacity of the cylindrical pipe is

V = πr²h

r = 8cm

if it takes the pipe 2m per second

then it's volume in one second is

V = 3.14 ×8 × 2× 100

V = 5024cm³/s

if it takes 24 minutes

24 minutes = 24 × 60 s

= 1440s

therefore volume of the tank = 1440 × 5024

= 7234560cm³

in litres = 7234560/1000

= 7234.56litres

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98% confidence interval for the proportion of all american adults who would report having earned money by selling something online in the previous year by using z-score. The correct answer is (0.1859, 0.2133)

The point estimate for the proportion of American adults who earned money by selling something online in the previous year is:

p-hat = 914/4579 = 0.1995

To construct a 98% confidence interval for the population proportion, we can use the formula:

p-hat ± z*(sqrt(p-hat*(1-p-hat)/n))

where z is the z-score associated with the desired confidence level (98% corresponds to a z-score of 2.33), and n is the sample size. Plugging in the values, we get:

0.1995 ± 2.33*(sqrt(0.1995*(1-0.1995)/4579))

Simplifying this expression, we get:

(0.1859, 0.2133)

Therefore, the correct answer is (0.1859, 0.2133). This means we are 98% confident that the true proportion of American adults who earned money by selling something online in the previous year lies between 0.1859 and 0.2133.

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The total area of the banner is approximately 800.54 square inches.

A quadrilateral is a four-sided polygon, having four edges and four corners

The area of the square is side length squared, or 24² = 576 square inches.

The diameter of the semicircle is also the side length of the square, so it is 24 inches.

Radius = 24/2=12 inches

The area of a semicircle is half of the area of a circle with the same radius. The area of a circle is π times the radius squared, so the area of the semicircle is:

1/2×π×12²=72π

Add Area of the square and the area of the semicircle:

576 + 72π = 800.54

Therefore, the total area of the banner is approximately 800.54 square inches.

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Answer:

here it is

Step-by-step explanation:

-3 represents the slope. Since its 3/1, this means which point on the slope is 3 to side and 1 either up or down. Since the slope is negative, it goes down.

The formula for a slope is y = mx + b. Since we don’t have the b, that means it is 0. B represents the y intercept or when the line crosses the y axis.

Answer:

p = 4.5

Step-by-step explanation:

0.5p - 3.45 = -1.2.

0.5p = -1.2 + 3.45

0.5p = 2.25

0.5p/0.5 = 2.25/0.5

p = 4.5

therefore p is equal to 4.5

The probability that the number of U.S. adults who oppose exactly 2, less than 4, and at least 3 will be 0.0727, 0.2925, and 0.9136, respectively.

Frequency distribution of the percentage of successful outcomes that might occur in a certain number of trials with the same chance of success. If X~B(n, p), then the probability is given as

[tex]\rm P(X=x) = \ ^nC_x \times p^x \times (1-p)^{n - x}[/tex]

The probability that the number of U.S. adults who oppose exactly 2 is given as,

P(2) = ⁶C₂ x (0.68)² x (1 - 0.68)⁴

P(2) = 0.0727

The probability that the number of U.S. adults who oppose less than four is given as,

P(x < 4) = ⁶C₁ x (0.68)¹ x (1 - 0.68)⁵ + ⁶C₂ x (0.68)² x (1 - 0.68)⁴ + ⁶C₃ x (0.68)³ x (1 - 0.68)³

P(x < 4) = 0.0137 + 0.0727 + 0.2061

P(x < 4) = 0.2925

The probability that the number of U.S. adults who oppose at least three is given as,

P (x ≥ 3) = 1 - ⁶C₁ x (0.68)¹ x (1 - 0.68)⁵ - ⁶C₂ x (0.68)² x (1 - 0.68)⁴

P (x ≥ 3) = 1 - 0.0137 - 0.0727

P (x ≥ 3) = 0.9136

The probability that the number of U.S. adults who oppose exactly 2, less than 4, and at least 3 will be 0.0727, 0.2925, and 0.9136, respectively.

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The measure of angle x is given as follows:

a. x = 30º.

Angle y is complementary with the angle of 60º, meaning that the sum of their measures is of 90º, hence it's measure is given as follows:

y + 60 = 90

y = 30º.

Angle y and angle x form vertical angles, meaning that they are congruent, that is, they have the same measure, hence the measure of angle x is given as follows:

x = y = 30º.

Hence the correct option is given by option a.

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Answer:  14.25x is the expression

It represents the total combined cost everyone paid.

=======================================================

Explanation:

Add up the price of a ticket, a medium drink, and a large popcorn.

7.50+2.75+4.00 = 14.25

Each person spends $14.25 for those three items.

If x is the unknown number of people, then 14.25x represents the total amount spent by everyone combined.

Example: x = 10 people, so 14.25x = 14.25*10 = 142.50 dollars total is spent by everyone combined.

No triangle can form with the given measurements.

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

The given angles are 53° and 27°.

By using angle sum of property of a triangle, we get

53°+27°+x=180°

x=100°

It is not possible to draw a unique triangle with any 3 possible measurements of angles.

Therefore, no triangle can form with given measurements.

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The net number of ATP produced from eight molecules of glucose during glycolysis is 32 ATP molecules.

Glycolysis is a metabolic pathway that breaks down glucose into two molecules of pyruvate, which in turn produces ATP. Each molecule of glucose yields two molecules of ATP and two molecules of NADH. Each NADH molecule, in turn, produces three more ATP molecules when it is oxidized in the electron transport chain. Therefore, the total number of ATP produced from one molecule of glucose is four. When eight molecules of glucose undergo glycolysis, the total number of ATP produced is 4 x 8 = 32 ATP molecules. hence 32 ATP molecules produced during the process of glycolysis.

The complete question is : select the net number of ATP produced from 8 molecules of glucose during the process of glycolysis is

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Answer: A, i think

Step-by-step explanation: edge 2020

Answer:

The 2nd option

Step-by-step explanation:

You can substitute values to replace X and if it alines with the graph then you know that is the correct answer choice

Option C, center at (0, 0) transverse axis is x - axis vertices at (-11, 0) and (11, 0) foci at ([tex]-\sqrt{265}[/tex], 0) and ([tex]\sqrt{265}[/tex], 0) is the correct option.

The transverse axis is a line segment with vertices as its endpoints that traverses the hyperbola's center. The transverse axis's containing line is where the foci are located. The co-vertices serve as the endpoints of the conjugate axis, which is perpendicular to the transverse axis.

The transverse axis is located on the y-axis because of the equation's form, which is y^2a^2-x^2b^2 = 1. The vertices act as the graph's y-intercepts since the hyperbola is centered at the origin. Set x=0 and then solve for y to discover the vertices. Hence, the formula for a hyperbola with foci along the x-axis is x^2a^2-y^2b^2 = 1. The solution can be seen on the attached image below.

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Question correction:

See attached image below.

We can start by finding the expected value of X and Y separately: (X) = (0+0+1+1+2+1+0+1+0)/9 = 6/9 = 2/3, E(Y) = (0+0+1+1+2+0+1+0+0)/9 = 5/9

Next, we can expand (X+Y)^2: (X+Y)^2 = X^2 + 2XY + Y^2

Taking the expected value of both sides, we get: E((X+Y)^2) = E(X^2) + 2E(XY) + E(Y^2)

To find E(XY), we can create a table of the possible values of X and Y, and their corresponding probabilities: [table in the attatchment]

So, we have:

E(XY) = 0*(3/9) + 0*(2/9) + 0*(1/9) + 0*(2/9) + 1*(1/9) + 2*(1/9) + 0*(1/9) + 2*(1/9) + 4*(1/9) = 1

Next, we need to find E(X^2) and E(Y^2): E(X^2) = (0^2+0^2+1^2+1^2+2^2+1^2+0^2+1^2+0^2)/9 = 8/9

E(Y^2) = (0^2+0^2+1^2+1^2+2^2+0^2+1^2+0^2+0^2)/9 = 5/9

Putting it all together, we get: E((X+Y)^2) = E(X^2) + 2E(XY) + E(Y^2) = 8/9 + 2*1 + 5/9 = 23/9. Therefore, the answer is 23/9.

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Answer:

Technology improvements allow someone to look up jobs and be able to apply. This is much easier than going around yourself as it takes less time and effort. With technology we are capable of looking at ads of jobs and finding jobs in and around your area. Places such as indeed and linkedin have options for filters to allow you to adjust your search to salaries and areas that suit you.

Hope this helps, have a lovely day! :)

The appropriate null hypothesis for a random sample of car's color and speeding tickets is equals to the observed counts are equal to the expected counts.

The curious newspaper columnist tabulate the car color on a random sample. The above table showed car color and their corresponding speeding tickets. Sample size, n = 120

Registed red colour cars in his state

= 14%

Registed white/silver colour cars in his state= 35%

Registed gray/black colour cars in his state = 23%

Registed others colour cars in his state

= 28%

We habe to determine the right choice for null hypothesis from the options. For this, here we have to use chi square test of goodness of fit to test this hypothesis. We know that in chi square test, they arevalready given the observed frequencies. Then we have to find out the expected frequencies using the given percentages. So here we have to findout whether the expected frequency and observed frequency are equal or not. So the null hypothesis is The observed counts are equal to the expected counts.

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Cartesian product are A.{aa, ab, ac, ad}   B. {ab}   C. {aa, ab, ad}   D.{ab}

Given the set notations A = {a} B = {b, c} C = {a, b, d}

BUC = {a, b, c, d}

B∩C = {b}

a) A × (BUC) = {aa, ab, ac, ad}

b) A × (B ∩ C) = {ab}

c) (A × B) ∪ (A × C)

A × B = {ab, ac} and A × C = {aa, ab, ad}

(A × B) ∪ (A × C) = {aa, ab, ac, ad}

d) For (A × B) ∩ (A × C)

(A × B) ∩ (A × C) = {ab}

The symbol ∩ represents the intersection of sets. For example, the intersection of two sets X and Y can be expressed as X ∩ Y.

The union of two sets P and Q is denoted by P ∪ Q. This is the set of all distinct elements contained in P or Q. The symbol used to represent the union of sets is ∪. The intersection of two sets P and Q is denoted by P ∩ Q. This is the set of all distinct elements in both P and Q. The symbol for the set intersection is ∩. The intersection of two given sets, H. P and Q, is the set containing all elements common to both P and Q.

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Answer:

The equation for the parabola (quadratic function) that passes through the points (-1, 1), (1, -5), and (2, 1) is y = (6/49)(x - 2/3)^2 - 1.

Step-by-step explanation:

To write the equation of a quadratic function (parabola) given three points, we can use the vertex form of the equation:

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola and a is a scaling factor that determines the shape of the parabola.

To find the vertex of the parabola, we can use the formula:

h = (x1 + x2 + x3) / 3

k = (y1 + y2 + y3) / 3

where (x1, y1), (x2, y2), and (x3, y3) are the given points.

Substituting the given points into these formulas, we get:

h = (-1 + 1 + 2) / 3 = 2/3

k = (1 - 5 + 1) / 3 = -1

So the vertex of the parabola is (2/3, -1).

Now, we can substitute this vertex and one of the given points (e.g. (-1, 1)) into the vertex form equation and solve for a:

1 = a(-1 - 2/3)^2 - 1

2 = a(7/3)^2

a = 6/49

So the equation of the parabola is:

y = (6/49)(x - 2/3)^2 - 1

Answer: y = -2x^2 + 6x - 4

Step-by-step explanation:

The equation for this parabola/quadratic function is y = -2x^2 + 6x - 4. To arrive at this equation, we use the fact that the equation for a parabola/quadratic function is y = ax^2 + bx + c, where a, b, and c are constants. We can then substitute in the coordinates of each point to solve for a, b, and c.

For the point (-1,1), we have 1 = -2(-1)^2 + 6(-1) + c, so c = 5.

For the point (1,-5), we have -5 = -2(1)^2 + 6(1) + 5, so -2 = -2.

For the point (2,1), we have 1 = -2(2)^2 + 6(2) + 5, so -4 = -4.

And therefore, the equation is y = -2x^2 + 6x - 4.

To calculate the property tax rate, you need to divide the property taxes by the appraised value of the property and then multiply by 100 to express the result as a percentage.

In this case, the property tax rate can be calculated as follows:

Property tax rate = (Property taxes / Appraised value) * 100%

= ($1,650.00 / $112,000.00) * 100%

= 0.014732142857142857 * 100%

= 1.47%

So, the property tax rate in your neighborhood is 1.47%, rounded to the nearest hundredth of a percent.

The line of best fit is given as follows:

y = 0.25x + 72.25.

The correct option regarding the slope is given as follows:

The slope of the line of best fit is 0.25. Each time the shoe size increases by one, the height increases by 0.25 inches.

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.

The points for this problem are given as follows:

(7.5, 63), (8, 80.5), (12, 68), (7, 71), (9, 69.5), (10, 70), (12, 75), (12.5, 63), (14,72)

Inserting these points into a calculator, the equation is given as follows:

y = 0.25x + 72.25.

The slope of 0.25 represents the rate of change of the output variable(height) relative to the input variable(shoe size).

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Answer:

15

Step-by-step explanation:

A right angle is 90 degrees

90 - 45 = 45

The remaining angle of 3x is equal to 45 degrees.

45/3 = x     x=15

Answer:

Step-by-step explanation:

To write the Taylor series for the function f(x) = e^(-x) about x = x0 = -1, we first need to find the k-th derivative of f(x) and evaluate it at x = -1.

f(x) = e^(-x)

f'(x) = -e^(-x)

f''(x) = e^(-x)

f'''(x) = -e^(-x)

f''''(x) = e^(-x)

...

The k-th derivative alternates between e^(-x) and -e^(-x), depending on the parity of k.

To evaluate the k-th derivative at x = -1, we substitute -1 into the k-th derivative expression and simplify:

f^k(-1) = (-1)^k * e^1

Now we can write the Taylor series using the formula:

f(x) = f(x0) + (x - x0) f'(x0) / 1! + (x - x0)^2 f''(x0) / 2! + (x - x0)^3 f'''(x0) / 3! + ...

Plugging in the values we obtained earlier, we have:

f(-x0) = e

f'(-x0) = -e

f''(-x0) = e

f'''(-x0) = -e

f''''(-x0) = e

...

Substituting these values into the formula, we get:

f(x) = e - (x + 1)e + (x + 1)^2 e / 2! - (x + 1)^3 e / 3! + (x + 1)^4 e / 4! - ...

Using sigma notation, we can write this as:

f(x) = ∑_{k=0}^∞ (-1)^k (x + 1)^k e / k!

where ∑_{k=0}^∞ represents the sum from k = 0 to infinity.

The range, given the cost of surfboard rentals, would be $ 140.

The interquartile range of the cost of surfboard rentals is $ 56.

There is an outlier which is the cost of 6 days of rentals which is $ 168.

To find the range, the formula is :

= Largest cost - Lowest cost

To find these costs, find the cost of the days of rentals :

1 day :                                  2 days                            3 days :

= 28 x 1                                = 28 x 2                         = 28 x 3

= $ 28                                   = $ 56                          = $ 84

6 days :

= 28 x 6

= $ 168

The range is therefore :

= 168 - 28

= $ 140

To find the Interquartile range, first find the First Quartile and the Third Quartile after ordering the costs:

Order of costs :

28, 28, 28, 56, 56, 56, 84, 84, 84, 168

First quartile position :

= 1 / 4 x ( n + 1 )

= 1 / 4 x ( 10 + 1 )

= 3 rd position which is $ 28

Third quartile position :

= 3 / 4 x ( n + 1 )

= 3 / 4 x ( 10 + 1 )

= 8 th position which is $ 84

The Interquartile range is :

= 84 - 28

= $ 56

The outlier is the cost of 6 days which is $ 168. This is a rental as it is much larger than other costs.

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As per the information provided, this all indicates that the function f is becoming more of a function r at end.

Three different factors affect the function that determines the balance in this account: the initial deposit amount, the interest rate compounded on this account, and the amount of time the money is kept in the account. The account balance changes if any one or all of these three values is altered.

Let us examine how the interest rate affects this balance. When money is kept in an interest-bearing account, the interest is added as a percentage of the balance to the value of the account. Accordingly, a higher interest rate would result in a larger sum being added to the balance because a larger portion of the balance would be deposited.

Thus, this indicates that the function f is becoming more of a function r at end.

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Note that the correct question is:

The balance, B, in dollars, in a bank account depends on the amount deposited, A dollars, the annual interest rate, r%, and the time, t, in months since the deposit, so B = f(A, r, t).

Is f an increasing or decreasing function of r? Explain your answer.

No, Earline won't have enough money in six weeks

Earline needs to save $367.50 for her summer vacation

She plans on saving $52.50 per week

The amount of money that Earline will get in six weeks can be calculated as follows

= 52.50 × 6

= 315

$315 is lesser that $367.50

Hence Earline will not be able to save enough money in six weeks

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Answer: She lost 78% percent of her money.

450-100 is 350. This means that Kelly lost 350 dollars.

350/450 is 0.777777778. Rounded to the next whole number the percent is 78%. This means Kelly lost 78% of her money.

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