Which graph represents the function f(x)=|x-6|+1

Answer: 15.

Step-by-step explanation: If one-third of the students are girls, then two-thirds of the students are boys:

number of boys = (2/3) * 30 = 20

Three-quarters of the boys play basketball, so the number of boys in the class who play basketball is:

number of boys who play basketball = (3/4) * 20 = 15

Therefore, the number of boys in the class who play basketball is 15.

None of the descriptive alternatives are correct.

What is the null hypothesis?

In statistical hypothesis testing, null and alternate hypotheses are utilized. The alternative hypothesis of a test expresses your research's prediction of an effect or relationship, whereas the null hypothesis of a test always predicts no effect or no association between variables.

Here, we have

Given:  if obtained from an experiment, would lead to rejecting the null hypothesis if a = .01.

for 1st choice ; p-value =fdist(5,3,18)= 0.0107

for 2nd choice : p-value =fdist(4.08,3,8)=0.0496

for 3rd choice : p-value =fdist(150,1,1)=0.052

since none of the choices have p value less than 0.01; none of these would lead to a rejected null hypothesis.

Hence, none of the descriptive alternatives are correct.

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In the given triangle, using the law of Cosines, the value of angle θ is 103°

From the question, we are to calculate the value of angle θ in the diagram.

From the given diagram,

We have a triangle ABC with given side lengths

From the given information,

a = 42 cm

b = 78 cm

c = 57 cm

From the law of Cosines, we have that

cos B = (a² + c² - b²)/2ac

Thus,

cos θ = (a² + c² - b²)/2ac

Substitute the parameters

cos θ = (42² + 57² - 78²)/2(42)(57)

cos θ = (1764 + 3249 - 6084) / (4788)

cos θ = -1071/4788

θ = cos⁻¹(-1071/4788)

θ = 102.9255

θ ≈ 103°

Hence, the value of θ is 103°

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The amount that each girl receives if they receive $200 more than each boy is: $1133.33

We are told that $2800 is shared among four boys and two girls.

Thus:

Fraction of boys = 4/6 = 2/3

Fraction of girls = 2/6 = 1/3

Amount received by each boy if shared equally = (4/6) * 2800 = $1866.67

Amount received by each girl if shared equally = (2/6) * 2800 = $933.33

Now, each girl gets $200 more than each boy. Thus:

Amount each girl gets = $933.33 + $200 = $1133.33

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There are 60,466,176 different license plates that consist of five symbols, either digits or letters.

To calculate the number of different license plates consisting of five symbols, we need to consider the number of choices for each symbol, which can be either digits (0-9) or letters (A-Z).
Determine the number of choices for each symbol.
There are 10 digits (0-9) and 26 letters (A-Z), so there are a total of 10 + 26 = 36 possible choices for each symbol.
Use the counting principle.
Since there are 5 symbols on the license plate and 36 choices for each symbol, we can use the counting principle to determine the number of different license plates.

The counting principle states that if there are n ways to do one thing and m ways to do another, then there are n x m ways to do both.

Calculate the number of different license plates.
The number of different license plates can be calculated as 36 × 36 × 36 × 36 × 36 = [tex]36^5[/tex] = 60,466,176.

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There are a total of 60,466,176 different license plates consisting of five symbols, either digits or letters. This is because there are 26 letters in the English alphabet and 10 digits, so the total number of symbols is 36.

To calculate the number of different license plates consisting of five symbols, we need to consider that each symbol can be either a digit (0-9) or a letter (A-Z). There are 10 digits and 26 letters, so there are 36 possible choices for each symbol.

To find the total number of different license plates, we use the following steps:

1. Determine the number of possible choices for each symbol (36, as explained above).
2. Since there are five symbols in the license plate, raise the number of choices (36) to the power of 5.
3. Calculate the result.

So, the calculation would be:

36^5 = 60,466,176

There are 60,466,176 different license plates that can be created using five symbols with either digits or letters.

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Since the calculated t-value (0.701) is less than the critical value (1.996), we fail to reject the null hypothesis. Therefore, we do not have convincing evidence that the ages at first marriage are higher in Spain than in Italy.

A two-tailed t-test is a statistical hypothesis test used to determine whether there is a significant difference between the means of two groups. It is called a "two-tailed" test because the alternative hypothesis is that the means are not equal, and the difference could be in either direction (i.e., the difference could be positive or negative). The null hypothesis is that the means are equal, and the test calculates the probability that the observed difference between the means could have occurred by chance if the null hypothesis were true. If this probability (known as the p-value) is less than a pre-determined level of significance (typically 0.05 or 0.01), the null hypothesis is rejected, and it is concluded that there is a significant difference between the means of the two groups.

Here,

To determine if there is convincing evidence that the ages at first marriage are higher in Spain than in Italy, we can perform a two-sample t-test for the difference in means.

The null hypothesis is that there is no difference in the mean ages at first marriage between Spain and Italy, while the alternative hypothesis is that the mean age at first marriage is higher in Spain than in Italy.

We can use the following formula to calculate the t-statistic:

t = (x1 - x2) / √(s1²/n1 + s2²/n2)

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Plugging in the values, we get:

t = (29.5 - 28.8) / √((2.5²/84) + (3.6²/73))

t = 0.701

Using a two-tailed t-test with degrees of freedom equal to the smaller of n1-1 and n2-1 (in this case, 73-1 = 72), and a significance level of 0.05, the critical value is 1.996.

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Answer: 729

Step-by-step explanation:

3^2 is the same has 3 to the power of 2

9^2 is the same as 9 to the power of 2

When you see an expression like 3^2 x 9^2, it means you must raise 3 and 9 to the power of 2, multiply those numbers, and then do it again.

3 raised to the power of 2, often known as 3 times itself or 3 x 3, equals 9.

9 raised to the power of 2, often known as 9 times itself (9 x 9), equals 81.

As a result, when we change these values in the original expression, we obtain:

3^2 x 9^2 = 9 x 81

Now that we have these two integers, we can easily multiply them to obtain the result:

9 x 81 = 729

Therefore, 729 is the answer to the equation 3^2 x 9^2.

The correct statement regarding the two functions is given as follows:

f(1) = g(1).

Considering the graph containing the equations for the system, the solution of the system of equations is given by the point of intersection of all the equations of the system.

The point of intersection for this problem is given as follows:

(1,3).

Which means that at x = 1, function f(x) and g(x) have the same numeric value, thus the correct statement is given as follows:

f(1) = g(1).

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The loose sweets are better value, as they cost only £0.0089 per gram, compared to £0.01242 per gram for the pre-packed sweets.

We need to calculate their price per gram.

Price per gram of pre-packed sweets:

120 g of pre-packed sweets cost £1.49

1 g of pre-packed sweets costs £1.49 / 120 = £0.01242 (rounded to 5 decimal places)

Price per gram of loose sweets:

100 g of loose sweets cost £0.89

1 g of loose sweets costs £0.89 / 100 = £0.0089

So, the loose sweets are better value, as they cost only £0.0089 per gram, compared to £0.01242 per gram for the pre-packed sweets.

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We can use the fact that angle ACB is 30° to find v. We can use the tangent function:DB = CD - 50

DB = 2950 / v

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

To solve this problem, we will use trigonometry and geometry.

First, let's draw a diagram to better understand the situation:

              /|

             / |

            /  | h

        b /   |

          ----

           d

    a         c

    |\        |

    | \       |

 H  |  \ h'   |

    |   \     |

    |    \    |

    |     \   |

    |      \  |

    |       \ |

    |        \|

   ------------

          D

In this diagram, we have the lighthouse at point A with height H, the boat at point C, and after traveling for 1 minute at a constant speed, it reaches point B. We are given that angle ACB is 30°, angle AHB is 90°, and angle ABH is 60°.

We need to find the height of the lighthouse and the speed of the boat from C to B.Let's start by finding the height of the lighthouse. We can use the tangent function:

tan(ABH) = H / d

tan(60) = H / d

sqrt(3) = H / d

H = sqrt(3) * d

Now, let's find the distance d. We can use the law of cosines:scss

d² = h² + (AB)² - 2 * h * AB * cos(ABH)

We know that AB = 50 meters, ABH = 60°, and h = CD - h', where CD is the distance the boat traveled from C to D and h' is the height of the boat at point D. We can also use the tangent function to find h':

tan(ACH) = h' / CD

tan(30) = h' / (CD + DB)

1/sqrt(3) = h' / (CD + 50)

h' = (CD + 50) / sqrt(3)

Substituting h' in the previous equation:

d² = (CD - (CD + 50) / sqrt(3))² + 50² - 2 * (CD - (CD + 50) / sqrt(3)) * 50 * cos(60)

d² = (CD² + 2 * CD * 50 / sqrt(3) + 2500 / 3) + 2500 - (CD² - CD * 50 / sqrt(3) + 2500 / 3)

d² = 10000 / 3 + CD * 100 / sqrt(3)

Finally, we can use the fact that angle ACB is 30° to find v. We can use the tangent function:

tan(ACB) = h' / (CD + DB)

tan(30) = (CD + 50) / sqrt(3) / (CD + DB)

1 / sqrt(3) = (CD + 50) / sqrt(3) / (CD + DB)

DB = CD - 50

DB = 2950 / v

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In a case whereby the sum of two consecutive numbers is 25 the largest of the consecutive numbers is 13.

Given that sum of two consecutive numbers is 25 , ans we were required to locatye the  largest of the consecutive numbers. The we can represent the consecutive numbers as x and x+1. According to the problem, the sum of these two consecutive numbers is 25:

x + (x+1) = 25

Simplifying the left side of the equation:

2x + 1 = 25

2x = 24

Dividing both sides by 2:

x = 12

So the first consecutive number is 12. The second consecutive number is 12 + 1 = 13. Therefore, the largest of the consecutive numbers is 13.

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The solutions for the given equation be written as: x = (2n + 1)π/10, where n is any integer.

An equation is a mathematical statement that shows that two expressions are equal. It usually contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, or exponentiation.

Starting from the given equation:

-4cos(5x) + 1 = 1

Simplifying the equation, we get:

-4cos(5x) = 0

Dividing both sides by -4, we get:

cos(5x) = 0

Now, we need to find the values of x that satisfy this equation. Recall that the cosine function is equal to 0 at odd multiples of π/2, i.e.,

cos(θ) = 0 for θ = (2n + 1)π/2, where n is an integer.

So, substituting θ = 5x, we get:

cos(5x) = 0 for 5x = (2n + 1)π/2

Dividing both sides by 5, we get:

x = (2n + 1)π/10

So, the solutions for the given equation are:

x = π/10, 3π/10, 5π/10, 7π/10, 9π/10, 11π/10, 13π/10, 15π/10, 17π/10, ...

which can be written as:

x = (2n + 1)π/10, where n is any integer.

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Answer: y=12

Step-by-step explanation:

So it says 2x - y = 10 so basically we have to find a number that gives you 10 and that number is 12 because 12-2=10.

I hope this helps!

Dodger Stadium: 37,036 more people can attend a Dodger game., Lambeau Field + Georgia Dome: 132,118 fans can be seated altogether in the two parks.

1) Dodger Stadium:

56,000 - 18,964 = 37,036 more people can attend a Dodger game.

2) Alamodome:

35,000 - 20,557 = 14,443 more people can be seated for special events.

3) Lambeau Field + Georgia Dome:

60,890 + 71,228 = 132,118 fans can be seated altogether in the two parks.

4) Arrowhead Pond + Staples Center:

17,174 + 18,118 = 35,292 fans can be held altogether in the two arenas.

5) United Center:

21,500 / 25 = 860 25-seat ticket packages could be sold for one game.

6) Comerica Park:

40,000 / 20 = 2,000 20-seat packages could be sold.

7) Fenway Park - Veterans Stadium:

62,409 - 33,871 = 28,538 more fans can attend a game in Philadelphia.

8) St. Louis Stadium:

66,000 / 8 = 8,250 ticket packages could be sold for one game.

9) Miami Dolphins stadium:

75,192 x 8 = 601,536 total fans could attend all 8 regular-season games.

10) Edison Field:

45,050 x 81 = 3,655,050 tickets could be sold for their 81 regular-season games.

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According to the equation, the monthly fee that Sara paid was $60.

Let's start by assigning some variables. Let x be the monthly fee that Sara paid and let y be the number of months that Sara was a member of the gym. We know that Sara paid $15.95 to become a member, so her total cost can be represented by the equation:

Total Cost = Initial Cost + Monthly Fee x Number of Months

$735.95 = $15.95 + x x y

Now we have an equation with two variables. To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting $15.95 from both sides of the equation:

$720 = x x y

Next, we need to solve for x. Since we don't know the value of y, we can't solve for x directly. However, we do know that Sara was a member for 12 months, so we can substitute y = 12 into the equation:

$720 = x x 12

Now we can solve for x by dividing both sides by 12:

$60 = x

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The statement is true: If x and y are linearly independent, and if z is in Span {x, y}, then {x, y, z} is linearly dependent.

The statement is true.
Let's first understand the terms used:
Linearly independent:

A set of vectors is linearly independent if none of them can be expressed as a linear combination of the other vectors. In other words, no vector in the set can be written as a sum of scalar multiples of the other vectors.
Span:

The span of a set of vectors is the set of all linear combinations of those vectors.

In this case, Span[tex]{x, y}[/tex] is the set of all vectors that can be formed by adding scalar multiples of x and y.
Now, let's consider the given statement:
If x and y are linearly independent, it means that neither x nor y can be expressed as a linear combination of the other. However, it is given that z is in the Span[tex]{x, y}.[/tex]

This means that z can be expressed as a linear combination of x and y:
[tex]z = ax + by[/tex], where a and b are scalar constants.
Let's analyze the set[tex]{x, y, z}[/tex]. We know that z can be expressed as a linear combination of x and y, as shown above. This implies that the set [tex]{x, y, z}[/tex]is linearly dependent, because one vector (z) can be expressed as a linear combination of the others [tex](x and y)[/tex].

Thus, the statement is true: If x and y are linearly independent, and if z is in Span[tex]{x, y}[/tex], then[tex]{x, y, z}[/tex] is linearly dependent.

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Answer:

x=0, 5 (-5±√15)/2

Step-by-step explanation:

see images for solution

To begin solving this problem, we need to determine the dimensions of the rectangular region that the farmer will fence in. Let's say the length of thr uses, is given by the equation:
e rectangle is L and the width is W. The perimeter of the rectangle, which will be the length of fencing the farme
2L + W = 350

Solving for W, we get:

W = 350 - 2L

Next, we need to divide the rectangular region into three smaller rectangles by placing two parallel fences. Let's say the two fences are placed along the length of the rectangle, dividing it into three sections with widths of x, y, and z. Therefore, we have:

L = x + y + z

Now, we can determine the area of the entire fenced-in region by summing the areas of the three smaller rectangles. The area of a rectangle is given by the equation:

Area = Length x Width

Therefore, the total area of the fenced-in region is:

Area = (xW) + (yW) + (zW)

Substituting W = 350 - 2L and L = x + y + z, we get:

Area = (x(350-2(x+y+z))) + (y(350-2(x+y+z))) + (z(350-2(x+y+z)))

Simplifying this equation, we get:

Area = 350(x+y+z) - 2(x^2 + y^2 + z^2)

To maximize the area, we need to take the derivative of this equation with respect to one of the variables (x, y, or z), set it equal to zero, and solve for the variable. This process is too complicated to do by hand, so we will use a calculator or computer program to find the maximum area.

After finding the maximum area, we can determine the dimensions of the region that give us this maximum area. We do this by using the equations we derived earlier:

W = 350 - 2L

L = x + y + z

With the maximum area and these equations, we can solve for the dimensions of the region that give us the maximum area.

In summary, the farmer should fence in a rectangular region with dimensions that maximize the total area of three smaller rectangles created by placing two parallel fences. The maximum area can be found by taking the derivative of the area equation and setting it equal to zero. The dimensions of the region that give us the maximum area can be found by using the equations we derived earlier.

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From the attached picture, it is proven that the diagonals of rectangle MNOP are congruent.

To show that the diagonals of rectangle MNOP bisect each other, we need to show that they intersect at their midpoint. Let's label the diagonals as AC and BD, where AC is the diagonal that goes from vertex M to vertex O, and BD is the diagonal that goes from vertex N to vertex P.

First, let's find the midpoint of AC. The midpoint of a line segment is the point that is exactly halfway between the two endpoints. The endpoints of AC are M and O, so we can find the midpoint by averaging their x-coordinates and y-coordinates:

midpoint of AC = ((Mx + Ox)/2, (My + Oy)/2)

Similarly, we can find the midpoint of BD:

midpoint of BD = ((Nx + Px)/2, (Ny + Py)/2)

Now we need to show that these midpoints are the same point. That is, we need to show that:

((Mx + Ox)/2, (My + Oy)/2) = ((Nx + Px)/2, (Ny + Py)/2)

To do this, we can set the x-coordinates equal to each other and the y-coordinates equal to each other:

(Mx + Ox)/2 = (Nx + Px)/2

(My + Oy)/2 = (Ny + Py)/2

Now we can solve for the values of x and y. First, we'll solve for x:

Mx + Ox = Nx + Px

2Mx + 2Ox = 2Nx + 2Px

Mx + Ox - Nx - Px = 0

(Mx - Nx) + (Ox - Px) = 0

Similarly, we can solve for y:

My + Oy = Ny + Py

2My + 2Oy = 2Ny + 2Py

My + Oy - Ny - Py = 0

(My - Ny) + (Oy - Py) = 0

Now we can see that the x-coordinate and y-coordinate of the midpoint of AC are equal to the x-coordinate and y-coordinate of the midpoint of BD, respectively. Therefore, the diagonals of rectangle MNOP bisect each other.

To show that the diagonals are congruent, we can use the Pythagorean theorem. Let's label the length of AC as a and the length of BD as b. Then we have:

a^2 = OM^2 + ON^2 (by the Pythagorean theorem in triangle OMN)

b^2 = PN^2 + PO^2 (by the Pythagorean theorem in triangle PON)

But we know that OM = ON and PO = PN, since MNOP is a rectangle. Therefore, we can simplify these expressions:

a^2 = 2OM^2

b^2 = 2PO^2

Since OM = PO (they are opposite sides of a rectangle), we can substitute to get:

a^2 = 2OM^2 = 2PO^2 = b^2

Therefore, a = b, and the diagonals of rectangle MNOP are congruent.

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[tex]cos^2(x) = cos^2(x)[/tex].

This equation is true for all values of x, so the solution is:
x ∈ ℝ (x is any real number).

To solve the equation[tex]cos^2(x)[/tex]= (power reducing formula),

we need to replace [tex]cos^2(x)[/tex] with the power reducing formula.

The power reducing formula for [tex]cos^2(x)[/tex] is:
[tex]cos^2(x) = (1 + cos(2x)) / 2[/tex]
Now, let's solve the equation:
[tex](1 + cos(2x)) / 2 = cos^2(x)[/tex]
We want to find x when this equation is true.

Since the left side is the power reducing formula for [tex]cos^2(x)[/tex],

we can simply write:
[tex]cos^2(x) = cos^2(x)[/tex].

The power reducing formula is a trigonometric identity that allows you to express a trigonometric function of a higher power in terms of a trigonometric function of a lower power.

It is most commonly used for reducing the power of the sine and cosine functions.

The power reducing formula for cosine is:

[tex]cos^2(x) = (1 + cos(2x))/2[/tex]

The power reducing formula for sine is:

[tex]sin^2(x) = (1 - cos(2x))/2[/tex]

These formulas can be derived using the Pythagorean identity, which states that [tex]sin^2(x) + cos^2(x) = 1.[/tex]

By solving for either [tex]sin^2(x) or cos^2(x)[/tex] in terms of the other, and then using the double angle formula for cosine [tex](cos(2x) = cos^2(x) - sin^2(x)),[/tex]we can arrive at the power reducing formulas.

The power reducing formulas can be used to simplify trigonometric expressions and make them easier to work with.

For example, if you have an expression such as [tex]sin^4(x)[/tex], you can use the power reducing formula for sine to express [tex]sin^4(x)[/tex] in terms of [tex]sin^2(x),[/tex]and then use the power reducing formula for cosine to express [tex]sin^2(x)[/tex]in terms of cos(2x).

This can make the expression simpler and easier to integrate or differentiate.

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The statement that is not necessarily correct is ΔTRS ≅ ΔVUW. So, correct option is D.

The given information states that two triangles are congruent based on the corresponding parts, RS ≅ UV, RT ≅ UW and ∠R ≅ ∠U.

To determine which statement is not necessarily correct, we need to use the congruence criteria that are sufficient to prove the congruence of triangles. These criteria are:

SSS (Side-Side-Side): If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

SAS (Side-Angle-Side): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

ASA (Angle-Side-Angle): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Using the given information, we can apply the SAS criterion to show that ΔRST ≅ ΔUVW. This is because we know that RS ≅ UV, RT ≅ UW, and ∠R ≅ ∠U. Therefore, the statement (a) ΔRST ≅ ΔUVW is correct.

Now, we can use the SAS criterion again to show that ΔSTR ≅ ΔVWU. This is because we know that RS ≅ UV, RT ≅ UW, and ∠R ≅ ∠U. Therefore, the statement (b) ΔSTR ≅ ΔVWU is also correct.

We can also use the SAS criterion to show that ΔTRS ≅ ΔVWU. This is because we know that RS ≅ UV, RT ≅ UW, and ∠R ≅ ∠U. Therefore, the statement (c) ΔTRS ≅ ΔVWU is correct.

However, we cannot use any of the above criteria to show that ΔTRS ≅ ΔVUW. This is because we do not know that TU ≅ VW. Therefore, the statement (d) ΔTRS ≅ ΔVUW is not necessarily correct.

So, correct option is D.

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Answer:

69/5 or 13.8

Step-by-step explanation:

..…........

Answer:

Nicole pays 629 dollars per month.

Step-by-step explanation:

I think Nicole pays $629.29 per month

Step-by-step explanation:

On solving the provided question we can say that As a result, the sequence's ninth term is -781250.

A sequence is a collection of numbers, sometimes known as "terms." Terms like 2, 5, and 8 are examples. Some sequences may be made infinitely long by utilising a specific pattern they follow. To continue the process, take the example of 2,5,8 and add 3. There are formulae that show where to search in a series for words. In mathematics, a sequence (or event) is a collection of items that are in some order. It is similar to a set in that it comprises parts (also known as elements or terms). The length of a series is defined as the total number of ordered items, which may be infinite. The act of arranging two or more elements in a logical sequence.  

To discover the nth term in a series, we must first figure out what pattern or rule guides the sequence.

In this situation, each term in the series may be generated by multiplying the previous term by -5. So the pattern or rule for this sequence is as follows:

an = -5 * an-1

where a1 = -2

[tex]a^9 = -5 * a8\\= -5 * (-2 * (-5)^7)\\= -781250\\[/tex]

As a result, the sequence's ninth term is -781250.

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The median length of time required to review an application is 105 minutes.

To find the median, the data needs to be arranged in order from least to greatest: 19, 48, 140, 220.

Since there is an even number of data points, the median is the average of the two middle values, which in this case are 48 and 140. Adding them together and dividing by 2 gives 94, which is less than the next highest value of 220.

Therefore, the median length of time required to review an application is 105 minutes.

To know more about median, refer here:

https://brainly.com/question/30759810#

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Answer:

15

Step-by-step explanation:

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