HELP PLEASE IT URGENT (BRAINLIEST) IM BEGGING
What is the fractional equivalent of the repeating decimal n = 0.1515... ?
Answer the questions to find out.
1. How many repeating digits does the number represented by n have? (2 points)




2. You need to multiply n by a power of 10 to help you find the fraction. Decide on the power of 10 to multiply by, and tell how you identified that number. (2 points)






3. Write an equation where the left side is your power of 10 times n and the right side is the result of multiplying 0.1515... by that power. (2 points)

4. Write the original equation, n = 0.1515... underneath your equation from question 3. Then subtract the equations. Show your work. (2 points)






5. Write n as a fraction in simplest form. Show your work. (2 points)

Answers

Answer 1

Answer:

[tex]\frac{5}{33}[/tex]

Step-by-step explanation:

1.

2

1 5 is what's repeating, and there are two digits.

2.

10² = 100

I chose 10 to the power of 2 because there are 2 digits repeating.

3.

n × 10² = 0.1515 x 10² (square 10)

100n = 0.1515 × 100 (combine like terms)

100n = 15.15

4.

   100n = 15.1515....

-         n = 0.1515....

-------------------------

99n = 15

5.

99n = 15 (divide both sides by 99)

n = [tex]\frac{15}{99}[/tex]

As it asks for simplified form:

[tex]\frac{15}{99}[/tex] ÷ [tex]\frac{3}{3} = \frac{5}{33}[/tex]

Therefore, the fractional equivalent of the repeating decimal n = 0.1515... is [tex]\frac{5}{33}[/tex].


Related Questions

CAN SOMEONE HELP WITH THIS QUESTION?✨

Answers

The marginal revenue is 2752 dollar per unit of revenue function is given by R(q)=-7q²+400g.

What is the marginal revenue formula?

The variance in the number of units sold is multiplied by the total change in revenue to determine marginal revenue. Here is how marginal revenue is determined: The difference between total income and output is the marginal revenue. Because it measures the increase in revenue from the sale of extra goods and services, marginal revenue is crucial. The law of diminishing returns, which asserts that any increase in production will result in smaller increases in output, has an impact on marginal revenue. The perfect level has been obtained as a result.

To find the marginal revenue, we obtain ,

R(q)=-7q²+400g.

q= 8

Marginal revenue= R(q)

MP(8)=-7(8)²+400×8

          =-7×64+3200=2752dollar per unit.

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The accompanying sample of six measurements was randomly selected from a normally distributed population. Complete parts a through c below. 2, 3, -1.5.1.2 a. Test the null hypothesis that the mean of the population is 3 against the alternative hypothesis, u <3. Use a =0.05. The test statistic is ____(Round to two decimal places as needed.) .

Answers

The t-test statistic of the data is -1.23

What is the test statistic

To test the null hypothesis that the mean of the population is 3 against the alternative hypothesis, u <3 with a significance level of 0.05, we can use a one-tailed t-test since the sample size is small and the population standard deviation is unknown.

The formula for the t-test statistic is:

t = (x(bar) - μ) / (s / √n)

Where:

x(bar) = sample mean

μ = population mean (null hypothesis)

s = sample standard deviation

n = sample size

Given the sample of six measurements: 2, 3, -1.5, 1.2

First, we need to calculate the sample mean, sample standard deviation, and t-test statistic.

Sample mean (x(bar)) = (2 + 3 - 1.5 + 1.2) / 4 = 1.93

Sample standard deviation (s) = √[(∑(x - x(bar))^2) / (n - 1)]

= √[((2 - 1.93)^2 + (3 - 1.93)^2 + (-1.5 - 1.93)^2 + (1.2 - 1.93)^2 +  / (4 - 1)]

= 1.92

t-test statistic = (x(bar) - μ) / (s / √n)

= (1.93 - 3) / (1.92 / √5)

= -1.23 (rounded to two decimal places)

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If S$1.00 = NRs 80.00 If Shyam wants to send NRs 20,000 to Nepal, how many S$ does he need?​

Answers

Answer:

S$ 250

Step-by-step explanation:

we can solve this by dividing 20,000 NRs by 80 since S$1.00 = NRs 80

the right isosceles triangle pqr has vertices p(3,3),, q(3,1) and r(x,y) and is rotated 90 degress counterclowise about the origin. find the missing vertex of the triangle.

Answers

The right isosceles triangle PQR has vertices p(3,3), q(3,1) and r(x,y) and is rotated 90 degrees counterclockwise about the origin. the missing vertex of the triangle is r (5, 1)

What is isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.

Properties are:

In a triangle, the angles that face the two equal sides are likewise equal.

An isosceles triangle has one base and two equal sides, which are known as the legs and the base, respectively.

Since the triangle is isosceles, the two legs have equal length. The coordinates of two vertices are given:

P(3,3)

Q(3,1)

Assuming that PQ and QR are the legs of equal length, the distance between Q and R must be the same as the distance between P and Q

d = √[(3-3)² + (3-1)²

d = 2

Therefore, the coordinates of r is: (5, 1)

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A lighthouse has a shadow that is 36 36 feet long. Zara is 4 4 feet tall, and has a shadow that is 3 3 feet long. The two triangles formed are similar because the angle to the sun is the same. Use this information to complete the statement about the lighthouse.

Answers

The height of the lighthouse is 48 feet.

To find the height of the lighthouse, we can use the concept of similar triangles. When two triangles are similar, it means that they have the same shape but different sizes. In this case, the two triangles are similar because they have the same angle to the sun. That is, the angle between the ground and the line from the top of the lighthouse to the sun is the same as the angle between the ground and the line from Zara to the sun.

This proportion is based on the fact that the two triangles are similar, so the corresponding sides are in proportion.

So, we have:

(height of lighthouse) / 36 feet = 4 feet / 3 feet

We can solve for the height of the lighthouse by cross-multiplying:

(height of lighthouse) = 36 feet × (4 feet / 3 feet)

Simplifying the expression, we get:

(height of lighthouse) = 48 feet

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The given question is incomplete, the complete question is

A lighthouse has a shadow that is 36 36 feet long. Zara is 4 4 feet tall, and has a shadow that is 3 3 feet long. The two triangles formed are similar because the angle to the sun is the same. Use this information to complete the statement about the lighthouse.

The height of the lighthouse is ___ feet .

a, b, c, and d are four different numbers and the proportion is true, which of the following is false?

Answers

If a, b, c, and d are four different numbers and the proportion a/b = c/d is true, then none of the statements is false.

What is proportion?

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.

Since a/b = c/d, are proportional then can cross-multiply to get ad = bc.

Now, evaluate each statement -

A. b/a = d/c

Cross-multiplying, it is obtained that bc = ad, which is true based on the original proportion.

Therefore, this statement is true.

B. a/c = b/d

Cross-multiplying, it is obtained ad = bc, which is also true based on the original proportion.

Therefore, this statement is true.

C. b/a = c/d

This is equivalent to the original proportion, so it is true.

D. (a + b)/b = (c + d)/d

Simplify the equation -

d(a + b) = b(c + d)

da + db = bc + bd

da = bc

Cross-multiplying, it is obtained that da = bc, which is true based on the original proportion.

Therefore, this statement is true.

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THE BASE OF THE TRIANGLE IS B IS THREE INCHES GREATER THAN THE HEIGHT

Answers

Answer:

14 in^2

Step-by-step explanation:

4+3=7 in. Area of the triangle is BH/2=7*4/2=14 in^2.

Need help, thanks!
Last question

Answers

The maximum total deduction that can be claimed is OE. $17,100.

What is deduction ?

Deduction refers to the process of subtracting or taking away something. In the context of taxes, a deduction is a specific amount of money that a taxpayer is allowed to subtract from their income before calculating their tax liability. Deductions are one way to reduce the amount of taxes owed and can help to lower a person's overall tax burden.

There are two main types of deductions in the U.S. tax system: standard deductions and itemized deductions. The standard deduction is a fixed amount that varies depending on the taxpayer's filing status, while itemized deductions are specific expenses that a taxpayer can deduct from their taxable income. Some common examples of itemized deductions include mortgage interest, charitable contributions, medical expenses, and state and local taxes.

It's important to note that not all deductions are available to all taxpayers, and there are specific rules and limits that apply to each type of deduction. It's also important to keep accurate records and documentation to support any deductions that are claimed on a tax return.

The maximum total deduction that can be claimed is OE. $17,100, because that is the sum of the deductible expenses and the standard deduction.

The question is asking for the maximum total deduction that can be claimed, given certain deductible expenses and a standard deduction.

The standard deduction for the tax year is $6,100, and the deductible expenses are $6,000 in mortgage interest and $5,000 in charitable contributions.

Since the deductible expenses ($6,000 + $5,000 = $11,000) are less than the standard deduction of $6,100, it makes sense to use the standard deduction instead of itemizing deductions.

Therefore, the maximum total deduction would be the sum of the deductible expenses and the standard deduction:

$11,000 + $6,100 = $17,100

So, the maximum total deduction that can be claimed is OE. $17,100.

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A satellite orbits earth at a speed of 12700 feet per second (ft/s). Use the following facts to convert this speed to miles per hour (mph).

1 mile = 5280 ft
1 min = 60 sec
1 hour = 60 min

Answers

The speed of the satellite around the earth in miles per hour is 8659.09 miles per hour.

What is meant by Measurements?

Measurement is the method of comparing the properties of a quantity or object using a standard quantity.

Measurement is important to determine the quantity of any object.

A same quantity can have more than one type of measurement which can be converted to each other.

Given,

Speed of the satellite in feet per second = 12700 feet per second (ft/s)

We have,

5280 feet = 1 mile

1 feet = 1/5280 mile

12700 feet = 12700/ 5280 miles

Also,

60 minute = 1 hour

1 minute = 1/60 hour

60 seconds = 1 minute = 1/60 hour

1 second = 1/3600 hour

12700 feet per second =  12700/ 5280 miles ÷ 1/3600 hour

                                      = 8659.09 miles per hour.

Hence the speed converted is 8659.09 miles per hour.

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Maureen has a Jump rope that is 62 inches long nancys jump rope is 10 inches longer how long is nancys jump rope?

Answers

Nancy's jump rope is 72 inches long.

Answer: 6 feet long

Step-by-step explanation:

1ft. = 12 in

62 inches = 5 feet and 2 inches

Break down 62 into 60 and 2

60 divided by 12 = 5 (12x5=60)

60in. = 5ft.

2in. = 2in.

5ft. and 2in.

10in.= 10in.

Add the inches

10in. + 2 in. = 12 in.

12in.= 1ft.

5ft. + 1ft. = 6ft.

Answer: Nancy’s rope is 6ft. long

These the graphs of f and g to find (fg)(0).

Answers

The composite function (fg)(0) has a value of -4

How to evaluate the composite function

From the question, we have the following parameters that can be used in our computation:

The graph

Also, we have

(fg)(0)

The notation (fg)(x) represents the composite function of two functions f(x) and g(x), where one function is applied to the result of the other function.

The formula for (fg)(x) is:

(fg)(x) = f(g(x))

So, we have

(fg)(0) = f(g(0))

This gives

(fg)(0) = f(3)

(fg)(0) = -4

Hence, the value is -4

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In Hillsdale, the library is due south of the courthouse and due west of the community
swimming pool. If the distance between the library and the courthouse is 15 miles and the
distance between the courthouse and the city pool is 25 miles, how far is the library from the
community pool?

Answers

The library is 20 miles from the community pool as calculated after performing mathematical operations.

What are mathematical operations?

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, In Hillsdale, the library is due south of the courthouse and due west of the community swimming pool.

Also given,

The distance between the library and the courthouse is 15 miles.

The distance between the courthouse and the city pool is 25 miles,

Using the Pythagorean theorem, we have:

x = 25² - 15²

x² = 625 - 225

x = 400

Taking the square root of both sides, we get:

x = 20

Therefore, the library is 20 miles from the community pool

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Solve for 0

sin(0-70)=cos0

Answers

The solution of the trigonometric equation for θ is given as follows:

θ = 80º.

How to solve the trigonometric equation?

The trigonometric equation for this problem is defined as follows:

sin(θ - 70) = cos(θ).

When two angles are complementary, that is, the sum of their measures is of 90º, we have that the sine of one angle is equals to the cosine of the other angle.

The angles for this problem are given as follows:

θ - 70.θ.

As the sine of one is equals to the cosine of the other, they are complementary, hence the angle θ is obtained as follows:

θ - 70 + θ = 90

2θ = 160

θ = 160/2

θ = 80.

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Find the measure of angle 1
Find the measure of angle 2

Answers

Answer:

Angle 1= 45°

Angle 2= 90°

Step-by-step explanation:

Angle is found when you divide 90 by 2

We do this because all edges of a square add up to 90 and this angle is split in half, which is why we divided by 2

The to find angle 2 you get 45 for the left side of the triangle, 45 on the right side add them, which will give you 90, then subtract from 180 because angles in triangle equals 180 when you do this you get 90.

a radio disc jockey has 8 songs on this upcoming hours playlist: 2 are rock songs, 3 are reggae songs, and 3 are country songs, The disc jockey randomly chooses the first song to play, and then she randomly chooses the second song from the remaining ones. what is the probability that both songs are rock songs? write your answer as a fraction in simplest form.

Answers

The disc jockey has a 1 in 8 chance of randomly choosing any of the 8 songs for the first song. After the first song is chosen, the disc jockey has a 1 in 7 chance of randomly choosing any of the remaining 7 songs for the second song.

What is 50/10 equivalent fractions for division 

Answers

The equivalent fractions are A = { 100 / 20 , 150 / 30 }

What is a Fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fractions be represented as A

Now , the value of A is

A = 50/10

On simplifying , the fraction , we get

The value of A = 5/1

Now , the equivalent fractions of A are

Multiply the numerator and denominator of the fraction by 2 , we get

A = 100/20

Multiply the numerator and denominator of the fraction by 3 , we get

A = 150/30

Hence , the equivalent fractions are 5/1 , 100/20 and 150/30

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Write an equation for the function graphed below. The y intercept is at (0,0.2)

Answers

The equation for the graphed function is [tex]y=\frac{8\left(x-1\right)^2}{5\left(x-2\right)^2\left(x+2\right)}[/tex]

How to determine the equation for the function

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have the following asymptotes

x = -2 and x = 2

This means that the denominator of the function is

(x + 2) and (x - 2)²

(x - 2) is squared because the graph appears to turn (not intersect) at the zeros of x = 1 (close to x = 2)

So, we have

y = a/(x + 2)(x - 2)²

Where a is a real value

The zero is x = 1 with a multiplicity of 2 (because the curve turns at x = 1)

So, we have

y = a(x - 1)²/(x + 2)(x - 2)²

The y-intercept is (0, 0.2)

This means that

0.2 = a(0 - 1)²/(0 + 2)(0 - 2)²

So, we have

0.2 = a/8

Evaluate

a = 1.6

So, we have

a = 8/5

The function becomes

y = 8(x - 1)²/5(x + 2)(x - 2)²

Express properly

[tex]y=\frac{8\left(x-1\right)^2}{5\left(x-2\right)^2\left(x+2\right)}[/tex]

Hence, the equation is [tex]y=\frac{8\left(x-1\right)^2}{5\left(x-2\right)^2\left(x+2\right)}[/tex]

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HELPPPP 100 POINTSSSSSSSSSS

Answers

what u need help with

CAN SOMEONE HELP WITH THIS QUESTION?✨

Answers

The population after 4 years is 1982.

What is a function?

function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.


We have.,

Current population = 1652 people

The population triples every 10 years.

This means,

We can make a function for the number of population after m years.

y = 1652 x 3(m/10)

Where M is the number of years.

Now,

Substitute m = 4.

y = 1652 x 3(m/10)

y = 1652 x 3 (4/10)

y = 1652 x 3 x 2/5

y = 1982.4

y = 1982

Thus,

1982 is the population after 4 years.

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Michelle is buying a 95,000 dollar home. She has been approved for a 4.95% APR, 30 year mortgage. She made a 15% down payment and will be closing on April 8th. How much should she expect to pay in prepaid interest at the closing

Answers

Answer:

b

Step-by-step explanation:

because u can tell

At the closing of her home purchase, Michelle should expect to pay prepaid interest of $6,934.50. This amount represents the interest accrued from April 8th to the end of the month.

The monthly payment for Michelle's mortgage is calculated as follows:

Principal and interest payment = (95,000 - 15,000) x 0.0495 / 12

This equals a monthly payment of $420.63.

Michelle's total interest over the life of the loan is $119,750. This amount is the sum of her prepaid interest and the total interest she pays over the life of the loan.

Consider the following data: x −2 −1 0 1 2 P(X=x) 0.1 0.1 0.2 0.2 0.4 Step 3 of 5 : Find the standard deviation. Round your answer to one decimal place.

Answers

The answer is the expected value is - 2. The equation for expected value is the sum of the values times their probabilities.

What is the frequency of the function f(x)? f(x)=14cos(2x)+5 express the answer in fraction form. Enter your answer in the box.

Answers

The frequency of the function f(x) is 1/π.

What is a function?

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable. In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

We need to find the frequency of given function;

f(x)=1/4 cos(2x)+5

To finding the period and then use the general relation frequency

frequency = 1/period

In the given function f(x)=1/4 cos(2x)+5 here, only the constant 2 which will multiply with x effects the period.

As we know that 2π is the period of cosx then the period of cos(2x) is

2x=2π

x=π

So, the period of cos(2x) is π

Now the frequency is F=1/π

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A square pen is made using four posts on each side. How many posts were used?​

Answers

Answer:

Step-by-step explanation:

If a square pen is made using four posts on each side, then the total number of posts used can be found by multiplying the number of sides by the number of posts per side. Since there are four sides to a square, we can multiply 4 by 4 to get:

4 x 4 = 16

Therefore, 16 posts were used to make the square pen.

Answer: 12 posts

Explanation: there are 4 posts on each side, but some posts will overlap because there must be posts on the 4 corners.
So first do
4x4=16
Then you have to subtract the overlapping posts on the 4 corners, so
16-4=12

Hey 1+1+1+1-4 x 50 +1 =

Answers

Answer:

-195

Step-by-step explanation:

1+1+1+1-200+1

1+1+1+1-4x50+1

-195

Hopes this helps!!

I don't know if you have this answer!!

Consider the following correct implementation of the insertion sort algorithm. The insertionsort method correctly sorts the elements of ArrayList data into increasing order. public static void insertionsort (ArrayList data) { for (int j - 1;) < data.size(); j++) intv - data.get()); int k - j; while (k > DEV data) { for (int ) - 1;) < date.size(); j++) int v - data.get(i); int k = while (k > de liv listo Words; public String word withCommas () String result = ""; int sizeofList - expression / for (int k - 0; i < sizeoflist; k++) result = result + listofwords.get(k): if ( /* condition */ ) ( result = result + , 1 result = result + ": return result; Which of the following can be used to replace /* expression and condition/ so thatwords WithCommas will work as intended? A expression /// A condition/ A listof words.size()-1/k!-0 B A expression/// condition/ listofWards.size(/k!:D C 1 * expression */ // * condition/ listOfWards.sizel - 1/k!= sizeofList - 1 / * expression // /* condition/ D listOfWords.size(/k! sizeofList 1 1 * expression */ // * condition/ result.length/k!-D The following sort method correctly sorts the integers in elements into ascending order public static void sort (int i elements) for (int j = 0; j < elements.length - 1; j++) = 1 int index = ji for (int k = 1 + l; kc elements.length; k++) Line 1: Line 2: Line 3: Line 4: Line 5. Line 6: Line 7: Line & Line 9: TE Line 10 Line 11: Line 12: Line 13: Line 14: Line 15: Line 16: Line 17: Line 18 Line 19 if (elements [k] C elements (index] { index= } int temp = elements (j); elements (] = elements (index); elements index) - temp: 1 Which of the following changes to the sort method would correctly sort the integers in elements into descending order? I. Replace line 9 with: Line 9: if (elements[x] > elements[index]) II. Replace lines 15-17 with: Line 15: int temp = elements (index): Line 16: elements [index] = elements (li Line 17 elements [= temp: III. Replace line 3 with: Line 3: for (int j = elements.length - 1; } > 0; j--) and replace line 7 with: Line 7 for (int k = 0; 1; k++) II. Replace lines 15-17 with: Line 15: int temp = elements (index); Line 16: elements (index] = elements[j; Line 17: elements (j = temp; III. Replace line 3 with: Line 3: for (int j = elements.length - 1; } > 0; i--) and replace line 7 with: Line 7: for (int k = 0; k

Answers

For the given insertion sort program the answer is (E) I, II, and III.

What is insertion sort?

Insertion sort is a simple sorting algorithm that works by repeatedly iterating through the elements of an array, or a list, and inserting each element into its proper position within the sorted portion of the array. The algorithm maintains a sorted sublist of elements, which starts as the first element of the array, and then iterates through the remaining unsorted elements one-by-one, comparing each element with the elements in the sorted sublist and moving them to the right until the correct position is found. In other words, insertion sort iteratively expands the sorted sublist by inserting each new element into its correct position, until the entire array is sorted. The time complexity of the insertion sort algorithm is O(n^2) in the worst-case scenario, where n is the number of elements in the array, but it can perform much better on small datasets or partially sorted arrays.

According to given conditions:

For the first question:

After the first pass of the outer loop, the array will be [2, 5, 4, 1, 3, 6]. After the second pass, the array will be [2, 4, 5, 1, 3, 6]. After the third pass, the array will be [1, 2, 4, 5, 3, 6]. Therefore, the answer is (C) [1, 2, 4, 5, 3, 6].

For the second question:

Statement 1 will execute 6 times because there are 6 elements in the array. Statement 2 will also execute 6 times because each element in the array will be moved to its correct position during the insertion sort. Therefore, the answer is (E) 6, 6.

For the third question:

To correctly separate the words in listofWords with commas and enclose them in braces, we need to iterate through the list and add each word to the result string followed by a comma (except for the last word) and a space. Then we need to remove the last comma and space and add the opening and closing braces. This can be achieved with the following expression and condition:

Expression: listofWords.get(k) + ", "

Condition: k != listofWords.size() - 1

Therefore, the answer is (A) expression: listofWords.get(k) + ", ", condition: k != listofWords.size() - 1.

For the fourth question:

To sort the integers in elements in descending order, we need to make two changes to the sort method:

I. Replace line 9 with: if (elements[k] > elements[index])

II. Replace lines 15-17 with:

Line 15: int temp = elements[index];

Line 16: elements[index] = elements[j];

Line 17: elements[j] = temp;

III. Replace line 3 with: for (int j = elements.length - 1; j > 0; j--) and replace line 7 with: for (int k = 0; k < j; k++)

Therefore, for the given insertion sort program the answer is (E) I, II, and III.

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A car was stopped at a red light. When the light turns green, the car reaches a speed of 47 miles per hour in 4 seconds. What is the acceleration, to 1 decimal place?
feet/s2.

Answers

Answer:

275.7 ft/s^2 appr.

Step-by-step explanation:

47mi*5280=248160 feet per hour.

4 seconds = 4/(60*60)=1/900 of an hour.

1/900*248160=275.7 feet/s^2 approx.

Answer:

The car's acceleration is 17.2 ft/s².

Step-by-step explanation:

First we need to do some unit conversions.

Unit Conversions

There is 60 seconds in 1 minute.

There is 60 minutes in 1 hour.

So therefore there is 3600 seconds in 1 hour.

There is 5280 feet in 1 mile.

Now we can create an expression convert mph to ft/s

Multiply the speed value in mph by [tex]\frac{5280}{3600}[/tex] to get the speed in ft/s

We can simplify [tex]\frac{5280}{3600}[/tex]  to [tex]\frac{22}{15}[/tex].

Multiply the speed value in mph by [tex]\frac{22}{15}[/tex] to get the speed in ft/s.

We are given a speed of 47 mph.

[tex]47*\frac{22}{15}=68.93[/tex]

Numerical Evaluation of Acceleration

Now we can solve for the acceleration.

The formula for acceleration is

[tex]a=\frac{v_f-v_i}{t}[/tex]

In this example we are given

[tex]v_f=68.93\\v_o=0\\t=4[/tex]

Substituting our values into the equation for acceleration yields

[tex]a=\frac{68.93-0}{4}[/tex]

Evaluate [tex]\frac{68.93-0}{4}[/tex]

[tex]a=17.23[/tex]

Rounding to 1 decimal place gives us

[tex]a=17.2[/tex]

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Analyzing Interest Rates
The Federal Reserve has control over the nation’s monetary policy. Through adjusting the required reserve ratio, buying and selling government bonds on the open market, or adjusting the discount rate, the Fed can influence interest rates and the money supply in the country. When we talk about interest rates, it’s important to distinguish between long-term and Short-term interest rates. Short-term interest rates are directly affected when the Fed changes its federal funds and discount rates and are for loans made for short periods. long-term interest rates are set by market forces. Lower long-term interest rates encourage investment by businesses and consumers because the cost of paying back the money over a long period is low. Keep this distinction in mind while you complete the following activity.

Part A
Considering the current state of the economy and what you know about monetary policy, do you think the Federal Reserve should increase interest rates, decrease interest rates, or keep interest rates constant? Why?















Space used (includes formatting): 0 / 15000
Part B
Using an Internet search engine, find a website or an article that contains an editorial or opinion piece that shares your opinion and copy the URL in the space below. Keep in mind that it might take you some time to find a good article, so don’t automatically take the first one you find.















Space used (includes formatting): 0 / 15000
Part C
List three main points from the source you found that explain the author’s reasoning.















Space used (includes formatting): 0 / 15000
Part D
Based on what you have read, what bias might the author bring to his or her opinion?















Space used (includes formatting): 0 / 15000
Part E
Using an Internet search engine, find a website or an article that expresses the opposite to your opinion and copy the URL in the space below. Keep in mind that it might take you some time to find a good article, so don’t automatically take the first one you find.















Space used (includes formatting): 0 / 15000
Part F
List three main points from the source you found that explain the author’s reasoning.















Part G
Based on what you have read, what bias might the author bring to his or her opinion?

Answers

Here are the answers part-wise.

Part A
Considering the current state of the economy and what you know about monetary policy, the Federal Reserve should keep interest rates constant. The reason is that the current environment is conducive to a low-interest rate environment, which encourages business and consumer investments and helps promote economic growth.

Part B
https://www.marketwatch.com/story/why-the-fed-should-not-raise-rates-now-2020-10-02

Part C
The three main points from the source are:
1. The economy is still recovering from the pandemic and raising interest rates could be detrimental to the recovery;
2. Low-interest rates help encourage borrowing for business investment, which helps promote economic growth;
3. Low-interest rates allow businesses and consumers to manage their debt payments more easily.

Part D
The bias that the author brings to their opinion is that low-interest rates are beneficial for the economy and should not be increased.

Part E
https://www.cnbc.com/2020/09/30/fed-should-hike-rates-because-economic-data-now-justifies-it-top-bank-ceo-says.html

Part F
The three main points from the source are:
1. The economy is performing well and raising interest rates would help maintain this momentum;
2. Low-interest rates have encouraged borrowing, which has created a potential for future inflation;
3. Low-interest rates have increased stock market volatility and therefore raising them could help to reduce it.

Part G
The bias that the author brings to their opinion is that high-interest rates are beneficial for the economy and should be increased.

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Seven friends are seated around a circular table at a wedding reception. In how many ways can they be arranged

Answers

Answer:

there are 720 ways to arrange the 7 friends around the circular table at the wedding reception

Step-by-step explanation:

The number of ways to arrange n distinct objects in a circle is (n-1)!, since there are n ways to choose the starting point, and then (n-1)! ways to arrange the remaining objects in a circle.

In this case, we have 7 friends seated around a circular table, so the number of ways to arrange them is:

(7-1)! = 6! = 720

Therefore, there are 720 ways to arrange the 7 friends around the circular table at the wedding reception.

Answer:

720

Step-by-step explanation:

(7-1)! = 6! = 720

After a 27% decrease the value of a game card was now on sale for $34.00. What was the original price?

Answers

The original price of the game card was approximately $46.58.

What purpose does a game serve?

When the game can be effectively described by a numerical "characteristic function," such as v(S), which expresses how much any coalition S of players may win with certainty, regardless of the behaviour of the other players, then we can most readily determine the value of the game.

Let x represent the game card's initial cost. So 1 - 0.27 = 0.73, the price would be 0.73x after a 27% drop.

We are aware that 34.00 = 0.73x. We can divide both sides by 0.73 to find x:

x = 34.00 ÷ 0.73

x ≈ 46.58

Thus, the game card's initial cost was only about $46.58.

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Solve the inequality |3x-2| ≤4

Simplify all fractions as much as possible. Express your answer as an integer or fraction, and not as a decimal. If the answer is a fraction, provide the answer as "a/b". Do not leave spaces between characters.
? ≤ x ≤ ?

Answers

The solution to inequality is -2/3 ≤ x ≤ 2. The value of x lies between -2/3 and 2.

What is inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the expression on the left should be greater or less than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using inequality symbols.

Given inequality is

|3x-2| ≤ 4

Applying the formula |x| ≤ a → -a ≤ x ≤ a:

-4 ≤ 3x-2 ≤ 4

Add 2 on both sides:

-4 + 2 ≤ 3x-2 + 2 ≤ 4 + 2

-2 ≤ 3x ≤ 6

Divide both sides by 3:

-2/3 ≤ x ≤ 2

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