Why does using the formula length × width to find the area of a rectangle give us the same answer as counting square units?

The distance between the landing pad ≈ 23.13 miles

The plane saw 2 landing pads in opposite direction . The angles of depression to pad A and pad B are 46° and 16°. The straight line distance from the helicopter to pad A is 5 miles .

The illustration forms a triangle with 2 half's of a right angle triangle.

Pad A right angle triangle

let us use this triangle to find the opposite sides which is the same for both right angle triangle formed .

tan 46° = opposite/adjacent

tan 46° = a/5

a = 5 tan 46°

a = 5 × 1.03553031379

a = 5.17765156895

a = 5. 2 miles

Pad B right angle triangle

Let us find the straight line distance from the helicopter to pad B.

The distance is the adjacent side of the triangle.

tan 16° = opposite/adjacent

tan 16° = 5.2/adjacent

adjacent = 5.2/0.28674538575

adjacent = 18.134555108

adjacent = 18.135

Straight line distance from the helicopter to pad B = 18.135 miles

The distance between the landing pad = 5 + 18.135 = 23.134555108  miles

The distance between the landing pads ≈ 23.13 miles

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The correct sentence is,

⇒ The IQR of 13 is the most accurate to use, since the data is skewed.

We have to given that;

A histogram is provided to display the data.

⇒ 5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20

Hence, To find range as;

Range = Highest - lowest value

          = 20 - 5

          = 15

And, We have to find IQR as;

In the data set;

First quartile is,

⇒ Q₁ = (6 + 8)/ 2 = 7

Second quartile is,

Q₃ = (20 + 20) / 2 = 20

Hence, The value of IQR is,

⇒ IQR = Q₃ - Q₁

⇒ IQR = 20 - 7

⇒ IQR = 13

Thus, The correct sentence is,

⇒ The IQR of 13 is the most accurate to use, since the data is skewed.

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Answer:

Step-by-step explanation:

A. Variability means the spread of the range for between the 3rd and 1st quartile meaning the actual box.  The actual box is wider with South Middle so the difference is greater and therefore greater variability

B. North Middle has greater distance in general because the box has bigger numbers.  That's where the majority of the kids are, so in general North Middle has kids that are further away  

At a rate of 1231 kilometers attendant to an hour, it will take an estimated 30 hours for a pilot to circumnavigate the whole earth and acquire the applicable standard.

In estimating the amount of time a pilot would require to fly around the globe while averaging 1231 kilometers per hour, we can easily employ the formula: Time = Distance ÷ Speed.

Multiplied passage this equation in tandem with the minimal distance necessary to qualify for an around-the-world speed record produces 36,763 kilometers: thus, these measurements yield 29.87 hours. To clarify, at a rate of 1231 kilometers attendant to an hour, it will take an estimated 30 hours for a pilot to circumnavigate the whole earth and acquire the applicable standard.

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Answer:

Step-by-step explanation:

If you have 1,000,000 number cubes, each measuring one inch on a side, then the height of the tower you can build with them can be found by multiplying the number of cubes by the height of a single cube.

The height of a single cube is also one inch, since all sides are equal in length. Therefore, the height of the entire tower would be:

1,000,000 cubes × 1 inch/cube = 1,000,000 inches

To convert this to a more manageable unit, we can divide by the number of inches in a typical measure of length, such as a foot or a mile. For example:

1,000,000 inches ÷ 12 inches/foot ≈ 83,333.33 feet

This is a very tall tower, almost 16 miles high!

It will take approximately 16.90 (about 16 years 11 months) years for a $25,000 investment to triple when invested at 6.5% interest compounded continuously.

The formula for continuous compounding is given by:

A = P[tex]e^{(rt)}[/tex]

Where:

A = Final amount

P = Initial amount

r = Annual interest rate (as a decimal)

t = time in years

We need to solve for t when the final amount A is 3 times the initial amount P, i.e. A = 3P.

So, we have:

3P =  P[tex]e^{(rt)}[/tex]

Simplifying:

3 = [tex]e^{(rt)}[/tex]

Taking the natural logarithm of both sides:

ln(3) = rt

t = ln(3) / r

Substituting the given values:

t = ln(3) / 0.065

t ≈ 16.90 years

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As per the unitary method, Bethany needs to buy 7 quarts of paint in order to paint 5 storage boxes.

Firstly, we need to find the surface area of one storage box that needs to be painted. The surface area of a box can be found using the formula:

Surface Area = 2(lw + lh + wh)

where l is the length, w is the width, and h is the height of the box.

Substituting the given values, we get:

Surface Area of one box = 2(6 x 3 + 6 x 5.12 + 3.12 x 5.12) square feet

= 131.52 square feet

Next, we need to find the total surface area of 5 boxes:

Total Surface Area of 5 boxes = Surface Area of one box x 5

= 131.52 x 5

= 657.6 square feet

Now, we need to find how many quarts of paint are required to cover this area. From the given information, we know that one quart of paint covers 100 square feet of surface area.

Using the unitary method, we can set up a proportion:

1 quart of paint covers 100 square feet

x quarts of paint cover 657.6 square feet

Solving for x, we get:

x = (657.6/100) quarts of paint

= 6.576 quarts of paint

Since we can only buy whole quarts of paint, we need to round up the answer to the nearest whole number.

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If we compare Jenna's original test score of 65% to her retake score of 80%, the test statistics do indeed demonstrate an improvement.

As her score grew by 15 percentage points, there was an improvement, which suggests that her performance improved or increased between the first exam and the second.

This represents an improvement in Jenna's test results, in our opinion. Her retake score was 80%, which is a greater percentage than her first score of 65%.

This demonstrates an improvement in her performance since it shows that she performed better on the second test than she did on the first.

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Answer:

In geometry, formal definitions are formed using other defined words or terms. There are, however, three words in geometry that are not formally defined. These words are point, line and plane, and are referred to as the " three undefined terms of geometry ".

Step-by-step explanation:

Answer:  

Step-by-step explanation:

The back-to-back stem-and-leaf plot or parallel boxplots can be use to compare. GPAs for successful students are generally higher. A significant relationship exists between GPA and credit hours for successful students. An applicant with a 3.5 GPA is likely to be successful, as the predicted value is closer to successful students' values.

To compare the GPAs for the two groups, an appropriate graphical display could be a back-to-back stem-and-leaf plot or parallel boxplots. Based on the graph, we can observe that successful students generally have higher GPAs than unsuccessful students.

To determine if there is a significant relationship between GPA and mean number of credit hours per semester for successful students, we can use a t-test for the slope or linear regression t-test.

Given the provided computer output, with a t-value of -5.90 and a p-value of 0.000, we can reject the null hypothesis and conclude that there is a significant relationship between GPA and mean number of credit hours per semester for successful students.

Using the regression equation to predict the number of credit hours for an applicant with a GPA of 3.5,

For the successful group predicted hours = 23.514 – 2.7555(3.5) = 13.86975

For the unsuccessful group predicted hours = 24.200 – 3.485(3.5) = 12.0025

we get a predicted value of 13.86975 for successful students and 12.0025 for unsuccessful students.

Since the actual value of 14 is closer to the predicted value for successful students, we can infer that this applicant is likely to be successful in the Ph.D. program.

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--The given question is incomplete, the complete question is given

" The statistics department at a large university is trying to determine if it is possible to predict whether an applicant will successfully complete the Ph.D. program or will leave before completing the program. The department is considering whether GPA (grade point average) in undergraduate statistics and mathematics courses (a measure of performance) and mean number of credit hours per semester (a measure of workload) would be helpful measures. To gather data, a random sample of 20 entering students from the past 5 years is taken. The data are given in photo.

a. Use an appropriate graphical display to compare the GPAs for the two groups.(provide names only) Write a few sentences commenting on your display.

b. For the students who successfully completed the Ph.D. program, is there a significant relationship between GPA and mean number of credit hours per semester?

Give a statistical justification to support your response.

c. If a new applicant has a GPA of 3.5 and a mean number of credit hours per semester of 14.0, do you think this applicant will successfully complete the Ph.D. program? Give a statistical justification to support your response. "--

Answer:

a)  $16,122

b) $4,246

c) $112,357

Step-by-step explanation:

What is depreciation

We should calculate the depreciation using the declining balance method
This uses the technique of computing the depreciation on the previous year's depreciated value

As an example
If the original cost is $100 and depreciation rate is 10%( 0.10 in decimal)

Depreciation Year 1 = 100 x 0.10 = $10

Depreciated value at end of year 1 = 100 - 10 = $90

For the second year, the depreciation amount is computed on $90
= 90 x 0.10 = $ 9

Depreciated amount at end of year 2 = 90 - 9 = $81

The depreciated value of an asset valued at $A at time of purchase at a depreciation rate of r (in decimal) for n years is given by the formula
A' = A(1 - r)ⁿ

We are given
A = $34,145
r = 8/100 = 0.08 therefore 1 - r = 1 - 0.08 = 0.92

a) Depreciated value after 9 years:
A' = 34145(0.92)⁹
    = 16121.95

Rounded to the nearest dollar that would be $16,122 ANSWER

b) Depreciated Value after 25 years

A' = 34145(0.92)²⁵

    = $4,246  rounded to the nearest dollar

c) Car's value after 50 years

At the end of 25 years, the Mustang has become a classic with a value of $4, 246

Then it starts to appreciate at the rate of 14% (0.14 in decimal)

The appreciated value each year after 25 years is given by
A'' = A'( 1 + r)ⁿ

where r is the rate of appreciation and n is the number of years

We are given r = 14% = 0.14

1 + r = 1.14

n = 25

A' = 4,246 the value after 25 years from purchase

Car value after 50 years = car value after 25 years appreciated for the next 25 years

= 4246(1.14)²⁵

= $112,357 rounded to the nearest $

So you can really make a killing after 25 years. As an interesting side note, the value of the car will reach the original value 16 years after 25 years or a total of 41 years after purchase

The height of the metal prism is 1/10 times the height of the tank.

The height h of the metal prism is calculated as follows;

Since the tank is half-filled with water, the height of the water in the tank is H/2.

let the height of the prism = h

Volume of the rectangular tank + volume of prism = total volume

1/2 x L x W x H + L x W x h = 3/5 x L x W x H

H/2  + h = 3H/5

h = 3H/5 - H/2

h = H/10

Therefore, the height of the metal prism is 1/10 times the height of the tank.

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If "employed-adults" were asked how likely they thought that they will lose their jobs, then percent of adults that are "fairly-likely" to lose jobs is 6.23%.

To find the percent of adults that are fairly-likely to lose their jobs, we  first add the total number of adults who responded to survey;

⇒ Total number of adults = 626 + 902 + 3745 + 9212 = 14,485

Next, we determine number of adults who responded "Fairly Likely";

⇒ Number of adults who responded "Fairly Likely" = 902,

To find the percentage, we use formula;

⇒ Percentage = (Number of adults responded "Fairly Likely"/Total number of adults) × 100,

Substituting the values,

We get,

⇒ Percentage = (902/14485) × 100 = 6.23%,

Therefore, 6.23% of employed adults in the survey are fairly likely to lose their jobs within next-year.

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The given question is incomplete, the complete question is

In a survey, employed adults were asked how likely they thought it was that they would lose their jobs within the next year. the results are :

 Response     Frequency

 Very Likely         626

 Fairly Likely        902

Not too Likely      3745

  Not Likely          9212

Find the percent of adults that are fairly likely to lose their jobs.  

The example of nonprobabilistic sampling among the given choices is judgment sampling.

In judgment sampling, the researcher uses their judgment or expertise to select a sample that they believe is representative of the population. This type of sampling does not involve random selection and is therefore nonprobabilistic. The sample may be selected based on certain criteria or characteristics that the researcher believes are important.

In contrast, simple random sampling, stratified simple random sampling, and cluster sampling are all examples of probabilistic sampling methods, which involve random selection of a sample from the population using a probability-based approach.

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Answer:

7/14 in simplest form is 1/2

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Answer:

The answer is d) 2/c.

Explanation :

If one of the zeroes of cubic polynomial x^3+ax^2+bx+c is 2, then the product of the other two zeroes can be found by dividing the polynomial by (x-2), which gives:

x^3+ax^2+bx+c = (x-2)(x^2+(a+2)x+(c-2a))

We can solve the quadratic equation x^2+(a+2)x+(c-2a) to find the other two zeroes. By Vieta's formulas, the product of the roots of a quadratic equation ax^2+bx+c=0 is c/a. Therefore, the product of the other two zeroes is:

pq = (c-2a)/1 * 1/(a+2) = (c-2a)/(a+2)

Substituting the value of c/2a from the cubic polynomial gives:

pq = (c-2a)/(a+2) = (2c-4a)/(2a+4) = -2(c/2a) + 2

Therefore, the answer is d) 2/c.

Leroy's total employment compensation last year was $46,650. Hence, the correct answer is option a, $46,650.

To find Leroy's total employment compensation, we need to consider his total job benefits and his total job expenses for traveling and professional development.

Leroy's total job benefits last year were $50,150. His total job expenses for traveling and professional development were $3,500. To calculate his total employment compensation, we need to subtract the job expenses from the job benefits.

Total employment compensation = Total job benefits - Total job expenses
Total employment compensation = $50,150 - $3,500
Total employment compensation = $46,650

The correct option is a. $46650.

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The graphs to match each inequality to its solution are added as an attachment

Analyzing the inequalities from the question, we have the following explanations

Next, we match the number lines and the inequalities

See attachment for number lines

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Using a significance level of 5%, we conclude that there is significant evidence that American adults who drink alcohol do not favor beer, wine, and liquor equally as the alcoholic drink they consume most often. So, the correct answer is D).

Using a significance level of 5%, the chi-square test statistic is 33.3815 with 2 degrees of freedom and a corresponding p-value of less than 0.0001.

Since the p-value is less than 0.05, we reject the null hypothesis of equal preference for beer, wine, and liquor and conclude that there is significant evidence that American adults who drink alcohol do not favor beer, wine, and liquor equally as the alcoholic drink they consume most often.

Therefore, the answer is (d) There is significant evidence that American adults who drink alcohol do not favor beer, wine, and liquor equally as the alcoholic drink they consume most often.

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--The given question is incomplete, the complete question is given

"  Gallup asked a nationally representative sample of adults about their alcohol consumption. Those in the sample who drank alcohol were asked which they drank most often-beer, wine, or liquor. Do the data provide evidence of an equal preference for beer, wine, and liquor as the favored alcoholic drink of American adults who drink alcohol? Here is an incomplete Minitab output for the corresponding chi-square test: Test Contribution Category Observed Proportion Expected to Chi-Sq beer 264 0.333333 216.667 10.3405 wine 237 0.333333 216.667 1.9082 liquor 149 0.333333 216.667 21.1328 N DF Chi-Sq P-Value 650 Using a significance level of 5%, what should you conclude?

a. There are significantly more American adult drinkers who favor beer over wine or liquor.

b. The data are consistent with an equal distribution of beer, wine, and liquor as the alcoholic drink consumed most often by American adults who drink alcohol.

c. We are unable to conclude anything, because the test assumptions are not met.

d. There is significant evidence that American adults who drink alcohol do not favor beer, wine, and liquor equally as the alcoholic drink they consume most often."--

To compare the two running times, we need to express them in the same units. We can convert Sylvester's time to seconds by multiplying by 60:

Sylvester: 4 minutes x 60 seconds/minute = 240 seconds

Lenworth: 4 minutes 12 seconds = 4 x 60 + 12 = 252 seconds

Now we can find the ratio of Lenworth's time to Sylvester's time:

Lenworth/Sylvester = 252/240 = 21/20

So the ratio of Lenworth's time to Sylvester's time is 21:20.

The two forms of writing that have a similar purpose of entertaining an audience are as follow,

A short story

An epic poem

Short stories and epic poems are both forms of literature.

That are designed to entertain readers through the use of compelling characters, interesting plots, and vivid descriptions.

A news article, a book report, and do-it-yourself instructions have different purposes.

A news article is designed to inform readers about current events.

The current event may relates to day day life or to the nature.

A book report is designed to summarize and analyze a book.

IN book report mostly famous books are included to spread the awareness about the book.

And do-it-yourself instructions are designed to provide step-by-step guidance on how to complete a task.

Do -t - yourself is consider as a individual task.

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The type of ticket that must have been sold are 100 adults and 400 students

Also, they were short by $360

Given that tickets are sold for adults and students

Let d = adults

Let s = students

So, we have

6.5d + 3.5s = 2050

d + s = 500

When solved graphically, we have

d = adults = 100

s = students = 400

Here, we have

s = 3d

s + d = 480

So, we have

4d = 480

Evaluate

d = 120

s = 360

So, we have

Total = 6.5 * 120 + 3.5 * 260

Total = 1690

Difference = 2050 - 1690

Evaluate

Difference = 360

They were short by $360

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Answer:Width=5, Length=10

Step-by-step explanation:

You can solve this by using a variable, x, and assigning it to the value that is the width.

Since the perimeter of a rectangle is the width times two plus the length times two, you can use an equation that looks like this:

(image shown)

This will give you the value of X, the width, and you can multiply this value by 2 to get the length.

Answer:

10 cm

Step-by-step explanation:

The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length and w is the width1. We know that the perimeter of this rectangle is 30 cm. So we can write:

2(2w + w) = 30

Simplifying this equation gives:

6w = 30

Therefore:

w = 5

So the width of the rectangle is 5 cm and its length is twice as long as its width which means it’s 10 cm.

Answer:

(x, -y)

(-x, y)

Step-by-step explanation:

If m(x) = -h(x), then each point (x, y) on the graph of h(x) becomes the point (x, -y) on the graph of m(x).

This is because the negative sign in front of h(x) in the equation for m(x) reflects the graph of h(x) across the x-axis. So, the y-coordinate of each point on the graph of h(x) becomes its opposite on the graph of m(x), while the x-coordinate remains the same.

If n(x) = h(-x), then each point (x, y) on the graph of h(x) becomes the point (-x, y) on the graph of n(x).

This is because the expression h(-x) means that we are replacing the variable x in the function h with -x. This reflects the graph of h(x) across the y-axis, since each value of x is replaced by its opposite. So, the x-coordinate of each point on the graph of h(x) becomes its opposite on the graph of n(x), while the y-coordinate remains the same.

Answer:  (a) (x,-y)   (b)(-x, y)

Step-by-step explanation:

Because it's saying that you need to take the negative of the function h(x)  which is y so  make y negative

(a) (x,-y)

The question now say that only the x is going to be come negative so

(b)(-x, y)

Answer:

Step-by-step explanation:

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, to find the perimeter of the triangle with sides a = 24, b = 45, and c = ?, we need to add up the lengths of the known sides:

Perimeter = a + b + c

Plugging in the values, we get:

Perimeter = 24 + 45 + c

Simplifying, we get:

Perimeter = 69 + c

We still need to find the length of the third side, c. However, we can use the fact that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words:

a + b > c

24 + 45 > c

69 > c

Therefore, we know that c must be less than 69.

On the other hand, we can also use the fact that the difference between the lengths of any two sides of a triangle must be less than the length of the third side. In other words:

|a - b| < c

|24 - 45| < c

21 < c

Therefore, we know that c must be greater than 21.

Putting these two inequalities together, we have:

21 < c < 69

So the perimeter is:

Perimeter = 69 + c

And we know that:

21 < c < 69

Therefore, we can say that the perimeter is somewhere between:

69 + 21 = 90

and

69 + 69 = 138

Rounding to the nearest tenth, we get:

Perimeter ≈ 90.0 - 138.0

Therefore, the perimeter is somewhere between 90.0 and 138.0, depending on the actual length of the third side, c.

An equivalent fraction of students that does not be a part of students who attended choir practice is given by 1/4 or 0.25 as a decimal.

Total number of students are equal to 20.

If 15 out of 20 students attended choir practice.

Then the fraction of students who attended can be written as 15/20.

An equivalent decimal fraction that does not represent the part of students who attended choir practice is

= Subtract the fraction of students who attended from 1 which represents the whole group of students.

= 1 - 15/20

= 20/20 - 15/20

= 5/20

= ( 1/ 4) as simplified fraction form.

= 0.25 as a decimal

Therefore, equivalent decimal fraction of students does not represent part of students who attended choir practice is 1/4 or 0.25 as a decimal.

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The above question is incomplete, the complete question is:

Yesterday 15 out of 20 students attended choir practice. Write an equivalent decimal fraction of students which does not represent the part of students who attended choir practice?

As a result, twenty-five percent of the responses were not cataloged in the table.

To begin with, discover the amount of replies that failed to be noted:

Complete Responses - Documented Responses = Unrecorded Responses

200 - 150 = 50

Next, estimate the proportion of responses not represented in the table:

(Unrecorded Responses / Total Responses) * 100%

(50 / 200) * 100% = 0.25 * 100% = 25%

As a result, twenty-five percent of the responses were not cataloged in the table.

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Cecilia collected a total of 200 service responses for her study. She noticed that only 150 responses were recorded in the table. What percent of the responses were not recorded in the table?

Answer:

13*

Step-by-step explanation:

Use the Pythagorean theorem.

a=1

b=x

c=13

so, [tex]1^2 + x^2 = 13^2[/tex]

[tex]x^2 = 169 - 1 = 168[/tex]

[tex]x = \sqrt{168}[/tex]

 [tex]\sqrt{168} = 12.961481396815720461931934872176[/tex] = 13

*If we round to the nearest tenth, we get 13. Because of this rounding, the other leg is the hypotenuse, but it is actually different.