Among fatal plane crashes that occurred during the past 65 years, 260 were due to pilot error, 62 were due to other human error, 315
were due to weather, 682 were due to mechanical problems, and 313 were due to sabotage.
Fill in the relative frequency for each category. Write answers in percentage form and round to one decimal place as needed. Do not include the percent symbol.

Among Fatal Plane Crashes That Occurred During The Past 65 Years, 260 Were Due To Pilot Error, 62 Were

Answers

Answer 1

Answer: Pilot Error: 15.9%

Human Error: 3.8%

Weather: 19.3%

Mechanical Problems: 41.8%

Sabotage: 19.2%

Step-by-step explanation:

260+62+315+682+313=

322+997+313=

1319+313=1632 total crashes

Pilot error: 260/1632=

0.159=

0.159*1=

0.159*100%=15.9%

Human error: 62/1632=

0.03799=

0.038=

0.038*100%=3.8%

Weather: 315/1632=

0.193=

0.193*100%=19.3%

Mechanical Problems: 682/1632=

0.41789=

0.418=41.8%

Sabotage: 313/1632=

0.191789=

0.192=19.2%


Related Questions

Which of the following describes a correct process for solving the equation 3(x + 6) = 21 and arrives at the correct solution? (1 point)
Divide both sides of the equation by 3, and then subtract 6 from both sides of the equation. The solution is x = 1.
Subtract 6 from both sides of the equation, and then divide both sides of the equation by 3. The solution is x = 5.
Distribute the 3, subtract 6 from both sides of the equation, and then divide both sides of the equation by 3. The solution is x = 5.
Add 6 to both sides of the equation, and then divide both sides of the equation by 3. The solution is x = 9.

Answers

Answer:

1st answer indeed

Step-by-step explanation:

ok so the steps are included in the given answer. hope you can figure it out. if not let me know. (:

which number class does -17 belong to

Answers

The abstract class Number is the superclass of classes BigDecimal , BigInteger , Byte , Double , Float , Integer , Long , and Short .

Step-by-step explanation:

Help asap im struggeling

Answers

The range and domain for the exponential function and logistics function are Expotentioal function : Domain= (2,  infinity )

Exponential function:

An exponential function is a mathematical function of the following form: f ( x ) = a x. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.

Exponential functions have the form f(x) = bx, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent. An example of an exponential function is the growth of bacteria. Some bacteria double every hour.

In exponential notation, a number usually is expressed as a coefficient between one and ten times an integral power of ten, the exponent. To express a number in exponential notation, write it in the form: c × 10n, where c is a number between 1 and 10 (e.g. 1, 2.5, 6.3, 9.8) and n is an integer (e.g. 1, -3, 6, -2

Definition of logarithmic function: a function (such as y = log x or y = ln x) that is the inverse of an exponential function (such as y = ax or y = ex) so that the independent variable appears in a logarithm.

Expotentioal funtion :

Domain= (2,  infinity )

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The exponential function's and the logistical function's range and domain are Exponential purpose: Domain= (2, infinite ) (2, infinity )

Explicit function

A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.

When b > 0 and b 1, an exponential function has the form f(x) = bx. The base is b, and the exponent is x, just like in any exponential expression. The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour.

The exponential function's and logistics's domain and range

When b > 0 and b 1, an exponential function has the form f(x) = bx. The base is b, and the exponent is x, just like in any exponential expression. The development of bacteria is an illustration of an exponential function. Some germs multiply by two per hour.

A number is typically written in exponential notation as a coefficient between one and ten times an integral power of ten, the exponent. When writing a number in exponential notation, use the format: c 10n, where c is an integer and n is a number between 1 and 10 (for example, 1, 2.5, 6.3, 9.8).

A logarithmic function is one that is the inverse of an exponential function, such as y = ax or y = ex, and causes the independent variable to appear in a logarithm. Examples of such functions include y = log x and y = ln x.

Expotentioal funtion :

Domain= (2,  infinity )

-3+p/7=-5 help step by step please ???

Answers

here’s an explanation! let me know if you need further clarification

Question 41

By the time Janet pays off the loan, what is the total cost of her trip?


Question 4 options:


$3,500



$4,441.17



$3,681.42



$3,685.05


Question 5

What is the equation to find your new balance after each month?


Question 5 options:


New balance = Previous balance - Interest paid



New balance = Previous balance - Principal paid



New balance = Principal paid - Interest paid



New balance = Previous balance - Total monthly payment

Answers

Доброе утро, отве    $3,500

Calculate the perimeter and area of the triangle formed by the coordinates K (-4,-1) ,L(-2, 2), and M (3,-1).

Answers

Perimeter = 16.4 units

Using the heron's formula, Area ≈ 10.4 units².

What is the Heron's Formula?

The heron's formula is used to find the area of a triangle with known side lengths of all its three sides, a, b, and c. The heron's formula is given as: Area = √[s(s - a)(s - b)(s - c)], where s = half the perimeter of the triangle

s = (a + b + c)/2.

Given the following:

K (-4,-1) ,

L(-2, 2),

M (3,-1)

Use the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex], to find KL, LM, and KM.

KL = √[(−2−(−4))² + (2−(−1))²]

KL = √13 ≈ 3.6 units

LM = √[(−2−3)² + (2−(−1))²]

LM = √34 = 5.8 units

KM = √[(−4−3)² + (−1−(−1))²]

KM = √49 = 7 units

Perimeter = 3.6 + 5.8 + 7 = 16.4 units

Semi-perimeter (s) = 1/2(16.4) = 8.2 units

KL = a ≈ 3.6 units

LM = b = 5.8 units

KM = c = 7 units

s = 8.2

Plug in the values into √[s(s - a)(s - b)(s - c)]

Area = √[8.2(8.2 - 3.6)(8.2 - 5.8)(8.2 - 7)]

Area = √[8.2(4.6)(2.4)(1.2)]

Area = √108.6336

Area ≈ 10.4 units²

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Look at this diagram:

C
D
E
F
G
H
I
J


If
DF
and
GI
are parallel lines and mFEH = 134°, what is mDEH?

Answers

Answer:

Step-by-step explanation:

ihe

The teacher wants to encourage her students by reporting that, overall, the scores were high. Should she use the mean or median to summarize the center of the distribution of scores? She could choose either one because they are equal. She should report the mean because it will be greater than the median. She should report the median because it will be greater than the mean. All the missing scores are needed in order to decide.

Answers

She should report the Mean because it will be greater than the Median.

Let's start with the example from before. Imagine you teach a class with 20 students, and they take a test with 20 multiple choice questions about the Revolutionary War. Imagine that the grades you get back from scoring their tests look like this:

Student #1: 20   Student #6: 12    Student #11: 10     Student#16:8Student #2: 17   Student #7: 12    Student #12: 10     Student#17:6 Student #3: 16  Student #8: 12    Student #13: 10     Student #18:6   Student #4: 14   Student #9: 10    Student #14: 8       Student #19:4 Student #5: 14  Student #10: 10   Student #15: 8      Student#20: 3

So you can see we have student #1 through student #20, and you can see that the scores range quite a bit. Looking at these scores you can see that one student, student #1, got a perfect score of 20 out of 20. Many students got scores somewhere in the middle, with five students getting half of the questions right - that would be a score of 10 out of 20. A few of the students did pretty well, only missing a few questions, While a few students did pretty badly but at least got a few of the questions right.

Let's say the principal of your school wants a quick summary of how your students did on their test. How would you summarize the results? The most common type of statistic, in either the context of the classroom assessment or in laboratory research projects, is statistics of summary. There are various types of Statistics of summary, but in general their purpose is to quickly give an general impression of the overall trend in results. So, just like you'd guess, based on the term Statistics of summary, these statistics just give you a ballpark idea of what happened on the test.

The most well-known statistic of summary is called the mean, which is the term we use for the arithmetic average score. When most people use the term 'average score,' what they're really referring to, technically, is what we call the mean. How do we calculate the mean? We simply add up all of the individual results, get the total, and then divide by the number of students in the class. In our example, you can see how this would look on the screen. If you add up the scores of 20 + 17 + 16 and so on through all 20 students, you get a total score of 210. You divide 210 by 20 (the number of students), and you get a mean of 10.5. You can see that this score, 10.5, is a pretty representative score of the middle score for this class, so it works nicely as a summary.

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Matsu wants to measure the dimensions of her vegetable garden. Which unit of measurement should she use to
eliminate the need to write the values in scientific notation?
inches
feet
cups
tons

Answers

For measuring the vegetable garden, Matsu should use the unit of feet.

What is defined as the measurement units?

Finding a number that represents the amount of anything is what measurement is all about.

A measurement unit is a unit of measurement that is used to represent a physical quantity. For example, the unit of measurement is the defined magnitude of quantity that is being used as the norm for measuring the same type of quantity, as adopted and specified by law or convention.The imperial unit, also known as the British imperial system, is the standard or default weights and measures system.Metric System: The metric system is by far the most recent and widely used international system of measurement.Natural System: Natural units are physical units of measurement that are entirely based on common physical constants.

For the given question;

The dimensions of the garden are the length. This could be calculated by using the two values in the option; That is inches and feet.

But as inches is a used for measuring the small length ad feet is the larger unit.

Thus, dimensions of the vegetable garden of Matsu are calculated by using feet.

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Answer:

For measuring the vegetable garden, Matsu should use the unit of feet.

What is defined as the measurement units?

Finding a number that represents the amount of anything is what measurement is all about.

A measurement unit is a unit of measurement that is used to represent a physical quantity.

For example, the unit of measurement is the defined magnitude of quantity that is being used as the norm for measuring the same type of quantity, as adopted and specified by law or convention.

The imperial unit, also known as the British imperial system, is the standard or default weights and measures system.

Metric System: The metric system is by far the most recent and widely used international system of measurement.

Natural System: Natural units are physical units of measurement that are entirely based on common physical constants.

For the given question;

The dimensions of the garden are the length. This could be calculated by using the two values in the option; That is inches and feet.

But as inches is a used for measuring the small length ad feet is the larger unit.

Thus, dimensions of the vegetable garden of Matsu are calculated by using feet.

Step-by-step explanation:

The ages of residents of a small town are given in the following frequency distribution, approximate the

mean age

Answers

The mean age of the residents of a small town will be 27.74.

How to calculate the mean?

Midpoints of classes are:

4.5, 14.5, 24.5, 34.5, 44.5, 54.5, 64.5, 74.5, 84.5, 94.5

Hence,

Mean = (4.5*283 + 14.5*202 + 24.5*215 + 34.5*256 + 44.5*175 + 54.5*90 + 64.5*23 + 74.5*21 + 84.5*15 + 94.5*3)/(283 + 202 + 215 + 256 + 175 + 90 + 23 + 21 + 15 + 3)

Mean = (1273.5 + 2929 + 5267.5 + 8832 + 7787.5 + 4905 + 1483.5 + 1564.5 + 1267.5 + 283.5) / 1283

= 35593.5/1283

= 27.74

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Solve for the unknown angle measures of the polygon.
A pentagon has angle measures of 100°, 103°, 111° and 114°. What must the fifth angle measure?
The fifth angle measures

Answers

The fifth angle measure of the polygon is 112°

What is a pentagon?

Since a pentagon is made up of three triangles, its total angles are 3 * 180 * 540. The following formula may be used to get the pentagon's total interior angles: We are aware that the interior angle sum of a polygon with n sides is equal to (n - 2) 180°.

Let the missing angle be x.

The sum of the angles of pentagon is 540°

540 = 100 + 103 + 111 + 114 + x

540 = 428 + x

x = 540 - 428

x = 112

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which data set would be best represented by a line graph?
j the change i population of a particular city over the last 100 years
k. the percentage of recent u.s. immigrants from different continents
l. the numbger of people living in each region of a state
m. the wages in dollars per hour o store employees
n. the heights oan weights of people in a city

Answers

The data set which would be best represented by a line graph is; Choice j: The change in population of a particular city over the last 100 years.

Which is best represented by a line graph?

It follows from the task content that the data set which is best represented by a line graph is.to.he identified.

On this note, since choice J measures the change in a dependent quantity, population according to a change in the independent variable, time.

Consequently, choice J is best represented by a line graph.

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Find three consecutive odd integers such that the sum of the first and third equals to the sum of the second and 43.
Be sure to show your work and list the integers in this format: (1, 2, 3)

Answers

Answer:

  (41, 43, 45)

Step-by-step explanation:

You want three consecutive odd integers such that the sum of the first and third is 43 more than the second.

Setup

Let n represent the middle (second) of the integers. Then the first is (n-2) and the third is (n+2). The given relation can be written as the equation ...

  (n -2) +(n +2) = n +43

Solution

Simplifying gives ...

  2n = n +43

  n = 43

  n-2 = 41

  n+2 = 45

The three integers are (41, 43, 45).

__

Additional comment

When working consecutive integer problems, it often works well to let a variable represent the middle one, or their average value.

The fifth term of the number parttern 15,10,5,0

Answers

Answer:

Step-by-step explanation: -5

Answer:

-5

Step-by-step explanation:

The pattern is decreasing by 5, so 0-5= -5

Hope this helps :D

( -5+1 ) + ( 6-11 ) + ( -3 - 17 )

Answers

-29 la después es -29
(-4)+(-5)+(-20)
(-9)+(-20)
(-29)

A company has $9721 to give out in bonuses. An amount is to be given out equally to each of the 24 employees

Answers

Answer:  $405 each:)

Step-by-step explanation:

You would subtract 24 from 9721 and then it will give you 405.041666666 so you will round and it will be 405 each

Answer:

$405

Step-by-step explanation:

24x405=9721$

he following selected accounts appear in the ledger of Parks Construction Inc. at the
beginning of the current year:
Preferred 2% Stock, $75 par (100,000 shares authorized, 80,000 shares issued) . . . . . . . $ 6,000,000
Paid-In Capital in Excess of Par—Preferred Stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420,000
Common Stock, $8 par (5,000,000 shares authorized, 3,000,000 shares issued) . . . . . . . 24,000,000
Paid-In Capital in Excess of Par—Common Stock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,850,000
Retained Earnings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115,400,000
During the year, the corporation completed a number of transactions affecting the
stockholders’ equity. They are summarized as follows:
a. Issued 400,000 shares of common stock at $11, receiving cash.
b. Issued 5,000 shares of preferred 2% stock at $90.
c. Purchased 150,000 shares of treasury common for $10 per share.
d. Sold 80,000 shares of treasury common for $13 per share.
e. Sold 20,000 shares of treasury common for $9 per share.
f. Declared cash dividends of $1.50 per share on preferred stock and $0.06 per share
on common stock.
g. Paid the cash dividends.

Answers

Based on the events that occurred on January 5, and February 10, journal entries for Parks Construction Inc. are:

Date                 Account title                                          Debit            Credit

Jan. 5               Cash                                                 $4,400,000

                         Common stock                                                  $3,200,000

                          Paid-in capital in excess of par- Common      $1,200,000

Feb 10               Cash                                                 $450,000

                         Common stock                                                     $375,000

                          Paid-in capital in excess of par - preferred       $75,000

How to find the common stock value?

The cash would be:

= 400,000 x 11

= $4,400,000

The common stock value would be:

= 400,000 x 8

= $3,200,000

The cash from preferred stock:

= 5,000 x 90

= $450,000

Preferred stock:
= 50,000 x 75

= $375,000

The question is:
Journalize the entries to record the transactions on January 5 and February 10. . Refer to the Chart of Accounts for exact wording of account titles.

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MN has a slope of 4/5 and PQ has a slope of -4/5.Are the lines parallel, perpendicular, or neither?

Answers

Answer:

neither

Step-by-step explanation:

En Vogue Menswear ordered short-sleeve shirts for $23.00 each and long-sleeve shirts for $28.50 each from Hugo Boss. If the total order amounted to $9,862.50 for 375 shirts, how many of each shirt was ordered?

Answers

The number of short-sleeve shirts ordered is 150.

The number of long-sleeve shirts ordered is 225.

What are the simultaneous equations that represent the question?

23s + 28.50l = $9,862.50 equation 1

s + l = 375 equation 2

Where:

s = number of short-sleeve shirts ordered

l =  number of long-sleeve shirts ordered

How many of each shirts were ordered?

The first step is to multiply equation 2 by 23

23s + 23l = 8,625 equation 3

Subtract equation 3 from equation 2

1237.50 = 5.5l

Divide both sides by 5.5

l = 225

s = 375 - 225 = 150

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Find the solution to the system of equations.y=-2x+7. y=5x-7

Answers

Answer:

  (x, y) = (2, 3)

Step-by-step explanation:

You want the solution to the system of equations.y=-2x+7, y=5x-7.

Solution

Equating the expressions for y gives ...

  -2x +7 = 5x -7

  14 = 7x . . . . . . . add 7+2x

  2 = x . . . . . . . . . divide by 7

  y = 5(2) -7 = 3 . . find y from the second equation

The solution is (x, y) = (2, 3).

Find the value of x the diagram is not a scale

○ 85

○ 95

○ 127

○ 42

Answers

Answer:

85°

Step-by-step explanation:

→ Find the sum of the angles in the triangle

53 + 42 = 95

→ Find what the sum of angles in a triangle should be

180

→ Subtract 95 from it

180 - 95 = 85°

A town has a population of 109,500 and grows at a rate of 7.4% every year. Which
equation represents the town's population after 2 years?

Answers

126305.622 is the town's population after 2 years on percentage  7.4.

What percentage means?

percentage , which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

P=  109,500

r = rate =7.4/100

t = time = 2 years

Based on the given conditions, formulate [tex]109,500 . ( 7.4 /100 + 1 )^{2}[/tex]

                                                   = 109500 ( 107.4)²

                                                    = 109500 × 107.4 × 107.4

Evaluate the equation/expression = 126305.622

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In an experiment, college students were given either four quarters or a $1 bill and they could either keep the money or spend it on gum. The results are summarized in the table. Complete parts (a)
K
through (c) below.
Students Given Four Quarters
Students Given a $1 Bill
Purchased Gum
33
11
Kept the Money
18
27
a. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters.
The probability is 0.589
(Round to three decimal places as needed.)
b. Find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill
The probability is
(Round to three decimal places as needed.)
c. What do the preceding results suggest?
OA A student given four quarters is more likely to have spent the money than a student given a $1 bill
OB. A student given a $1 bill is more likely to have spent the money than a student given four quarters.
OC. A student was more likely to have spent the money than to have kept the money
OD. A student was more likely to be given four quarters than a $1 bill

Answers

Using the probability concept, it is found that:

a) The probability is 0.682.

b) The probability is 0.578.

c) A student given a $1 bill is more likely to have spent the money than a student given four quarters.

What is a probability?

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For item a, we have that out of the 44 students that were given four quarters, 30 students spent money purchasing gum, hence:

p = 30/44 = 0.682.

The probability is 0.682.

For item b, we have that out of 45 students that were given a $1 bill, 26 kept the money, hence:

p = 26/45 = 0.578.

The probability is 0.578.

Hence the correct option for item c is:

A student given a $1 bill is more likely to have spent the money than a student given four quarters.

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Joan bought a radio and later sold it for $360 . She mad a profit of %20. How much money did Joan pay for the radio?

Answers

The answer is $72 it’s easy

Use the graph of y=f(x)

Answers

The right answer is ( A )
Cause the function is shifted 2 units to the left
And it's shifted 3 units down

A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph.

Shifts are added/subtracted to the x or f(x) components. If the constant is grouped with the x, then it is a horizontal shift, otherwise it is a vertical shift.

- My first language isn't english so I hope this helped a bit .

After 2 minutes an ant traveled 120 meters and after 6 minutes the ant will have traveled 260 meters.

Assuming a linear equation can be used to model the change in distance traveled over time between 2 and 6 minutes, let y be the distance traveled (in meters) after x minutes and complete this linear model in slope-intercept form:


Question 2
The significance of the slope in the context of this situation is:

The ant travels 50 meters in 35 minutes.
The ant travels at an average of 35 meters per minute.
The ant travels at an average of 50 meters per minute.
The ant travels at an average of 50 minutes per meter.
The ant travels at an average of 35 minutes per meter.

Question 3
The distance that the ant will have traveled after 14 minutes is


Question 4
The number of minutes that will pass from the time the ant begins moving until it has traveled 610 meters is

Answers

1. The equation is: y = 35x + 50

2. The significance of the slope is: A. The ant travels at an average of 35 meters per minute.

3. Distance would be 490 meters.

4. Number of minutes will be: 16.

How to Model a Linear Equation?

Given that x = minutes, and y = distance, then we would have the following coordinates:

(2, 120)

(6, 260)

1. The slope (m) = change in y / change in x = 260 - 120 / 6 - 2

Slope (m) = 35

Substitute m = 35, and (x, y) = (2, 120) into y = mx + b to find b

120 = 35(2) + b

120 = 70 + b

120 - 70 = b

b = 50

Substitute m = 35 and b = 50 into y = mx + b to write the equation

y = 35x + 50

2. The slope of the graph 35.

The significance of the slope is: A. The ant travels at an average of 35 meters per minute.

3. When x = 14, we have:

y = 35(14) + 50

y = 490

Distance would be 490 meters.

4. Substitute y = 610 into y = 35x + 50

610 = 35x + 50

610 - 50 = 35x

560 = 35x

560/35 = 35x/35

16 = x

x = 16

Number of minutes will be: 16.

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Find the solution to the given system of equations.







5
x
+
6
y
+
8
z
=

17

5
x
+
5
y
+
9
z
=

13

x
+
y
+
2
z
=

2

Answers

break down the equations into parts and use simultaneous equation method to solve it

A car dealer will sell you the $16,850 car of your dreams for $3,290 down and payments of $333.97 per month for 48 months. What is the APR? (Round your answer to the nearest tenth of a percent.)

Answers

The APR of the given transaction to the nearest tent of a percent is; 4.8%

What is the APR?

We find how much you will pay for the car using the down and monthly payments:

3290 + 333.97(48) = $19608.56

Thus, the interest is:

I = (19608.56 - 16450) = $3158.56

Use the simple interest formula:

I = Prt

where;

I is the interest.

P is the principal.

r is the interest rate is the time in years.

Substitute I = $3158.56, P = $16450, and t = 4 years (48 months):

Thus;

3158.56 = (16450)r(4)

Expanding gives;

​3158.56 = 65800r

r = 3158.56/65800

r ≈ 0.048 = 4.8%

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The marching band needs to create rows for its performance. There are 48 instruments and 32 flag bearers. Only one type of performer can be in each row. What is the maximum number of performers in each row so that all the rows are equal in length?

48
32
16
2

Answers

The maximum number of performers in each row so that all the rows are equal in length is C. 16.

How to calculate the value

It should be noted that there are 48 instruments and 32 flag bearers and only one type of performer can be in each row.

The maximum number of performers in each row so that all the rows are equal in length will be the highest common factor between both numbers.

It should be noted that the highest common factor between 32 and 48 is 16

Therefore the correct option is C.

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Determine the whole number of standard deviations from the mean that include all
data values.
The mean price of the nonfiction books on a best-sellers list is $25.07; the standard
deviation is $2.62.
$26.95, $22.95, $24.00, $24.95, $29.95, $19.95, $24.95, $24.00, $27.95, $25.00

Answers

The number of standard deviations from the mean that include all

data values is two.

Standard Deviation could be a live that shows what proportion variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean.it's a well-liked live of variability as a result of it returns to the initial units of live of the information set

From the gathering of information, we will see that the minimum worth is $19.95 and also the most worth is $29.95. So , we would like to seek out the amount of normal deviations, let's decision it "a" , such that[tex]\overline x $\color \ - a\cdot\sigma \le 19.95}[/tex] and   [tex]\overline x $\color \ +a\cdot\sigma \geq 29.95}[/tex]

Use the given values of mean  [tex]\overline x[/tex] and normal deviation (σ) to notice the worth of "a".

         [tex]\overline x $\color \ - a\cdot\sigma \le 19.95}\\25.07\ - 2.62a \leq 19.95\\5.12\leq 2.62a\\1.9541\leq a[/tex]

On rounding off we get a = 2

Checking another inequality

         [tex]\overline x $\color \ + a\cdot\sigma \geq 29.95}\\25.07 \ + 2(2.62) \geq 29.95\\25.07 + 5.24 \geq 29.95\\30.31\geq 29.95[/tex]

Thus , 2 standard deviation include the all values from the given set of data .

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