Identify the interquartile range from the box and whisker plot above

Therefore, 65% of all nurses have a starting salary of more than $71,725.31.

Random variable: X, the starting salary of a randomly selected nurse.

b) P(X ≥ 78371.8) = 1 - P(X < 78371.8)

Using the Z-score formula:

z = (X - μ) / σ = (78371.8 - 67694) / 10333 ≈ 1.03

Looking up the probability in the standard normal table or using a calculator, we get:

P (Z ≥ 1.03) ≈ 0.1492

Therefore, P (X ≥ 78371.8) ≈ 0.1492.

c) P (X ≤ 91407.1)

Using the Z-score formula:

z = (X - μ) / σ = (91407.1 - 67694) / 10333 ≈ 2.30

Looking up the probability in the standard normal table or using a calculator, we get:

P(Z ≤ 2.30) ≈ 0.9893

Therefore, P (X ≤ 91407.1) ≈ 0.9893.

d) P (78371.8 < X < 91407.1) = P(X < 91407.1) - P(X < 78371.8)

Using the Z-score formula:

z1 = (78371.8 - 67694) / 10333 ≈ 1.03

z2 = (91407.1 - 67694) / 10333 ≈ 2.30

Looking up the probabilities in the standard normal table or using a calculator, we get:

P(Z < 1.03) ≈ 0.8498

P(Z < 2.30) ≈ 0.9893

Therefore, P (78371.8 < X < 91407.1) ≈ 0.9893 - 0.8498 ≈ 0.1395.

e) P (X ≤ 41861.5)

Using the Z-score formula:

z = (41861.5 - 67694) / 10333 ≈ -2.50

Looking up the probability in the standard normal table or using a calculator, we get:

P (Z ≤ -2.50) ≈ 0.0062

Therefore, P (X ≤ 41861.5) ≈ 0.0062.

f) Yes, a starting salary of 41861.5 dollars is unusually low for a randomly selected nurse, because it is more than 3 standard deviations below the mean. A salary this low would be in the bottom 0.62% of all nurse salaries.

g) To find the starting salary that 65% of all nurses have more than, we need to find the z-score that corresponds to the 65th percentile, and then use the Z-score formula to solve for X.

Using a standard normal table or calculator, we find that the z-score corresponding to the 65th percentile is approximately 0.3853.

Using the Z-score formula:

z = (X - μ) / σ

Substituting μ = 67694, σ = 10333, and z = 0.3853, we get:

0.3853 = (X - 67694) / 10333

Solving for X, we get:

X = 10333(0.3853) + 67694 ≈ 71725.31

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Answer: To find the derivative of the function h(x), we can use the quotient rule, which states that if f(x) = u(x) / v(x), then f'(x) = [v(x)u'(x) - u(x)v'(x)] / [v(x)]^2.

Using this rule, we can find the derivative of h(x) as follows:

h(x) = (x + 2) / (x - 2)

h'(x) = [(x - 2)(1) - (x + 2)(1)] / (x - 2)^2 // apply the quotient rule and differentiate numerator and denominator

h'(x) = (-2 - 2x) / (x - 2)^2

Therefore, the derivative of h(x) is h'(x) = (-2 - 2x) / (x - 2)^2.

Step-by-step explanation:

Answer:

d. x > 2 or x < -2

Step-by-step explanation:

Domain describes the range of x-values in a function.

Domain

The domain of a graph is all of the x-values covered by the function. The domain does not reflect the y-values of a function. This means that answers A and B are automatically wrong.

By looking at the graph, we can tell that there is a gap where some x-values are not covered. This gap is known as a discontinuity. The discontinuity begins at -2 and ends at 2. All of the x-values in the discontinuity are not a part of the domain, and any parts of the graph that are continuous, are included in the domain. The graph is continuous at all points greater than 2 and less than -2, so all of those values are included in the domain. Now, we just need to find out if the endpoints are included in the domain.

Included Values

We know that the domain includes all x-values greater than 2 and less than -2, but we need to know if the domain includes 2 and -2. On a graph, included values will be shown as a closed circle and non-included values will be shown as an open circle. By looking at the graph, we can tell that 2 is not included but -2 is. This means that the domain is x > 2 or x < -2 because the domain does not include x = 2.

Question A) A 99% confidence interval estimate of his population mean finishing time of 100 meters race is (12.8081,15.5919)

Question B) Option II) narrower is the correct Option.

Let X be the time required to finish 100 meters race competition with Tom ( in seconds.)

A) A 99% confidence interval estimate of his population mean finishing time of 100 meters race is (12.8081,15.5919)

x = 14.2

s^2= 0.9867

s= 0.9933

t \aplha/2, n-1 = 3.7074

Margin of error= 1.3919

lower bound= 12.8081

upper bound= 15.5919

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In the exponential function F(x) = ab^x, the variable x is an exponent.

In the exponential function F(x) = ab^x, the variable x is an exponent.

The function F(x) represents a value that grows or decays exponentially with respect to x.

The base b is a positive constant that determines the rate of growth or decay, and the coefficient a determines the initial value of the function.

The variable x can be any number

However, it is always the exponent that determines the value of the function F(x) for a given input x.

Therefore, the correct answer is A. an exponent.

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Answer: f'(x) = 10

Step-by-step explanation: To find f'(x), we need to take the derivative of g(x) with respect to x.

The derivative of 3x is 3, and the derivative of 7x is 7. Since the derivative of a constant is 0, the derivative of -1 is 0. Therefore, we can simplify g(x) to:

g(x) = 3x + 7x - 1 = 10x - 1

The derivative of 10x is 10, and the derivative of a constant is 0. Therefore, f'(x) = 10.

The equation of p(x) in vertex form is;

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

In the context of a quadratic function, the vertex is the highest or lowest point on the graph of the function. It is the point where the parabola changes direction. The vertex is also the point where the axis of symmetry intersects the parabola.

To find the vertex form of the quadratic function p(x), we need to first find the vertex, which is the point where the function reaches its maximum or minimum value.

To find the vertex, we can use the formula:

x = -b/2a, where a is the coefficient of the x²  term, b is the coefficient of the x term, and c is the constant term.

Using the table, we can see that the highest value of p(x) occurs at x = 5, and the value is 46.

We can then use the formula to find the vertex:

x = -b/2a = -5/2a

Using the values from the table, we can set up two equations:

46 = a(5)² + b(5) + c

1 = a(0)²  + b(0) + c

Simplifying the second equation, we get:

1 = c

Substituting c = 1 into the first equation and solving for a and b, we get:

46 = 25a + 5b + 1

-20 = 5a + b

Solving for b, we get:

b = -20 - 5a

Substituting b = -20 - 5a into the first equation and solving for a, we get:

46 = 25a + 5(-20 - 5a) + 1

46 = 15a - 99

145 = 15a

a = 9.67

Substituting a = 9.67 and c = 1 into b = -20 - 5a, we get:

b = -20 - 5(9.67) = -71.35

Therefore, the equation of p(x) in vertex form is:

p(x) = 9.67(x - 5)²  + 1

Simplifying, we get:

p(x) = 9.67(x²  - 10x + 25) + 1

p(x) = 9.67x²  - 96.7x + 250.85 + 1

p(x) = 9.67x²  - 96.7x + 251.85

Rounding to the nearest hundredth, we get:

p(x) = 9.67(x - 5²  + 1 = 9.67(x + 1.04)²  - 10.25

Therefore, the answer is:

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

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tan = 1/√3= perpendicular/ base

1/√3 = AB / AC

AB / 6 = 1/√3

AB = 6/√3

Answer:

Least: 565

Greatest: 574

Step-by-step explanation:

564 would round down to 560 and 575 would round to 580

Helping in the name of Jeus.

The least whole number that rounds to 570 when rounded to the nearest ten is 570. The greatest whole number that rounds to 570 when rounded to the nearest ten is 580.

To find the least whole number that rounds to 570 when rounded to the nearest ten, we need to look at the digit in the tens place. In this case, the tens digit is 7. Since the number can only round up or down, we need to determine if rounding 570 to the nearest ten would be up or down. Since 570 is closer to 570 than to 580, we can round down to 570. Therefore, the least whole number that rounds to 570 when rounded to the nearest ten is 570 itself.

On the other hand, to find the greatest whole number that rounds to 570 when rounded to the nearest ten, we again need to look at the digit in the tens place. Since the tens digit is 7, we need to determine if rounding 570 to the nearest ten would be up or down. Since 570 is closer to 580 than to 570, we can round up to 580. Therefore, the greatest whole number that rounds to 570 when rounded to the nearest ten is 580.

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Answer:

No: n=3; 90

No: n=4; 480

Yes: n=5; 540

Yes: n=6; 720

Step-by-step explanation:

(n-2)180

if the sum of the interior angles is not equal to the above equation when substituting the variable for however many sides there are in the polygon, then it is not the correct sum

Joel will have 12000 after 20 years. The solution has been obtained by using simple interest.

What is simple interest?

Simple interest is the cost of borrowing that is computed using the original principal amount alone and a constant interest rate.

We are given that Joel received a 5,000 gift from his grandmother when he turned 18 and he deposited that money into a savings account that offered 7 percent simple interest.

So, the total interest earned

⇒ Interest = (7% of 5000) * 20

⇒ Interest = 350 * 20

⇒ Interest = 7000

So, the total amount after 20 years will be,

⇒ Amount = Interest + Principal

⇒ Amount = 7000 + 5000

⇒ Amount = 12000

Hence, Joel will have 12000 after 20 years.

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Answer: $624.24.

Step-by-step explanation:

To find the total amount of interest paid on the loan, we first need to find the total amount of money repaid over the course of 36 months.

The total amount repaid is the monthly payment multiplied by the number of months:

Total amount repaid = Monthly payment x Number of months

Total amount repaid = $79.84 x 36 = $2,874.24

To find the total amount of interest paid, we need to subtract the original amount borrowed from the total amount repaid:

Total interest paid = Total amount repaid - Original amount borrowed

Total interest paid = $2,874.24 - $2,250 = $624.24

Therefore, the total amount of interest paid on the loan is $624.24.

Answer:

Shinto worshippers believed in Kami, which were divine spirits that lived in nature. The Kami were believed to be present in all things, including rocks, trees, animals, and humans, and were worshipped and honored through various rituals and ceremonies. Shinto is the traditional religion of Japan, and while it does not have a single founder or doctrine, the belief in Kami is a central tenet of the faith. Today, many Japanese people practice Shinto alongside other religions such as Buddhism or Christianity.

The simplified expression is adbc - bc - abd√c - b√ad√c + acd√b + cd√ab.

In mathematics, the distributive property is a property of operations that involves multiplying a factor by a sum or difference of terms. The distributive property states that the product of a factor and a sum or difference of terms is equal to the sum or difference of the products of the factor with each term individually. In other words, for any numbers a, b, and c, the distributive property can be expressed as:

a(b + c) = ab + ac

Given expression

(a√b+c√d)-b√a)×(d√c-√ab+abc)

Simplifying the expression

(a√b+c√d-b√a)×(d√c-√ab+abc)

by simplifying the given expression using the distributive property of multiplication:

(a√b+c√d-b√a)×(d√c-√ab+abc)

= adbc + acd√b - abd√c - b√ad√c + cd√ab - bc

= adbc - bc - abd√c - b√ad√c + acd√b + cd√ab

Therefore, the simplified expression is adbc - bc - abd√c - b√ad√c + acd√b + cd√ab.

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Answer:

0.909

Step-by-step explanation:

Absolute value is basically the positive value of a number in this case. The symbol of absolute value is ||, and so, the answer is:
|-0.909| = 0.909

Hence, the answer is 0.909, just make the answer positive if they ask for the absolute value of a number.

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Answer: Increase in percentage by 42% and with baggage 43.2%.

Step-by-step explanation:

we know that the price is increased from $250 to $ 335

the percentage change by increasing the price is

$355 - $ 250 = $105

percentage change will be change/original = 105/250*100 = 42%

additional charges $ 50, $105+ $50 = 155

percentage change = 155/355*100 = 43.2%

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40 students have red hair.

We have,

Red color= 5%

Black = 25%

Brown = 40%

Blonde= 30%

Total middle school students = 800

So, the number of red haired student

= 5% of 800

= 5/100 x 800

= 5 x 8

= 40 students

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The transformations which must be applied to object A to place it in the position of object B include the following: B. reflection and translation.

In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;

In Mathematics and Geometry, a reflection can be defined as a type of transformation which moves every point of the geometric figure such as a triangle, by producing a flipped, but mirror image of the geometric figure.

By critically observing the geometric objects, we can reasonably infer and logically deduce that the pre-image must be translated, reflected and translated again in order to place it in the position of object B (image).

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Answer:

b. reflection and translation

Step-by-step explanation:

Ramiro has three credit cards with limits of $7,000, $5,000, and $9,500, respectively. Assuming he charged each of them up to 75 percent of its limit, the amount he owes on each card is:

Card 1: 75% of $7,000 = $5,250

Card 2: 75% of $5,000 = $3,750

Card 3: 75% of $9,500 = $7,125

To calculate the total amount Ramiro owes, we add up the amounts he owes on each card: $5,250 + $3,750 + $7,125 = $16,125

Therefore, Ramiro currently owes a total of $16,125 on his three credit cards.

91.3 pounds of fruit are left

Jason bought = 91.5 pounds

class ate = 0.2 pounds

You subtract the amount the class ate from the amount Jason bought to get the amount of fruit left.

91.5 - 0.2 = 91.3 pounds

Answer: 17999640

Step-by-step explanation:

The number of sides (100000) - 2. This gives you 99998 sides. Then you multiply it by 180. This equals 17999640

Answer: The sum of the exterior angles of a polygon is always 360 degrees. This is because when you travel around the exterior of a polygon, you make one complete revolution of 360 degrees.

To find the measure of each exterior angle of a regular n-gon (a polygon with n sides and angles of equal measure), you divide the total sum of the exterior angles (360 degrees) by the number of sides or angles in the polygon.

So for a regular 100000-gon, each exterior angle measures 360/100000 = 0.0036 degrees.

To find the sum of all the exterior angles in a 100000-gon, we multiply the measure of one exterior angle by the number of exterior angles (which is also equal to the number of sides/vertices in the polygon).

The number of exterior angles in a 100000-gon is also 100000, so:

Sum of exterior angles = 0.0036 degrees/angle × 100000 angles = 360 degrees

Therefore, the sum of the exterior angles of a 100000-gon is 360 degrees.

Step-by-step explanation:

Answer: Let's call the speed of the boat "b" and the speed of the current "c". We can set up two equations based on the information given:

Downstream: distance = rate × time

78 = (b + c) × 3

Upstream: distance = rate × time

80 = (b - c) × 4

Now we have two equations with two unknowns, which we can solve simultaneously. We can start by simplifying each equation:

78 = 3b + 3c

80 = 4b - 4c

We can solve the second equation for "b" by adding 4c to both sides and then dividing by 4:

80 + 4c = 4b

20 + c = b

Now we can substitute this expression for "b" into the first equation and simplify:

78 = 3(20 + c) + 3c

78 = 60 + 6c

18 = 6c

c = 3

So the speed of the current is 3 km/h. We can use the expression we found for "b" earlier to find the speed of the boat:

b = 20 + c = 20 + 3 = 23 km/h

Therefore, the speed of the boat is 23 km/h.

Step-by-step explanation:

Answer: 104%

Step-by-step explanation: 26% times 4 years

The percent increase in the cost of an airline ticket is 62.22% (approx)  

The percent increase in the cost of the airline ticket with the additional $50 baggage fee is 84.44% (approx)

To find the percentage of increase find the difference between the old and new cost of tickets. Now multiply the ratio of the resultant difference and the intial cost of the ticket by 100.

Here we have

Two weeks ago, the cost to fly from Hartford to Denver was $225.

Now the cost is $365.

The percent increase in the cost of the airline ticket from $225 to $365 can be calculated as follows:

Here the difference between the old and new ticket prices is given by

=> $365 - $225 = $140

The percentage of change = 140/225 (100) = 62.22%

The airline charges an additional $50 baggage fee

The new ticket price = $365 + $50 = $415.

Hence, the difference between the old and new ticket prices is

=>  $415 - $225 = $190

The percentage of change = [190/225] × 100 = 84.44%

Therefore,

The percent increase in the cost of an airline ticket is 62.22% (approx)  

The percent increase in the cost of the airline ticket with the additional $50 baggage fee is 84.44% (approx)

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The formula for finding revolution ​is

Revolutions = Distance traveled / Circumference of the object.

In physics and mechanics, revolutions refer to the number of times an object completes a full circular motion around an axis or a point.

A revolution is a complete turn around a fixed point or axis, and it is often measured in terms of rotations per minute (RPM) or cycles per second.

For example, a car tire completes one revolution when it turns once completely around its axis. Similarly, a planet completes one revolution when it completes one full orbit around its star.

The formula for finding revolution:  ​

The formula for finding the number of revolutions of a rotating object is:

Revolutions = Distance traveled / Circumference of the object

Where distance traveled is the linear distance that the object has covered, and circumference is the distance around the circular cross-section of the object.

Therefore,

The formula for finding revolution ​is

Revolutions = Distance traveled / Circumference of the object.

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To complete the grouped frequency distribution for the data with a class width of 4, you can start by first obtaining the range of the data, determining the lower limit of the first class interval, and the upper limit of each class interval.

After you have determined the upper limit of each class interval, the next thing to do will be constructing a table that shows the columns for the class intervals, the frequency of each interval, and the cumulative frequency.

Count the number of data points that fall into each class interval, and record these frequencies in the frequency column of the table. Add up the frequencies to get the cumulative frequencies. Finally, use the figures obtained to determine the mean, median and mode.

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The height of the plant, the time Anthony plants the seed and the number of months, analyzed using an assumption of a constant growth rate indicates;

PT1.A; 1 5/8 inches

PT2.B; 4 1/8 inches per month

A growth rate is the rate at which the a quantity being measured increases per unit time.

The height of the plant at the beginning of the summer in June = 12 3/8 inches

Height of the plant at the end of the summer in September = 14 inches

PT1.A. The amount by which the plant grows is therefore;

14 - 12 3/8 = 14 - 99/8 = (112 - 99)/8 = 13/8

13/8 = 1 5/8

The length in inches by which the plant had grown from June to September = 1 5/8 inches

PT2.B. The amount by which the plant had grown per month, can be found by assuming a linear relationship in the growth rate of the plant

The number of months between March and June = 6 - 3 = 3 months

The growth rate of the plant per month is therefore;

Growth rate = (12 3/8)/3 = (99/8)/3 = 33/8

33/8 = 4 1/8

The growth rate of the plant = 4 1/8 inches per month

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