The stem-and-leaf plot shows test scores Charlie received for the year.
What is the total number of test scores recorded on the stem-and-leaf plot?
Also here is a snip.

Answer:

[tex] \sqrt{ {20}^{2} + {44}^{2} } = \sqrt{400 + 1936} = \sqrt{2336} = 4 \sqrt{146} = 48.3[/tex]

The length of DG is about 48.3 cm.

The probability is based on actual observations or data, which makes it an experimental probability. It is important to note that experimental probabilities may not always match theoretical probabilities due to factors such as bias or chance.

The given scenario is an example of experimental probability. Experimental probability refers to the probability of an event based on actual observations or data collected through experimentation or observation. In this case, the experiment involved rolling a die containing the numbers 1-6, and observing the number that appears on the top face of the die. Out of the 15 times the die was rolled, it landed on an even number 8 times. The experimental probability of rolling an even number can be calculated by dividing the number of times an even number was rolled by the total number of rolls, which is 8/15 in this case.

Theoretical probability, on the other hand, refers to the probability of an event based on mathematical calculations and assumptions. For instance, the theoretical probability of rolling an even number on a fair six-sided die can be calculated as 3/6 or 1/2, since there are three even numbers (2, 4, and 6) and six possible outcomes. However, in this case, the probability is based on actual observations or data, which makes it an experimental probability. It is important to note that experimental probabilities may not always match theoretical probabilities due to factors such as bias or chance.

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Answer:

Step-by-step explanation:

First question :

The summation of the angles given in the figure is 360 degrees.So :

3x+4x+5x+6x=360°

⇒ 18x=360°

⇒ x=(360÷18)

⇒ x=20°

Second Question :

Two opposite vertical angles formed when two lines intersect each other are always equal ,So:

5x=3x+58°

⇒ 2x=58°

⇒x=29°

80 students gained more than 48 mark from box plot.

Since 120 students gained less than 70, and

70 is the upper quartile from box plot

120 people are in the 75% of all the students

we need to find the total number of students.

we need to multiply 0.75 (75%) by something to get 120. which is 160 (the total number of all students).

and since 48 is the median score, find 50% of 160 which is 80

Hence, 80 students gained more than 48 mark

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A class hierarchy is a diagram that shows the inheritance relationship between classes.

It is similar to a family tree in that it shows the parent-child relationships between classes. In a class hierarchy, the parent class is called the superclass and the child class is called the subclass. The subclass inherits the properties and behaviors of the superclass, and can also add new properties and behaviors of its own.

The class hierarchy is an important concept in object-oriented programming, as it allows for code reuse and the creation of complex systems with modular, reusable components.

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The units for da/dx are pounds per foot squared.

The units for da/dx would be pounds per foot squared. This is because da/dx represents the rate of change of the function a(x), which has units of pounds per foot, with respect to x, which has units of feet. When we take the derivative of a(x), we essential do division of the change in a(x) by the change in x.  

The change in a(x) has units of pounds, and the change in x has units of feet. Therefore, the units for da/dx are pounds per foot squared.

To further explain this, imagine that a(x) represents the weight of a beam that is x feet long. The units for a(x) would be pounds per foot, as it gives us the weight of the beam per unit of length. The derivative of a(x), or da/dx, would give us the rate at which the weight of the beam changes as we increase its length by one foot.

This rate of change would be in units of pounds per foot squared, as we are dividing the change in weight (pounds) by the change in length (feet squared).

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The sample proportions of northern and southern residents of this state will depend on the actual preferences of the individuals in the samples.

We have a sample of 33 Northerners and 41 Southerners from a certain state. The sample proportions of northern residents (pN) and southern residents (ps) who prefer flour tortillas over corn tortillas can be calculated based on the provided information.

According to the claim by agriculturists, 43% of northern residents and 59% of southern residents prefer flour tortillas. To estimate the proportions in the population, we use the sample proportions.

For the northern residents:

pN = Number of northerners preferring flour tortillas / Total number of northerners in the sample

Assuming that the sample is representative, we can multiply the sample size by the claimed proportion to estimate the number of northerners preferring flour tortillas:

pN = 33 * 0.43 = 14.19 (approximately)

For the southern residents:

ps = Number of southerners preferring flour tortillas / Total number of southerners in the sample

Again, assuming the sample is representative, we can estimate the number of Southerners preferring flour tortillas:

ps = 41 * 0.59 = 24.19 (approximately)

The sample proportions pN and ps are estimates of the proportions in the respective populations. They provide an indication of the preferences of the residents in the northern and southern portions of the state based on the selected samples.

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Finally, we just need to use the z-coordinate of the point as the third coordinate in our cylindrical coordinates. So our final answer is: (r, θ, z) = (sqrt(x2 + y2), arctan(y/x), z)

To express a point given in Cartesian coordinates (x, y, and z) in cylindrical coordinates (r,, and z), we need to use some trigonometry. Here's how it works:
First, we need to find the distance from the origin to the point in question. This distance is given by the formula:
r = sqrt(x2 + y2)
where sqrt() means "square root" and 2 means "squared". So we take the square of the x-coordinate, add it to the square of the y-coordinate, and then take the square root of the result. This gives us the distance from the origin to the point in the x-y plane.
Next, we need to find the angle that the point makes with the positive x-axis. This angle is given by the formula:
= arctan(y/x)
where arctan() means "inverse tangent." This formula gives us the angle in radians (not degrees) between the positive x-axis and the line from the origin to the point. Note that we need to be careful about the signs of x and y when using this formula since arctan() can only give us angles between -pi/2 and pi/2 (i.e., the first and fourth quadrants).
Finally, we just need to use the z-coordinate of the point as the third coordinate in our cylindrical coordinates. So our final answer is: (r, θ, z) = (sqrt(x2 + y2), arctan(y/x), z)

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Therefore, the point (3,4,5) in Cartesian coordinates can be expressed in cylindrical coordinates as (5,0.93,5), where r = 5, θ ≈ 0.93 radians, and z = 5.

Sure, I can definitely help you with that! To express a point given in Cartesian coordinates (x,y,z) in cylindrical coordinates (r,θ,z), we use the following formulas:

r = √(x^2 + y^2)
θ = arctan(y/x)
z = z

So, if we have a point (x,y,z) in Cartesian coordinates, we can convert it to cylindrical coordinates using these formulas. For example, let's say we have the point (3,4,5) in Cartesian coordinates. To express this point in cylindrical coordinates, we first find r, θ, and z using the formulas above:

r = √(3^2 + 4^2) = √25 = 5
θ = arctan(4/3) ≈ 0.93 radians
z = 5


I hope this helps! Let me know if you have any further questions or if you need me to explain anything in more detail.

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Answer: 40.8

Step-by-step explanation: :)

Answer:

  236 minutes

Step-by-step explanation:

You want to know the time to fill a cylindrical pool with radius 5 feet and depth 4 feet if 1 cubic foot is 7.5 gallons and the fill rate is 10 gallons per minute.

The volume of the pool is ...

  V = πr²h

  V = π(5 ft)²(4 ft) = 100π ft³ ≈ 314.159 ft³

The time to fill the pool will be found by dividing the number of gallons by the fill rate in gallons per minute.

  t = V/rate

  t = (314.159 ft³)(7.5 gal/ft³)/(10 gal/min) ≈ 236 min

It will take about 236 minutes to fill the pool.

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Answer is B g(x)=-1/2x+1

A frustum is one of two pieces of a double cone divided at the vertex. A double cone is a three-dimensional shape that is created by connecting two cones with their vertices touching.

When the double cone is cut through the vertex, it creates two pieces known as frustums. A frustum has a circular base and a smaller circular top, which are parallel to each other. The height of the frustum is the distance between the two circular bases.

The volume of a frustum can be calculated using the formula V = (1/3)h(a^2 + ab + b^2), where h is the height, a is the radius of the larger base, and b is the radius of the smaller top. Frustums are commonly found in architecture and engineering, such as in the design of buildings and bridges.

A "napped cone" is one of two pieces of a double cone divided at the vertex. When a double cone is bisected through its vertex, it results in two identical, mirror-image napped cones. These geometric shapes have various applications in mathematics, engineering, and design due to their unique properties.

Napped cones share some characteristics with regular cones, such as having a circular base, but their pointed vertex is replaced by a flat plane where the double cone was divided. This creates a shape that is both symmetrical and easy to manipulate for various purposes.

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-$217,400 is the amount of money needed to cover the purchase of your new home by selling the old house at $389,000.

Cost of home = $264,000

Selling price = $389,000

Purchase price of new home = $428,000

Deposit percentage = 20%

The total amount received from selling the house is:

The amount received from the sale = selling price - purchase price

The amount received from sale = $389,000 - $264,000

Amount received from sale = $125,000

The amount spent on the new home is:

Amount spent on new home = purchase price - deposit

Amount spent on new home = $428,000 - 20% of $428,000

Amount spent on new home = $428,000 - $85,600

Amount spent on new home = $342,400

Finally, the leftover money is calculated as:

The amount left over = amount received from sale - the amount spent on a new home

The amount left over = $125,000 - $342,400

Amount left over = -$217,400

The negative amount indicates that you did not have enough money from the sale of your old home to cover the purchase of your new home.

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x = -4 and y = 5 is the solution to the given system of equations.

The given equations are:

y = -2x - 3

4y + x = 16

To solve this system of equations, we can use either the substitution method or the elimination method. Let's use the substitution method here:

Solve one equation for one variable in terms of the other variable. Let's solve the first equation for y:

y = -2x - 3

Substitute the expression for that variable from Step 1 into the other equation. Substitute y = -2x - 3 into the second equation:

4y + x = 16

4(-2x - 3) + x = 16

Simplify and solve for the remaining variable. Distribute the 4:

-8x - 12 + x = 16

-7x = 28

x = -4

Substitute the value found in Step 3 into one of the original equations and solve for the other variable. Let's use the first equation:

y = -2x - 3

y = -2(-4) - 3

y = 5

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Complete Question:

Solve the system of equations:

y = -2x - 3

4y + x = 16

Answer: 67,500

Step-by-step explanation:

75,000 divided by 10% = 7,500

75,000 - 7,500 = 67,500

Approximately 68% of callers are on hold between 2.6 and 3.4 minutes. To find the per cent of callers on hold between 2.9 and 4.4 minutes, we need to find the area under the normal distribution curve between these two values.

Using a standard normal distribution table or calculator, we can find the z-scores for 2.9 and 4.4, which are -0.63 and 1.5, respectively. Then, we can use the cumulative distribution function (CDF) to find the area under the curve between these z-scores. The result is approximately 65.6%. Therefore, we can conclude that about 65.6% of callers are on hold between 2.9 and 4.4 minutes.

To explain the calculation in more detail, we can use the formula for the standard normal distribution, which is:

z = (x - μ) / σ

where z is the z-score, x is the value we are interested in, μ is the mean, and σ is the standard deviation. Using the given values, we can find the z-scores for 2.9 and 4.4 as follows:

z1 = (2.9 - 3.4) / 0.8 = -0.63

z2 = (4.4 - 3.4) / 0.8 = 1.25

We need to use the CDF to find the area under the curve between these two z-scores. The CDF gives the probability that a random variable is less than or equal to a certain value. We can use a standard normal distribution table or calculator to find the CDF for each z-score.

The CDF for z1 is approximately 0.2643, and the CDF for z2 is approximately 0.8944. To find the area between these two values, we subtract the smaller CDF from the larger CDF:

0.8944 - 0.2643 = 0.6301

This means that about 63.01% of the area under the normal distribution curve is between z1 and z2. However, we are interested in the per cent of callers who are on hold between 2.9 and 4.4 minutes, not the per cent of the area under the curve. To convert this percentage to the per cent of callers, we can multiply by 100:

0.6301 * 100 = 63.01%

Therefore, approximately 65.6% of callers are on hold for between 2.9 and 4.4 minutes.

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The  quotient, expressed in rectangular form, is 1/2 - 1/2 - i(√(3)/2).

We can simplify this complex division by multiplying the numerator and denominator by the complex conjugate of the denominator.

The complex conjugate of 8(cos210° + isin210°) is 8(cos(-210°) + isin(-210°)), so we have:

2(cos150° + isin150°) ÷ 8(cos210° + isin210°)

= 2(cos150° + isin150°) x (8(cos(-210°) + isin(-210°))) / (8(cos210° + isin210°)) x (8(cos(-210°) + isin(-210°)))

= 28 x (cos150°cos(-210°) - sin150°sin(-210°) + i(cos150°sin(-210°) + sin150°cos(-210°))) / 88

= (1/4)(4cos(-60°) + 4isin(-60°))

= (1/4)(4cos60° - 4isin60°)

= cos60° - isin60°

= 1/2 - i(√(3)/2)

Therefore, the quotient, expressed in rectangular form, is 1/2 - 1/2 - i(√(3)/2).

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Answer:

A ≈ 25.6°, B ≈ 52.3°, C ≈ 68.8° or A

Step-by-step explanation:

To solve the triangle ABC, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of the angles opposite those sides. The law states that:

c^2 = a^2 + b^2 - 2ab cos(C)

where c is the length of the side opposite angle C, a is the length of the side opposite angle A, and b is the length of the side opposite angle B.

Using the given values of a, b, and c, we can substitute into the formula and solve for cos(C):

41^2 = 19^2 + 45^2 - 2(19)(45) cos(C)

1681 = 361 + 2025 - 1710 cos(C)

cos(C) = (361 + 2025 - 1681) / (21945)

cos(C) = 0.37103

Now we can use the inverse cosine function to find the measure of angle C:

C = cos^-1(0.37103)

C ≈ 68.8°

Next, we can use the Law of Sines to find the measures of angles A and B:

sin(A)/a = sin(C)/c

sin(A)/19 = sin(68.8°)/41

sin(A) ≈ 0.4250

A ≈ 25.6°

Similarly, we can find the measure of angle B:

sin(B)/b = sin(C)/c

sin(B)/45 = sin(68.8°)/41

sin(B) ≈ 0.7873

B ≈ 52.3°

Therefore, the solution for the triangle ABC is:

A ≈ 25.6°, B ≈ 52.3°, C ≈ 68.8° or A

The equation of the circle with center (-5, 2) and radius 7 is ( x + 5 )² + ( y - 2 )² = 49.

The standard form equation of a circle with center (h, k) and radius r is:

( x - h )² + ( y - k )² = r²

Given that the center of the circle is (-5, 2) and the radius is 7.

Hence, we can substitute these values into the formula to get the equation of the circle:

Plug in h = -5, k = 2 and r = 7

( x - h )² + ( y - k )² = r²

(x - (-5) )² + ( y - 2 )² = 7²

Simplifying and expanding the equation, we get:

( x + 5 )² + ( y - 2 )² = 49

Therefore, the equation of the circle is ( x + 5 )² + ( y - 2 )² = 49.

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The area of the triangle is 4.5 square unit.

We have, y= 4x/ (1 + x³)

Now, differentiating the above equation wrt to x we get

y' = 4(1 + x³)- 4x . 3x² / (1+ x³)²

y'= -8x³ + 4/ (1+x³)²

When x = 1 then y' = -4/4 = -1

so, y -2 = -1 (x-1)

y= -x+ 3

Here the x intercept is (3, 0) and y intercept is (0, 3).

so, Area of Triangle is

= 1/2 x 3 x 3

= 9/2

= 4.5 square unit

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the probability of obtaining a sample mean within 500 of the population mean is approximately 0.6827.

To solve this problem, we need to use the central limit theorem which states that the distribution of the sample means will be approximately normal with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.

Given that the population mean is 51800 and the population standard deviation is 4000, we can calculate the standard error of the mean as follows:

Standard error of the mean = 4000 / sqrt(64) = 500

We want to find the probability of obtaining a sample mean within 500 of the population mean. This can be written as:

P(51800 - 500 < X < 51800 + 500)

where X is the sample mean.

We can standardize this interval using the standard error of the mean:

P(-1 < Z < 1)

where Z is a standard normal variable.

Using a standard normal table, we find that the probability of Z being between -1 and 1 is approximately 0.6827.

Therefore, the probability of obtaining a sample mean within 500 of the population mean is approximately 0.6827.

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The probability that the cook adds the right ingredients and cooks the noodles well is 3/4 or 75%.

I understand that you need help calculating the probability of a cook adding the right ingredients while preparing noodles.

To determine the probability, we need to consider the number of successful attempts and the total number of attempts. In this scenario, the cook adds the right ingredients nine times and makes an error three times.

Therefore, there have been 12 attempts in total (9 successful attempts + 3 erroneous attempts).

The probability of adding the right ingredients is calculated by dividing the number of successful attempts (9) by the total number of attempts (12).

So, the probability is:

P(success) = 9 successful attempts / 12 total attempts

By simplifying this fraction, we get:

P(success) = 3/4

Therefore, the probability that the cook adds the right ingredients and cooks the noodles well is 3/4 or 75%. This means that out of every 12 attempts, the cook is likely to add the right ingredients and cook the noodles well nine times.

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The equation that shows the number of signatures that can be expected after w weeks is N = 2000 + 500w, where N is the number of signatures and w is the number of weeks.

The initial number of signatures is 2,000 and the petition gains 500 signatures each week. Therefore, the equation can be written in slope-intercept form as y = mx + b, where m is the slope (500) and b is the y-intercept (2,000). So, the equation becomes N = 500w + 2000. This means that for each additional week, Tisha can expect to gain 500 more signatures on the petition.

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The Angle of Attack is the term used to describe the angle between an airfoil's chord line and the relative wind.

The angle between the chord line of an airfoil and the relative wind is known as the angle of attack. This angle is a crucial factor in determining the lift and drag of the airfoil, and is affected by factors such as the speed of the airfoil and the shape of its surface.

                                 In aviation, maintaining the proper angle of attack is essential for achieving optimal performance and safety during flight.

The angle between the chord line of an airfoil and the relative wind is known as the Angle of Attack (AOA).

Chord Line: This is the imaginary straight line connecting the leading edge to the trailing edge of an airfoil.
Relative Wind: This is the flow of air as it interacts with the airfoil. It's the direction of airflow relative to the airfoil's motion.
Angle of Attack (AOA): This is the angle formed between the chord line of an airfoil and the direction of the relative wind.

In summary, the Angle of Attack is the term used to describe the angle between an airfoil's chord line and the relative wind.

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The total amount paid by Maddy is $14.65.

It is given in the question that Maddy paid $2.15 for each pair of socks. She also had a coupon for $1.75 off the total purchase amount.

So, the total amount paid by Maddy will be the sum of the amount paid for 6 pairs of socks and the coupon amount i.e.

Total amount = $2.15*6 + $1.75

Total amount = $14.65

Hence, the total amount Maddy paid for the socks is $14.65.

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The equation that represents circle N include the following: C. (x + 7)² + (y - 6)² = 50.

In Geometry, the standard or general form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Radius, r = √[(x₂ - x₁)² + (y₂ - y₁)²]

Radius, r = √[(-2 + 7)² + (11 - 6)²]

Radius, r = √[(5)² + (5)²]

Radius, r = √50 units.

By substituting the given radius and center into the equation of a circle, we have;

(x - h)² + (y - k)² = r²

(x - (-7))² + (y - 6)² = (√50)²

(x + 7)² + (y - 6)² = 50.

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From the chi-square test, the p-value is greater than significance level so, we can't reject the null hypothesis. The distribution of patients in this data set of wards in community hospital has not changed.

We have a community hospital is studying its distribution of patients. Random sample with

number of patients = 317

There is a table present in above figure contains the type of patients, old rate and present rate of occurrence of type of patients.

Level of significance = 0.05

We have to test the claim that the distribution of patients in these ward is same or not.

Now, For testing the claim we will use the chi-square test, null and alternative hypothesis are defined as [tex]H_0[/tex]: the distribution of patients has not Changed

[tex]H_a[/tex]: the distribution of patients has Changed

Patients observed Expected

Maternity ward 65 20% of 317 = 63.4

Cardiac ward 100 32% of 317 = 101.44

burn ward 29 10% of 317 = 31.7

children ward 48 15% of 317 = 47.55

All wards 75 23% of 317 = 72.91

Now, calculate the χ² statistic : [tex]χ² = \frac{ \sum( O_i - E_i)²} {E_i}[/tex]

where, Oᵢ --> observed value for iᵗʰ

Eᵢ --> excepted value for iᵗʰ

[tex]χ² = \frac{ \sum( 65 - 63.4)²} {63.4} + \frac{ \sum( 100 - 101.44)²} {101.4} + \frac{ \sum( 29 - 31.7)²} {31.7} + \frac{ \sum( 48 - 47.55)²} {47.55} + \frac{ \sum( 75 - 72.91)²} {72.91} \\ [/tex]

= 0.355

Now, we calculate p-value for χ² > 0.355, from the calculater the critical value for

[tex]χ² = 0.355[/tex] and degree of freedom = n - 1 = 5 - 1 = 4 , where 5 is number of categorical variables. So, [tex] P( χ² > 0.355)[/tex] = 0.99

Since, the p-value = 0.99 > 0.05, so we fail to reject the null hypothesis. Hence, from the above test we can accept the claim that the distribution of patients has not changed.

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Complete question:

the community hospital is studying its distribution of patients. a random sample of 317 patients presently in the hospital gave the following information: type of patient, old rate of occurrences of these types of patients and present number of occurrence of type of patients. Using a 5% level of significance, test the claim that the distribution of patients in these wards has not changed.

Answer:

9,100

Step-by-step explanation:

We have a rectangle with a length of 130 and a width of 70.

We are asked to find how much turf will cover the entire field.

We can multiply:

130·70

=9100

This means that 9,100 yds² is needed.

Hope this helps! :)

The profit P(x) = -0.5x² + 23x - 13.

We have,

Q(x) = 45x - 0.5x² and L(x) = 12x + 13

To calculate the profit the formula used

P(x) = Q(x) - L(x)

P(x) = 45x - 0.5x² - (12x+ 13)

P(x) = 45x - 0.5x² -12x - 13

P(x) = -0.5x² + 23x - 13

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