Determine how many liters a right circular cylindrical tank holds if it is 6 m long and 13 m in diameter.​

The percent of data within the following interval from 28 to 82 is 99.73%

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

Mean = 55

Standard deviation = 9

Scores = from 28 to 82

So, we have

z = (28 - 55)/9 = -3

z = (82 - 55)/9 = 4

This means that it is between a z-score of -3 and a z-score of 3

This is represented as

Probability = (-3 < z < 3)

Using a graphing calculator, we have

Probability =  0.9973

Express as percentage

Probability =  99.73%

Hence, the probability is 99.73%

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The solution of the equation 1/(x-3) + 1/(x+5) = 1/3 is x=-3, x=7, option D is correct

The given equation is 1/(x-3) + 1/(x+5) = 1/3

Take LCM on left hand side

(x+5)+(x-3)/(x-3)(x+5)= 1/3

2x+2/(x-3)(x+5) = 1/3

2(x+1)/(x-3)(x+5) = 1/3

6(x+1)=(x-3)(x+5)

6x+6 = x²+5x-3x-15

6x+6 = x²+2x-15

x²+2x-6x-15-6=0

x²-4x-21=0

x² -7x+3x-21=0

x(x-7)+3(x-7)

(x+3)(x-7)

The solutions are x=-3, x=7

Hence, the solution of the equation 1/(x-3) + 1/(x+5) = 1/3 is x=-3, x=7, option D is correct

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Answer: 9.66666667

Step-by-step explanation:

To find the number of days it would take to build a similar house, we would need to create a proportion.

Workers: 27:9

Days: 29:?

Let's simplify.

Workers: 3:1

Days: 29:?

Now, we divide 29 by 3 to see how many days it would take to build a similar house.

29/3=9.666666667 (9.6 repeating)

So, your answer would be 9.6

Hope this helps!

The requried amount of fencing needed t cover the pond in this backyard is 319.36 meters.

A figure of Robert's backyard has been shown, we have to determine the perimeter of his backyard,

The perimeter of backyard = 2L + 2[πw/2]
The perimeter of backyard = 2*78 + 2[π*52/2]
The perimeter of the backyard = 319.36 meters

Thus, the requried amount of fencing needed t cover the pond in this backyard is 319.36 meters.

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-1 is the value of the slope.

To find the slope of a line that is perpendicular to the line x - y = 0, we need to find the slope of the given line first.

To do this, we can rearrange the equation x - y = 0 to solve for y:

x - y = 0

y = x

So the given line has a slope of 1 since the coefficient of x is 1.

Since a line perpendicular to this line will have a slope that is the negative reciprocal of the slope of the given line, we can find the slope of the perpendicular line by taking the negative reciprocal of 1:

the slope of the perpendicular line = -1/1

the slope of the perpendicular line = -1

Therefore, the slope of a line that is perpendicular to the line x - y = 0 is -1.

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The mean number of ice chests in a section is 46.75.

The mean is the average or the most common value in a collection of numbers. In statistics, it is a measure of central tendency along median and mode..

To find the mean number of ice chests in a section, we need to calculate the sum of the ice chests and then divide total number of sections sampled.

Sum of ice chests = 48 + 51 + 26 + 73 + 51 + 48 + 26 + 51

Sum of ice chests = 374

Mean number of ice chests will be:

= (Sum of ice chests) / (Total number of sections sampled)

= 374 / 8

= 46.75

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The number name of 97600305 in international system of numeration Ninety-Seven Million, Six Hundred Thousand, Three Hundred and Five.

The number 97600305 can be written with commas as,

Place the commas after hundred.

That is after 305.

Read as three hundred five.

then place the commas after thousands.

Place the comma after 600.

Read as six hundred thousands.

and place the comma after million.

that is after 97.

Read as Ninety-Seven Million.

Combine all and write in the international system of numeration,

The number 97600305 is read as,

Ninety-Seven Million, Six Hundred Thousand, Three Hundred and Five.

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The given question is incomplete, I answer the question in general according to my knowledge:

Write the number name for the numeral 97600305 by inserting commas and write the number name in international system of numeration.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-8})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{- \cfrac{5}{4}}(x-\stackrel{x_1}{(-4)}) \implies y +8 = - \cfrac{5}{4} ( x +4)[/tex]

The range is greater for the girls and the mean is greater for the girls. So, correct option is B.

A) The statement "The range is greater for the girls" is true. The range is the difference between the highest and the lowest values in a data set.

Looking at the line plots, the highest value for the boys is 10, and the lowest is 3, giving a range of 7 hours. The highest value for the girls is 9, and the lowest is 5, giving a range of 4 hours. Therefore, the range is greater for the boys.

B) The mean is the sum of all values divided by the total number of values. To calculate the mean for the boys, we add up all the hours and divide by 10, which gives us:

(3 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 10) / 10 = 7.4 hours

To calculate the mean for the girls, we add up all the hours and divide by 10, which gives us:

(5 + 6 + 6 + 6 + 7 + 7 + 7 + 8 + 8 + 9) / 10 = 7.1 hours

Therefore, the mean for the boys is 7.4 hours and the mean for the girls is 7.1 hours, so the statement "The mean is greater for the girls".

So, correct option is B.

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The total number of subsets is 128 and the total number of proper subsets is 127 and this can be determined by using the given data.

Given :

The set of days of the week.

The following steps can be used in order to determine the number of subsets and the number of proper subsets:

Step 1 - According to the given data, the set is given below:

S = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}

Step 2 - Now, the total number of subsets is given by the formula  where 'n' is the number of elements of the set.

The total number of subsets is 128.

Step 3 - Now, the total number of proper subsets is given by the formula  where 'n' is the number of elements of the set.

The total number of proper subsets is 127.

a) The total number of subsets is 128.

b) The total number of proper subsets is 127.

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complete question:

Find (a) the number of subsets and (b) the number of proper subsets of the set.

The set of days of the week.

(a) The number of subsets is

(b) The number of proper subsets is

The collection of rivers of Nepal is a well defined value.

Nepal boasts a finite number of well-defined rivers, each identified and named for easy reference. Given the geographically diverse landscape of Nepal with intricate topography, the task of accurately delineating the sources and tributaries of its waterways is challenging.

Further compounding such complexity are seasonal variations that cause some rivers to dry up at specific times—rendering the precise marking of their borders an especially arduous undertaking.

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The acceleration of the car at that time was 3 m/s².

We have,

From the kinematic equation to find the acceleration:

v = u + at

where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

Initial velocity u = 15 m/s

Final velocity v = 45 m/s,

Time t = 10 s

We can rearrange the equation to solve for acceleration:

a = (v - u) / t

Substituting the values, we get:

a = (45 m/s - 15 m/s) / 10 s

a = 3 m/s^2

Therefore,

The acceleration of the car at that time was 3 m/s².

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The complete question in english.

A car moving on a straight track increases its speed from 15 m/s to 45 m/s using a

po of 10 seconds. Assuming that the acceleration was uniform, calculate:

acceleration at that time.

The value of coordinates of fourth vertex of rectangle is, (0, 3)

We have to given that;

A rectangle is made up from points (-2,-1), (4,-1), (4,3),

Since, Midpoints of the points are same both diagonal.

Hence, Let the fourth vertex = \(x, y)

Midpoint of point (- 2, - 1) and (4, 3) is,

(- 2 + 4) / 2,. (- 1 + 3) / 2

(2, 1)

Midpoint of (x, y) and (4, - 1) is,

(x + 4)/2, (y - 1)/2

Which is same as (2, 1).

Hence, We can compare as;

(x + 4) / 2 = 2

x + 4 = 4

x = 0

y - 1 / 2 = 1

y - 1 = 2

y = 3

Thus, The value of coordinates of fourth vertex of rectangle is, (0, 3)

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Complete question is,

If a rectangle is made up from points (-2,-1), (4,-1), (4,3),

Then, The value of fourth coordinate is?

The second data set best shows asymmetric distribution.

To identify the weekend whose data best shows asymmetric distribution, we need to look for the data set that is skewed, or "lopsided", meaning it has a longer tail on one side than on the other.

We can begin by creating a histogram for each of the data sets to visualize their distributions

The second data set, however, shows a clear skew to the left, with a longer tail of observations on the left side of the center than on the right side.

This makes the second data set the one that best shows asymmetric distribution.

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Answer:

0125

Step-by-step explanation:

The answer is equal to 0125

If total sales including tax are $2739.45 , the portion that is the tax amount is $155.06. So, correct option is C.

To find the portion that is the tax amount, we need to first determine the portion of the total sales that is the cost of the item before taxes. To do this, we can use the fact that the sales tax is 6%, which means that the total sales including tax is 106% of the cost before taxes.

Thus, we can set up the equation:

total sales including tax = cost before taxes + tax amount

Or, in terms of percentages:

106% cost before taxes = cost before taxes + tax amount

Simplifying this equation, we get:

0.06 cost before taxes = tax amount

Now we can substitute the given information into this equation. If total sales including tax are $2739.45, then the cost before taxes is:

cost before taxes = total sales including tax / 1.06

cost before taxes = $2584.39

Finally, we can calculate the tax amount:

tax amount = 0.06 * $2584.39

tax amount = $155.06

Therefore, the answer is option C, $155.06.

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The statement "the product of two negative rational numbers is greater than either factor" is never true.

The statement "the product of two positive rational numbers is greater than either factor" is only sometimes true.

We have,

Part A:

The statement "the product of two negative rational numbers is greater than either factor" is never true.

This can be proved by considering a negative rational number, say -1/2, and multiplying it by a negative rational number that is greater in magnitude, say -2/3.

The product of these two negative rational numbers is 1/3, which is less than either factor.

Another example is -3/4 multiplied by -1/2 which results in 3/8, again less than either factor.

Part B:

The statement "the product of two positive rational numbers is greater than either factor" is only sometimes true.

For example, if we take 1/2 and 2/3, the product is 1/3 which is less than either factor.

Similarly, if we take 3/4 and 4/5, the product is 3/5 which is less than either factor.

Therefore, the statement is only sometimes true and not always true.

Thus,

The statement "the product of two negative rational numbers is greater than either factor" is never true.

The statement "the product of two positive rational numbers is greater than either factor" is only sometimes true.

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The scale factor of the given drawing is expressed as: 1:5

We are given the dimensions of the scale drawing of the blanket as:

Length = 10 inches

Width = 6 inches

We are given that the actual dimensions of the baby blanket are:

Length = 50 inches

Width = 30 inches

The size by which a shape is enlarged or reduced is called as its scale factor. It is used when we need to increase the size of a 2D shape, such as circle, triangle, square, rectangle, etc. If y = Kx is an equation, then K is the scale factor for x.

The scale factor is:

50/10 = 30/6 = 5

Thus, we have 1:5

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The probability of drawing two green marbles in a row is 4/9.

Given that, a box has 1 red marble, 1 blue marble, and 4 green marbles.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Number of favorable outcomes = 4

Total number of outcomes = 6

Probability of drawing 1st green marble = 4/6

= 2/3

Probability of drawing 2nd green marble = 4/6

= 2/3

Probability of drawing two marbles = 2/3 × 2/3

= 4/9

Therefore, the probability of drawing two green marbles in a row is 4/9.

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The percentage of the can that is not occupied by tennis balls is approximately 80.14%.

We have,

The volume of the can = The volume of the cylinder - The volume of the three tennis balls.

The volume of the cylinder.

V(cylinder) = πr²h

where r is the radius and h is the height of the cylinder.

Since the can holds three tennis balls snugly, the height of the cylinder is equal to three times the diameter of a tennis ball.

= 3 × 2(3.5 cm)

= 21 cm.

V(cylinder)

= π (3.5 cm)² (21 cm)

= 2709.38 cm³

The volume of one tennis ball.

V (ball) = (4/3)πr³

where r is the radius of the tennis ball. Thus,

V(ball) = (4/3)π(3.5 cm)³ = 179.594 cm³

The total volume of the three tennis balls is:

V(3balls) = 3 V(ball)

= 3(4/3) π (3.5 cm)³

= 538.782 cm³

The volume of the can not be occupied by tennis balls.

V(not occupied) = V(cylinder) - V(3 balls)

= 2709.38 - 538.782

= 2170.598 cm³

The percentage of the can that is not occupied by tennis balls.

percentage = (V(not occupied / V(cylinder)) × 100%

= (2170.598 cm^3/2709.38 cm^3) × 100%

= 80.14%

Therefore,

The percentage of the can that is not occupied by tennis balls is approximately 80.14%.

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The volume of the hemisphere as given in the task content to the nearest tenth is; 718.4 mm³.

It follows from the task content that the volume of the hemisphere as represented in the attached image is to be determined.

Since the volume of the hemisphere is given by;

V = 2/3πr³

where radius = diameter/2 = 14/2 = 7.

Consequently, the volume, V is;

V = 2/3 × π × 7³

V = 718.4 mm³.

Ultimately, the volume is; 718.4 mm³.

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The length x in the similar triangle is 7.06 units.

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.

Therefore, let's use the similarity of the triangle to find the value of x in the triangle.

Hence, using the proportion,

y / 8 = 8 / 17

cross multiply

17y = 64

y = 64 / 17

y = 3.76470588235

y = 3.76

Therefore,

17 - 3.76 = 13.24

Hence,

13.24 / x = x / 3.76

cross multiply

x² = 49.7824

x = √49.7824

x = 7.05566439111

Hence,

x = 7.06 units

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The solution of the inequality is y > 32.

We have the inequality,

1/4 y > 8

Now, solving the inequality for y

Multiply both side by 4 we get

1/4 y(4) > 8 (4)

y > 32

Thus, the solution of the inequality is y > 32.

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The Average Order's Gross Profit for the clothing eCommerce company in this scenario is USD 15.

For the Average Order's Gross Profit for the clothing eCommerce company in this scenario, we need to subtract the cost of production and shipping from the Average Order Value as;

⇒ Gross Profit = Average Order Value - Cost of production - Cost of shipping Gross Profit

⇒ Gross Profit = USD 65 - USD 35 - USD 15

⇒ Gross Profit = USD 15

Therefore, the Average Order's Gross Profit for the clothing eCommerce company in this scenario is USD 15.

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On Solving the equations "6x + 3y = 45"  and "2x - 2y = 6", we get that the solution is x = 6 and y = 3.

An "Equation" is defined as a mathematical statement which shows the equality of "two-expressions", which are separated by equal sign.

To solve the simultaneous equations:

6x + 3y = 45      ...equation(1)

2x - 2y = 6         ...equation(2)

We Multiplying the equation(2) by 3, we get:

⇒ 6x - 6y = 18,

Subtracting this equation to the first equation, we get:

⇒ 6x + 3y - 6x + 6y = 45 - 18,

⇒ 9y = 27,

⇒ y = 3,

Now, we can substitute this value of "y" into any of the original equations to find "y". Let's use the first equation:

⇒ 6x + 3y = 45,

Substituting y = 3, we get:

⇒ 6x + 3(3) = 45,

⇒ 6x + 9 = 45,

⇒ 6x = 45 - 9,

⇒ x = 6,

Therefore, the solution to the simultaneous equations is x = 6 and y = 3.

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The given question is incomplete, the complete question is

Solve the following simultaneous equation

6x + 3y = 45  and 2x - 2y = 6.

Tom's ploy to get other boys to do his work:  through Tom's use of persuasion and trickery to get the work done. Option B

The reader is left wondering if Tom will be caught and punished for his conduct because he uses persuasion and deceit to persuade other lads to perform his work for him.

The reader is also left wondering whether the other lads will finally grasp what Tom is up to and cease assisting him, or whether they will continue to be duped by him. The use of persuasion and cunning adds a sense of danger and risk-taking to the situation, heightening the story's tension.

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The total interest that the credit card holder paid at 11.99% APR for $6,299.59 is D. $559.56.

The total interest is a function of the APR, the principal, and the period involved.

The total interest can be determined using an online finance calculator with some adjustments.

N (# of periods) = 11 months

I/Y (Interest per year) = 11.99%

PV (Present Value) = $6,299.59

PMT (Periodic Payment) = $-350

Results:

FV = $-2,979.39

Sum of all periodic payments = $-3,850.00

Total Interest = $529.80

12th Month Interest = $29.76 ($2,979.39 x 11.99% x 1/12)

Total interest up to the 12th month = $559.56 ($529.80 + $29.76)

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Hello! Here are the recursive definitions of the given sequence:

A) The sequence is increasing by 7 for each term, so the recursive definition can be written as:

a1 = 3

an = an-1 + 7

So, the recursive definition of the sequence is: 3, 3+7=10, 10+7=17, 17+7=24, ...

B) The second option given, "anan-1 + 10 a1 = 3" is not a recursive definition of the sequence.

C) The third option given, "San = 10an-1" is also not a recursive definition of the sequence because it uses a different variable 'S' instead of 'a'.

The simplified expression is determined as 2x³ - 6x +  4x⁻².

The expression is simplified by applying the principle of exponent rules of division as shown below;

The given function = 2x⁵ - 6x³ + 4 / x²

So we will divide each of the numerator with the denominator as shown below;

2x⁵/x² = 2x⁵⁻² = 2x³

6x³/x² = 6x³⁻² = 6x

4/x² = 4x⁻²

The simplified expression = 2x³ - 6x +  4x⁻²

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