A cylindrical tank is one-fifth full of oil. The cylinder has a base radius of 80 cm. The height of the cylinder is 200 cm. 1 litre 1000 cm3 How many litres of oil are in the tank? Round your answer to the nearest litre

Answer:

0.005

Step-by-step explanation:

Answer:

Step-by-step explanation:

You can’t solve this equation as none of the numbers have the same coefficient to solve. If you wanted to solve for x and y, you will need two equations as there are two unknown variables in the equation and the only way to solve for x and y is to use simultaneous method which includes two equations.

Answer:

Step-by-step explanation:

348.55

The scale factor of the following pair of similar polygons after the dilation is 0.7

Given

The pair of similar polygons

From the pair of similar polygons, we have the following corresponding side lengths

Pre-image of the polygon = 30

Image of the polygon = 21

The scale factor of the similar polygons is then calculated as

Scale factor = 21/30

Evaluate the quotient

Scale factor = 0.7

Hence, the scale factor is 0.7

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The number we are looking for is N = 2 × 2^3 × 3^2 = 72.

Let's first recall some properties of the number of divisors of an integer. If we factorize an integer n as a product of prime powers, say

n = p_1^a_1 × p_2^a_2 × ... × p_k^a_k

then the number of divisors of n is given by

d(n) = (a_1 + 1) × (a_2 + 1) × ... × (a_k + 1).

Using this fact, we can deduce some information about the number we are looking for. Let's call it N. We know that N has 8 divisors, so it must be of the form

N = p_1^2 × p_2^2, or N = p_1^7,

where p_1 and p_2 are distinct prime numbers.

Now, we are told that each of N/2 and N/3 has four divisors. We can use the same fact about the number of divisors to conclude that

N/2 = q_1^3 × q_2, or N/2 = q_1^1 × q_2^3,

and

N/3 = r_1^3 × r_2, or N/3 = r_1^1 × r_2^3,

where q_1, q_2, r_1, and r_2 are distinct prime numbers.

To simplify the notation, let's introduce the variables a, b, c, d, e, and f, defined by

p_1 = q_1^a × q_2^b,

p_2 = r_1^c × r_2^d,

N/2 = q_1^e × q_2^f,

N/3 = r_1^g × r_2^h.

Using the information we have so far, we can write down equations for a, b, c, d, e, f, g, and h in terms of unknown exponents:

a + 1 × (b + 1) = e + 1 × (f + 1) = 4,

c + 1 × (d + 1) = g + 1 × (h + 1) = 4,

2a × 2b = ef,

2c × 2d = gh.

We can solve this system of equations by trial and error. For example, we can start by trying all possible values of a and b such that 2a × 2b = 4. This gives us two possibilities: a = 0, b = 2, or a = 1, b = 1. Using the first possibility, we get e = 3, f = 1, which leads to N/2 = q_1^3 × q_2, and hence N = 2 × q_1^3 × q_2^2. Substituting this into the equation for the sum of divisors, we get

(1 + q_1 + q_1^2 + q_1^3) × (1 + q_2 + q_2^2) = 216.

We can solve this equation by trial and error as well, or by observing that 216 = 2^3 × 3^3, and hence the two factors on the left-hand side must be equal to 2^3 and 3^3, respectively. This gives us the unique solution q_1 = 2 and q_2 = 3, and hence N = 2 × 2^3 × 3^2 = 72.

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Answer:

24 cm (to nearest cm)

Step-by-step explanation:

XLV = extra large tin volume (cm³)

LV = large tin volume (cm³)

XLR = extre large tin radius (cm)

LR = large tin radius (cm) = 20

XLV = 1.75 × LV

Since the tins are geometrically similar cylinders, we can infer that the volumes and radii of the 2 tins are related;

We know the relationship between the volume of the two tins, i.e. the XL tin is 75% greater in volume than the L tin;

This means the volumetric scale factor or multiplier is ×1.75;

Subsequently, we know:

XLV = 1.75 × LV

Similarly, there is a relationship between the radii of the tins;

The relationship is, however, slightly different;

[tex]XLR = (\sqrt[3]{1.75}) \times LR[/tex]

We need to take the cube root of the volumetric scale factor, reason being, the radius is a linear dimension unlike volume;

Easy way to figure this is radius is in cm, volume is in cm³;

So:

XLR = 1.205... × LR

XLR = 1.205... × 20

XLR = 24.101... --> 24 cm (to nearest cm)

The given lengths of 3 feet, 3 feet, and 7 feet cannot form a triangle because they do not satisfy the Triangle Inequality Theorem, which is the sum of the lengths of any two sides is greater than the length of the third side.

To form a triangle, the sum of the lengths of any two sides of the triangle must be greater than the length of the third side. This is known as the Triangle Inequality Theorem.

Let's apply this theorem to the given lengths of 3 feet, 3 feet, and 7 feet:

The sum of the first two sides is 3 + 3 = 6 feet, which is less than the length of the third side of 7 feet. So, the first two sides cannot form a triangle.

The sum of the first and third sides is 3 + 7 = 10 feet, which is greater than the length of the second side of 3 feet. However, the sum of the second and third sides is 3 + 7 = 10 feet, which is also greater than the length of the first side of 3 feet.

Therefore, neither of the two combinations of sides satisfy the Triangle Inequality Theorem, and so it is impossible to form a triangle with sides of 3 feet, 3 feet, and 7 feet.

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We can graph this solution on the number line by placing a point at 7.6.

Graphs are visual representations of data or information. They are used to show relationships between different pieces of data and display numerical data in a more meaningful way. Graphs are made up of individual elements called nodes which are connected by edges. Nodes represent individual data points or pieces of information. Edges represent the relationship between two nodes and can represent either a physical or a logical link. Graphs can be used to represent many different types of data or information, such as social networks, transportation networks, and even biological relationships. Graphs are a powerful tool for understanding complex data sets, making them an essential tool for data analysis.

80∠ 10x + 4 = 20

80 10x + 4 = 20

80 - 4 = 10x

76 = 10x

7.6 = x

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We can graph this solution on the number line by placing a point at 7.6.

Graphs are visual representations of data or information. They are used to show relationships between different pieces of data and display numerical data in a more meaningful way. Graphs are made up of individual elements called nodes which are connected by edges. Nodes represent individual data points or pieces of information. Edges represent the relationship between two nodes and can represent either a physical or a logical link. Graphs can be used to represent many different types of data or information, such as social networks, transportation networks, and even biological relationships. Graphs are a powerful tool for understanding complex data sets, making them an essential tool for data analysis.

80∠ 10x + 4 = 20
80 10x + 4 = 20
80 - 4 = 10x
76 = 10x
7.6 = x

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There will be a total of 28 handshakes when the 3 late members arrive.

The first n-1 positive integers are added together using the formula n(n-1)/2, where n is the total number of terms being added together.

The number of combinations or arrangements of a given collection of items may be determined using this formula, which can be obtained using the process of mathematical induction. It is often used in combinatorics and discrete mathematics. For instance, the formula was used to determine how many times a group of individuals shook hands in the scenario above. It might also be used to determine the number of pathways in a network of nodes or vertices or the number of ways to choose a portion of an object set from a bigger set in other settings.

Given that, 3 members arrive late, and 5 members are already present.

The total members are 5 + 3 = 8.

Now, using the sum of positive integer formula:

n(n-1)/2

We can determine the number of handshakes.

8(8-1)/2 = 28

Hence, there will be a total of 28 handshakes when the 3 late members arrive.

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In Rosettenville, a suburb of Johannesburg, South Africa, Robert Brozin and Fernando Duarte acquired the Chicken Land restaurant in 1987, launching Nando's.

The eatery was renamed Nando's in honor of Fernando. The restaurant incorporated influences from former Mozambican Portuguese colonists, many of whom had relocated to Johannesburg's southeast after their country gained independence in 1975. Expansion was an essential component of their vision from the beginning. Nando's had already grown from one restaurant in 1987 to four by 1990. It became increasingly difficult to implement a common strategy and decision-making became inefficient as new outlets were maintained as separate businesses.

In 1995, Nando's International Holdings (NIH) was established as a new international holding because managing this growingly complex global structure had become extremely challenging. The South African branch of Nando's Group Holdings (NGH) was successfully listed on the Johannesburg Stock Exchange on April 27, 1997. NGH was 54% owned by NIH, with the remaining 26% available to the general public and former joint venture partners. The main goals of the share offer and listing were to broaden the group's capital base and enable group restructuring.

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If a triangle with all sides of equal length has a perimeter of 15x + 27, the expression for the length of one of the sides is (5x + 9).

The perimeter of a triangle is the sum of the lengths of all three sides. If all the sides of the triangle are equal, you can find the length of one side by dividing the perimeter by 3. Here, the perimeter is given as 15x + 27. Therefore, the length of one side will be (15x + 27) / 3 = 5x + 9. Hence, an expression for the length of one of the sides is (5x + 9).

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The given probability distribution "a teacher monitored the number of people texting during class each day and calculated the corresponding probability distribution." is a type of discrete probability distribution.

The probability distribution is used to describe the probability of each outcome in a series of possible outcomes. It is a mathematical representation of the outcomes of an experiment.

The teacher likely used a discrete probability distribution to calculate the probability of a certain number of people texting during class each day.

A discrete probability distribution is used to analyze data where the outcome is counted in whole numbers, such as the number of people texting in a given class period.

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Answer:

5/37

Step-by-step explanation:

There are 37 possible outcomes when rolling a 37-sided die, so the probability of rolling any one specific number is 1/37.

To find the probability of rolling any of the given numbers (35, 25, 33, 9, or 19), we need to add the probabilities of rolling each individual number.

Probability of rolling 35: 1/37

Probability of rolling 25: 1/37

Probability of rolling 33: 1/37

Probability of rolling 9: 1/37

Probability of rolling 19: 1/37

The probability of rolling any one of these numbers is the sum of these probabilities:

1/37 + 1/37 + 1/37 + 1/37 + 1/37 = 5/37

So the probability of rolling any of the given numbers is 5/37, which is approximately 0.1351 when rounded to four decimal places.

The value of the unknown lengths in these similar triangles is FH is 6.67 units and EG is 27 units.

A triangle is a polygon with three sides and three angles. It is a two-dimensional shape that is commonly studied in mathematics, geometry, and other fields. The sum of the angles in a triangle is always 180 degrees, and the lengths of the sides can vary. Triangles can be classified based on the lengths of their sides and the measures of their angles. Common types of triangles include equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles have many important properties and are used in various applications, including construction, engineering, and physics.

Here,

1. Let x be the length of FH. We have:

AB/EF = BD/FH

12/8 = 10/x

Cross-multiplying, we get:

12x = 80

x = 80/12

x ≈ 6.67

Therefore, FH ≈ 6.67.

2. Let y be the length of EG. We have:

AC/BD = FH/EG

15/9 = 5/y

Cross-multiplying, we get:

5y = 135

y = 135/5

y ≈ 27

Therefore, EG ≈ 27.

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The types of inferences that will be made about population parameters are causation, estimation, and regression on the basis of relationship.

Causation is the process of showing the cause-and-effect relationship between two variables. In this case, one variable influences the other variable. This type of inference is significant when making decisions because it helps us understand how a change in one variable leads to a change in another variable.

Estimation: In statistical analysis, estimation refers to determining the possible value of an unknown population parameter. It is impossible to calculate the population parameters directly, and hence we use sample statistics to estimate them.

Regression analysis is the statistical technique used to identify the relationship between two variables. It involves estimating the coefficients of the model that best fit the data.

This type of inference helps us predict the value of a dependent variable based on an independent variable.

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The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.

An equation is a statement that shows the equality between two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, exponentiation, or roots. An equation can be solved by finding the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, science, engineering, and other fields to describe relationships between different quantities and to make predictions or solve problems.

Here,

Since line B is perpendicular to line A, the product of their gradients is -1. Therefore, the gradient of line B is 1/5.

a) To find the y-intercept of line B, we need to know a point on the line. Since we don't have one, we can use the fact that the y-intercept is the point where the line intersects the y-axis. To find this point, we can set x = 0 in the equation of line B:

y = (1/5)x + c

0 = (1/5)(0) + c

c = 0

Therefore, the y-intercept of line B is (0,0).

b) The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.

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11.87 m² metal sheet would be needed to make the base area of tank.

Volume of cylinder, determines how much material it can carry, is determined by the cylinder's volume. A cylinder is a three-dimensional structure having two parallel, identical bases that are congruent.

It is given that capacity of a closed cylindrical vessel of height 2 m is 3080 liters

Let us assume that Radius of cylinder = r

Then Volume of cylinder = π ×r² ×h

= 2π ×r²× m³

1 m³ = 1000 liters

= 2000 π r²  liters

Volume of tank = Capacity

2000 π r² = 3080

=> 2000 × (22/7) × r² = 3080

=> r² = 49/100

=> r = 7/10 m

=> r = 0.7 m

Base Area of tank = TSA = 2πrh + 2πr²

= 2×(22/7)(0.7)×2 + 2×(22/7)×(0.7)²

= 3.0772 +8.792

= 111.87 m²

Hence, 11.87 m² metal sheet would be needed to make it.

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Answer:

-12 is the y intercept while your slope is -4

Step-by-step explanation:

The point that partitions segment AB in a 1:4 ratio is (-1/2, -1).

What is Segment?

In geometry, a segment is a part of a line that has two endpoints. It can be thought of as a portion of a straight line that is bounded by two distinct points, called endpoints. A segment has a length, which is the distance between its endpoints. It is usually denoted by a line segment between its two endpoints, such as AB, where A and B are the endpoints. A segment is different from a line, which extends infinitely in both directions, while a segment has a finite length between its two endpoints.

To find the point that partitions segment AB in a 1:4 ratio, we need to use the midpoint formula to find the coordinates of the point that is one-fourth of the distance from point A to point B. The midpoint formula is:

((x1 + x2)/2, (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the segment.

So, let's first find the coordinates of the midpoint of segment AB:

Midpoint = ((-3 + 7)/2, (2 - 10)/2)

= (2, -4)

Now, to find the point that partitions segment AB in a 1:4 ratio, we need to find the coordinates of a point that is one-fourth of the distance from point A to the midpoint. We can use the midpoint formula again, this time using point A and the midpoint:

((x1 + x2)/2, (y1 + y2)/2) = ((-3 + 2)/2, (2 - 4)/2)

= (-1/2, -1)

So, the point that partitions segment AB in a 1:4 ratio is (-1/2, -1).

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Answer:

yes it is right now you can write it

The expressions that are equivalent to (x-2)² is x² - 4x + 4. (option B)

Now, let's look at the expression (x-2)². This is a binomial expression that can be simplified by applying the rules of exponents. Specifically, we can expand this expression as follows:

(x-2)² = (x-2) * (x-2)

= x * x - 2 * x - 2 * x + 2 * 2

= x² - 4x + 4

So, the expression (x-2)² is equivalent to x² - 4x + 4.

However, the problem asks us to identify other expressions that are equivalent to (x-2)². To do this, we can use the process of factoring. We know that (x-2)² can be factored as (x-2) * (x-2). Using this factorization, we can rewrite (x-2)² as:

(x-2)² = (x-2) * (x-2)

= (x-2)²

So, (x-2)² is equivalent to itself.

Hence the correct option is (B).

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Complete Question:

Which expressions are equivalent to (x−2)²?

Select the correct choice.

A. (x + 2) (x - 2)

B. x² - 4x + 4

C. x² - 2x + 5

D. x² + x - 2x

We have that, using Euclid's algorithm, we find the inverse of 200 modules 1001 is -5 (or 1001+5).

To find the inverse of a module m using Euclid's algorithm, the steps are as follows:

1. Calculate the greatest common divisor (GCD) of a and m using the Euclidean algorithm.

2. Let a = GCD * s + m*t, where s is the inverse of a module m.

3. The GCD in terms of a and my is written as 1 = m-s*a.

4. Find s = -a, so the inverse of a module m is -a (or m+s).

For example, a = 2, m=17, so GCD = 1 = 17-8*2 and the inverse of 2 modulo 17 is -8 (or 17+8). Similarly, for a = 34, m= 89, the GCD = 1 = 89-34*2 and the inverse of 34 modulo 89 is -34 (or 89+34). Finally, for a = 200, m= 1001, the GCD = 1 = 1001-5*200 and the inverse of 200 modulo 1001 is -5 (or 1001+5).

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The length of a side of the square is 8 cm.

What do you mean by perimeter of a rectangle and square?

When a wire is bent into the shape of a rectangle, its length becomes the perimeter of the rectangle. Similarly, when the wire is reshaped into a square, its length becomes the perimeter of the square.

The perimeter of a rectangle is given by the formula [tex]P=2(l+w)[/tex] , where [tex]l[/tex] is the length and [tex]w[/tex] is the width.

The perimeter of a square is given by the formula [tex]P=4s[/tex] , where [tex]s[/tex] is the length of a side.

Calculating the length of a side of the square:

The length of the rectangle is 11 cm and the width is 5 cm.

Therefore, the perimeter of the rectangle is [tex]P=2(11+5)=32[/tex] cm.

Since the wire is reshaped into a square, the perimeter of the square is also 32 cm.

Using the formula [tex]P=4s[/tex], we can solve for the length of a side of the square:

[tex]32 = 4s[/tex]

[tex]s = 32/4[/tex]

[tex]s = 8[/tex]

Therefore, the length of a side of the square is 8 cm.

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The 12 months of age) as percentiles of the CDC growth chart reference population.

The most likely description of Sarah's weights (at 3, 6, 9, and 12 months of age) as percentiles of the CDC growth chart reference population is: 85th percentile at 3 months; 85th percentile at 6 months; 90th percentile at 9 months; 95th percentile at 12 months.What is percentile in statistics?In statistics, a percentile is a value below which a specific percentage of observations in a group falls. It is used to split up data into segments that represent an equal proportion of the entire group, resulting in a data set split into 100 equal portions, with each portion representing one percentage point. Sarah's weight is in the 85th percentile at 3 months, 85th percentile at 6 months, 90th percentile at 9 months, and 95th percentile at 12 months is a most likely description of her weights (at 3, 6, 9, and 12 months of age) as percentiles of the CDC growth chart reference population.

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Answer:

30 minutes

Step-by-step explanation:

Use ratios. This is an inverse function, as speeding up makes the time traveling go down. So, when dividing the speed by 3 (done so 15 can get to 5), we multiply the time traveled by 3.

10 minutes * 3 = 30 minutes

Answer:

-1/3

Step-by-step explanation:

Answer:

-1/3

Step-by-step explanation:

The factorizations of these integers above represent their factorizations into their respective prime numbers.

(a) 756 = 2^2.3^3.7, (b) 819 = 3^2.7.11, (c) 9,075 = 3^2.5^2.7The unique factorization theorem refers to an essential theorem in standard algebraic theory that characterizes the unique factorization properties of integers. Standard factored form, on the other hand, refers to an expression in which an integer is factored into its standard, irreducible components.In view of this, the three provided integers, 756, 819, and 9,075 can be factored as follows:756 = 2^2.3^3.7 (in standard factored form)819 = 3^2.7.11 (in standard factored form)9,075 = 3^2.5^2.7 (in standard factored form)Note that the factorizations of these integers above represent their factorizations into their respective prime numbers.

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Answer: 15

Step-by-step explanation:

13--2 = 13 + 2 = 15

Total seats in plane: 186

108+64+14

5/7 of 14 is: 10

14÷7= 2

2x5= 10

5/16 of 64 is: 20

64÷16=4

5×4= 20

5/9 of 108 is: 60

108÷9= 12

12x5= 60

60+20+10=90

90/186 of seats are being used

simplified: 15/31

No

When the radius of circle 2 is twice the radius of circle 1, the size of circle 2 is larger than circle 1.

In geometry, a triangle is a polygon with three sides and three angles. The sum of the angles in a triangle is always 180 degrees. Triangles are one of the most basic and fundamental shapes in geometry and are used in many mathematical and real-world applications, such as in architecture, engineering, and physics. There are different types of triangles based on the length of their sides and the measures of their angles, such as equilateral triangles, isosceles triangles, scalene triangles, acute triangles, obtuse triangles, and right triangles.

Here,

2. This is because the circumference and area of a circle are directly proportional to the radius.

3. To determine if triangles ABC and DEF are similar, we need to check if their corresponding angles are congruent and if their corresponding sides are in proportion. From the diagram, we can see that angle A is congruent to angle D, angle B is congruent to angle E, and angle C is congruent to angle F. This satisfies the angle-angle (AA) similarity criterion. Additionally, we can use the side-side-side (SSS) similarity criterion to determine if the corresponding sides are in proportion. From the diagram, we can see that side AB is parallel to side DE, side AC is parallel to side DF, and side BC is parallel to side EF. Therefore, we can conclude that triangles ABC and DEF are similar.

4. To find the coordinates of D using the coordinates of A, we need to determine the translation from A to D. From the diagram, we can see that A is translated two units to the right and three units down to get to D. Therefore, we can find the coordinates of D by adding two to the x-coordinate of A and subtracting three from the y-coordinate of A. If the coordinates of A are (x1, y1), then the coordinates of D would be (x1 + 2, y1 - 3).

A= (-0.87,0.5)

D=(-0.87 + 2, 0.5 - 3)

D=(1.13,-2.5)

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