The Cost Of 6 Liters Of Petrol Is 48. 60. What Is The Cost Of 1 Liter? (2024)

In order to guarantee that the Simpson's rule approximation is accurate to within 0.00001, n should be larger than 8.

This is because Simpson's rule assumes that the function is composed of cubic polynomials, and the larger the n, the more finely the polynomials represent the function. To ensure accuracy, n should be large enough so that the cubic polynomials are an accurate approximation of the function. Increasing n also increases the number of subintervals, which helps the approximation to be more precise. For this particular example, n should be at least 8 in order to guarantee accuracy to within 0.00001.

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Answer: 6.857

11+42-5=48

11-4=7

So 48/7= 6.857142857142857
Rounded is 6.857

The average rate of temperature change decreased from 2.4 °C to −3.2 °C in 3.5 h is −1.6 °C/hour.

By dividing the entire change in temperature by the amount of time passed, the average rate of temperature change per hour can be computed.

First, determine the overall temperature change.

The temperature dropped from 2.4 °C to 3.2 °C, making the overall temperature change:

ΔT is the product of the beginning and final temperatures.

ΔT = (−3.2) °C - 2.4 °C

ΔT = −5.6 °C

Step 2: Calculate the time elapsed.

The temperature decreased from 2.4 °C to −3.2 °C in 3.5 hours, so the time elapsed is:

Δt = 3.5 hours

Step 3: Calculate the average rate of change in temperature per hour.

The average rate of change in temperature per hour is:

ΔT/Δt = (−5.6 °C)/(3.5 hours)

ΔT/Δt = −1.6 °C/hour

Therefore, the average rate of change in temperature per hour is −1.6 °C/hour.

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Answer:

The perimeter is 150

Multiply 10x2 x 15x2 (so 30x20)

Answer:

-1/3

Step-by-step explanation:

rise over run and its a negative slope

Answer:

-1/3

Step-by-step explanation:

Use Rise/Run. Since the line goes down from left to right, it is negative. Also, since it goes down 1 unit and over 3 units it is -1/3

Answer:

85

Step-by-step explanation:

Total angles formula (n-2) * 180 - memorize this formula

so 4 sides means 4 angles sum = 360

a kite is symmetrical,

so y= 360- 105-105 -65 =85

the dimensions of the lot is 100 yards by 400 yards. In this problem, a parking lot has a rectangular area of 40,000 square yards, and the length is 200 yards more than twice the width.

Determining the dimensions of a rectangular area, such as a parking lot, can be a useful task for many purposes, such as planning and designing a new lot or estimating the amount of space available for parking.

Let's call the width of the parking lot "w". Then, the length of the parking lot can be represented as 2w + 200.

The total area of the parking lot is 40,000 square yards, so we can set up an equation to solve for w: w * (2w + 200) = 40,000.

Solving for w, we get w = 100. This means that the width of the parking lot is 100 yards and the length is 2 * 100 + 200 = 400 yards.

The dimensions of the parking lot are 100 yards by 400 yards.

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The rectangular pyramid is cut by a plane containing its altitude and perpendicular to its base and will be divided into two rectangular oblique pyramids.

What is Geometry?

One of the first areas of mathematics is geometry, along with maths. It is preoccupied with spatial characteristics including the separation, form, size, and relative placement of objects. A geometer is a mathematician who specializes in shape.

A straight plane passes through the apex point of the given pyramid when it is intersected by a plane that is orthogonal to its foundation and contains its altitude. The perpendicular planes are parallel to the base at all times. Therefore, this kind of cross-section is a form of continuous passing through the triangle's vertex point.

The rectangular pyramid is cut by a plane containing its altitude and perpendicular to its base and will be divided into two rectangular oblique pyramids.

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By using the volume of a cube formula, The length of one side of the shipping box is 12.5 cm.

To find the length of one side of the box, we can use the formula for the volume of a cube, which is V = s^3, where s is the length of one side. Given that the volume of the box is 1525 cubic centimeters, we can solve for s:

V = 1525

s^3 = 1525

s = cubic root of 1525

s = 12.5 cm

So, the length of one side of the box is 12.5 cm.

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The two 2 digit number Mumtaz chose are 70 and 33, which when further divided by the other number gives 2.12121212

We need to find the two 2 digit numbers used by Mumtaz

Therefore we let x be = 2.12121212........(1)

then, we can say that x = 2 + 0.12121212

then taking 2 as a whole and making the rest fraction we get, x = 2 + [tex]\frac{12}{99}[/tex]

then x =[tex]\frac{198+n}{99}[/tex]

then simplifying this we get x = [tex]\frac{210}{99}[/tex]

so therefore we can say that we know, x = [tex]\frac{70}{33}[/tex]

clearly it shows that when divided it gives, [tex]\frac{70}{33}[/tex] = 2.12121212

therefore, we know that when 70 divided by 33 gives 2.12121212

hence, the numbers used my Mumtaz are 70 and 33

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Answer: The given system of equations is a linear system in two variables and can be solved either by substitution or elimination method.

Substitution method:

Solve one of the equations for one of the variables and substitute it into the other equation.

Starting with the first equation:

y = 3x - 7

Substitute this into the second equation:

6x - 2(3x - 7) = 12

Expanding the right side:

6x - 6x + 14 = 12

Simplifying:

14 = 12

This is not a valid solution, so the system has no solution.

Elimination method:

Multiply one of the equations by a constant to make the coefficients of one of the variables equal, then add the two equations to eliminate that variable.

Starting with the first equation:

y = 3x - 7

Multiply the second equation by -2:

-12x + 4y = -24

Adding the two equations:

4y - 12x = -24 - (-7)

Expanding the right side:

4y - 12x = -17

Solving for y:

y = (-12x - 17) / 4

Substituting this expression for y back into either equation to solve for x:

y = 3x - 7

(-12x - 17) / 4 = 3x - 7

Expanding both sides:

-12x - 17 = 4(3x - 7)

Expanding the right side:

-12x - 17 = 12x - 28

Adding 12x to both sides:

-17 = 24x - 28

Adding 28 to both sides:

11 = 24x

Dividing both sides by 24:

x = 11/24

Substituting this value of x back into either equation to find y:

y = 3x - 7

y = 3(11/24) - 7

Expanding:

y = 11/8 - 7

y = 11/8 - 56/8

y = -45/8

So, the solution to the system of equations is (x, y) = (11/24, -45/8).

This solution can be plotted on the coordinate plane to graph the two lines. The two lines intersect at the point (11/24, -45/8), which is the solution to the system of equations.

Step-by-step explanation:

Answer:

P = 4sqrt2 meters

Step-by-step explanation:

The diagonal of the square is the diameter of the circle. The radius is given, it is 1 meter. The diameter would then be 2 meters.

If you just consider the diagonal and just two sides, it is a 45°-45°-90° triangle. If the hypotenuse is 2, then the legs are sqrt2. This is a side of the square. Each side of the square is ssqrt2. There are four sides.

To find the perimeter, add up all four sides. Or since its a square and all four sides are the same, times by 4

Perimeter = 4sqrt2 meters

The terms missing from the diagram will be – 6x and – 3x. Then the right choice is option C.

What is factorization?

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The quadratic expression is given below.

⇒ x² – 9x + 18

Factorize the expression, then we have

⇒ x² – 9x + 18

⇒ x² – 6x – 3x + 18

⇒ x(x – 6) – 3(x – 6)

⇒ (x – 6)(x – 3)

The terms missing from the diagram will be – 6x and – 3x. Then the right choice is option C.

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In 1960, there were 53,719,840 deaths worldwide if there were 3.032 billion people.

The world's population was predicted to be 3.032 billion people in 1960, and there were 17.7 fatalities for every 1000 persons. This translates to 17.7 deaths per 1000 persons. We multiply the population by the death rate to determine the total number of fatalities worldwide in 1960. 53,719,840 people pass away as a result, which is a sizable amount of people lost in a single year. This emphasises the effect of mortality on population growth as well as the significance of addressing the factors that contribute to death, such as illnesses and way of life decisions. Additionally, this data serves as a baseline for advancements in lowering death rates and raising life expectancy, which has been a goal of the global health community for many years.

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The answers are pi/3, 2pi/3.

Explanation:

Because of our special triangles, we know cos(pi/6) is root 3 over 2. therefore we plug in root 3 over 2 instead of cos(pi/6)

sinx= root 3/2

Next, because of CAST, we know sin is positive in quadrants 1 and 2.

To find our reference angle, we use the special triangles again and see that our reference angle is pi/3.

The reference angle pi/3 in quadrant 1 is pi/3 and in quadrant two it is 2pi/3.

Those are your answers!

The vertex of the function defined as g(x) = f(x+2) is (8, 4).

How to determine the vertex of the function

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

Vertex of f(x) = (6, 4)

For the function defined as g(x) = f(x+2), we have

Vertex = (x + 2, y)

Where

x = 6 and y = 2

Substitute the known values in the above equation, so, we have the following representation

Vertex = (6 + 2, 4)

Evaluate

Vertex = (8, 4)

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Simply said, a trend line is a line drawn over a pivot to indicate the direction in which prices are moving most frequently.

What is a trend line equation?

A linear relationship is depicted by a trend line. Y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope of the line, and b is the y-intercept, is the equation for a linear relationship.

Simply said, a trend line is a line drawn over a pivot to indicate the direction in which prices are moving most frequently.

It should be mentioned that trend lines are used to help traders decide which trades to make.

For instance,

In a restaurant = 4 employees

salary of 1 = $ 2340

Then,

Total salary = 4 x 2340 = $ 9360

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The minimum coefficient of friction needed between your back and the barrel wall ride (room spins, floor drops away) if the diameter of the circle is 2.8 m and it makes 1 revolution every 1.9 seconds is 0.45.

Barrel Wall Friction

To determine the minimum coefficient of friction needed, we can use the centripetal force equation:

F = (mv²)/r

where:

F is the centripetal force

m is the mass of the person

v is the speed of the person

r is the radius of the circle

The speed of the person can be found by dividing the circumference of the circle by the time it takes to make one revolution:

v = (2πr)/t

where:

π is pi (approximately 3.14)

t is the time to make one revolution

Combining these equations, we get:

F = (m(2πr/t)²)/r

Simplifying, we get:

F = 4π²mr/t²

The force of gravity pulling the person down is given by:

Fg = mg

where:

g is the acceleration due to gravity (approximately 9.8 m/s²)

To find the minimum coefficient of friction needed, we need to find the ratio of the centripetal force to the force of gravity:

F/Fg = (4π²mr/t²)/(mg) = 4π²r/(gt²)

The minimum coefficient of friction needed is then:

μmin = (F/Fg) - 1 = 4π²r/(gt²) - 1

Substituting the given values, we get:

μmin = (4π² x 1.0 kg x 2.8 m)/(9.8 m/s² x (1.9 s²) - 1

Solving for μmin, we get:

μmin ≈ 0.45

Therefore, the minimum coefficient of friction needed between the person's back and the barrel wall ride is approximately 0.45.

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Using the measure of the diagonal of the rectangular prism box, the pole can't be stored in the box because it is longer than the diagonal of the box.

What is the Measure of the Diagonal of a Rectangular Prism?

To determine if the fishing pole that is 6 feet long can be stored in the rectangular prism box, find its diagonal.

Find the Diagonal of the rectangular box:

The diagonal of a rectangular prism can be found using the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the other two sides.

In this case, the diagonal length is the hypotenuse of a right triangle with sides 4 feet, 3 feet, and 2 feet. So, we can find the diagonal by using the theorem:

diagonal = √(4^2 + 3^2 + 2^2) = √(16 + 9 + 4) = √(29) = 5.385 feet

So, the diagonal of the rectangular prism is approximately 5.385 feet.

Since the length of the pole is 6 feet, which is greater than 5.385, therefore, it can't be stored in the rectangular prism box.

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Answer:

The slopes of these two lines are different.

The perimeter of the rectangle whose sides are 2/3 and 1/3 is 6/3 and answer as a reduced fraction is the perimeter of the rectangle is 2units.

The perimeter of a rectangle is equal to the sum of the lengths of all four sides. To find the perimeter of a rectangle with the sides of length 2/3 and 1/3, we need to add up the length of all four sides. Perimeter = 2×(2/3) + 2×(1/3). Perimeter = 4/3 + 2/3 = 6/3. To simplify this fraction we can divide the numerator by the denominator which is 3, Perimeter = 6/3 = 2 units. Hence, the reduced fraction for the perimeter of the rectangle with sides of length 2/3 and 1/3 is 2units.

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The distance from home plate to second base is 180 feet, which is double the distance from home plate to first base.

A baseball diamond is a square with four bases, with home plate in the middle. 90 feet separate first base from home plate, and 90 more feet separate first base from second base. Therefore, the total distance from home plate to second base is twice that distance, or 180 feet. The same applies to all of the bases; the distance between them is always 90 feet, so the total distance from home plate to any base is twice that of the distance from home plate to first base. This means that the distance from home plate to second base, third base, and home plate is all 180 feet.

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The average rate of change in revenue as the number of bluetooth speakers sold increases from 20 to 40 units is approximately $34.994 per unit.

The average rate of change in revenue as the number of bluetooth speakers sold increases from 20 to 40 units can be found using the formula for average rate of change:

average rate of change = (final value - initial value) / (final x - initial x)

Plugging in the values, we get:

average rate of change = (R(40) - R(20)) / (40 - 20)

Where R(x) = 35x - 0.01x^2 is the revenue equation.

First, we need to find the values of R(40) and R(20).

R(40) = 35x40 - 0.01x40^2 = 1400 - 0.16 = 1399.84

R(20) = 35x20 - 0.01x20^2 = 700 - 0.04 = 699.96

So,

average rate of change = (1399.84 - 699.96) / (40 - 20) = 699.88 / 20 = 34.99

So, the average rate of change in revenue as the number of bluetooth speakers sold increases from 20 to 40 units is approximately $34.994 per unit.

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There are 20 different arrangement that three married couples can sit at a round table together.

What does number arrangement mean?

The number of ways that a number of things can be ordered or arranged is known as an arrangement number, also known as a permutation number or simply a permutation. Generally speaking, a grouping of objects constitutes an arrangement. Both combinations and permutations can be used to determine how many "arrangements" there are of the components (order is significant). An arrangement is another term for the split of space into cells by a set of hyperplanes (Agarwal and Sharir 2000).

What is the procedure for making arrangements?

Let's say we have n objects, and we need to make arrangements for r of them. The numbers of ways in which the arrangement can take place are given by permutation as [tex]nPr = \frac{n!} {(n-1)!}.[/tex]

There are 6 guests, so the total number of arrangements is 6!.

The number of distinct arrangements for 6 guests at a round table is[tex]6!/6 = 720/6 = 120.[/tex]

This gives us 3! arrangements for each group of identical arrangements, so the final answer is[tex]120/3! = 120/6 = 20.[/tex]

There are 20 distinct arrangements where three married couples can sit together at a round table.

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Three married couples (6 guests altogether) attend a dinner party. They sit at a round table randomly in such a way that each outcome is equally likely. What is the probability that somebody sits next to his or her spouse?

Hint. Label the seats, the individuals, and the couples. There are 6! = 720 seating arrangements altogether. Apply inclusion-exclusion to the events A₁ = {ith couple sit next to each other), i = 1, 2, 3. Count carefully the numbers of arrangements in the intersections of the A;s.

The area of figure is,

⇒ 26 units²

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Here, The given figure is made up of a parallelogram and a rectangle.

Hence, The area of the parallelogram is

⇒ Base × Height

Here, The base of the parallelogram is 6 units (Just count the boxes).

And, The height is also 1 unit.

This implies that the area of the parallelogram is

⇒ Base × Height

⇒ 6 × 1

⇒ 6 units²

And, To find the area of the rectangle, we need to find the width and the length using the distance formula or the Pythagoras Theorem.

Using the Pythagoras Theorem as;

⇒ l² = a² + b²

⇒ l² = 2² + 6²

⇒ l² = 4 + 36

⇒ l² = 40

⇒ l = 2√10

And, We get;

⇒ w² = 1² + 3²

⇒ w² = 1 + 9

⇒ w² = 10

⇒ w = √10

Hence, Area of rectangle is,

⇒ l × w

⇒ 2√10 × √10

⇒ 2 × 10

⇒ 20 unit²

Hence, The area of figure is,

⇒ 20 + 6

⇒ 26 units²

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The graph of y = 5x + 6 is the graph of y = x + 1 stretched and shifted

How to determine the relationship between the graphs

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

y = x + 1

y = 5x + 6

Using the above as a guide, we have the following:

g(x) = 5f(x + 1) + 1

This means that y = x + 1 is stretched by 5 and then shifted up by 1 units to get y = 5x + 6

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Complete question|

How do the graphs of y = x + 1 and y = 5x + 6 compare?

Answer:

Step-by-step explanation:

Answer:

X = 0.9

Step-by-step explanation:

step-by-step.

4x+9

2

1

3

=

3x

0.5

Step 1: Simplify both sides of the equation.

12

7

x+

27

7

=6x

Step 2: Subtract 6x from both sides.

12

7

x+

27

7

−6x=6x−6x

−4.285714x+

27

7

=0

Step 3: Subtract 27/7 from both sides.

−4.285714x+

27

7

−

27

7

=0−

27

7

−4.285714x=

−27

7

Step 4: Divide both sides by -4.285714.

−4.285714x

−4.285714

=

−27

7

−4.285714

x=0.9

Answer:

Sue can fill 72 / 10 = 7 10-fluid ounce bowls of soup.

There will be 72 - 10 * 7 = 12 fluid ounces of soup left over.

Step-by-step explanation:

The can of soup shown is 32 ounces, and a full can of water is 40 fluid ounces. So, the total amount of soup that Sue made is 32 + 40 = 72 fluid ounces.

Sue can fill 72 / 10 = 7 10-fluid ounce bowls of soup.

There will be 72 - 10 * 7 = 12 fluid ounces of soup left over.

According to the above information, assembler B requires less time to assemble more than assembler A.

How to select the correct option?

To select the correct option we must analyze the image of the tables in which the time in hours is related to the number of assembled toasters. Based on this information, we can infer that the number of assemblers B assembles a greater number of toasters in a similar or less time than the other assembler. For example:

3 - 14584 - ?3 * 1458 / 4 = 1,093.5

While assembler A assembles 1,093 toasters in 4 hours, assembler B assembles 1,956.

Note: This question is incomplete. Here is the complete information:

Options:

Jointer A requires less time to assemble more than jointer B.Jointer B requires less time to assemble than Jointer A.Both jointers assembled the same.

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The area of the parallelogram will be 180 square cm. Then the correct option is B.

What is the area of the parallelogram?

Let H be the height and W be the width of the parallelogram.

Then the area of the parallelogram will be

Area of the parallelogram = H × W square units

The height and width of the parallelogram are 12 cm and 15 cm, respectively. Then the area of the parallelogram is given as,

A = 12 x 15

A = 180 square cm

The area of the parallelogram will be 180 square cm. Then the correct option is B.

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