Can somebody help me please

Wonderful quote, have a nice day!

Answer:

nicee

Step-by-step explanation:

Value of r is different for every series

let

a , b , c , d ..... be geometric series then

r = b/a or d/c and so on

where r is common ratio

You can travel 11 kilometers per litre of petrol.

You can calculate the number of kilometers per litre by dividing the distance travelled by the amount of petrol used. In this case, you would divide 220km by 20Lt to get the number of kilometers per litre.

Here is the step-by-step calculation:

1. Distance travelled = 220km

2. Amount of petrol used = 20Lt

3. Kilometers per litre = Distance travelled / Amount of petrol used

4. Kilometers per litre = 220km / 20Lt

5. Kilometers per litre = 11km/Lt

Therefore, you can travel 11 kilometers per litre of petrol.

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The ratio of the short side to the long side is 9/4 and the ratio of the hypotenuse to the long side is 5/4.

What is triangle ?

A triangle is a two-dimensional shape with three straight sides and three angles. It is one of the most basic and important shapes in geometry.

The three sides of a triangle can be of different lengths, or they can be of the same length, in which case it is called an equilateral triangle. The angles of a triangle can also vary, and they always add up to 180 degrees. Triangles can have acute angles (less than 90 degrees), right angles (exactly 90 degrees), or obtuse angles (greater than 90 degrees).

According to given information :

Ratio of short to long sides:

x/9 = 9/4

To solve for x, we can cross-multiply:

4x = 9 * 9

4x = 81

x = 81/4

So the ratio of the short side to the long side is:

x/9 = (81/4) / 9 = 81/36 = 9/4

Ratio of hypotenuse to long sides:

y/9 = 15/12

To solve for y, we can cross-multiply:

12y = 9 * 15

12y = 135

y = 135/12 = 45/4

So the ratio of the hypotenuse to the long side is:

y/9 = (45/4) / 9 = 45/36 = 5/4

Therefore, the ratio of the short side to the long side is 9/4 and the ratio of the hypotenuse to the long side is 5/4.

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The error in the given solution was adding the numerators while ignoring the Denominators.

Solve the expression:$$\frac{3x+2}{x^2-4x-12} + \frac{2x-1}{x^2-x-12}$$

$$\frac{3x+2}{x^2-4x-12} + \frac{2x-1}{x^2-x-12}$$$$= \frac{3x+2}{(x+2)(x-6)} + \frac{2x-1}{(x+3)(x-4)}$$$$= \frac{(3x+2)(x+3)}{(x+2)(x-6)(x+3)} + \frac{(2x-1)(x+2)}{(x+3)(x-4)(x+2)}$$

Using the least common denominator and adding, we get$$\frac{(3x+2)(x+3)}{(x+2)(x-6)(x+3)} + \frac{(2x-1)(x+2)}{(x+3)(x-4)(x+2)}$$$$= \frac{(3x+2)(x+3) + (2x-1)(x+2)}{(x+2)(x-6)(x+3)}$$$$= \frac{3x^2 + 11x + 4}{(x+2)(x-6)(x+3)}$$

Correct Answer:$$\frac{3x+2}{x^2-4x-12} + \frac{2x-1}{x^2-x-12}$$$$= \frac{(3x+2)(x-4) + (2x-1)(x+3)}{(x-6)(x+3)(x-4)}$$$$= \frac{3x^2 - 10x - 5}{(x-6)(x+3)(x-4)}$$

Error Analysis:The given problem was solved using the correct approach to add or subtract rational expressions. However, the calculations made were incorrect.

The error made in the solution was the addition of the numerators while ignoring the denominators, which is not allowed. The correct method to add or subtract rational expressions is to find the least common denominator (LCD) of the given expressions.

The LCD of the given expressions is $(x+2)(x-6)(x+3)(x-4)$.After finding the LCD, we rewrite each term with the same denominator, and then add or subtract the numerators.

In this problem, the correct solution would be$$\frac{3x+2}{x^2-4x-12} + \frac{2x-1}{x^2-x-12}$$$$= \frac{(3x+2)(x-4) + (2x-1)(x+3)}{(x-6)(x+3)(x-4)}$$$$= \frac{3x^2 - 10x - 5}{(x-6)(x+3)(x-4)}$$

Therefore, the error in the given solution was adding the numerators while ignoring the denominators.

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The weight that separates the bottom 5% is approximately 5.02 ounces.

To find the weights that separate the top 5% and the bottom 5%, we need to use the z-score formula and the standard normal distribution table.

First, let's find the z-score for the top 5%. Using the standard normal distribution table, we find that the z-score for the top 5% is approximately 1.645.

Next, we can use the formula z = (x - μ) / σ, where z is the z-score, x is the weight we're trying to find, μ is the mean, and σ is the standard deviation.

For the top 5%, we have:

1.645 = (x - 5.12) / 0.07

Solving for x, we get:

x = 5.12 + 1.645 * 0.07

x ≈ 5.22 ounces

Therefore, the weight that separates the top 5% is approximately 5.22 ounces.

To find the weight that separates the bottom 5%, we use the same process but with a negative z-score. The z-score for the bottom 5% is approximately -1.645.

-1.645 = (x - 5.12) / 0.07

Solving for x, we get:

x = 5.12 - 1.645 * 0.07

x ≈ 5.02 ounces

Therefore, the weight that separates the bottom 5% is approximately 5.02 ounces.

These weights could serve as limits used to identify which components should be rejected. Any component with a weight less than 5.02 ounces or greater than 5.22 ounces should be rejected.

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In order to draw a line that is parallel to given lines and is midway between them, the given lines also will be parallel.

So first let's draw two given lines:

Now, a line parallel to both lines and located midway between them looks like:

So the green line is the loci that fits the description: a line that is parallel to the given lines and midway between them.

A story that can be represented using the equation y=x+1/5x is "John has an apple and he cut another apple into 5 equal parts and took on part. What's the rural fraction of apple that he has?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, if John has an apple and he cut another apple into 5 equal parts and took on part.

This can be illustrated as:

y = x + 1/5x

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Answer:

( 8,7 )

Step-by-step explanation:

Answer:

\(\sqrt{113}\)

Step-by-step explanation:

Answer:

\(\left[\begin{array}{cc}-230&380\\-170&60\end{array}\right]\)

Step-by-step explanation:

Notice that you are being asked to perform the product of a scalar (the number "-10" times a 2 by 2 matrix.

Such type of product requires the multiplication of each element of the matrix by the scalar "-10"

That means that the element 23 gets transformed into "-230"

The element -38 gets transformed into "380"

The element 17 gets transformed into "-170"

and lastly, the element -6 gets transformed into "60"

\(\left[\begin{array}{cc}1-230&380\\-170&60\\end{array}\right]\)\(\left[\begin{array}{cc}-230&380\\-170&60\end{array}\right]\)

Such modification gets reflected in the second matrix listed among the possible answers.

A triangle's internal angles add up to a total of 180°. This indicates that a triangle's complete turn from one angle to another is equivalent to 180 degrees. Regardless of the triangle's size or shape, there is a link between the measurements of its internal angles.

The sum of the two angles' measurements would also equal 180° if we think of a straight line as a degenerate triangle with two of its angles each measuring 180°. So, the equation for the connection between two angles' measurements is:

Mangle1 + Mangle2 = 180°

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Answer:

5x^3-4x^2+3x+

Step-by-step explanation:

According to the question the length of the third side is \(5x^3 - 4x^2 + 3x + 12\)

A triangle is a geometric shape that is formed by three line segments that intersect at three non-collinear points. The three line segments are called the sides of the triangle, while the three points where they intersect are called the vertices of the triangle.

According to the option we can see the third side is greater than the sum of other two sides of triangle if the length of the third side is

So we can write;

\((5x^3 - 4x^2 + 3x + 12) > [(3x^2 - 4x - 1) + (4x - x^2 + 5)]\\(5x^3 - 4x^2 + 3x + 12) > [(2x^2 - 4)]\)

Therefore, the correct option is last one which is; the third side is

\(5x^3 - 4x^2 + 3x +12\)

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Answer: 512

Step-by-step explanation:

2^ (3^2)

2^ (9)

512

Answer:

B

Step-by-step explanation:

Answer:

\(\frac{1}{2}\)

Step-by-step explanation:

\(--------------------------------------------\)

\(\frac{1}{3}\cdot\frac{1}{4}+\frac{5}{12}\) = \(?\)

\(\frac{1}{12}+\frac{5}{12}\) = \(?\)

\(\frac{6}{12}\) = \(\frac{3}{6}\) = \(?\)

\(\frac{1}{2}\)

\(--------------------------------------------\)

Hope this helps! <3

\(--------------------------------------------\)

Answer:

y=x^2-4x+12

Step-by-step explanation:

Vertex to standard form is simple once you know how to look at it.

Standard form is x^2+bx+c=y.

Vertex form is f(x) = a(x – h)2 + k

So we know h=-2 and k =8.

Then, you need to graph it.

Since the y intercept is 12, 12=c.

b=k/h so b=8/-2 or -4. So -4=b

Answer:

$18.73

Step-by-step explanation:

$16.55 + $2.18

(sorry if I'm wrong)

Answer:

214

Step-by-step explanation:

Answer:

432 square feet

Step-by-step explanation:

We know perimeter of rectangle is 2(length + width)

we already know that length is 8 yards

and perimeter is 84 feet

we need to find width first

then

we find area of garden by using formula

area of rectangle = length * width

first we need to convert yards into feet as perimeter is in yards

1 yard = 3 feet

8 yards = 3*8 feet = 24 feet

now we plug value of length and perimeter in formula

perimeter = 2(length + width)

84 = 2(24 + width)

84/2 = 24 + width

=> 42 = 24 + width

=> width = 42 - 24 = 18

Thus, width of garden is 18 feet

now

area of the garden =  length * width = 24* 18 feet square

area of the garden= 432 square feet

Other way to explain:

perimeter = 2 *length + 2 *width

length = 24 feet (8 yards = 24 feet)

since perimeter = 84 feet

84 = 2 * 24 + 2 * width

36 = 2 * width

18 = width

width = 18 feet

area of rectangle is length * width = 24 * 18 = 432 square feet

The z-score for a data value of 84 in a normal distribution with a mean of 86 and a standard deviation of 5 is approximately -0.40.

The z-score is a measure of how many standard deviations a data value is away from the mean. It is calculated using the formula: \(\(z = \frac{x - \mu}{\sigma}\)\), where x is the data value, \(\(\mu\)\) is the mean, and \(\(\sigma\)\) is the standard deviation. In this case, the data value is 84, the mean is 86, and the standard deviation is 5.

Plugging these values into the formula, we get: \(\(z = \frac{84 - 86}{5} = -0.40\)\). Since the z-score represents the number of standard deviations, a negative value indicates that the data value is below the mean. Rounding to two decimal places, the z-score for a data value of 84 is approximately -0.40.

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The statement is false. The arc length of the curve defined by x = 4(3 + y)² on the interval [1, 4] is not approximately 131 units.

To find the arc length of a curve, we use the formula ∫ √(1 + (dx/dy)²) dy, where the integral is taken over the given interval.

In this case, the equation x = 4(3 + y)² represents a parabolic curve. By differentiating x with respect to y and substituting it into the arc length formula, we can calculate the exact arc length over the interval [1, 4].

However, it is clear that the arc length of the curve defined by x = 4(3 + y)² cannot be approximately 131 units, as this would require a specific calculation using the precise integral formula mentioned above.

Therefore, the statement is false, and without further calculations, we cannot determine the exact arc length of the given curve on the interval [1, 4].

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Answer:

she messed up at -17=34x

Step-by-step explanation:

she added 8x to each side but she was actually supposed to subtract

The error is 8(x - 3) + 7 = 2x(13) and -17 = 34x.

4 - 17 = -13, not 13

8x - 17 = 26x

-17 = 26x -8

-17 = 18x ( it should be like this, but this is still wrong because it should -26)

The solution is:

8(x - 3) + 7 = 2x(4 - 17)

8(x - 3) + 7 = 2x(-13)

8x - 24 + 7 = -26x

8x - 17 = -26x

8x + 26x = 17

34x = 17

x = 17/34

x = 1/2

Hope it helps!

To determine the percentage of times the machine will dispense more than 7.1 oz of coffee, we need to calculate the z-score and find the corresponding area under the normal distribution curve.

The z-score is calculated using the formula:

z = (x - μ) / σ

where x is the value we're interested in (7.1 oz), μ is the mean (7.6 oz), and σ is the standard deviation (0.5 oz).

Let's calculate the z-score:

z = (7.1 - 7.6) / 0.5

z = -0.5 / 0.5

z = -1

Now we need to find the area under the normal distribution curve for a z-score of -1. We can use a standard normal distribution table or a statistical calculator to find this area.

The area corresponds to the probability that the machine will dispense more than 7.1 oz.

Using a standard normal distribution table, we can find that the area to the left of z = -1 is approximately 0.1587. Since we're interested in the area to the right (more than 7.1 oz), we subtract this value from 1:

P(X > 7.1) = 1 - 0.1587

P(X > 7.1) ≈ 0.8413

Therefore, the vending machine will dispense more than 7.1 oz approximately 84.13% of the time.

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Answer:

18 tons

Step-by-step explanation:

1 pound = 0.0005 ton

Therefore,

36,000 pounds

= 36000*0.0005

= 18 tons

The radius and center of the translated circle are,

Radius = 7 units

Center = (10, - 2)

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The equation of circle is,

x² + y² - 18x + 8y + 48 = 0

Now, We can simplify the equation as;

x² + y² - 18x + 8y + 48 = 0

x² - 18x + 81 - 81 + y² + 8y + 16 - 16 + 48 = 0

(x - 9)² + (y + 4)² = 49

(x - 9)² + (y + 4)² = 7²

Hence, The radius of circle = 7

And, Center = (9, - 4)

Let the center of circle after translated one unit right and two units down is, (h', k')

Hence, We get;

h' = 9 + 1 = 10

k' = - 4 + 2 = - 2

Thus, The equation of the translated circle is,

(x - 10)² + (y - (- 2))² = 7

Hence, the radius and center of the translated circle are,

Radius = 7 units

Center = (10, - 2)

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Answer:

15 ft^3

Step-by-step explanation:

Sand needed can be determined by calculating the volume of a pyramid

Volume of a pyramid = 1/3 x ( length base x height)

1/3 x ( 4.5 x 4 x 2.5) = 15 ft^3

axis of symmetry would be where it becomes symmetrical

Answer:

Clean air has no smell

Despite all of our best intentions to make a home smell clean, the truth is that clean air should smell like nothing at all.

Step-by-step explanation:

Before the rain begins, one of the first odors you may notice as winds pick up and clouds roll in is a sweet, pungent zing in your nostrils. That's the sharp, fresh aroma of ozone—a form of oxygen whose name comes from the Greek word ozein (to smell).

Answer:

x + 3

Step-by-step explanation:

Since the fractions have the same denominator we can add them. Adding them gives us (x + 3) / y so the numerator is x + 3.

Answer:

x + 3

Step-by-step explanation:

When the weight moves from x = -8 cm to x = 8 cm, the spring moves from its maximum stretched position to its maximum compressed position.Hence, the spring oscillates between its maximum stretched and compressed positions when the weight is set in motion. Therefore, the spring is a simple harmonic oscillator.

Given: Displacement x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0. To find: What is the spring?Explanation:We know that displacement is given by x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0.Comparing this with the standard equation, x

= Acos(ωt+ φ)A

= amplitude

= 8 cmω

= angular frequencyφ

= phase angleWhen the spring is at equilibrium position, the weight attached to the spring does not move. Hence, no force is acting on the weight at the equilibrium position. Therefore, the spring is neither stretched nor compressed at the equilibrium position.Now, the spring is set in motion resulting in a displacement of x

= 8 cos t

= Acos(ωt+ φ) where A

= 8 cm, ω

= 1 and φ

=0. The maximum displacement of the spring is 8 cm in the positive x direction. When the weight is at x

= 8 cm, the restoring force of the spring is maximum in the negative x direction and it pulls the weight towards the equilibrium position. At the equilibrium position, the weight momentarily stops. When the weight moves from x

= 8 cm to x

= -8 cm, the spring moves from its natural length to its maximum stretched position. At x

= -8 cm, the weight momentarily stops. When the weight moves from x

= -8 cm to x

= 8 cm, the spring moves from its maximum stretched position to its maximum compressed position.Hence, the spring oscillates between its maximum stretched and compressed positions when the weight is set in motion. Therefore, the spring is a simple harmonic oscillator.

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The displacement of the weight attached to the spring is given by the equation x = 8 cos t. The amplitude of the motion is 8 centimeters and the period is 2π seconds.

The equation x = 8 cos t represents the displacement of a weight attached to a spring in simple harmonic motion. In this equation, x is measured in centimeters and t is measured in seconds.

The amplitude of the motion is 8 centimeters, which means that the weight oscillates between x = 8 and x = -8.

The period of the motion can be determined from the equation T = 2π/ω, where ω is the angular frequency. In this case, ω = 1, so the period T is 2π seconds.

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