Graph the Auctsin. \[ g(v)=-x^{2} \] sroph-a-function button.

The volume of the cylinder when its radius is tripled is 405π unit³.

The volume of the cylinder when its radius is tripled is calculated by applying the formula for volume of a cylinder as follows;

V = πr²h

where;

V₁/r₁² = V₂/r₂²

where;

V₁ is the initial volume = 45π unit³

r₁ = 3 units

when the radius is tripled, r₂ = 3r₁

V₁/r₁² = V₂/r₂²

V₂ = (V₁/r₁²) x r₂²

V₂ = (V₁/r₁²) x (3r₁)²

V₂ = 9V₁

V₂ = 9 x 45π unit³

V₂ = 405π unit³

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It take 22.22 minutes for the two math students to finish the assignment together.

To determine how long it would take for the two math students to finish the assignment together, we can use the concept of "work done per unit of time."

Let's assume that the amount of work required to complete the assignment is represented by 1 unit.

If the first math student can complete the assignment in 50 minutes, then their work rate is 1/50 units per minute. Similarly, the second math student's work rate is 1/40 units per minute.

When they work together, their work rates are additive. So, the combined work rate of both students is (1/50 + 1/40) units per minute.

To find out how long it would take for them to finish the assignment together, we can calculate the reciprocal of the combined work rate:

1 / (1/50 + 1/40) = 1 / (0.02 + 0.025) = 1 / 0.045 = 22.22 minutes (approximately)

Therefore, it would take approximately 22.22 minutes for the two math students to finish the assignment together.

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Step-by-step explanation:

After taking over the throne, Ly Thai To found out that Hoa Lu land was narrow and surrounded by mountains, which was not worthy of the capital of an independent nation; it was more difficult to build a prosperous country. The King thought of moving the capital

Answer:

x = 2

Step-by-step explanation:

\( \rm Solve \: for \: x: \\ \rm \longrightarrow 4 (3 x - 1) = 20 \\ \\ \rm Divide \: both \: sides \: of \: 4 (3 x - 1) = 20 \: by \: 4: \\ \rm \longrightarrow \dfrac{4(3x - 1)}{4} = \dfrac{20}{4} \\ \\ \rm \dfrac{4}{4} = 1: \\ \rm \longrightarrow 3 x - 1 = \dfrac{20}{4} \\ \\ \rm \dfrac{20}{4} = 5: \\ \rm \longrightarrow 3 x - 1 = 5 \\ \\ \rm Add \: 1 \: to \: both \: sides: \\ \rm \longrightarrow 3 x + (1 - 1) = 1 + 5 \\ \\ \rm 1 - 1 = 0: \\ \rm \longrightarrow 3 x = 5 + 1 \\ \\ \rm 5 + 1 = 6: \\ \rm \longrightarrow 3 x = 6 \\ \\ \rm Divide \: both \: sides \: of \: 3 x = 6 \: by \: 3: \\ \rm \longrightarrow \dfrac{3x}{3} = \dfrac{6}{3} \\ \\ \rm \dfrac{3}{3} = 1: \\ \rm \longrightarrow x = \dfrac{6}{3} \\ \\ \rm \dfrac{6}{3} = 2 : \\ \rm \longrightarrow x = 2\)

H0: p1 ≥ p2 (Null hypothesis: Proportion of ADHD-diagnosed students in School A is equal to or greater than in School B)

Null Hypothesis: The proportion of students diagnosed with ADHD in School A is equal to or greater than the proportion of students diagnosed with ADHD in School B.

Symbolically, the null hypothesis can be stated as:

H0: p1 ≥ p2

Where:

H0: Null Hypothesis

p1: Proportion of students diagnosed with ADHD in School A

p2: Proportion of students diagnosed with ADHD in School B

In other words, the null hypothesis assumes that there is no significant difference or that School A may have an equal or higher proportion of students diagnosed with ADHD compared to School B.

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Answer:

x = 18

Step-by-step explanation:

According to the property of the angle, 2x = 36, so x = 36/2 = 18.

The graphs of triangle XYZ and its image after a dilation by a scale factor of 3 centered at the origin are shown below.

In Mathematics and Geometry, a dilation refers to a type of transformation that is typically used for altering the side lengths (dimension) of a geometric figure, but not its shape.

In this scenario and exercise, we would have to dilate the coordinates of the pre-image (triangle XYZ) by using a scale factor of 3 centered at the origin in order to produce triangle X'Y'Z' as follows:

Coordinate X (6, -1)        →       (6 × 3, -1 × 3) = X' (18, -3).

Coordinate Y (-2, -4)        →      (-2 × 3, -4 × 3) = Y' (-6, -12).

Coordinate Z (1, 2)        →       (1 × 3, 2 × 3) = Z' (3, 6).

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Complete Question:

Use the given vertices to graph △XYZ and its image after a dilation centered at the origin with scale factor k=3.

X(6, -1), Y(-2,-4), Z(1, 2)

So the vector  form of the equation is: y = -1(x - 2)² + 3.

To convert from standard form to vertex form, we complete the square by following these steps:

Factor out the coefficient of the x-squared term:

y = -x² + 4x - 1

= -1(x² - 4x) - 1

To complete the square inside the parentheses, add and subtract the square of half of the coefficient of the x-term (-4/2)^2 = 4:

y = -1(x² - 4x + 4 - 4) - 1

Simplify the expression inside the parentheses by factoring a perfect square:

y = -1((x - 2)² - 4) - 1

Distribute the -1 and simplify:

y = -1(x - 2)² + 3

Therefore, the vertex of the parabola is at (2, 3), and the negative coefficient of the x-squared term means that the parabola opens downwards.

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Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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Answer:

The center of this circle is (5, -4) and the radius is 1.

Step-by-step explanation:

First regroup these terms according to x and y :

x^2 - 10x + y^2 + 8y = -40

Next, complete the square for x^2 - 10x:  x^2 - 10x + 5^2 - 5^2.

and the same for y^2 + 8y:  y^2 + 8y + 16 - 16

Substituting these results into x^2 - 10x + y^2 + 8y = -40, we get:

x^2 - 10x + 5^2 - 5^2 y^2 + 8y + 16 - 16 = -40.

Next, rewrite x^2 - 10x + 25 and y^2 + 8y + 16 as squares of binomials:

Then x^2 - 10x + 5^2 - 5^2 y^2 + 8y + 16 - 16 = -40 becomes:

(x - 5)^2 + (y + 4)^2 - 25 - 16 = -40, or:

(x - 5)^2 + (y + 4)^2 = 1

This equation has the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.  Matching like terms, we get h = 5, k = -4 and r = 1.

The center of this circle is (5, -4) and the radius is 1.

Answer:

Center (5,-4) Radius = 1

Step-by-step explanation:

Put it in the form of the standard circle equation after dividing everything by 2. (-10x/2=-5x) (8y/2=4y) Since the radius wasn't given, it's just going to be a 1.

(x-5)^2+y(-(-4))^2 = 1^2

Hence, center (5, -4) and radius 1.

The equation sin(2x) + sin(x) = 0 is satisfied by two solutions on the interval [0, 2π): x = 0 and x = π.

To solve the equation sin(2x) + sin(x) = 0, we can rewrite it as sin(2x) = -sin(x).

Using the double-angle formula for sine, we have 2sin(x)cos(x) = -sin(x).

Now, we can consider two cases:

Case 1: sin(x) ≠ 0

In this case, we can divide both sides of the equation by sin(x), giving 2cos(x) = -1. Solving for cos(x), we find cos(x) = -1/2. This occurs at x = π/3 and x = 5π/3. However, we need to check if these values fall within the given interval [0, 2π). Only x = π/3 satisfies this condition.

Case 2: sin(x) = 0

If sin(x) = 0, then x must be an integer multiple of π. Within the given interval [0, 2π), x = 0 and x = π are solutions.

Therefore, the equation sin(2x) + sin(x) = 0 is satisfied by two solutions on the interval [0, 2π): x = 0 and x = π.

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Answer: it is D

Step-by-step explanation:

Answer:

\(r=2\)

Step-by-step explanation:

\(7r - 1 = 2r + 9\)

Add 1 to both sides:

\(7r-1+1=2r+9+1\)

\(7r=2r+10\)

Subtract 2r from both sides:

\(7r-2r=2r+10-2r\)

\(5r=10\)

Divide both sides by 5:

\(\frac{5r}{5}=\frac{10}{5}\)

\(r=2\)

Answer:

2

Step-by-step explanation:

Answer:

b. the triangle is not a right triangle

Step-by-step explanation:

Answer:

The triangle in this particular question may or may not be a right angled triangle

Step-by-step explanation:

~basically triangle are known to have 3 sides otherwise we would not call it a triangle...however in this particular question they may be no definite answer and triangle with 3 sides can be any sort of triangle:

-isosceles triangle with 3 uneven sides

-right angled triangle like stated with an hypotenuse

or

-scalene triangle with simply to equal sides...

glad I could help thumbs

disclaimer this answer may not be accurate and I do not take any responsibility if this answer is wrong thank you

Step-by-step explanation:

sorry di ko rin alam wala ako kasi akong ganyan

Answer:

all angles add up to 360 degrees

Step-by-step explanation:

Answer:

one solution i believe

Step-by-step explanation:

hoped I helped:)

Answer: one solution

Step-by-step explanation: it has one solution because it equals 0 so yes it has one solution

Answer:

i dont get this why is it crossed out

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

This is a two-stage problem

  for the first 12 years use cont compounding formula

        FV = PV e^(rt)     Future value  Presnt value   r = decimal int   t = years

         = 2000 e^(.05 * 12) = 3644.24    use this amount for the second stage

     Fv = pv e^(rt)  = 3644.24 ( e^(.08*8) ) = $ 6911.23

The vertices of the ellipse are (-4,2) and (4,2), since these points lie on the major axis of the ellipse which is horizontal.

Two of the focuses given in the issue, (−4,2) and (4,2), are both situated on a similar even line. This implies that the significant hub of the oval should be level. Two different focuses given in the issue, (2,2) and (- 9,2), are likewise situated on this level line. Thusly, the focal point of the oval is the midpoint between the focuses (- 4,2) and (4,2), which is (0,2).

The other two focuses given in the issue, (−5,5) and (−5,−1), are situated on an upward line that goes through the focal point of the oval. This implies that the minor pivot of the oval should be vertical.

The vertices of the oval are the places where the significant hub meets the circle. Since the significant hub goes through the focuses (−4,2) and (4,2), the vertices of the oval are (- 4,2) and (4,2).

In this way, the vertices of the oval are (- 4,2) and (4,2).

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200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

The absolute difference between the predicted and actual values must be determined, added together, and divided by the total number of periods.

Forecasted values are as follows: 1,500 and 1,400

Values in actuality: 1,200 and 1,500

Absolute differences:

|1,500 - 1,200| = 300

|1,400 - 1,500| = 100

Now, we calculate the MAD:

MAD = (300 + 100) / 2 = 400 / 2 = 200

Therefore, 200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

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Answer:

14

Step-by-step explanation:

The values after bubble sort is called on an input array of length n has the complexity O(n²)

Bubble sort is a simple sorting algorithm that is commonly taught in high school. It works by repeatedly swapping adjacent elements that are in the wrong order until the entire array is sorted.

To better understand the values of the array after bubble sort, let's take an example. Suppose we have the following input array of length 5:

[4, 2, 8, 5, 1]

After the first pass of bubble sort, the largest element (8) is at the end of the array:

[2, 4, 5, 1, 8]

After the second pass, the second largest element (5) is at the second-to-last position:

[2, 4, 1, 5, 8]

After the third pass, the third largest element (4) is at the third-to-last position:

[2, 1, 4, 5, 8]

After the fourth and final pass, the array is fully sorted:

[1, 2, 4, 5, 8]

As you can see, bubble sort swaps adjacent elements until the largest element "bubbles up" to the end of the array, and the process repeats until the entire array is sorted in ascending order.

It's worth noting that bubble sort has a worst-case time complexity of O(n²), meaning that the number of comparisons and swaps required grows quadratically with the size of the input array.

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The change in real GDP when government spending increases from 200 to 400 is 400. The multiplier effect measures how changes in government spending impact the overall economy.

To start, let's calculate the initial level of real GDP. The short-run aggregate supply equation tells us that Y (real GDP) equals 6,000 + 200P (price level). Since the price level is not given, we can assume it to be constant for simplicity.
Thus, the initial real GDP (Y) is 6,000.
Next, we'll calculate the change in government spending (ΔG). ΔG is the increase in government spending, which is 400 - 200 = 200.

The multiplier effect formula is given as 1 / (1 - MPC), where MPC is the marginal propensity to consume. In this case, the marginal propensity to consume is 0.5, as indicated by the consumption function C = 200 + 0.5(Y - NT).
Using the formula, the multiplier effect is 1 / (1 - 0.5) = 2.
To find the change in real GDP, we multiply the change in government spending (ΔG) by the multiplier effect.
Change in real GDP = ΔG * Multiplier effect = 200 * 2 = 400.
Therefore, the change in real GDP when government spending increases from 200 to 400 is 400.

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The area of the resulting surface of this infinite curve is π units.

In this question,

The infinite curve is y = e^−2x, x ≥ 0.

The curve is rotated about x-axis.

Since x ≥ 0, the limits will be 0 to ∞.

Then the area of the resulting surface is,

\(A= 2\pi \lim_{b\to \infty} (\int\limits^\infty_0{e^{-2x} } \, dx )\)

Now substitute,

u = -2x

⇒ du = -2dx

⇒ dx = \(-\frac{1}{2} du\)

Then,

\(\int\limits{-\frac{1}{2}e^{u} } \, du =-\frac{1}{2}\int\limits{e^{u} } \, du\)

Now substitute u and du, we get

⇒ \(-\frac{1}{2} \int\limits {e^{-2x} }(-2) \, dx\)

⇒ \(-\frac{-2}{2} \int\limits {e^{-2x} } \, dx\)

⇒ \((1) \int\limits {e^{-2x} } \, dx\)

⇒ \(\int\limits {e^{-2x} } \, dx\)

Thus the area of the resulting surface is

\(A= 2\pi \int\limits^\infty_0{e^{-2x} } \, dx\)

⇒ \(A= 2\pi [{e^{-2x}(\frac{1}{-2} ) } \,]\limits^\infty_0\)

⇒ \(A= \frac{2\pi}{-2} [{e^{-2(\infty)}-e^{-2(0)} } \,]\\\)

⇒ \(A= -\pi [0-1} \,]\\\)

⇒ \(A= \pi\)

Hence we can conclude that the area of the resulting surface is π units.

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The interesting or surprising thing we can learn about converting between improper fractions and mixed numbers is that to know how large or small a fraction formed from mixed number.

A mixed number, or fraction is a number having two parts one is integer (whole number) and other is a proper fraction (having numerator is less than its denominator). An example of a mixed number is \(2\frac{1}{\\ 2} \\ \). An improper fraction is defined when the top number (numerator) is larger than the bottom number (denominator). For example, \( \frac{8}{5} \).

To change an improper fraction to a mixed number follow these steps.

The conversion between improper fractions and mixed numbers or mixed to improper is a best way to be able to understand fractions and recognize how large or small a fraction is.

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Answer:

Approximately 1.2078566715...

Step-by-step explanation:

Very tricky question! Because the picture doesn't seem to be drawn to scale...

With point O being the center of the circle, construct segments KO, LO, and MO, all of them are the radius of the circle, thus, equivalent.

Since KL=LM, then triangle KLM is an isosceles triangle and angle K is equal to angle M.

\(m<K=m<M\\17=m<M\)

(Yes that means "measure of angle")

And because both angles K and M are 17 degrees, then angle L must be 146 degrees.

Now, focus on triangle LOK, since KO=LO, triangle LOK is also an isosceles triangle, thus:

\(m<LKO=m<KLO\\m<LKO=73\)

(Since half of angle L is 73)

Then m<KOL must be 34 degrees, and m<KOM will be 68 degrees.

After that, we can use the law of cosine to solve for KM:

\((KM)^2=1.08^2+1.08^2-2(1.08)(1.08)Cos(68)\\(KM)^2=1.1664+1.1664-2.3328(0.37460659341...)\\(KM)^2=2.3328-0.87388226112...\\(KM)^2=1.45891773888...\\KM=1.2078566715...\)

The only thing that bothers me is angle KOM being 68 degrees because in the figure angle KOM is clearly an obtuse angle.

I hope I am not tripping.

Answer:

Step-by-step explanation:

Draw a really careful diagram of Circle with center O and ΔKLM Then make <K = 17° and <M = 17°

Draw line Segment LO

Draw line Segment KO

Mark the intersection point of LO and KM as C

Since KL = LM the vertex is  

<KLM + 17 + 17 = 180

<KLM + 34 = 180

<KLM = 180 - 34

<KLM = 146

The diagonal LO bisects < KLM

Therefore <KL0 = 1/2 <KLM

<KLO = 73

KM and LO intersect at right angles because ΔKCL and MCL are congruent making <KCL = <MCL

2x = 180

x = 90

Now consider ΔKLO

It isosceles because it is made up of 2 radii.

That means that <OKL = 73

But OKC + OKL = 73

<OKC + 17 = 73

<OKC = 56

Now we are home free. We have the hypotenuse and an angle. We can find KC

Cos(56) = KC/KO

Cos(56) = KC/1.08

0.5592 * 1.08 = KC

kc = 0.6039

KM = twice that amount which is 1.2079

From the computation done, it can be denoted that the total price that will be paid will be $12.90.

1 Krispy Kosmos at $2.89 = $2.89

2 Chewy Chocos at $3.19 each = 2 × $3.19 = $6.38

1 Gooey Globs at $2.99 = $2.99

Total = $2.89 + $6.38 + $2.99 = $12.26

We'll then add the sales tax of 5.2%, therefore, the total value will be:

= $12.26 + (5.2% × $12.26)

= $12.26 + $0.638

= $12.90

In conclusion, the correct option is $12.90.

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Answer:

C

Step-by-step explanation:

Edg 2022