Part E
For any diagonal line segment on the coordinate grid, you can create two triangles that have the line segment as the hypotenuse. Are the lengths of the vertical line segments the same for both triangles? Are the lengths of the horizontal line segments the same for both triangles? What does that mean?

Along with proof of (a.) and (d.), (b.) Power tower: one level is a, (k + 1) levels is a raised to the power of a power tower with k levels, (c.) A(2, n) <= 2 ↑↑ n for all positive integers n, where ↑↑ denotes power tower notation.

The idea of a fully computable function that is not primitive recursive is illustrated by the recursively constructed mathematical function known as the Ackermann function. Since m and n are non-negative integers, it is commonly written as A(m, n).

a.) Prove using regular induction that \(A(1, n) \leq 2^n\) for all positive integers n:

Base Case: For n = 1, A(1, 1) = 2, which is equal to \(2^1\).

Inductive Hypothesis: Assume that \(A(1, k) \leq 2^k\) for some positive integer k.

Inductive Step: We need to show that \(A(1, k + 1) \leq 2^{(k + 1)}\). Using the recursive definition of A(m, n), we have \(A(1, k + 1) = A(0, A(1, k)) = 2^{(A(1, k))}\leq 2^{(2^k)}\) (by inductive hypothesis)\(< = 2^{(2^{(k + 1)})}\).

Therefore, by regular induction, we have proved that \(A(1, n) \leq 2^n\) for all positive integers n.

b.) A power tower with one level is defined as a, and a power tower with (k + 1) levels is defined as a raised to the power of a power tower with k levels.

c.) \(A(2, n) \leq 2\) ↑↑ n for all positive integers n, where ↑↑ denotes power tower notation.

d.) The recursive definition of a triple arrow-up notation for power towers is:

a ↑↑↑ 1 = a (base case)

a ↑↑↑ (k + 1) = a ↑↑ (a ↑↑↑ k) (recursive step)

This definition states that a triple arrow-up notation with one level is equal to the base value "a", and a triple arrow-up notation with (k + 1) levels is equal to "a" raised to the power of a triple arrow-up notation with "k" levels.

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Complete Question: ( Refer to image)

The calculated volume of the prism is 702 cubic cm

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

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

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Answer:

Step-by-step explanation:

use Y- Y1 = m ( X - X1 )

3.

y1 = 2

x1= -4

m= 3

Y- Y1 = m ( X - X1 )

y - 2 = 3 (x + 4)

y-2= 3x + 12

y = 3x + 14

4.

y1= -1

x1= 6

m = -1

Y- Y1 = m ( X - X1 )

y + 1 = -1 (x - 6)

y + 1 = -x + 6

y = 5 - x

The two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion. We denote the similarity of triangles here by ‘~’ symbol.

It is given that two triangles that are JKL and MNP are considered in which:

Now, from ΔJKL and ΔMNP, we have

∠K = ∠N (Given in the question)

∠L = ∠P(Given in the question)

Thus, by AA rule of similarity,

ΔJKL is similar to ΔMNP.

Therefore, the two considered triangles JKL and MNP are similar by the AA rule of similarity as the two angles that is ∠K = ∠N and ∠L = ∠P are there.

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Answer:

  acute

Step-by-step explanation:

An acute angle measures less than 90°.

1. Written as a power, the expression for the volume of the artifact cube is 3w³.

2. A simple expression for the case's volume is 27w³.

The volume of a cube is the total space enclosed by the cube in a three-dimensional space.

The volume of a cube is given as a³ where a is each side length.  The dimensions for volume include the length, width, and height, which for a cube are equal.

The width of the artifact = w

Each side of the display cube = 3w

The volume of the display cube = 3w x 3w x 3w

= 3w³

= 27w

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\(\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=15\pi \end{cases}\implies 15\pi =2\pi r\implies \cfrac{15\pi }{2\pi }=r\implies \cfrac{15}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{15}{2} \end{cases}\implies A=\pi \left( \cfrac{15}{2} \right)^2\implies A=\cfrac{225\pi }{4}\implies A=56.25\pi\)

Answer:

36%

Step-by-step explanation:

25÷100=0.25

1% = 0.25

9÷0.25=36

Answer:

0.92

Step-by-step explanation:

Hope this helps!

Answer:

0.92

Step-by-step explanation:

0.60 + 0.20 = 0.80

0.04 + 0.08 = 0.12

0.80 + 0.12 = 0.92

Answer:

I assume around 700 people vist the zoo

Answer:

B

Step-by-step explanation:

rewrite 1.27 in the calculater and math enter enter

Answer: only 2 groups of 8

Step-by-step explanation: because your dividing and 8 goes into 19 only twice but there would still be 1 volunteer left

Hope it helps :)

\(x + 4y = 9 \\

-x - 2y = 3 \\ eliminate \: one \: variable \: by \\ adding \: the \: equations \\ 2y = 12 \\ divide \: both \: sides \\ y = 6 \\ substitute \: the \: value \: of \: y \\ \: into \: equation \: ...2 \\ - x - 2(6) = 3 \\ solve \: the \: equation \\ - x - 12 = 3 \\ - x = 3 + 12 \\ - x = 15 \\ x = - 15 \\ SOLUTION \\ x = - 15 \\ y = 6 \\ Hope \: it \: helps :)\)

Answer:

The graph below shows the answer to

2x - 3y < 12

Also shown as

-3y < -2x + 12

Step-by-step explanation:

You can rearrange the inequality by subtracting 2x from both sides to isolate the y.

You now have -3y < 12 -2x

which can be put into the standard linear equation form of

-3y < -2x + 12

Then you divide both sides by -3 to get singular value of y, which is something like

-3/-3y < -2/-3x + 12/-3

which is

y > 2/3x -4

Note: I switched direction of the inequality because you are dividing both sides by a negative value.

After answering the provided question, we can conclude that The slope answer is not listed as a choice, but this is the correct equation.

In mathematics, slope is the slope of the regression of a line or curve. It is a measure of the degree to which a function's y-value varies once the x-value changes. A line's slope is usually expressed as a letter m and is able to be calculated as follows: m = (y2 - y1) / (x2 - x1) (x1, y1) and (x2, y2) is some two important points on the line. The slope of a line can be favorable, negative, equal to 0, or unknown. A positive slope means the line rises up from left to right, whereas a slope means the line falls back from left to right.

To find the equation of the line passing through the point (4,-5) with slope 2, we can use the point-slope form of the equation of a line.

y - y1 = m(x - x1)

y - (-5) = 2(x - 4)

y + 5 = 2x - 8

y = 2x - 13

y = 2x - 13

The answer is not listed as a choice, but this is the correct equation.

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the answer is 10.125

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

using the rule of logarithms

\(log_{b}\) x = n ⇒ x = \(b^{n}\)

given

\(log_{3}\) (2x + 5) = 3 , then

2x + 5 = 3³ = 27 ( subtract 5 from both sides )

2x = 22 ( divide both sides by 2 )

x = 11

Answer

the best answer is D

Answer:

  $50,000

Step-by-step explanation:

The given relations can be used to write and solve an equation for the amount invested in stocks.

Let s represent the amount invested in stocks. Then (120,000-s) is the amount invested in bonds. The total earnings by the two investments were ...

  0.18s +0.12(120,000 -s) = 17,400

Simplifying the equation, we have ...

  0.06s +14,400 = 17,400

  0.06s = 3000 . . . . . . . . . . subtract 14,400

  s = 50,000 . . . . . . . . . . . . divide by 0.06

Neal invested $50,000 in stocks.

__

Additional comment

The amount invested in bonds was 70,000. The profit earned was ...

  0.18(50,000) +0.12(70,000) = 9,000 +8,400 = 17,400

The number of defective bulbs in shipment is 25+33=58bulbs.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Median represents the middle value of the given data when arranged in a particular order.

We are given that;

Mean of yellow bulb= 6.6

Mean of green bulb= 5

Now,

For 1000 yellow bulb

=1000/200

=5

Mean= 5*6.6

=33

For 1000 green bulb

=1000/200

=5

Mean= 5*5

=25

Therefore, the mean of green and yellow bulb will be 25 and 33.

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The cost of 9 smoothies at the rate is $87.75.

Rate demonstrates how many times one number can fit into another number. It contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point to another data point

In this case, three smoothies cost $9.75. The cost of 9 smoothies will be:

= $9.75 × 9

= $87.75

The cost is $87.75.

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Answer:

4 e

Step-by-step explanation:

dz6dxrx xrrx6 xz33x4xr4x xrx

Answer: x = -3/2 , x = -1 1/2 , x = -1.5

Step-by-step explanation:

6/-4.5 = 8/4x

first determine the defined range --> x ≠ 0

cancel out the common factor 4 --> 6/-4.5 = 2/x

the convert the decimal into a fraction --> 6/-9/2 = 2/x

now use -a/b = a/-b = -a/b to rewrite the fraction --> 6/-9/2 = 2/x

then simplify the complex fraction --> -4/3 = 2/x

simplify the equation using cross-multiplication --> -4x=6

divide both side of the equation by -4 --> x = -3/2 , x ≠ 0

lastly, check if the solution is in the defined range --> x = -3/2

solution : x = -3/2

Alternative form: x = -1 1/2 , x = -1.5 (simplified)

The increase will be the original price x the increase rate.

15649 x 0.035 = $547.72

The new price would be original price + increase

15649 + 547.72 = $16,196.72

Answer:

The answer is a

Step-by-step explanation:

it’s a because each dude is 1/2 and you add another one half that’s one and you keep on doing until the last one.

brainliest pls

I hope this helped and was right.

Step-by-step explanation:

Length: 6

width: 4

height:3

Formula :

Volume= l x w x h

6x4x3 =72

72 x 1/2= 36in3/A

Answer:

ggg

Step-by-step explanation:

gggggg

Answer:

angle ced is a right ange

so the m angels debate =135 m angle aeb =35

so the answer is 135+35 =170

180 is a all side sim

=180-170=10 answer

Answer:

∠CED is a right angle.

∠CEA is a right angle.

m∠CEB = m∠BEA

m∠DEB = 135°

Answer:

1. The wind has blown all the leaves off the tree.

2. All the leaves have fallen to the ground.

3. My kite is being flown in the wind.

4. A shower of acorns have fallen from the sky

5. A busy squirrel dug for his acorns.

6. In the garden, pumpkins have grown.

7. Yesterday my friend and I rode to the park.

8. We have rode to the skate park.

9. My brother wrote me a letter.

10. He has written a essay.

11. Our neighbor had given us a pie.

12. Mom and Dad have spoken to me about cleaning my room.

Step-by-step explanation:

Based on Amy Schorling's driver rating factor, vehicle classification and bodily injury coverage, her annual premium is $576.46.

If she includes the $50-deductibel collision coverage, her insurance premium becomes $1,067.08.

At $25,000 property damage, her 25/50 bodily injury coverage premium is $206.40.

This should be added to her $50 comprehensive deductible D-14 vehicle classification of $105.20.

Annual base premium:

= 206.40 + 105.20

= $311.60

Annual premium:

= Annual base premium x Driver rating factor

= 311.60 x 1.85

= $576.46

The annual base premium becomes:

= 311.60 + 265.20

= $576.80

Annual premium becomes:

= 576.80 x 1.85

= $1,067.08

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