26. Let S be the subset of the set of ordered pairs of integers defined recursively by
Basis step: (0, 0) ∈ S.
Recursive step: If (a, b) ∈ S, then (a + 2, b + 3) ∈ S and (a + 3, b + 2) ∈ S.
a) List the elements of S produced by the first five applications of the recursive definition.
b) Use strong induction on the number of applications of the recursive step of the definition to show that 5 | a + b when (a, b) ∈ S.
c) Use structural induction to show that 5 | a + b when (a, b) ∈ S

Answer:

Choice D

Step-by-step explanation:

(x-1)²

Choice D is accurate.

Answer:

Equation A is not equivalent in the options given .

To evaluate the line integral ∫ γ y^2 dz + x^2 dy along the given paths, we need to parameterize each path and compute the corresponding integrals.

(a) Path along the arc of the parabola y = x^2:

We can parameterize this path as γ(t) = (t, t^2) for t in the interval [0, 2].

The line integral becomes:

∫ γ y^2 dz + x^2 dy = ∫[0,2] t^4 dz + t^2 x^2 dy

To express dz and dy in terms of dt, we differentiate the parameterization:

dz = dt

dy = 2t dt

Substituting these expressions, the line integral becomes:

∫[0,2] t^4 dt + t^2 x^2 (2t dt)

= ∫[0,2] t^4 + 2t^3 x^2 dt

= ∫[0,2] t^4 + 2t^5 dt

Integrating term by term, we have:

= [t^5/5 + t^6/3] evaluated from 0 to 2

= [(2^5)/5 + (2^6)/3] - [0^5/5 + 0^6/3]

= [32/5 + 64/3]

= 192/15

= 12.8

Therefore, the line integral along the arc of the parabola y = x^2 is 12.8.

(b) Path along the horizontal interval followed by the vertical interval:

We can divide this path into two segments: γ1 from (0, 0) to (2, 0) and γ2 from (2, 0) to (2, 4).

For γ1, we have a horizontal line segment, and for γ2, we have a vertical line segment.

For γ1:

Parameterization: γ1(t) = (t, 0) for t in the interval [0, 2]

dz = 0 (since it is a horizontal segment)

dy = 0 (since y = 0)

The line integral along γ1 becomes:

∫ γ1 y^2 dz + x^2 dy = ∫[0,2] 0 dz + t^2 x^2 dy = 0

For γ2:

Parameterization: γ2(t) = (2, t) for t in the interval [0, 4]

dz = dt

dy = dt

The line integral along γ2 becomes:

∫ γ2 y^2 dz + x^2 dy = ∫[0,4] t^2 dz + 4^2 dy

= ∫[0,4] t^2 dt + 16 dt

= [t^3/3 + 16t] evaluated from 0 to 4

= [4^3/3 + 16(4)] - [0^3/3 + 16(0)]

= [64/3 + 64]

= 256/3

≈ 85.33

Therefore, the line integral along the horizontal and vertical intervals is approximately 85.33.

(c) Path along the vertical interval followed by the horizontal interval:

We can divide this path into two segments: γ3 from (0, 0) to (0, 4) and γ4 from (0, 4) to (2, 4).

For γ3:

Parameterization: γ3(t) = (0, t) for t in the interval [0, 4]

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Step-by-step explanation:

First sentence

Let the number be X

second sentence

X-5

Third sentence

X-5=14

X=19

The number is 19

Hi there!  

»»————-　★　————-««

I believe your answer is:

19

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(\text{"I am thinking of a number. l take away 5. The result is 14."}\\\\\text{5 taken away from 'said number' would be 14.}\\\\\boxed{n-5=14}\\\\\\\boxed{\text{Solving for 'n'...}} \\\\\rightarrow n - 5 + 5 = 14 + 5\\\\\rightarrow \boxed{n = 19}\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

c

Step-by-step explanation:

Because it shows 6 with the 10 therefore there are going to be 10 zeros so thag would mean that its c

The ratio of the blue fish in the small tank to red fish in the large tank is 10 to 69.

Ratio is the relationship between two quantities.

Let x : y = ratio of the blue fish in the small tank to red fish in the large tank

Hence, there are x blue fish in the small tank for every y red fish in the large tank.

If in each tank, the ratio of red fish to blue fish is 3 to 4, then in each tank, in terms of x and y, the ratio is:

small tank :

red : blue = 3 : 4 = (3/4)x : x

large tank :

red : blue = 3 : 4 = y : (4/3)y

If the ratio of fish in the large tank to fish in the small tank is 46 to 5, then

(y + (4/3)y) : ((3/4)x + x) = 46 : 5

Simplifying the proportion,

(y + (4/3)y) : ((3/4)x + x) = 46 : 5

(7/3)y : (7/4)x = 46 : 5

(161/2)x = (35/3)y

x/y = (35/3) / (161/2)

x/y = x : y = 10 : 69

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Answer:

Option D is the correct option.

solution,

Probability that you are given to lead role:

\( \frac{probability \: you \: are \: chosen \: to \: be \: in \: team\: }{probability \: that \: you \: are \: chosen \: to \: lead}\)

\( = \frac{0.1}{0.5} \\ = 0.2\)

hope this helps...

Good luck on your assignment..

Answer:

1/4 inches

Step-by-step explanation:

To get 4 equal pieces you need to cut the 2 equal pieces in half, which half of 1/2 inches is 1/4 inches.

a. the safe speed for this curve is approximately 45.1 km/h.

b. the stations for PC and PT are approximately 02+506.7864 and 02+146.55, respectively.

c. the minimum Horizontal Side Offset Clearance for Sight Distance is approximately 2.504 meters.

d. The lane widening in the curve is approximately 9.73 meters.

e. the transition length (Superelevation Runoff length) is approximately 154 mm.

f. The maximum service volume for this curved segment (LOS-C) depends on various factors such as the number of lanes, lane width, and design vehicle (WB20)

To determine the various values and parameters for the given curved segment, we'll follow the steps outlined below:

a. The safe speed for the curve can be calculated using the formula:

V = √(R * g * e)

Where:

V = Safe speed (in km/h)

R = Radius of the curve (in meters)

g = Acceleration due to gravity (approximately 9.8 m/s²)

e = Super elevation (%)

Given:

R = 200 m

e = 8% (converted to decimal: 0.08)

Substituting the values into the formula:

V = √(200 * 9.8 * 0.08) ≈ √156.8 ≈ 12.52 m/s ≈ 45.1 km/h

Therefore, the safe speed for this curve is approximately 45.1 km/h.

b. The stations for the Point of Curvature (PC) and the Point of Tangency (PT) can be calculated using the given STAPI (Station at the Point of Intersection) and the I (Intersection Angle).

Given:

STAPI = 02+146.55

I = 360° 14' 11" (converted to decimal: 360.2364°)

To calculate the stations for PC and PT, we add the Intersection Angle to the STAPI:

STAPC = STAPI + I

STAPT = STAPI

Substituting the values:

STAPC = 02+146.55 + 360.2364 ≈ 02+506.7864

STAPT = 02+146.55

Therefore, the stations for PC and PT are approximately 02+506.7864 and 02+146.55, respectively.

c. The minimum Horizontal Side Offset Clearance for Sight Distance can be calculated using the formula:

S = 0.2V

Where:

S = Minimum Side Offset Clearance (in meters)

V = Safe speed (in m/s)

Given:

V = 12.52 m/s

Substituting the value into the formula:

S = 0.2 * 12.52 ≈ 2.504 m

Therefore, the minimum Horizontal Side Offset Clearance for Sight Distance is approximately 2.504 meters.

d. The lane widening in the curve can be calculated using the formula:

W = V * (1 - (1 / √(1 + R / K)))

Where:

W = Lane widening (in meters)

V = Safe speed (in m/s)

R = Radius of the curve (in meters)

K = Rate of change of lateral acceleration (typically 9.81 m/s²)

Given:

V = 12.52 m/s

R = 200 m

K = 9.81 m/s²

Substituting the values into the formula:

W = 12.52 * (1 - (1 / √(1 + 200 / 9.81))) ≈ 12.52 * (1 - (1 / √(20.36))) ≈ 12.52 * (1 - (1 / 4.513)) ≈ 12.52 * (1 - 0.2217) ≈ 12.52 * 0.7783 ≈ 9.73 m

Therefore, the lane widening in the curve is approximately 9.73 meters.

e. The transition length (Superelevation Runoff length) can be calculated using the formula:

L = (V² * T) / (127 * e)

Where:

L = Transition length (in meters)

V = Safe speed (in m/s)

T = Rate of superelevation runoff (typically 0.08 s/m)

e = Super elevation (%)

Given:

V = 12.52 m/s

T = 0.08 s/m

e = 8% (converted to decimal: 0.08)

Substituting the values into the formula:

L = (12.52² * 0.08) / (127 * 0.08) ≈ 1.568 / 10.16 ≈ 0.154 m ≈ 154 mm

Therefore, the transition length (Superelevation Runoff length) is approximately 154 mm.

f. The maximum service volume for this curved segment (LOS-C) depends on various factors such as the number of lanes, lane width, and design vehicle (WB20). Without additional information, it's not possible to determine the maximum service volume accurately. Typically, a detailed traffic analysis is required to determine LOS (Level of Service) for a curved segment based on traffic demand, lane capacity, and other factors.

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The point x=0 is a regular singular point, x=1 is an irregular singular point, and x=4 is an ordinary point.

To determine the type of each point, we need to find the indicial equation and examine its roots.

At x=0, the equation becomes (16-x²)³ x y'' - 2x² y' = 0, which is of the form x²(16-x²)³ y'' - 2x³(16-x²) y' = 0. By inspection, we can see that x=0 is a regular singular point.

At x=1, the equation becomes (225)(x-1)y'' - 2xy' = 0, which is of the form (x-1)y'' - (2x/15)y' = 0 after dividing by (225)(x-1). The coefficient of y' is not analytic at x=1, so x=1 is an irregular singular point.

At x=4, the equation becomes 0y'' - 32x y' = 0, which is of the form y' = 0 after dividing by -32x. Since the coefficient of y' is analytic at x=4, x=4 is an ordinary point.

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Answer: C. 16:28 & E. 20:35

Please mark as brainliest!

Answer:

Option A , Option E and Option C are the same.

Step-by-step explanation:

Option A :

\(4:7\)

Can not be simplified further

Option B :

\(8:15\)

Can not be simplified further

Option C :

\(16:28 \\ = \frac{16}{28} = \frac{4}{7} \\ 4:7\)

Option D :

\(2:3\)

Can not be simplified further

Option E :

\(20:35 \\ = \frac{4}{7} \\ 4:7\)

Can not be simplified further

Answer:

500 cubic feet

Step-by-step explanation:

5 * 20 * 5 = 500 cubic feet

Answer: 83.5

Step-by-step explanation:

\(\frac{\sin x}{34}=\frac{\sin 26^{\circ}}{15} \\\\\sin x=\frac{34 \sin 26^{\circ}}{15}\\\\x=sin^{-1} \left(\frac{34 \sin 26^{\circ}}{15} \right) \approx \boxed{83.5}\)

Answer:

  x ≈ 83.5° or 96.5°  (two possible values)

Step-by-step explanation:

The relationship between side lengths of a triangle and their opposite angles is given by the Law of Sines: side lengths are proportional to the sines of their opposite angles.

__

In this problem, the Law of Sines tells us ...

  sin(A)/BC = sin(C)/AB

  sin(C) = sin(A)·AB/BC

Using x for angle C, solving for x, and using the inverse sine function, we find ...

  x = arcsin(sin(26°)·34/15) ≈ arcsin(0.993641)

The arcsine function returns a value in the range 0–90°, but the supplemental angle in the rangle 90°–180° can have the identical sine value.

  x ≈ 83.5° or 96.5°

_____

Additional comment

For the graph in the attachment, we have set the angle mode to degrees. The solutions to f(x)=0 are solutions to the problem: 83.5° and 96.5°.

The triangle in the figure appears to be an acute triangle. The value of x for an acute triangle would be 83.5°. Often, we cannot take these figures at face value.

Answer:

$21.25

Step-by-step explanation:

100 - 15 = 85

25 * 0.85 = 21.25

Answer:

w^3(4 + u^2)(2 + u)(2 - u)

Step-by-step explanation:

6w^3 – u^4w^3

w^3(16 – u^4)

w^3(42 - ((u^2)^2)

w^3(4 + u^2)(4 - u^2)

w^3(4 + u^2)(22 - u^2)

w^3(4 + u^2)(2 + u)(2 - u)

To find slope, we must use the slope formula*.

\(m = \frac{2 - 0.5}{2 - (-2.5)} = \frac{1.5}{4.5}\)

The slope is 1.5/4.5.

For the first part, the number of license plates is: 65,780,800 and for the second part, the number of license plates with 3 consecutive digits is: 16,524,288.

If there are no restrictions on where the digits and letters are placed, the number of 8-place license plates consisting of 5 letters and 3 digits with no repetitions allowed can be found using the permutation formula:

nPr = n! / (n-r)!

where n is the number of available characters (26 letters and 10 digits) and r is the number of characters needed for the license plate (8).

Therefore, the number of license plates is:

(26 P 5) x (10 P 3) = (26!/21!) x (10!/7!) = 65,780,800

If the 3 digits must be consecutive, there are 8 possible positions for the block of digits (either the first 3, second 3, or last 3). Once the position of the block is chosen, the number of license plates can be found by counting the number of ways to arrange the letters and the block of digits. The number of ways to arrange the letters is 26 P 5, and the number of ways to arrange the block of digits is 10 (since there are only 10 possible sets of consecutive digits).

Therefore, the number of license plates with 3 consecutive digits is:

8 x (26 P 5) x 10 = 16,524,288

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The complete question goes thus:

If there are no restrictions on where the digits and letters are placed, how many 8

-place license plates consisting of 5

letters and 3

digits are possible if no repetitions of letters or digits are allowed? What if the 3

digits must be consecutive?

Answer: If the x2-9 is x^2-9, then this is the answer. If not and it's supposed to be 2x then the answer is x=2 or x=−7 or x=9/2

Step-by-step explanation:

3(x−2)(x2−9)(x+7)=0

3x4+15x3−69x2−135x+378=0

Step 1: Factor left side of equation.

3(x−2)(x+3)(x−3)(x+7)=0

Step 2: Set factors equal to 0.

x−2=0 or x+3=0 or x−3=0 or x+7=0

x=2 or x=−3 or x=3 or x=−7

Answer:

w = 33

Step-by-step explanation:

w ÷ 3.3 = 10

multiply both sides by 3.3:

w ÷ 3.3 x 3.3 = 10 x 3.3

⇒ w = 33

Answer:

ranalllldooo

Step-by-step explanation:

suiiiiiii

Answer:

$154.07

Step-by-step explanation:

\(\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

First find the Future Account Value (target amount) you need at the beginning of your retirement in order to earn $50,000 of interest each year whilst leaving the principal untouched.

Given:

Substitute the values in the compound interest formula to find the Future Account Value:

\(\implies P+50000=P\left(1+\dfrac{0.11}{12}\right)^{12 \cdot 1}\)

\(\implies P+50000=P\left(\dfrac{1211}{1200}\right)^{12}\)

\(\implies 50000=P\left(\dfrac{1211}{1200}\right)^{12}-P\)

\(\implies 50000=P\left(\left(\dfrac{1211}{1200}\right)^{12}-1\right)\)

\(\implies P=\dfrac{50000}{\left(\left(\dfrac{1211}{1200}\right)^{12}-1\right)}\)

\(\implies P=432081.77\)

Therefore, the Future Account Value needed at the beginning of your retirement is $432,081.77 to allow you to earn $50,000 per year from interest alone.

\(\boxed{\begin{minipage}{8.5 cm}\underline{Savings Plan Formula}\\\\$ FV=PMT\left[\dfrac{\left(1+\frac{r}{n}\right)^{nt}-1}{\frac{r}{n}} \right]$\\\\where:\\\\ \phantom{ww}$\bullet$ $FV =$ future value\\ \phantom{ww}$\bullet$ $PMT =$ periodic payment \\ \phantom{ww}$\bullet$ $r =$ APR (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ years \\ \phantom{ww}$\bullet$ $n =$ number of payments per year \\ \end{minipage}}\)

Given:

Substitute the values into the Savings Plan formula and solve for PMT to find the monthly payments:

\(\implies 432081.77=PMT\left[\dfrac{\left(1+\frac{0.11}{12}\right)^{12 \cdot 30}-1}{\frac{0.11}{12}} \right]\)

\(\implies 432081.77=PMT\left[\dfrac{\left(\frac{1211}{1200}\right)^{360}-1}{\frac{11}{1200}} \right]\)

\(\implies 432081.77=PMT\left[2804.519736 \right]\)

\(\implies PMT=\dfrac{432081.77}{2804.519736}\)

\(\implies PMT=154.0662255\)

Therefore, you should deposit $154.07 at the end of each month to be able to withdraw $50,000 per year from interest alone at the end of each year after you retire in 30 years.

Answer: The answer to this question is 5. The picture will explain

we have: ∠P + ∠Q + ∠R = 180°

<=> (4x – 14)º + (5x + 6)° + (x - 2)° = 180°

<=> 4x – 14 + 5x + 6 + x - 2 = 180°

<=> 10x - 10 = 180°

<=> 10x = 190

<=> x = 19°

So: ∠R = (x - 2)° = (19 - 2)° = 17°

ok done. Thank to me :>

Answer:

h = 4

Step-by-step explanation:

Calculate the slope m using the slope formula and equate to 2

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = M (h, 3 ) and (x₂, y₂ ) =  N (- 2, - 9 )

m = \(\frac{-9-3}{-2-h}\) = \(\frac{-12}{-2-h}\) , then

\(\frac{-12}{-2-h}\) = 2 ( multiply both sides by - 2 - h )

2(- 2 - h) = - 12 ( divide both sides by 2 )

- 2 - h = - 6 ( add 2 to both sides )

- h = - 4 ( multiply both sides by - 1 )

h = 4

The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed

The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.

To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.

On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.

So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.

Therefore, the correct answer is: The total number of tasks Terrence completed.

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Answer:

-1 = x              1 = x  

Step-by-step explanation:

We want to factor this first

-4x^2 = -4

x^2=1

sqrt x^2 = sqrt 1

x = ± 1

x=-1        x=1

The value of z* that should be used to construct a 90% confidence interval of a population mean is 1.65.

The value of z* that should be used to construct a 90% confidence interval of a population mean depends on the level of significance or alpha (α) we choose.

Since we want to construct a 90% confidence interval, the level of significance or alpha (α) can be calculated as:

α = 1 - confidence level = 1 - 0.9 = 0.1

We divide alpha (0.1) equally among the two tails of the standard normal distribution to get the critical value, which is denoted by z*. We can find z* by using a standard normal distribution table.

For a two-tailed test with a 0.1 level of significance, the critical value z* can be found as follows:

z* = 1 - (0.1 / 2) = 0.95

Using a standard normal distribution table, we find that the z-score corresponding to 0.95 is 1.645, rounded to the hundredth place.

Therefore, the answer is a.) 1.65.

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