If gdp is $20 trillion how many years will it take for a gdp to increase to 80$ trillion if growth is 7 percent

The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

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Answer:

185 anle with the postive measure and a negative measure

Answer:

abc = - 126

Step-by-step explanation:

(2x + 3)(3x - 1) ← expand product using FOIL

= 6x² + 7x - 3 ← in standard form

with a = 6, b = 7, c = - 3

Then

abc = 6 × 7 × (- 3) = - 126

Answer:2x(3-1) +3(3x-1)

6x^2 -2x+9x-3

6x^2+7x-3

a=6 b=7 c=3

product (x)=6x7x-3=-126

Answer:

D

Step-by-step explanation:

Answer:

39.44

Step-by-step explanation:

Answer:

39.4418605

Step-by-step explanation:

One of the options is c=d because matching angles are made and the same corners are congruent when a line joins two parallel lines.

In geometry, parallel lines are coplanar, straight lines that don't intersect anywhere. Parallel planes are those in the same three-dimensional space that never cross one another. Curves do not touch or intersect when they are parallel to one another and keep a predetermined minimum distance between them. Lines in a plane are considered to be parallel if their spacing is constant. Objects cannot cross parallel lines. Perpendicular lines are those that intersect at a precise angle of 90 degrees.

Due to vertical angles, A = d is also a possible answer. The outcome is that b+d=180 since b+c=180 and c=d, and b+d=180 as a result. Therefore, the answer is B, C, E, where a=d, c=d, and b+d=180.

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Answer:

x = 11

z = 86

Step-by-step explanation:

8x + 6 and 10x-16 are vertical angles

Vertical angles are pairs of angles that are opposite each other and have the same vertex, or point of intersection. They are formed when two lines intersect at a point, and are always congruent, or of equal measure.

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by subtracting 6 from both sides of the equation:

8x + 6 - 6 = 10x - 16 - 6

8x = 10x - 22

Now we can subtract 8x from both sides of the equation:

8x - 8x = 10x - 22 - 8x

0 = 2x - 22

To solve for x, we can add 22 to both sides of the equation:

0 + 22 = 2x - 22 + 22

22 = 2x

Finally, we can divide both sides of the equation by 2 to find the value of x: 22 / 2 = 2x / 2

x = 11

Therefore, the solution to the equation is x = 11.

Now that we have x, z is a supplementary angle to 8x + 6 (or you could do 10x - 16)

Supplementary angles are pairs of angles that add up to 180 degrees. They are formed when two lines intersect at a point, and the angles formed at the intersection are supplementary.

First plug in x, 8x + 6 = 8(11) + 6 = 88 + 6 = 94

180 - 94 = z

z = 86

Answer:

£225

Step-by-step explanation:

12.5% × £200

>> £25

Since we want to increase £200 by 12.5%, then we will add the increment to the £200 to get;

£200 + £25 = £225

Answer: £25

Step-by-step explanation: Take £200 and multiply by 12.5% and you get  £25. I hope this helped!

Answer: C

Step-by-step explanation: The answer is C because x is equivalent to 10 in both problems. X is equal to 10 in the problem 2x + 7 =27 because 2 x 10 = 20 + 7 = 27. X is also equal to 10 in the problem 5x - 15 = 35 because 5 x 10 = 50 - 15 = 35. This means the answer is C.

Answer:

1500

Step-by-step explanation:

18 = 1.2%

100% ÷ 1.2% = 83 and 1/3

1.2% × 83 and 1/3 = 100%

18 × 83 and 1/3 = 1500

The slope intercept form has the next form

We have

we need to isolate the y

ANSWER

y=3x-3

Answer: 41/75 or 54.67%

Step-by-step explanation:

Buttons --- yes,  zips --- yes = 45  (compute as 150 - 37 - 45 - 23)

Buttons --- yes,  zips --- no  = 37

Buttons --- no, zips --- yes = 45

Buttons --- no, zips --- no = 23

Therefore, 82 out of 150 bags have buttons so probability = 82/150 = 41/75

Yes, its true that the questionnaire is very carefully constructed by an individual to provide the measurement instrument.  

A questionnaire is a studies device which includes a sequence of questions for the motive of amassing facts from respondents. Questionnaires may be concept of as a form of written interview. A questionnaire is a listing of questions or gadgets used to collect facts from respondents approximately their attitudes, experiences, or opinions.

Questionnaires may be used to acquire quantitative and/or qualitative facts. Questionnaires are generally utilized in marketplace studies in addition to withinside the social and fitness sciences. Questionnaires are typically taken into consideration to be excessive in reliability. This is due to the fact it's miles feasible to invite a uniform set of questions. Any troubles withinside the layout of the survey may be ironed out after a pilot study. The greater closed questions used, the greater dependable the studies.

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Answer:

The interval notation for the set of all numbers greater than or equal to 1 and less than 6 is [1, 6).

Step-by-step explanation:

Answer:

√441=21

√361=19

√401=20.02 or 20

The planned order releases for each item are as follows: A: 20 units in period 1, B: 10 units in period 1, C: 40 units in period 3, D: No planned order release, E: 100 units in period 5, F: 100 units in period 5

To determine the planned order releases for all items, we need to calculate the net requirements for each period based on the given information. We will start with the highest-level item and work our way down the bill of materials.

Item A:

Period 1: Gross requirement of 20 units.

Since A uses lot-for-lot (L4L) as the lot-sizing technique, we release an order for 20 units of A.

Item B:

Item B is a component of A, and each A requires 2 units of B.

We need to calculate the net requirements for B based on the planned order release for A.

Period 1: Gross requirement of 20 units * 2 (requirement multiplier for B) = 40 units.

B has a scheduled receipt of 30 units in period 1.

Net requirement for B in period 1: 40 units - 30 units = 10 units.

Since B also uses L4L as the lot-sizing technique, we release an order for 10 units of B.

Item C:

Item C is a component of A, and each A requires 3 units of C.

We need to calculate the net requirements for C based on the planned order release for A.

Period 1: Gross requirement of 20 units * 3 (requirement multiplier for C) = 60 units.

C has a lead time of two periods, so we need to account for that.

Net requirement for C in period 3: 60 units - 20 units (scheduled receipt for A in period 1) = 40 units.

Since C uses L4L as the lot-sizing technique, we release an order for 40 units of C.

Item D:

Item D is a component of C, and each C requires 1 unit of D.

We need to calculate the net requirements for D based on the planned order release for C.

Period 3: Gross requirement of 40 units * 1 (requirement multiplier for D) = 40 units.

D has a lead time of one period, so we need to account for that.

Net requirement for D in period 4: 40 units - 60 units (scheduled receipt for C in period 3) = -20 units (no requirement).

Since the net requirement is negative, we do not release any planned order for D.

Item E:

Item E is a component of C, and each C requires 1 unit of E.

We need to calculate the net requirements for E based on the planned order release for C.

Period 3: Gross requirement of 40 units * 1 (requirement multiplier for E) = 40 units.

E has a lead time of two periods, so we need to account for that.

Net requirement for E in period 5: 40 units - 0 units (no scheduled receipt for E) = 40 units.

Since E requires a multiple of 100 to be purchased, we release an order for 100 units of E.

Item F:

Item F is a component of B and C, and each B requires 1 unit of F, while each C requires 2 units of F.

We need to calculate the net requirements for F based on the planned order releases for B and C.

Period 1: Gross requirement for B = 10 units * 1 (requirement multiplier for F) = 10 units.

Period 3: Gross requirement for C = 40 units * 2 (requirement multiplier for F) = 80 units.

F has a lead time of two periods, so we need to account for that.

Net requirement for F in period 5: 10 units + 80 units - 0 units (no scheduled receipt for F) = 90 units.

Since F requires a multiple of 100 to be purchased, we release an order for 100 units of F.

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Answer:

\(5.29 \times {10}^{1} \)

Expanding log(r^2 s^11)/t^14 = 2 loga(r) + 11 loga(s) - 14 loga(t)

To expand log(r^2 s^11)/t^14 using properties of logarithms, follow these steps:

Step 1: Apply the quotient rule. The quotient rule states that log(a/b) = log(a) - log(b). So we have: log(r^2 s^11) - log(t^14)

Step 2: Apply the product rule. The product rule states that log(ab) = log(a) + log(b). So we have: (log(r^2) + log(s^11)) - log(t^14)

Step 3: Apply the power rule. The power rule states that log(a^n) = n*log(a). So we have: (2*log(r) + 11*log(s)) - 14*log(t)

Thus, the expanded form of log(r^2 s^11)/t^14 is: 2*log(r) + 11*log(s) - 14*log(t)

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The number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

The number of calories that Darrell will burn in 1 minute while kayaking is obtained applying the proportions in the context of the problem.

For each input-output pair in the table, the constant of proportionality is of 4, hence the number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

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Step-by-step explanation:

Finding b

If we use the given slope and use one of the points to write the equation in point-slope form (y - y₁) = m(x - x₁)), we can rearrange it to find the y-intercept:

Using (4,4)  

                                ⇒  y - 4 =  - 0.5 (x - 4)

                                     y - 4 = - 0.5 x + 2

                                          y = -0.5 x + 6

Calculating 'n' and 'p'

We can find n and p by plugging the points into the newly found equation   y = -0.5 x + 6.

For n using (7, n)

             since  y = -0.5 x + 6

                        n = -0.5 (7) + 6

For p using (3,p)

               since y = -0.5 x + 6

                         p = - 0.5 (3) + 6

                         p = - 1.5 + 6

Checking the answer

We can check the answer we got in two ways:

         Using the points (4, 4) and (7, n) as (x₁, y₁) & (x₂, y₂)   respectively

         The slope of the line (m) = (y₂ - y₁) ÷ (x₂ - x₁)  

                               - 0.5  =  (n - 4) ÷ (7 - 4)

                               - 0.5 =  ⁿ⁻⁴/₃          [multiply both sides by 3]

                                - 1.5 = n - 4           [add four to both sides]

                                    n = 2.5     [this matches the value of n we found]

Answer:

  40

Step-by-step explanation:

Any solution x will mod 23 will also have x+23n as a solution, for some integer n. Since 900/23 = 39 3/23, we know there are 39 or 40 three-digit integers of this form.

As it happens, 100 is the smallest 3-digit solution. So, there are 40 three-digit numbers that are of the form 100 +23n, hence 40 solutions to the equation.

_____

The equation reduces, mod 23, to ...

  10x = 11

Its solutions are x = 23n +8.

Answer:

x= -0.5

Step-by-step explanation:

You want to isolate x on one side of the equation

15-12x=21

-15          -15

-12x=6

/-12     /-12

x= -0.5

Let \(\vec K,\vec L,\vec M,\vec N\) be vectors pointing the vertices K, L, M, and N, respectively.

The side KL is parallel to and has the same length as the vector

\(\vec L - \vec K = (2\,\vec\imath + 3\,\vec\jmath + 3\,\vec k) - (2\,\vec\imath+2\,\vec\jmath+\vec k) = \vec\jmath + 2\,\vec k\)

Similarly, the side KN is parallel and as long as

\(\vec N - \vec K = (6\,\vec\imath+8\,\vec\jmath+\vec k) - (2\,\vec\imath+2\,\vec\jmath+\vec k) = 4\,\vec\imath+6\,\vec\jmath\)

These vectors have magnitudes

\(\|\vec L - \vec K\| = \sqrt{0^2 + 1^2 + 2^2} = \sqrt5\)

\(\|\vec N - \vec K\| = \sqrt{4^2 + 6^2 + 0^2} = 2\sqrt{13}\)

and their dot product is

\((\vec L - \vec K) \cdot (\vec N - \vec K) = 0\cdot4 + 1\cdot6+1\cdot0 = 6\)

The parallelogram spanned by the vectors \(\vec L-\vec K\) and \(\vec N-\vec K\) has area equal to the magnitude of their cross product, for which we have the identity

\(\bigg\|(\vec L - \vec K) \times (\vec N - \vec K)\bigg\| = \|\vec L - \vec K\| \|\vec N - \vec K\| \sin(\theta) \\\\ \implies \text{area} = 2\sqrt{65} \, \sin(\theta)\)

where \(\theta\) is the angle between the sides KL and KN.

From the dot product identity, we have

\((\vec L - \vec K) \cdot (\vec N - \vec K) = \|\vec L - \vec K\| \|\vec N - \vec K\| \cos(\theta) \\\\ \implies 6 = 2\sqrt{65} \cos(\theta)\)

Then

\(\cos(\theta) = \dfrac3{\sqrt{65}} \implies \sin(\theta) = \sqrt{1-\cos^2(\theta)} = 2\sqrt{\dfrac{14}{65}} \\\\ \implies \text{area} = 2\sqrt{65} \cdot 2\sqrt{\dfrac{14}{65}} = \boxed{4\sqrt{14}}\)

Answer:

13/12

Step-by-step explanation:

Hope this helps <3

Answer:

answer is 1 1/12 is the correct answer

Answer:

$7

Step-by-step explanation:

Since 100/20 = 5, 20% is 1/5, so 20% of 35 is 35/5, or 7

Answer:

If someone leave a 20% tip and the meal is 35$how much was the tip :

$35.00 ÷ 20% = $7.00

Answer:

please give brainliest

Step-by-step explanation:

396.253521127

Answer:

360 inch^3

Step-by-step explanation:

Volume of 1 box = 1 x 1 x 9 = 9 inch^3

Volume of 40 boxes = 40 x 9 = 360 inch^3

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Answer:

360 in

Step-by-step explanation:

L × W × H

1 × 1 ×9 = 9in

9 × 40 = 360 in

A. The equations for the amounts of money Lyle and Shaun have in their accounts are represented as:

f(x) = 20x + 100

g(x) = 10x + 500

B. When f(x) = g(x), x = 40.

A linear equation can be written in slope-intercept form y = mx + b. Here, the value of m is the unit rate or slope, while the value of b is its y-intercept or initial value.

Part A:

Equation for Lyle:

y-intercept / initial value (b) = $100

Slope / unit rate (m) = $20

To write the equation, substitute m = 20 and b = 100 into f(x) = mx + b:

f(x) = 20x + 100.

Equation for Lyle:

y-intercept / initial value (b) = $500

Slope / unit rate (m) = $10

To write the equation, substitute m = 10 and b = 500 into g(x) = mx + b:

g(x) = 10x + 500.

Part B: To solve the system, we would do the following:

20x + 100 = 10x + 500

20x - 10x = -100 + 500

10x = 400

x = 400/10

x = 40

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