Which of these graphs is the solution set for the equation y = -4?

Answer:

x = 7

Step-by-step explanation:

Solve equation [2] for the variable  y

[2]    y = - 2

Plug this in for variable  y  in equation [1]

[1]    (-2) - 2x = -16

[1]     - 2x = -14

Solve equation [1] for the variable  x

[1]    2x = 14

[1]    x = 7

Solution:
y = -2
x = 7

The rule for the nth term of arithmetic sequence is a + (n - 1)d.

Here also,

We use the definition for the nth term of an arithmetic sequence:

an = a1 + (n - 1) d

Here first term (a1) = 51

common difference (d) = a2 - a1

                                      = 48 - 51

                                      = -3

We have to find 20th term,

a[20] = a1 + (20 - 1) d

         = 51 + 19 x -3

         = 51 - 57

         = - 6

Therefore 20th term of the sequence 51,48,45,42,... is -6.

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The general solution of the ODE 4y'' - 20y' + 25y = (1 + x + x²) cos(3x) is y = c₁ e²(2.5x) + c₂ x e²(2.5x) + A + Bx + Cx² + D cos(3x) + E sin(3x).The general solution of the ODE d²y + 49y = 2x² sin(7x) is y = c₁ e²(7ix) + c₂ e²(-7ix) + (Ax²+ Bx + C) sin(7x) + (Dx² + Ex + F) cos(7x).

Exercise 5: To find the general solution of the given ordinary differential equation (ODE), 4y'' - 20y' + 25y = (1 + x + x²) cos(3x)

Step 1: Find the complementary solution:

Assume y = e²(rx) and substitute it into the ODE:

4(r² e²(rx)) - 20(r e²(rx)) + 25(e²(rx)) = 0

Simplify the equation by dividing through by e²(rx):

4r² - 20r + 25 = 0

Solve this quadratic equation to find the values of r:

r = (20 ± √(20² - 4 ×4 × 25)) / (2 × 4)

r = (20 ± √(400 - 400)) / 8

r = (20 ± √0) / 8

r = 20 / 8

r = 2.5

y-c = c₁ e²(2.5x) + c₂ x e²(2.5x)

Step 2: Find the particular solution:

To find the particular solution the method of undetermined coefficients the particular solution has the form

y-p = A + Bx + Cx² + D cos(3x) + E sin(3x)

Substitute this into the ODE and solve for the coefficients A, B, C, D, and E by comparing like terms.

Step 3: Combine the complementary and particular solutions

The general solution is obtained by adding the complementary and particular solutions

y = y-c + y-p

Exercise 6: To find the general solution of the given ODE d²y + 49y = 2x² sin(7x),

Step 1: Find the complementary solution

Assume y = e²(rx) and substitute it into the ODE

(r² e²(rx)) + 49(e²(rx)) = 0

Simplify the equation by dividing through by e²(rx)

r² + 49 = 0

Solve this quadratic equation to find the values of r:

r = ±√(-49)

r = ±7i

The complementary solution is given by:

y-c = c₁ e²(7ix) + c₂ e²(-7ix)

Step 2: Find the particular solution:

To find the particular solution the method of undetermined coefficients  the particular solution has the form:

y-p = (Ax² + Bx + C) sin(7x) + (Dx² + Ex + F) cos(7x)

Substitute this into the ODE and solve for the coefficients A, B, C, D, E, and F

Step 3: Combine the complementary and particular solutions:

The general solution is obtained by adding the complementary and particular solutions:

y = y-c + y-p

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Answer:

≈ 5.6954

Step-by-step explanation:

Answer:

B. \(\frac{-3}{4}\)±\(\frac{\sqrt{41} }{4}\)

Step-by-step explanation:

First, substitute the equation into the quadratic formula.

\(x=\frac{b+-\sqrt{(b^{2} )-4(a)(c)} }{2a}\)

x=\(\frac{-3+-\sqrt{(3)^2-4(-2)(4)} }{4}\)

Solve for x.

x= \(\frac{-3+-\sqrt{9+32} }{4}\)

x=\(\frac{-3+-\sqrt{41} }{4}\)

The answer is x= \(-\frac{3}{4}\)±\(\frac{\sqrt{41} }{4}\)

Answer:

Hello! answer: 7

Heres an image to explain I hope this helps you!

Answer:

i belive th answer is 58

Step-by-step explanation:

so you have 3 right angles so thais 90 x 90x90

The probability of getting at least one question right is 96.875%.

The question states that at least one guess should be right. This ultimately means that all guesses cannot be wrong, which is the only possibility being excluded here.

Probability for wrong guess =12=0.5

Probability for all wrong guesses =0.5*0.5*0.5*0.5*0.5=0.03125 or 3.125%

There is only 3.125% chance of all wrong guesses. Rest of the possibilities are our favorable conditions, i.e. at least one correct guess.

Therefore,

Probability of at least one correct guess=1-0.03125=0.96875 or 96.875%

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The margin for the runners is 50% and the Margin percentage is 33.33% (to the nearest percent).

When the shop sells runners at a mark-up of 50%, we need to find out the margin for these runners.

What is markup?

The mark-up is a percentage that you add to the cost price of a product to get the selling price. The mark-up percentage is calculated based on the cost price of the product.

Let the cost price of the runner be CP and the markup percentage be M%

Since the shop is selling the runners at a 50% markup, the selling price of the runners would be 150% of their cost price.

Selling price = (100 + M)% × Cost priceSelling price = (100 + 50)% × CP = 150% × CP = 1.5 × CP

Therefore, the margin for the runners can be calculated as follows:

Margin = Selling price - Cost price

Margin = 1.5 × CP - CP = 0.5 × CP

Clearly, the margin on runners is 50% of their cost price.

The percentage of margin can be calculated as follows:

Margin percentage = (Margin / Selling price) × 100Margin percentage = (0.5 × CP / 1.5 × CP) × 100Margin percentage = (1/3) × 100Margin percentage = 33.33%

Therefore, the margin for the runners is 50% and the margin percentage is 33.33% (to the nearest percent).

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Step-by-step explanation:

Scores of Australia in all four matches starting from 1st 208, 192, 241, 203 respectively.

Similarly, scores of Pakistan in all four matches starting from 1st 102, 202, 360, 276 respectively.

The avg of  Pakistan in one match = (102+202+360+276)/4 = 235

The avg of  Australia in one match = (208+192+241+203)/4= 211

Since, the avg score of Pakistan is more than that of Australia, Pakistan performed better.

Answer:

41.2

Step-by-step explanation:

By the alternate interior angles theorem, the angle of depression is congruent to the angle of elevation.

This means that tan(27)=21/x.

x(tan 27)=21

x=21/(tan 27), which is about 41.2

The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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a. The expected potential profit for firm I is $60,000.

b. The expected potential profit for firms I and II together is $120,000.

In this scenario, there are three firms—firm I, firm II, and firm III—and two construction contracts that need to be randomly assigned. Each contract has a potential profit of $90,000.

To find the expected potential profit for firm I, we need to calculate the probability of firm I receiving one or both contracts and multiply it by the potential profit of each contract. Since the contracts are randomly assigned, firm I can receive one contract or both contracts.

If firm I receives only one contract, there are two possible scenarios: (1) firm I receives the first contract and firm II receives the second contract, or (2) firm II receives the first contract and firm I receives the second contract. Both scenarios have equal probabilities. In each scenario, firm I would earn a potential profit of $90,000.

If firm I receives both contracts, there is only one scenario with a probability of 1/3. In this case, firm I would earn a potential profit of $180,000.

To calculate the expected potential profit for firm I, we need to find the weighted average of the potential profits in each scenario, considering their probabilities. The probability of firm I receiving one contract is 2/3, and the probability of firm I receiving both contracts is 1/3.

Expected potential profit for firm I = (2/3) * $90,000 + (1/3) * $180,000

= $60,000

To find the expected potential profit for firms I and II together, we need to consider the scenarios where both firms receive one contract or both contracts.

If both firms receive one contract, there are two possible scenarios: (1) firm I receives the first contract and firm II receives the second contract, or (2) firm II receives the first contract and firm I receives the second contract. Both scenarios have equal probabilities. In each scenario, firm I and firm II would earn a potential profit of $90,000.

If both firms receive both contracts, there is only one scenario with a probability of 1/3. In this case, both firms would earn a potential profit of $180,000 each.

To calculate the expected potential profit for firms I and II together, we need to find the weighted average of the potential profits in each scenario, considering their probabilities. The probability of both firms receiving one contract is 2/3, and the probability of both firms receiving both contracts is 1/3.

Expected potential profit for firms I and II together = (2/3) * $90,000 + (1/3) * $180,000

= $60,000 + $60,000

= $120,000

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it would be 24 hours or 1 day long

Answer:

24 hours

Step-by-step explanation:

72 divided by 3

Finding the square root of non-perfect square numbers typically results in an irrational number, which has a non-repeating and non-terminating decimal representation.

Finding the square root of a number involves determining the value that, when multiplied by itself, gives the original number. Here are a few methods to find the square root:

Prime Factorization: This method involves breaking down the number into its prime factors. Pair the factors in groups of two, and take one factor from each pair. Multiply these selected factors to find the square root. For example, to find the square root of 36, the prime factors are 2 * 2 * 3 * 3. Taking one factor from each pair (2 * 3), we get 6, which is the square root of 36.

Estimation: Approximate the square root using estimation techniques. Find the perfect square closest to the number you want to find the square root of and estimate the value in between. Refine the estimate using successive approximations if needed. For example, to find the square root of 23, we know that the square root of 25 is 5. Therefore, the square root of 23 will be slightly less than 5.

Using a Calculator: Most calculators have a square root function. Simply input the number and use the square root function to obtain the result.

It's important to note that finding the square root of non-perfect square numbers typically results in an irrational number, which has a non-repeating and non-terminating decimal representation.

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The chemicals under considerationm an important quantity is the total proportion Y1 +Y2 found in any sample.V(Y1 + Y2) = Var(Y1) + Var(Y2) + 2Cov(Y1, Y2) = 1/18 + 1/18 + 2(1/144) = 5/72.

To find E(Y1 + Y2), we first find the marginal distribution of Y1 and Y2 by integrating the joint density function over the other variable as follows:

f1(y1) = ∫f(y1,y2)dy2 = ∫2dy2 from 0 to 1-y1 = 2(1-y1) for 0 ≤ y1 ≤ 1

f2(y2) = ∫f(y1,y2)dy1 = ∫2dy1 from 0 to 1-y2 = 2(1-y2) for 0 ≤ y2 ≤ 1

Now we can find E(Y1 + Y2) as follows:

E(Y1 + Y2) = ∫∫(y1 + y2)f(y1,y2)dy1dy2

= ∫∫(y1 + y2)2dy1dy2 over the region 0 ≤ y1 ≤ 1-y2, 0 ≤ y2 ≤ 1

E(Y1 + Y2) = ∫0^1∫0^(1-y1) (y1 + y2)2dy2dy1

= ∫0^1[y1(y1/2 + 2/3) + 1/3]dy1

= 7/12

To find V(Y1 + Y2), we can use the fact that V(Y1 + Y2) = V(Y1) + V(Y2) + 2Cov(Y1, Y2), where Cov(Y1, Y2) is the covariance of Y1 and Y2. First, we need to find the variances of Y1 and Y2:

Var(Y1) = E(Y1^2) - [E(Y1)]^2 = ∫∫y1^22dy1dy2 - [∫∫y1f(y1,y2)dy1dy2]^2

= ∫0^1∫0^(1-y1) y1^22dy2dy1 - [∫0^1(2y1-2y1^2)dy1]^2

= 1/18

Var(Y2) = E(Y2^2) - [E(Y2)]^2 = ∫∫y2^22dy1dy2 - [∫∫y2f(y1,y2)dy1dy2]^2

= ∫0^1∫0^(1-y2) y2^22dy1dy2 - [∫0^1(2y2-2y2^2)dy2]^2

= 1/18

Now we need to find the covariance of Y1 and Y2:

Cov(Y1, Y2) = E(Y1Y2) - E(Y1)E(Y2) = ∫∫y1y2f(y1,y2)dy1dy2 - (∫∫y1f(y1,y2)dy1dy2)(∫∫y2f(y1,y2)dy1dy2)

= ∫0^1∫0^(1-y1) 2y1y2dy2dy1 - (7/12)(7/12)

= 1/144

Therefore, V(Y1 + Y2) = Var(Y1) + Var(Y2) + 2Cov(Y1, Y2) = 1/18 + 1/18 + 2(1/144) = 5/72.

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The area of the quadrilateral given, can be found to be 84 square units

To find the area of the quadrilateral ABCD with vertices A(-8, 5), B(-2, -5), C(8, 1), and D(2, 11), we can divide it into two triangles, use the distance formula to find the lengths of the sides of the triangles:

Distance formula: d = √((x2 - x1)² + (y2 - y1)²)

AB = √((-2 - (-8))² + (-5 - 5)²) = √136

AC = √((8 - (-8))² + (1 - 5)²) = √272

Find the area of triangle ABC:

Area ABC = √(31.485 x (31.485 - √136) x (31.485 - √136) x (31.485 - √272)) = 42

Find the area of triangle ACD:

Area ACD = √(31.485 x (31.485 - √136) x (31.485 - √136) x (31.485 - √272)) = 42

Now, add the areas of the two triangles to find the area of the quadrilateral ABCD:

Area ABCD = 42 + 42

Area ABCD = 84 square units

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Compute the speed of the car:

\(\dfrac{2\pi\,\rm ft}{1\,\rm rev} \cdot \dfrac{13\,\rm rev}{1\,\rm s} \cdot \dfrac{1\,\rm mi}{5280\,\rm ft} \cdot \dfrac{3600\,\rm s}{1\,\rm h} = \dfrac{195\pi}{11} \dfrac{\rm mi}{\rm h} \approx 55.6919 \dfrac{\rm mi}{\rm h}\)

So after 1 hour, Sal will have driven about 56 mi.

Answer:

4

Step-by-step explanation:

When multiplying those fractions, you multiply the top (numerators) by each other and you'll get 60

Then when you divide the denominators you'll get 15.

60 divided by 15 is 4.

10/3 x 6/5 = 4

Step-by-step explanation:

You multiply the numerators together, same with the denominator. You get 60/15. You divide those numbers so you get 4 as your answer. Hope this helps!

Answer:

1.6x10^5

Step-by-step explanation:

moving decimal places 5 times to the left will give you an exponent of 5

1.6x10^5 has 2 sig figs (1 and 6)

comment your question if this is still unclear :))

In a 6-dimensional data cube with no hierarchies associated with any dimension, the total number of cuboids can be calculated as 63, using a formula based on the inclusion-exclusion principle.

For a 6-dimensional data cube, there are 2^6 - 1 = 63 non-empty subsets of dimensions. Each subset represents a cuboid. Therefore, there are 63 cuboids in a 6-dimensional data cube without any hierarchies associated with the dimensions.

This calculation is based on the concept that each subset of dimensions corresponds to a unique cuboid in the data cube. By summing up the cardinalities of all possible subsets, excluding the empty set, we arrive at the total count of 63 cuboids in the given scenario.

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A student club is designing a trebuchet to launch a pumpkin into projectile motion. The trajectory of the launched pumpkin is predicted to be parabolic, and can be described by the equation y(x). This means that as the pumpkin moves through the air, its path will follow a parabolic shape, which is common in projectile motion scenarios.

Based on the student club's design, they predict that the trajectory of the launched pumpkin will follow a parabolic path. This means that the height of the pumpkin (y) will depend on its horizontal distance from the launch point (x). The equation that describes this relationship is known as the "trajectory equation" or "equation of motion."

The general form of the trajectory equation for projectile motion is:

y(x) = ax^2 + bx + c

where a, b, and c are constants that depend on the initial velocity, angle of launch, and other factors.

To determine the specific values of a, b, and c for the student club's trebuchet, they will need to conduct experiments or simulations to measure the pumpkin's height at different horizontal distances. They can then use this data to fit the trajectory equation to the observed data points.

Once they have the trajectory equation, they can use it to make predictions about the pumpkin's flight path and adjust their design accordingly. For example, if the pumpkin is not landing where they want it to, they can tweak the launch angle, velocity, or other factors to get a better result.

Based on your question, a student club is designing a trebuchet to launch a pumpkin into projectile motion. The trajectory of the launched pumpkin is predicted to be parabolic, and can be described by the equation y(x). This means that as the pumpkin moves through the air, its path will follow a parabolic shape, which is common in projectile motion scenarios.

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Yes, the forester was justified in using a Normal model to analyze the woods, because the histogram is unimodal and symmetric. So option A is correct.

A histogram is a type of graph that uses vertical bars to show the distribution of a set of data. This particular histogram is unimodal, meaning that it has one peak which is an indication that the data is distributed normally. Additionally, the histogram is symmetric, which is another indication that the data is normally distributed.
Using a Normal model to analyze the woods is a valid approach because it allows the forester to identify the average diameter of the trees, as well as the spread of the data. It also allows him to check for any outliers, or points that fall outside the normal range. With this information, the forester can determine if the woods is suitable for sale, or if the buyer should be aware of any unexpected features.
Overall, the histogram is an effective way for the forester to analyze the data and determine if a Normal model is appropriate. By noting the unimodal and symmetric nature of the histogram, the forester can be sure that a Normal model will accurately represent the data, allowing him to make an informed decision about the woods.

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The complete response of the system described by the given difference equation, \(y(n) = f(n-1) - y(n-2) + 0.5k(n) + 0.5x(n-1)\), with the input \(x(n) = 0.5^n \cdot u(n)\) and initial conditions \(y[-1] = 0.75\) and \(y[-2] = 0.25\), is as follows:

\(y(n) = 1.5 \cdot 0.5^{n+1} - 0.5^n + 0.5 \cdot k(n) + 0.5 \cdot 0.5^{n-1}\),

To derive the complete response, we substitute the given input \(x(n)\) into the difference equation and solve for \(y(n)\) iteratively. The initial conditions \(y[-1]\) and \(y[-2]\) provide the base values for the recursion.

The first paragraph provides the final equation for the complete response of the system, taking into account the input signal, initial conditions, and the recursive nature of the difference equation. The second paragraph explains the process of deriving the complete response by substituting the input signal into the difference equation and solving iteratively, considering the initial conditions as the base values for the recursion.

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The declaration states that the value of Arc EFC = 253°.

A measure is indeed a quantitative concept used to express how large a collection is. Each unique measure represents a different method for determining how large a collection is. It would initially appear that a set's cardinality is the only logical way to determine its number.

We can tell we are working with a circular that has 360 degrees because of the connection.

We can infer that we have it if we look at that file.

Arc EFC

Arc CD

Arc DE

And everything together give us 360,

Arc EFC + Arc CD + Arc DE = 360

If we examine the figure again, we can see that the central angle of an intercepted arc is identical to the arc's measure.

Arc CD is 90 degrees since the central angle is 90 degrees given

Arc DE is 17 degrees

Arc EFC + Arc CD + Arc DE = 360

If we input all the figures

Arc EFC + 90 + 17 = 360

Arc EFC + 107 = 360

Arc EFC = 360 - 107

Arc EFC = 253

Therefore, Arc EFC = 253°

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The correct questions is:

Circle O, and are diameters. Arc ED measures 17°. Circle O is shown. Line segments F C and A E are diameters. Line segments C O and B O are radii. Point B is between points A and C, and point C is between points E and C. Angle D C is a right angle. What is the measure of Arc E F C? 107° 180° 253° 270°

Answer:

x = -2,1, 2

Step-by-step explanation:

g(x) = (x + 2)(x − 1)(x − 2)

Assuming we are looking for the roots

0  = (x + 2)(x − 1)(x − 2)

Using the zero product property

0 = x+2    0 =x-1    0 = x-2

x=-2         x = 1            x =2

9 and -4
7 and -2
5 and 0

Each and every pair has a total of 5.

Answer:

9 and-4

7 and -2

5 and 0

Step-by-step explanation:

When ya subtract 4 from 9 you get 5

the same applies to the rest.

Answer:

A:)

Step-by-step explanation:

l and lll

Answer:

x = 15

Step-by-step explanation:

-2x= -25-5

-2x=-30

x= 15

In a circle, 5 ones and 4 zeros are arranged randomly. Between any two equal digits, you write 0, and between any two different digits, you write 1.

To understand the process, consider the arrangement of the digits around the circle. Let's start with the first digit and compare it with the next digit. If they are the same, we write 0 in between them. If they are different, we write 1.

We continue this process for all adjacent pairs of digits around the circle until we reach the starting point again. This creates a new arrangement of zeros and ones based on the original arrangement of the digits.

By following this rule, we ensure that between any two equal digits, we have a 0, and between any two different digits, we have a 1. The resulting arrangement reflects the pattern described in the problem statement.

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