What is the slope of the line that contains the points -2- 0-1/1/2 1 2 and (4,-4)?
ill give brainiest to first great answer​

The differential equation of the ellipse in terms of x and y only: (x/2) ^2 + (y/3)^2 = 1. To eliminate the parameter t for a parametric equation of an ellipse, we can solve for t in terms of x or y and substitute it into the other equation.

Consider the parametrization of an ellipse given by x = 2cos(t) and y = 3sin(t).

We can eliminate t by solving for cos(t) and sin(t) in terms of x and y, respectively. From the first equation, we have cos(t) = x/2, so t = Arcos(x/2). Substituting this expression for t into the second equation, we get y = 3sin(arccos (x/2)) = 3sqrt(1-(x/2)^2). This gives us the equation of the ellipse in terms of x and y only:

(x/2)^2 + (y/3)^2 = 1.

This is the standard form equation of an ellipse with center at the origin and semi-axes of length 2 and 3 in the x and y directions, respectively.

In general, to eliminate the parameter t for a parametrization of an ellipse, we can use trigonometric identities to express cos(t) and sin(t) in terms of x and y, respectively. Substituting these expressions for cos(t) and sin(t) into the parametric equations and simplifying should give us the equation of the ellipse in terms of x and y only.

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We can find a vector v in h by choosing any value of t and constructing the vector [4t, t, 9t]. For example, if we choose t = 1, then v = [4, 1, 9] is a vector in h.

We can verify that v satisfies the condition that [4t, t, 9t] + [4s, s, 9s] = [4(t+s), t+s, 9(t+s)] for all t and s in the set of real numbers. If we add v to itself, we get: [4, 1, 9] + [4, 1, 9] = [8, 2, 18]

which is also a vector in h. Therefore, h is closed under vector addition. Similarly, if we multiply v by a scalar, say 2, we get:

2[4, 1, 9] = [8, 2, 18]

which is again a vector in h. Therefore, h is closed under scalar multiplication. Since h contains the zero vector, is closed under vector addition, and is closed under scalar multiplication, it satisfies the three properties required for a set to be a subspace of R^3. Hence, h is a subspace of R^3.

In summary, we can find a vector v in h by choosing any value of t and constructing the vector [4t, t, 9t]. By verifying that v satisfies the conditions required for a set to be a subspace, we can show that h is a subspace of R^3.

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The target costing process is a cost management technique used to determine the maximum cost that a company can incur while still earning a desired profit margin. It involves setting a target cost for a product or service and then working backwards to identify the cost of materials, labor, and overhead that will enable the company to achieve that target.

While finding a low-cost supplier is certainly one way to reduce the overall cost of production, it is not necessarily the starting point of the target costing process. Before selecting a supplier, a company must first understand its customers' needs and preferences, identify the features and benefits that will add value to the product or service, and determine the price that customers are willing to pay.

Once these factors are established, the company can then analyze the cost structure of the product or service and identify areas where costs can be reduced without sacrificing quality or customer satisfaction. This may involve exploring alternative materials or production methods, streamlining processes, or outsourcing certain tasks to lower-cost providers.

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The volume of the cone is approximately 84.78 cubic inches.To find the volume of a cone with a diameter of 6 inches and a slant height of 9 inches, we need to first find the radius of the cone. The diameter is 6 inches, so the radius is half of that, which is 3 inches.

Next, we can use the Pythagorean theorem to find the height of the cone. The slant height is 9 inches, which is the hypotenuse of a right triangle with legs equal to the radius and the height of the cone. We can write the following equation:

r^2 + h^2 = l^2

where r is the radius, h is the height, and l is the slant height. Substituting the given values, we get:

3^2 + h^2 = 9^2

9 + h^2 = 81

h^2 = 72

h = sqrt(72)

h ≈ 8.485 inches

Now that we have the radius and height, we can use the formula for the volume of a cone:

V = (1/3)πr^2h

Substituting the values we found, we get:

V = (1/3)π(3^2)(8.485)V ≈ 84.78 cubic inches.

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A sample size of 139 is required in order to estimate the time its trucks take to drive from city A to city B with a margin of error of ±2 minutes and 95% confidence, assuming the standard deviation is known to be 12 minutes.

To calculate the sample size required for this scenario, we need to use the formula for the sample size for a mean:
n = (z² * s²) / E²

where:
n = sample size
z = z-score for desired confidence level (95% = 1.96)
s = standard deviation (12 minutes)
E = desired margin of error (2 minutes)

Substituting in the values given, we get:
n = (1.96^2 * 12^2) / 2^2
n = 138.2976

We round up to the nearest whole number to get:
n = 139

Therefore, a sample size of 139 is required in order to estimate the time its trucks take to drive from city A to city B with a margin of error of ±2 minutes and 95% confidence, assuming the standard deviation is known to be 12 minutes.

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The probability of getting all three tosses to head is 1/8.

We have,

When a coin is tossed, there are two possible outcomes:

heads (H) or tails (T).

Since there are three tosses, the total number of possible outcomes.

2³ = 8.

The probability of getting heads on one toss is 1/2.

The probability of getting heads on all three tosses is the product of the probabilities of getting heads on each individual toss:

P(HHH) = P(H) x P(H) x P(H) = (1/2) x (1/2) x (1/2) = 1/8.

Therefore,

The probability of getting all three tosses to head is 1/8.

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Answer: The probability of event B, P(B), is 2.00.

Step-by-step explanation:

1. The formula for the probability of two independent events A and B occurring together is P(A and B) = P(A) * P(B).

2. We know that P(A) = 0.02 and P(A and B) = 0.04.

3. Substituting these values into the formula, we get 0.04 = 0.02 * P(B).

4. Solving for P(B), we divide both sides of the equation by 0.02.

5. This gives us P(B) = 0.04 / 0.02 = 2.00.

Please note that probabilities typically range from 0 to 1, so a probability of 2.00 seems unusual. It might be worth double-checking the provided probabilities for events A and B.

We do not have enough evidence to conclude that the proportion of students being bullied at school has decreased at a 5% level of significance.

Hypothesis testing is a statistical method used to determine whether a hypothesis about a population parameter is supported by the data. In this case, the hypothesis is that the proportion of students being bullied at school has decreased.

The one-sample proportion test is a type of hypothesis test used to determine whether a proportion in a sample is significantly different from a known population proportion.

In this case, we are testing whether the proportion of students who reported being bullied in the sample of 75 sixth grade students is significantly different from the population proportion of 43%.

To test whether the proportion of students being bullied at school has decreased, we can use a hypothesis test with the null hypothesis that the proportion is still 0.43 and the alternative hypothesis that the proportion is less than 0.43.

Let p be the true proportion of students being bullied at school, then we have:

H₀ : p = 0.43

Hₐ : p < 0.43 (one-tailed test)

Using the sample data, we can calculate the sample proportion of students who reported being bullied at school:

=> [tex]\hat{p}[/tex] = 30/75 = 0.4

We can use this to calculate the test statistic:

=> z = ( [tex]\hat{p}[/tex]  - p) / √(p×(1 - p)/n) = (0.4 - 0.43) /√(0.43×0.57/75) = -0.81

At the 5% level of significance with a one-tailed test, the critical z-value is -1.645. Since our calculated test statistic (-0.81) is greater than the critical value, we fail to reject the null hypothesis.

Therefore,

We do not have enough evidence to conclude that the proportion of students being bullied at school has decreased at a 5% level of significance.

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The answer is "inelastic". When demand is inelastic, changes in price do not significantly affect the quantity of goods or services demanded.

This means that increases in price result in increases in total revenue, while decreases in price result in decreases in total revenue. Inelastic demand occurs when consumers are not very responsive to changes in price and do not have good alternatives to the product or service being offered. Examples of products with inelastic demand are necessities like food, medicine, and gasoline, where consumers will continue to purchase the product regardless of price changes because they need it for daily living. On the other hand, products with elastic demand, like luxury items or non-essential goods, will see a significant decrease in demand when prices increase.

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Shaylen's score is at the 42nd percentile, which means that 42% of the students who took the test scored lower than Shaylen.

To find the percentile for Shaylen's score, we can use the formula:

percentile = (number of scores below Shaylen's score / total number of scores) x 100

We are given that Shaylen's score of 455 was higher than the scores of 4226 students. This means that there were 7246 - 4226 = 3020 students who scored higher than Shaylen. Therefore, we can calculate the percentile as:

percentile = (3020 / 7246) x 100

= 0.417 x 100

= 42 (rounded to the nearest percent)

So Shaylen's score is at the 42nd percentile, which means that 42% of the students who took the test scored lower than Shaylen.

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The cubic function only has one real zero, which is x = -2 - √5/3  = -2.75

Here we want to find the zeros of the cubic function:

y = 27(x + 2)³ + 5

The zeros of a function are the values of x such that the outcome is y, then we need to solve the equation:

0 =  27(x + 2)³ + 5

-5 =  27(x + 2)³

-5/27 = (x + 2)³

∛(-5/27) = x + 2

-√5/3 = x + 2

-2 - √5/3 = x

That is the only zero of the function (with a multiplicity of 3).

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Answer:

C

Step-by-step explanation:

sinx=9/19

sinx=0.47

opposite function on calculator

x= ~28

Answer:

28˚

Step-by-step explanation:

Answer: =133.3%

Step-by-step explanation:

Formula for percent change:

[tex]\frac{difference of 2 numbers}{original} *100[/tex]                 >substitute

[tex]\frac{\frac{7}{8} -\frac{3}{8} }{\frac{3}{8} } *100[/tex]                                         >subtract top

[tex]=\frac{\frac{4}{8} }{\frac{3}{8} }*100[/tex]                                         >simplify/reduce top

[tex]=\frac{\frac{1}{2} }{\frac{3}{8} }*100[/tex]                                         >Divide fractions(Keep the first, Change

                                                           the sign, Flip the 2nd fraction

= [tex]\frac{1}{2} *\frac{8}{3} *100\\[/tex]                                     >Reduce fractions and multiply

= [tex]\frac{4}{3} *100[/tex]

=133.3%

According to the statement the total probability is approximately 0.026, which is the second option in the list provided.

The probability that Brandon will earn a free homework pass can be found using the binomial probability formula. In this case, the number of trials (n) is 10, the probability of success (p) is 1/5 (since there are five answer choices per problem), and the probability of failure (q) is 4/5. We need to calculate the probability of getting at least 5 correct answers, meaning we will consider 5, 6, 7, 8, 9, and 10 correct answers.
The binomial probability formula is:
P(x) = C(n, x) * (p^x) * (q^(n-x))
Where P(x) is the probability of x successes, C(n, x) is the number of combinations of n items taken x at a time, and p and q are the probabilities of success and failure, respectively.
Calculating the probabilities for each of the desired outcomes (5 to 10 correct answers) and summing them up will give us the probability of Brandon earning a free homework pass. After doing the calculations, the total probability is approximately 0.026, which is the second option in the list provided.

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A smaller cylinder rod in the example of question 5 would provide a greater retraction force.

To understand why this is the case, we need to look at the formula for force: force = pressure x area. In the case of a hydraulic cylinder, the force is generated by pressure acting on the surface area of a piston. A smaller cylinder rod would have a smaller surface area than a larger one, which means that the same amount of pressure would generate a greater force.

For example, let's say that we have two hydraulic cylinders with the same pressure and the same fluid flow rate, but one has a smaller cylinder rod than the other. The smaller cylinder rod would have a smaller surface area, so the force generated by the pressure would be greater. This greater force would result in greater retraction of the rod, making it move faster and with greater force.

In conclusion, a smaller cylinder rod would provide a greater retraction force due to the smaller surface area on which pressure acts, resulting in a greater force for the same amount of pressure.

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If a survey is taken at a movie theater in Winterville. The first 150 people who entered the theater were asked about their favorite type of movie. The  true about this situation is: C. The population is the total number of people who go to the movie theater, and the sample is the first 150 people at the theater.

In this situation, the survey was taken of the first 150 people who entered the movie theater. Therefore, the sample is the group of 150 people who were surveyed. The population of interest is the total number of people who go to the movie theater, as these are the individuals who could potentially have a favorite type of movie.

However, it is not practical to survey every person who goes to the movie theater, so a sample of 150 people was taken from the population.

Therefore, option C is the correct answer.

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To find a potential function for the vector field f = 4xyi + (1-2x^2y^2)j over the region {(x,y): y>0}, we can use the method of partial derivatives to check if the vector field is conservative.

If it is conservative, we can find a potential function by integrating the components of the vector field.To determine if the vector field f is conservative, we need to check if the curl of f is equal to zero. In this case, the curl of f can be calculated as:

curl(f) = (∂f_y/∂x - ∂f_x/∂y)k = (-8xy)k

Since the z-component of the curl is not zero, the vector field is not conservative. Therefore, we cannot find a potential function for the entire region {(x,y): y>0}.

However, if we restrict the region to the subset {(x,y): y>0, 1-2x^2y^2>0}, we can find a potential function. In this case, we can integrate the x-component of f with respect to x, treating y as a constant, and add a constant of integration that depends on y. This gives:

F(x,y) = 2x^2y + g(y)

where g(y) is a constant of integration that depends only on y. We can then differentiate F(x,y) with respect to y and equate it to the y-component of f to find g(y). This gives:

g(y) = C - 2y^3

where C is an arbitrary constant. Therefore, the potential function for f over the restricted region {(x,y): y>0, 1-2x^2y^2>0} is:

F(x,y) = 2x^2y - 2y^3 + C

where C is a constant of integration.

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By failing to reject the null hypothesis with an observed p-value of 0.18% in a 2-tailed test with an alpha level of 0.05, the researcher runs the risk of a Type II error.

In hypothesis testing, a Type II error occurs when the null hypothesis is not rejected even though it is false. It means that the researcher fails to detect a significant effect or relationship that actually exists.

By accepting the null hypothesis when it should be rejected, the researcher may overlook an important finding or draw incorrect conclusions. In this case, with a low observed p-value of 0.18%, the researcher is likely to commit a Type II error by not rejecting the null hypothesis and missing a potentially significant result.


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The particular solution is y = (-9/8) * (9x + 81) e^(-x/9) + 85.125.

To solve this differential equation, we can use separation of variables.

dy/dx = -9x/8 e^(-x/9)

dy = (-9/8)x e^(-x/9) dx

Integrating both sides, we get:

y = (-9/8) * (9x + 81) e^(-x/9) + C

where C is the constant of integration.

To find the particular solution, we need to use the initial condition. Let's say that y(0) = 4.

Then, when x = 0, we have:

4 = (-9/8) * (0 + 81) e^(0) + C

C = 4 + (9/8) * 81

C = 85.125

Therefore, the particular solution is:

y = (-9/8) * (9x + 81) e^(-x/9) + 85.125

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The slope of the line is m = 2.49

Given data ,

Let's denote the number of meals delivered as x and the total cost as y.

Now , the cost is determined by two components

$4.98 for every 2 meals delivered and a $2.00 service fee

The first component, $4.98 for every 2 meals delivered, can be represented by the expression (4.98/2)x, which simplifies to 2.49x.

The second component is a fixed $2.00 service fee, which remains the same regardless of the number of meals delivered.

So , the total cost equation is:

y = 2.49x + 2.00

And , slope of this situation is the coefficient of x in the equation, which is 2.49

Hence , the slope of this situation is 2.49

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(a)The moment generating function of X is Mx(t) = [tex](e^(6t) + e^(7t) + e^(8t) + e^(9t)).[/tex]

(b)The moment generating function of X+Y is MX+Y(t)= [[tex](e^(6t) + e^(7t)[/tex] + [tex]e^(8t) + e^(9t)[/tex])] × [([tex]e^(18t) + e^(19t[/tex]) + [tex]e^(20t) + e^(21t[/tex]) + [tex]e^(22t) + e^(23t)[/tex] + e^(24t) + [tex]e^(25t) + e^(26t)[/tex])]

The moment generating function (MGF) of a random variable can be determined by taking the expected value of the exponential function raised to the product of the variable and a parameter. For a uniformly distributed random variable, we use the probability mass function (PMF) to calculate the MGF. By applying the formula and summing the contributions from each value in the support of the uniform distribution, we can obtain the MGF of the variable.

(a) To find the moment generating function (MGF) of a uniformly distributed random variable, we can use the formula:

Mx(t) = E[e^(tX)]

Since X is uniformly distributed on the set {6, 7, 8, 9}, the probability mass function (PMF) is:

P(X = 6) = P(X = 7) = P(X = 8) = P(X = 9) = 1/4

Using this PMF, we can calculate the MGF:

Mx(t) = E[e^(Xt)] = (e^(6t) × P(X = 6)) + (e^(7t) ×P(X = 7)) + (e^(8t) ×P(X = 8)) + (e^(9t) ×P(X = 9))

= (e^(6t) ×1/4) + (e^(7t) ×1/4) + (e^(8t) × 1/4) + (e^(9t) × 1/4)

So, the moment generating function of X is Mx(t) =  (e^(6t) + e^(7t) + e^(8t) + e^(9t)).

(b) Since X and Y are independent, the MGF of the sum X + Y is the product of their respective MGFs:

MX+Y(t) = Mx(t)× My(t)

The moment generating function of Y can be found similarly. Since Y is uniformly distributed on the set {18, 19, 20, 21, 22, 23, 24, 25, 26}, with equal probabilities for each value, we have:

My(t) = (e^(18t) + e^(19t) + e^(20t) + e^(21t) + e^(22t) + e^(23t) + e^(24t) + e^(25t) + e^(26t))/9

Therefore, the moment generating function of X + Y is:

MX+Y(t) = Mx(t) × My(t) = [(e^(6t) + e^(7t) + e^(8t) + e^(9t))] × [(e^(18t) + e^(19t) + e^(20t) + e^(21t) + e^(22t) + e^(23t) + e^(24t) + e^(25t) + e^(26t))]

:Therefore,the moment generating function of X is Mx(t) =  (e^(6t) + e^(7t) + e^(8t) + e^(9t)) and the moment generating function of X+Y is MX+Y(t)= [(e^(6t) + e^(7t) + e^(8t) + e^(9t))] × [(e^(18t) + e^(19t) + e^(20t) + e^(21t) + e^(22t) + e^(23t) + e^(24t) + e^(25t) + e^(26t))]

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Based on the demonstration of feasibility and optimality, we conclude that the solution (x1, x2, x3) = (3/2, 1/2, 0) is indeed optimal for the given linear program.

What is Optimality?

Optimality refers to the quality or state of being the best or most favorable among a set of alternatives or solutions. In various contexts, optimality is often associated with achieving the maximum or minimum value of an objective function, reaching an optimal solution, or attaining the best possible outcome.

To prove that the solution (x1, x2, x3) = (3/2, 1/2, 0) is optimal for the given linear program, we need to demonstrate two conditions: feasibility and optimality.

Feasibility: We need to show that the solution satisfies all the constraints of the linear program.

From the given constraints:

x1 - x2 ≤ 1: (3/2) - (1/2) = 1, which satisfies the inequality.

2x2 - x3 ≤ 1: 2(1/2) - 0 ≤ 1, which satisfies the inequality.

x1, x2, x3 ≥ 0: All the variables are non-negative, so this constraint is satisfied.

Therefore, the solution (x1, x2, x3) = (3/2, 1/2, 0) is feasible.

Optimality: We need to demonstrate that the solution provides the maximum value for the objective function.

The objective function is max x1 - 2x3.

Plugging in the values from the solution: (3/2) - 2(0) = 3/2.

We need to show that no other feasible solution can yield a higher value for the objective function.

By examining the constraints, we find that the upper bounds for x1 and x2 are 1, and x3 is non-negative.

Considering all possible values within these constraints, we observe that (3/2, 1/2, 0) provides the maximum value of 3/2 for the objective function.

Thus, the solution (x1, x2, x3) = (3/2, 1/2, 0) is optimal.

Therefore, based on the demonstration of feasibility and optimality, we conclude that the solution (x1, x2, x3) = (3/2, 1/2, 0) is indeed optimal for the given linear program.

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Complete Question -

Question: Linear Programming: For The Linear Program: Max X1-2x3 X1-X2 <= 1 2x2-X3 &Lt;= 1 X1, X2, X3 >= 0 Prove That The Solution (X1, X2, X3) = (3/2, 1/2, 0) Is Optimal

Linear programming:

For the linear program:

max x1-2x3

x1-x2 <= 1

2x2-x3 <= 1

x1, x2, x3 >= 0

prove that the solution (x1, x2, x3) = (3/2, 1/2, 0) is optimal

Answer: Your answer is B.

Step-by-step explanation:

The center of mass of the system of objects is at (1, 2)

Here we have a system  of objects that have masses 1 , 1 and 1 at the point (-2,2), (2,1) and (3,3), because all the objects have the same mass, then the center of mass will just be in the center of these 3 points.

To get the center we need to get the means for the two coordinates, for x we have:

x = (-2 + 2 + 3)/3 = 1

For y we have.

y = (2 + 1 + 3)/3 = 2

The center of mass is at (1, 2)

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Answer:

3.8%

Step-by-step explanation:

The solution is:

the probability that the two butterflies she spots will both be type A butterflies is 0.0044

The computation of the  probability that the two butterflies she spots will both be type A butterflies is shown below:

= 1 ÷ Type A × 1 ÷ Type A

= 1 ÷ 15 × 1 ÷ 15

= 1 ÷ 225

= 0.0044

Hence, the  probability that the two butterflies she spots will both be type A butterflies is 0.0044

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complete questio:

Susie is looking for butterflies in an area where: 15% of the butterflies are of type A 30% of the butterflies are of type B 55% of the butterflies are of type C Suppose that she spots two butterflies on her walk, and that the types of the two butterflies are independent from each other (perhaps because they are spotted in different locations). (a) What is the probability that the two butterflies she spots will both be type A butterflies

The  equation of the tangent line to the curve x(t) = 2/t, y(t) = t^2 + 1 at the point (2, 2) is y = -x + 4.

To find the equation of the tangent line to the curve x(t) = 2/t, y(t) = t^2 + 1 at the point (2, 2), we need to find the slope of the curve at that point and then use the point-slope form of a linear equation.

First, we need to find the derivative of y with respect to x:

dy/dx = (dy/dt) / (dx/dt)

To find dy/dt and dx/dt, we differentiate y(t) and x(t) with respect to t:

dy/dt = 2t
dx/dt = -2/t^2

So, we have:

dy/dx = (dy/dt) / (dx/dt) = (2t) / (-2/t^2) = -t^3

Now, we can find the slope of the tangent line at the point (2, 2) by plugging in t = 1:

dy/dx = -1

Therefore, the slope of the tangent line is -1.

Next, we use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where (x1, y1) is the point on the curve where the tangent line intersects it, and m is the slope of the tangent line.

Since the point (2, 2) lies on the curve, we have x1 = 2 and y1 = 2. Plugging in the slope and the point, we get:

y - 2 = -1(x - 2)

Simplifying, we get:

y = -x + 4

Therefore, the equation of the tangent line to the curve x(t) = 2/t, y(t) = t^2 + 1 at the point (2, 2) is y = -x + 4.

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The probability that the first spinner lands on "C" AND the second spinner lands on a "2" is 1/20.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences. Then the probability is given as,

P = (Favorable event) / (Total event)

The probability that the first spinner lands on the "C" is calculated as,

P = 1/5

The probability that the second spinner lands on "2" is calculated as,

P = 1/4

The probability that the first spinner lands on "C" AND the second spinner lands on a "2" is calculated as,

P = (1/5) x (1/4)

P = 1/20

More about the probability link is given below.

https://brainly.com/question/795909

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