find all solutions of the given equation. (enter your answers as a comma-separated list. let k be any integer. round terms to two decimal places where appropriate.) 4 sin2() − 3 = 0 = rad

The coefficient of correlation (r) being -0.30 indicates a weak negative linear relationship between the variables x and y. The value of r ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship. Therefore, an r value of -0.30 suggests that there is a weak negative relationship between x and y, but the relationship is not strong enough to be considered a significant predictor of y based on x.

The negative value of r indicates that as the value of x increases, the value of y tends to decrease, although the relationship is weak. It is important to note that while a weak correlation does not necessarily imply causation, it does suggest that there may be some underlying relationship between the variables that should be further explored. Therefore, it is recommended to use other statistical measures in conjunction with the coefficient of correlation to determine the strength and significance of the relationship between x and y.

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Marked price: 39 dollars

Selling price: 31 dollars

Discount: ???

Subtract the post-discount price from the pre-discount price.

31-39=-8

Divide this new number by the pre-discount price.

-8/39=-0.20512820512

Multiply the resultant number by 100.

-0.20512820512×100= -20.512820512

Round the number

-20.512820512 → -20.5

The discount was %20.5 off

I hoped I solved your question, if I did not you can tell me and I would be more than glad to fix it ૮ ˶ᵔ ᵕ ᵔ˶ ა

Sam needs to study approximately 4.6 hours per week to earn a 4.0 GPA. The answer is (d) 4.6 hours.

We know that Sam wants to earn a 4.0 GPA, and his class attendance hours are fixed at 4. Therefore, we can solve for the number of hours he needs to spend studying to achieve this goal by setting the equation equal to 4.0 and solving for the hours spent studying:

4.0 = (0.50 x hours spent studying) + (0.25 x 4) + (0.25 x 2.75)

4.0 = (0.50 x hours spent studying) + 1 + 0.6875

2.3125 = 0.50 x hours spent studying

hours spent studying = 4.625

The correct option is (d) 4.6 hours.

The complete question is:

Sam wants to improve his GPA. to earn a 4.0 this semester. His prior GPA was a 2.75. Imagine that there is an equation that says his new GPA could be calculated based on the number of hours he spends studying, his class attendance, and his prior GPA. Written as an equation, it is Grade = (0.50 x hours spent studying) + (0.25 x class attendance hours) + (0.25 x prior GPA). Sam plans to attend class for 4 out of 4 hours each week. Use the equation to determine approximately how many hours per week Sam needs to study to earn a 4.0.

Select one:

a. 2.3 hours

b. 4.0 hours

c. 1.7 hours

d. 4.6 hours

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The measure of the various angles are:

∠1= 130°

∠3 = 130°

∠5= 50°

∠6= 130°

Lines m and l are the parallel lines and a line 'n' is a transverse intersecting these lines.

m∠2 = 50°

m∠1 + m∠2 = 180° [Linear pair of angles]

m∠1 = 180° - 50°

m∠1 = 130°

m∠3 = m∠1 = 130° [Vertically opposite angles]

m∠3 + m∠5 = 180° [Consecutive interior angles]

m∠5 = 180° - m∠3

       = 180° - 130°

m∠5   = 50°

m∠6 + m∠5 = 180° [Linear pair of angles]

m∠6 = 180° - 50°

m∠6= 130°

Hence,  the measure of the various angles are:

∠1= 130°

∠3 = 130°

∠5= 50°

∠6= 130°

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See the attached image.

Answer:

We have vertical angles, so:

b = 37°

a = c = 180° - 37° = 143°

Answer:

g = [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

4 - [tex]\frac{1}{12}[/tex] g - 2 = [tex]\frac{3}{2}[/tex] g + 1 - [tex]\frac{5}{6}[/tex] g

multiply through by 12 ( the LCM of 12, 2 and 6 ) to clear the fractions

48 - g - 24 = 18g + 12 - 10g

- g + 24 = 8g + 12 ( subtract 8g from both sides )

- 9g + 24 = 12 ( subtract 24 from both sides )

- 9g = - 12 ( divide both sides by - 9 )

g = [tex]\frac{-12}{-9}[/tex] = [tex]\frac{12}{9}[/tex] = [tex]\frac{4}{3}[/tex]

The correct answer option is: B. the IQR remains a 2.

IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.

Mathematically, interquartile range (IQR) is the difference between quartile 1 (Q₁) and quartile 3 (Q₃):

IQR = Q₃ - Q₁

Based on the given data set, the following interquartile ranges was calculated by using Microsoft Excel:

Q₃ = 8

Q₁ = 6

Now, the interquartile range (IQR) is given by:

IQR = Q₃ - Q₁

IQR = 8 - 2

IQR = 2

Adding a shoe size of 6 to the data set, the first and third and interquartile ranges remained the same, which implies that the interquartile range (IQR) would remain as two (2).

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Yes; using proportions, Andy is correct to believe that he has enough builders to finish this wall in less than 11 days.

Proportion refers to the ratio of one quantity or value compared to another.

Proportions are fractional values that are depicted in decimals, fractions, or percentages.

The number of builders that build Andy's wall in 15 days = 8

The number of days it would take 8 builders to finish the wall = 15 days

Proportionately, if 8 builders would take 15 days to build the wall, 11 builders would take 10.9 days (15 × 8) ÷11], which is approximately 11 days.

Thus, we can conclude that Andy is correct as 11 builders would take less than 11 days to finish the wall.

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There are 66,295,011,200 ways for six teachers to each choose two children with no one getting a pair of twins.

The given problem deals with six pairs of non-identical twins and six teachers who need to choose two children each, ensuring that no teacher selects a pair of twins.  

Let's begin by understanding the total number of ways the teachers can choose two children from the twelve available. To do this, we need to find the number of combinations of choosing two children from a set of twelve.

This can be calculated using the formula for combinations:

C(n, r) = n! / (r!(n-r)!)

Here, n represents the total number of items to choose from (in our case, 12 children), and r represents the number of items to be chosen at a time (2 children per teacher).

Substituting the values, we have:

C(12, 2) = 12! / (2!(12-2)!)

            = 12! / (2! * 10!)

            = (12 * 11 * 10!) / (2! * 10!)

            = 12 * 11 / 2

            = 66

Therefore, there are 66 different ways for each teacher to choose two children without any restrictions.

However, we need to account for the fact that no teacher should select a pair of twins. Let's consider the scenario where all six teachers choose two children without any restrictions. In this case, each teacher can choose from the available twelve children. The first teacher has twelve choices, the second teacher has eleven choices (as one child has been already selected), the third teacher has ten choices, and so on.

Using the multiplication principle, we can determine the total number of ways all six teachers can select two children without any restrictions:

Total ways without restrictions = 12 * 11 * 10 * 9 * 8 * 7

Now, let's consider the number of ways that result in a teacher selecting a pair of twins. Since there are six pairs of twins, each teacher has a 1/66 chance of selecting a specific pair of twins. Therefore, we need to subtract the number of ways a teacher can choose a pair of twins from the total ways without restrictions.

Number of ways a teacher can choose a pair of twins = 6 * (12 * 11 * 10 * 9 * 8 * 7) / 66

Finally, to find the number of ways for the six teachers to each choose two children with no one getting a pair of twins, we subtract the number of ways a teacher can choose a pair of twins from the total ways without restrictions:

Number of ways = Total ways without restrictions - Number of ways a teacher can choose a pair of twins

= (12 * 11 * 10 * 9 * 8 * 7) - (6 * (12 * 11 * 10 * 9 * 8 * 7) / 66)

= 66,355,443,200 - (3,991,680 / 66)

= 66,355,443,200 - 60,432,000

= 66,295,011,200

There are 66,295,011,200 ways for six teachers to each choose two children with no one getting a pair of twins.

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True, it is often not feasible to study the entire population because it may be impossible to observe all the items in the population. This is especially true in larger populations where it may be impractical or too costly to collect data on every single item. Therefore, researchers often use statistical sampling techniques to select a representative subset of the population. This sample is then studied and used to make inferences about the population as a whole. While sampling is not perfect, it can provide a reliable estimate of the population parameters with a certain level of confidence. Therefore, it is essential to carefully choose the sample to ensure that it accurately represents the population.

The question is about the feasibility of studying the entire population. It is often not possible to observe all the items in a population due to various constraints such as time, money, and practicality. Therefore, researchers use sampling techniques to select a representative subset of the population, which can provide a reliable estimate of the population parameters.

In conclusion, it is true that it is often not feasible to study the entire population. However, researchers can use statistical sampling techniques to select a representative subset of the population, which can provide a reliable estimate of the population parameters. It is essential to carefully choose the sample to ensure that it accurately represents the population.

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If y follows a chi-squared distribution with v = 10, then its expected value and variance are given by: E(y) = v = 10, Var(y) = 2v = 20. The probability that X^2 exceeds 6.737 is approximately 0.4238.

Now, let X = √y. Then X follows a chi distribution with v = 10 degrees of freedom. We have:

E(X) = E(√y) = √E(y) = √10

Var(X) = Var(√y) = 1/4 Var(y) = 5

To find P(X^2 > 6.737), we can use the definition of the chi-squared distribution. We have:

P(X^2 > 6.737) = P(X > √6.737) + P(X < -√6.737)

The chi distribution is symmetric, so P(X < -√6.737) = P(X > √6.737). Therefore,

P(X^2 > 6.737) = 2P(X > √6.737)

We can standardize X by subtracting its mean and dividing by its standard deviation:

Z = (X - √10) / √5

Then,

P(X > √6.737) = P(Z > (√6.737 - √10) / √5)

Using a standard normal table or calculator, we find that:

P(Z > 0.798) = 0.2119

Therefore,

P(X^2 > 6.737) = 2P(X > √6.737) = 2(0.2119) = 0.4238

So the probability that X^2 exceeds 6.737 is approximately 0.4238.

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The absolute maximum of f(x) on [3,4] is f(3) = 2 and the absolute minimum is f(4) = -7.The extreme value theorem does guarantee the existence of an absolute maximum and minimum for f(x) on this interval.

The extreme value theorem states that if a function is continuous over a closed interval, then it must have an absolute maximum and an absolute minimum on that interval.

In this case, the function f(x) is continuous over the closed interval [3,4], as it is a square root function and the square root of a non-negative number is always defined.

To find the absolute maximum and minimum of f(x) on [3,4], we need to evaluate f(x) at the endpoints and any critical points in the interval. However, since f(x) is a decreasing function on [3,4], the maximum value of f(x) occurs at the left endpoint x=3 and the minimum value occurs at the right endpoint x=4.

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Por lo tanto, la tasa de disminución de la temperatura en grados Celsius por día debe ser menor o igual a 10/3 para que la piscina esté abierta el jueves.

Para resolver este problema, necesitamos utilizar la siguiente fórmula:

Temperatura final = Temperatura inicial - tasa de disminución x días

Sea x la tasa de disminución en grados Celsius por día. Entonces, la temperatura alta el jueves fue:

30 - x(3)

Como se menciona en el problema, la piscina está abierta cuando la temperatura alta es mayor de 20 ∘ C20, degrees, start text, C, end text. Por lo tanto, la temperatura alta el jueves debe ser mayor o igual que 20 ∘ C20, degrees, start text, C, end text. Entonces, tenemos la siguiente desigualdad:

30 - x(3) ≥ 20

Resolviendo para x, obtenemos:

x ≤ 10/3

Por lo tanto, la tasa de disminución de la temperatura en grados Celsius por día debe ser menor o igual a 10/3 para que la piscina esté abierta el jueves.

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The range of y when x belongs to the set of real numbers is

y ≥ -4

To find the range of y when x belongs to the set of real numbers, we can consider the shape of the graph of the function

y = x² - 2x - 3.

Plotting the graph shows that the graphs opens upward and the parabola opens upward and the range of y is all real numbers greater than or equal to the y coordinate of the minimum point.

In this case, the range is y ≥ -4.

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To find the P-value, we need to find the probability of getting a test statistic less than or equal to the -1.38 under a null hypothesis.

Using a standard normal distribution table or calculator, we find that the area to the left of -1.38 is 0.0844.

Therefore, the P-value is 0.0844.

To decide whether to reject the null hypothesis at a significance level of α = 0.05, we compare the P-value to α. Since the P-value (0.0844) is greater than α (0.05), we fail to reject the null hypothesis. We do not have enough evidence to support the alternative hypothesis at the 0.05 level of significance.

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In the schedule of cost of goods sold, the cost of goods available for sale represents the total cost of all goods that were available for sale during a particular period.

The schedule of cost of goods sold is an important financial statement that shows the cost of goods that a company has sold during a particular period. The cost of goods available for sale is a key component of this statement and represents the total cost of all goods that were available for sale during the period.

The cost of goods available for sale is calculated by adding the beginning inventory to the cost of goods purchased during the period. This calculation gives the total cost of all goods that a company had available for sale during the period.

Once the cost of goods available for sale is determined, the cost of goods sold can be calculated by subtracting the ending inventory from the cost of goods available for sale. This calculation gives the cost of all goods that were sold during the period.

Overall, the schedule of cost of goods sold is an important financial statement that helps companies track their inventory and understand their cost of goods sold. The cost of goods available for sale is a critical component of this statement and represents the total cost of all goods that a company had available for sale during a particular period.

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The 3rd (third term )of the sequence with  a₁ = 6 and aₙ = aₙ₋₁ • 2 using Geometric Sequence is 24.

To find the third term of the geometric sequence with a recursive formula, we can use the given formula which is a GP formula:

a₁ = 6

aₙ = aₙ₋₁ • 2

Given

First term (a₁) = 6

Therefore

Second term (a₂) = a₁ • 2

                            = 6 • 2 = 12

Third term (a₃) = a₂ • 2

                        = 12 • 2 = 24

Therefore, the third term of the sequence is 24.

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When a system of equations has infinitely many solutions, it is considered consistent and dependent.

This means that the equations are not contradictory and there are multiple solutions that satisfy both equations. In contrast, an inconsistent system of equations has no solutions and a consistent, independent system has exactly one unique solution.

For the given system of equations y = x + 5 and y = -5x - 1, we can see that both equations can be rearranged to the form y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slopes are different (-5 and 1) and the y-intercepts are different (-1 and 5). Therefore, the two lines intersect at a single point and the system has only one solution. So, the answer is option 4 - two.

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Answer:

72.588

or rounded 72.6

Step-by-step explanation:

The two binomials are:

x² + 7x + 12

6x² - 13x + 6

We have,

One possible set of binomials whose product includes the term 12 is:

(x + 4)(x + 3)

Expanding this product, we get:

x^2 + 7x + 12

And,

Another set of binomials whose product includes the term 12 is:

(2x - 3)(3x - 2)

Expanding this product, we get:

6x^2 - 13x + 6

Thus,

The two binomials are:

x² + 7x + 12

6x² - 13x + 6

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Answer: C 3

Step-by-step explanation:

Each of the sides from D have been multiplied by 3 to get D'

3 is the factor

C 3

Thus, the equation of the curve that satisfies the differential equation and passes through the point (4,-3) is y = -3x^2/5 + 57/5.

To find the particular solution to the given differential equation, we first need to separate the variables. We can do this by rearranging the equation as follows:

4y^2 dx = 9x^2 dy
dy/dx = 4y^2/9x^2

Now, we can integrate both sides with respect to their respective variables. Integrating the left-hand side gives us y as a function of x:

∫dy = ∫4y^2/9x^2 dx
y = -3x^2/5 + C

To find the value of the constant C, we can use the initial condition provided in the problem. When x = 4 and y = -3, we have:

-3 = -3(4)^2/5 + C
C = 57/5

Therefore, the particular solution to the differential equation is:

y = -3x^2/5 + 57/5

This is the equation of the curve that satisfies the differential equation and passes through the point (4,-3).

In summary, the process of finding a particular solution to a differential equation involves separating the variables, integrating both sides, and using the initial conditions to determine the value of the constant of integration. The resulting function is the particular solution to the differential equation.

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The deadweight loss in this scenario can be calculated as the difference between the consumer surplus and producer surplus at the equilibrium price. In this case, the equilibrium price is $15.

To calculate the consumer surplus, we first need to calculate the quantity demanded at the equilibrium price, which is qd = 55 – 15 = 40. The consumer surplus can be calculated as the area under the demand curve above the equilibrium price, which is 1/2*(55-15)*40 = $800.

To calculate the producer surplus, we first need to calculate the quantity supplied at the equilibrium price, which is qs = 615 - 15 = 75. The producer surplus can be calculated as the area above the supply curve below the equilibrium price, which is 1/2(15-0)*(75-15) = $900.

The deadweight loss is the difference between the consumer surplus and producer surplus, which is $800 - $900 = -$100. This negative value indicates that there is no deadweight loss in this scenario, and both the consumers and producers are benefiting from the equilibrium price.

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The probability that the mean weight of a 24-bag case of potato chips is below 10 ounces is approximately 0.

Here,

Let X = weight of potato chips in medium size bag.

The random variable X follows a Normal distribution with mean, μ = 10.2 ounces and standard deviation, σ = 0.12 ounces.

A sample of n = 24 bags of chips is selected.

Compute the probability that the mean weight of these 24 bags is less than 10 ounces as follows:

P (X < 0) = 1 - P(Z < 8.16)

            ≈ 0

Thus, the probability that the mean weight of a 24-bag case of potato chips is below 10 ounces is approximately 0.

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complete question:

The weight of potato chips in a medium-size bag is stated to be 10 ounces the amount that the packaging machine puts in these bags is believed to have a normal model with mean 10.2 and standard deviation 0.12 ounces. What's the probability that the mean weight of a 24-bag case of potato chips is below 10 ounces?

After considering all the options we conclude that the debut of the 911 and 988 hotlines was for 54 years, which is Option B.

The first 911 emergency call was made in 1968 in Alabama. The 988 hotline is a new national mental health crisis hotline that was mandated by the federal government in October 2020 with an official nationwide start date on July 16, 2022. Therefore, the number of years between the debut of the 911 and 988 hotlines is 54 years.

A hotline refers to a phone line which is provided for  the public so that they can apply it to contact an organization about a particular subject. Hotlines gives people opportunity express their concerns and to obtain information from an organization.
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A sample size of at least 538 freshmen to estimate the proportion of freshmen who do not visit their advisors regularly with a margin of error of 4% and a confidence level of 95%.

To answer your question, we need to use the formula for sample size calculation for proportion:
n = [(Z-score)^2 * p(1-p)] / E^2

Where:
n = required sample size
Z-score = the critical value for the desired confidence level (95% confidence level corresponds to a Z-score of 1.96)
p = the estimated population proportion (34% or 0.34)
1-p = the complement of p
E = the desired margin of error (4% or 0.04)

Plugging in the values:
n = [(1.96)^2 * 0.34(1-0.34)] / (0.04)^2
Simplifying the equation:
n = [(3.8416) * 0.2244] / 0.0016
n = 537.38

We need a sample size of at least 538 freshmen to estimate the proportion of freshmen who do not visit their advisors regularly with a margin of error of 4% and a confidence level of 95%. Keep in mind that this is just an estimate based on the historical data and assumes that the population proportion has not changed significantly.

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The estimated value of the frequency parameter lambda using the method of moments is approximately 0.20.

To estimate the value of the frequency parameter lambda using the method of moments, we equate the sample mean with the population mean, which is equal to 1/lambda.

The sample mean can be calculated by summing the waiting times and dividing by the sample size:

mean = (2+7+9+1+6+7+7+3+5+2+8+3+4)/13 = 4.92

Therefore, we have:

4.92 = 1/lambda

Solving for lambda, we get:

lambda = 1/4.92

             ≈ 0.20

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the expression for x would be:
x = 24 / y.

To determine the expression for x, we need to consider the total amount of oil that needs to be pumped out of the tanker. As given in the question, the tanker can hold 24 tonnes of oil. Therefore, the expression for the total amount of oil that needs to be pumped out is:
Total amount of oil = 24 tonnes
Now, let's consider the rate at which oil can be pumped out of the tanker in cold weather. Let's assume that the tanker can pump out y tonnes of oil in one minute. Therefore, the expression for the amount of oil pumped out in x minutes would be:
Amount of oil pumped out = y * x tonnes
However, we know that the amount of oil pumped out should be equal to the total amount of oil in the tanker, which is 24 tonnes. Therefore, we can write the following equation:
y * x = 24
To find the expression for x, we can rearrange this equation as:
x = 24 / y
So, the expression for x would be:
x = 24 / y
This expression gives us the number of minutes it would take to empty the tanker in cold weather, based on the rate at which oil can be pumped out of the tanker in that weather condition

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The gradient vector field of f is a field of vectors that points in the direction of the steepest increase of f at each point in the xy-plane. To find the gradient vector field of f(x, y) = tan(2x − 3y), we need to calculate the partial derivatives of f with respect to x and y.

∂f/∂x = 2sec^2(2x - 3y)
∂f/∂y = -3sec^2(2x - 3y)

The gradient vector field is then given by the vector [2sec^2(2x - 3y), -3sec^2(2x - 3y)]. This field shows the direction and magnitude of the steepest increase of f at each point. The field will be perpendicular to the level curves of f, which are the curves where f is constant. In this case, the level curves are given by the equation tan(2x − 3y) = constant.
To find the gradient vector field of f(x, y) = tan(2x - 3y), we first need to compute the partial derivatives of f with respect to x and y.

1. Calculate the partial derivative with respect to x:
∂f/∂x = (2)(sec^2(2x - 3y))

2. Calculate the partial derivative with respect to y:
∂f/∂y = (-3)(sec^2(2x - 3y))

3. Form the gradient vector field using the partial derivatives:
∇f = (∂f/∂x, ∂f/∂y) = (2sec^2(2x - 3y), -3sec^2(2x - 3y))

The gradient vector field of f(x, y) = tan(2x - 3y) is (∇f) = (2sec^2(2x - 3y), -3sec^2(2x - 3y)).

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The relationship between x and y is neither linear nor exponential. To determine if the relationship between x and y is linear, exponential, or neither, we can create a table of values and see if there is a constant rate of change or a constant ratio between the values of x and y.

x | y
---|---
5 | -1
19 | -6
33 | -36
47 | -216
Looking at the table, we can see that there is no constant rate of change between the values of x and y. Therefore, the relationship is not linear. To determine if the relationship is exponential, we can check if there is a constant ratio between the values of y and x.
y/x = (-1)/5 = -0.2
(-6)/19 = -0.3158
(-36)/33 = -1.0909
(-216)/47 = -4.5957
Since the ratio between y and x is not constant, the relationship is not exponential either.

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