The required answer is based on the given data, we do not have sufficient evidence to support the claim that less than 10 percent of the test results are wrong at a 0.05 significance level.
To test the claim that less than 10 percent of the test results are wrong, use a hypothesis test with a significance level of 0.05. Let's define the null and alternative hypotheses:
Null Hypothesis (H0): The proportion of wrong test results is 10 percent or more.
Alternative Hypothesis (Ha): The proportion of wrong test results is less than 10 percent.
Use the binomial distribution to analyze the data. Let p be the true proportion of wrong test results. Since we want to test that the proportion is less than 10 percent, set p = 0.10 for the null hypothesis.
Given that 29 out of 308 tested subjects had wrong test results, calculate the sample proportion, denoted by p^, as follows:
p^ = 29 / 308 = 0.094
To conduct the hypothesis test, we can use the z-test for proportions. The test statistic is calculated as:
z = (p^ - p) / [tex]\sqrt{}[/tex]((p x (1 - p)) / n)
In this case, since we are testing whether the proportion is less than 10 percent, calculate a one-tailed z-test.
Substituting the values into the formula:
z = (0.094 - 0.10) / [tex]\sqrt{}[/tex]((0.10 x (1 - 0.10)) / 308)
Simplifying the expression:
z = -0.006 /[tex]\sqrt{}[/tex] (0.09 / 308)
z ≈ -0.006 / 0.017
Calculating the z-value:
z ≈ -0.353
To determine the critical value for a one-tailed test at a significance level of 0.05, we can consult the z-table or use statistical software. For a significance level of 0.05, the critical z-value is approximately -1.645 (since we are testing for less than 10 percent, in the left tail).
Since the calculated z-value (-0.353) is greater than the critical z-value (-1.645), we fail to reject the null hypothesis. There is not enough evidence to conclude that the proportion of wrong test results is less than 10 percent.
Therefore, based on the given data, we do not have sufficient evidence to support the claim that less than 10 percent of the test results are wrong at a 0.05 significance level.
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Tucker purchased $4,600 in new equipment for a catering business. He estimates that the value of the equipment is reduced by approximately 40% every two years. Tucker states that the function V(t)=4,600(0.4)2t could be used to represent the value of the equipment, V, in dollars t years after the purchase of the new equipment. Explain whether the function Tucker stated is correct, and, if not, determine the correct function that could be used to find the value of the equipment purchased.
show work
Answer:
The function stated by Tucker is incorrect.
V(t) = 4600(0.8)^t
Step-by-step explanation:
Given the function :
V(t)=4,600(0.4)2t
The initial value of equipment = 4600
Decay rate = 40% of very 2 years
The value of equipment t years after purchase
The exponential decat function goes thus :
V(t) = Initial value * (1 - decay rate)^t
The Decay rate per year = 40% /2 = 20% = 0.2
V(t) = 4600(1 - 0.2)^t
V(t) = 4600(0.8)^t
solve elimination method 3x+4y=0 and x - 2y =-5
Answer:
x=−2 and y=3/2
Step-by-step explanation:
see picture
Sketch two periods of the graph of the function h(x)=4sec(π4(x+3)). Identify the stretching factor, period, and asymptotes.
Enter the exact answers.
Stretching factor = ____________
Period: P=
__________
Enter the asymptotes of the function on the domain [−P,P].
To enter π, type Pi.
The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1). The order of the list does not matter.
Asymptotes: x=
__________
Select the correct graph of h(x)=4sec(π4(x+3)).
(a) (b) (c) (d)
The function h(x) = 4sec(π/4(x+3)) represents a graph with a stretching factor of 4 and a period of 8π/4 = 2π. The correct graph representation of h(x) = 4sec(π/4(x+3)) needs to show these characteristics. The correct answer would be (b).
The function h(x) = 4sec(π/4(x+3)) has a stretching factor of 4, which means that the amplitude of the function is multiplied by 4, causing the graph to be vertically stretched.
The period of the function is given by P = 2π/π/4 = 8π/4 = 2π. This means that the graph will complete two periods within the interval [-P, P], which in this case is [-2π, 2π].
The asymptotes of the function occur at x = -P/2 and x = P/2. Substituting the value of P = 2π, the asymptotes are x = -π and x = π. These vertical asymptotes indicate where the graph approaches infinity or negative infinity as x approaches these values.
To determine the correct graph representation of h(x) = 4sec(π/4(x+3)), you would need to choose the graph option that shows the stretching factor of 4, a period of 2π, and vertical asymptotes at x = -π and x = π.
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find an example of a commutative ring R with 1 in R, and a prime ideal P (of R) with no zero divisors but R is not an integral domain.
An example of a commutative ring R with 1, a prime ideal P, and no zero divisors but R is not an integral domain is the ring R = Z/6Z, where Z is the set of integers and 6Z is the ideal generated by 6.
The ring R = Z/6Z consists of the residue classes of integers modulo 6. The elements of R are [0], [1], [2], [3], [4], and [5], where [a] denotes the residue class of a modulo 6.
In this ring, addition and multiplication are performed modulo 6. For example, [2] + [3] = [5] and [2] * [3] = [0].
R has a multiplicative identity, which is the residue class [1]. It is commutative since addition and multiplication are performed modulo 6.
The ideal P = 2R consists of the elements [0] and [2]. P is a prime ideal since R/P is an integral domain, which means there are no zero divisors in R/P. However, R itself is not an integral domain because [2] * [3] = [0] in R, showing that zero divisors exist in R.
Therefore, the ring R = Z/6Z, with the prime ideal P = 2R, satisfies the given conditions.
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Identify if they are function or not
Answer:
1=function
2=not function
3=function
4=function
5=function
6=not function
7=not function
8=function
Each side of a square is increased 3 inches. When this happens, the area is multiplied by 25. How many inches in the side of the original square?
Answer:
s = 0.75 inches
Step-by-step explanation:
Let s = side length of the original square
s + 3 = side length of the new square
Area of a square = s²
A = s²
A = (s+3)²
A = s² + 6s + 9
Area multiplied by 25 = 25 * s²
So,
s² + 6s + 9 = 25s²
25s² - s² - 6s - 9 = 0
24s² - 6s - 9 = 0
8s² - 2s - 3 = 0
a = 8
b = -2
c = -3
s = -b ± √b² - 4ac / 2a
= -(-2) ± √(-2)² - 4(8)(-3) / 2(8)
= 2 ± √4 - (-96) / 16
= 2 ± √100 / 16
= 2 ± 10/16
s = 2 + 10/16 or 2-10/16
= 12/16 or -8/16
= 0.75 or -0.5
side length can not be negative
Therefore, s = 0.75
A = s²
A = (0.75)²
= 0.5625
A = (s+3)²
= (0.75+3)²
= 3.75²
= 13.95
Which of the following points is not an ordered pair for the function
ƒ(x ) =5/2 x + 6?
(4, 16)
(2, 7)
(-2, 1)
Answer:
(2, 7) is not an ordered pair for the function.
Step-by-step explanation:
evan has 4 chocolate bars with a total of 48 pices are in each bar
Answer:
what is your question? it seems the answer would be 12 just by looking at this, but still what is the question exactly?
Step-by-step explanation:
Answer: if you are dividing the answer will be 12
(i wrote two since it dosent say what we need to do
if you are multiplying you answer will be 192
hope it helped!
Step-by-step explanation:
Determine if the following linear maps are surjective or injective. You may assume each map is linear. (a) The derivative map T : P3(R) → P₂(R); P₂ (R); p(x) → d dx -p(x). (b) The linear map T: R³ → Rª defined by the matrix 1 1 -3 1 1 1 A 0 1 2 1 0 -1 (c) The linear map T: R³ → R³ defined by the matrix 0 5 5 A = 2 1 2 2 3 4
The linear map is not surjective but injective.
A linear map is an operation between two vector spaces that preserves the properties of addition and scalar multiplication; therefore, it is a linear transformation.
Here is how to determine if the following linear maps are surjective or injective.
(a) The derivative map T: P3(R) → P₂(R); P₂(R); p(x) → d/dx -p(x) is an example of a linear map,
where P3(R) and P₂(R) are the vector spaces of polynomials of degree at most 3 and 2 with coefficients in R, respectively.
Moreover, d/dx is the derivative operator acting on the polynomial p(x).
The kernel of the linear map T is the subspace of P3(R) consisting of polynomials p(x) with T(p(x)) = d/dx -p(x) = 0, i.e., p(x) is constant.
However, a constant polynomial of degree zero is not in the range of T, since it has no derivative. Therefore, the linear map T is injective and not surjective.
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Evaluate 4 + (m - n)
When m = 7 and n = 5.
What is the length of AC?
Answer:
AC=6
Step-by-step explanation:
You can see that ABC is 4 times bigger that HIJ because of lines AB and HI. HI(with a value of one) had to be multiplied by four to equal AB (a value of 4). Use this same rule to find the side AC.
1.5(the length of HJ) times 4 =6.
which tool is not needed to construct a perpendiculer bisecter
Answer:
a protractor is not needed to constant a perpendicular bisecter
Step-by-step explanation:
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Mario paid $44.25 in taxi fare from the hotel to
the airport. The cab charged $2.25 for the first
mile plus $3.50 for each additional mile. How
many miles was it from the hotel to the airport?
A. 10
B. 11
C. 12
D. 13
Answer:
C. 12
hope they help
first mile $2.25 plus $3.50 ×12= $42.00+2.25=44.25
Approximate the area under the graph of F(x)=0.2x³+2x²-0.2x-2 over the interval (-9,-4) using 5 subintervals. Use the left endpoints to find the height of the rectangles.
To approximate the area under the graph of the function F(x) = 0.2x³ + 2x² - 0.2x - 2 over the interval (-9, -4) using 5 subintervals and left endpoints, we can use the left Riemann sum method. The total area under the graph of F(x) over the interval (-9, -4).
To approximate the area using the left Riemann sum method, we start by dividing the interval (-9, -4) into 5 subintervals of equal width. The width of each subinterval can be calculated as (b - a) / n, where b is the upper limit of the interval (-4), a is the lower limit of the interval (-9), and n is the number of subintervals (5 in this case).
Next, we evaluate the function F(x) at the left endpoint of each subinterval to find the height of the rectangles. For the left Riemann sum, the left endpoint of each subinterval is used as the height. In this case, we evaluate F(x) at x = -9, -7, -5, -3, and -1.
Once we have the width and height of each rectangle, we can calculate the area of each rectangle by multiplying the width and height. Finally, we sum up the areas of all the rectangles to approximate the total area under the graph of F(x) over the interval (-9, -4).
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Rachel has 42 stickers she wants give to her friends. Rachel put the stickers in 7 equal groups. Then Rachel found more stickers and put 3 more in each pile. If Rachel gives 5 stickers to each of her 12 friends, how many stickers does she have left over?
Answer:
3 stamps
Step-by-step explanation: 42 stamps in equal groups would be 6 stickers/group.
6+3 = 9 stickers in each pile
there was 7 piles so multiply 7 by the 9 stickers in each pile
7· 9 = 63
5 · 12 = 60, so she gave her friends 60 stickers
63-60 = 3
A boy who is on the second floor of their house watches his dog lying on the ground. The angle between his eye level and his line of sight is 32º. a. Which angle is identified in the problem, angle of elevation or depression? b. If the boy is 3 meters above the ground, approximately how far is the dog from the house? c. If the dog is 7 meters from the house, how high is the boy above the ground?
As per the given details, the dog is approximately 0.6249 * 3 = 1.8747 meters from the house.
The angle recognized in the problem is the angle of depression. The angle of depression is the attitude between the horizontal line and the line of sight from an observer looking downward.
To calculate approximately how a ways the canine is from the residence, we are able to use trigonometry.
Since the angle of despair is given as 32º and the boy is 3 meters above the floor, we will use the tangent characteristic to find the space.
tan(32º) = (dog's distance / boy's height)
tan(32º) = d / 3
3 * tan(32º) = d
The dog is approximately 0.6249 * 3 = 1.8747 meters from the house.
To calculate how high the boy is above the floor, we are able to again use trigonometry. Since the canine is 7 meters from the residence and the attitude of melancholy is given as 32º, we are able to use the tangent characteristic to discover the peak of the boy.
tan(32º) = (boy's height / dog's distance)
tan(32º) = h / 7
7 * tan(32º) = h
Therefore, the boy is approximately 0.6249 * 7 = 4.3743 meters above the ground.
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write five other iterated integrals that are equal to the iterated integral
∫¹₀ ∫¹ᵧ ∫ʸ ₀ f(x, y, z)dx dx dy
Here are five other iterated integrals that are equal to the given iterated integral:
∫₀ʸ ∫⁺∞ₓ ∫¹₀ f(x, y, z)dz dx dy
∫₀ʸ ∫¹₀ ∫ʸ ∞ f(x, y, z)dz dx dy
∫⁺∞₁₀ ∫₀ʸ ∫ʸ ₀ f(x, y, z)dz dy dx
∫¹ᵧ ∫⁺∞₁₀ ∫₀ x f(x, y, z)dz dx dy
∫⁺∞₀ ∫⁺∞₁₀ ∫ʸ ₀ f(x, y, z)dz dx dy
The given iterated integral ∫¹₀ ∫¹ᵧ ∫ʸ ₀ f(x, y, z)dx dx dy represents the integration of a function f(x, y, z) over a region defined by the limits of integration. To obtain five other equivalent iterated integrals, we can rearrange the order of integration and modify the limits accordingly. Each integral represents the same volume or value as the given iterated integral, but the order of integration and limits may vary.
The key is to ensure that the new integrals cover the same region as the original one. The limits in each integral should define the appropriate range for each variable to maintain the equivalence. By rearranging the order of integration and adjusting the limits accordingly, we can obtain these alternative expressions that are equal to the given iterated integral.
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Help me please I have an f in this class I will give you 44 points
8 x 7s = 56s
8 x (-2) = -16
so 8(7s - 2) = 56s - 16
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Step-by-step explanation:
g a tank contains 90 kg of salt and 1000 l of water. a solution of a concentration 0.045 kg of salt per liter enters a tank at the rate 8 l/min. the solution is mixed and drains from the tank at the same rate what is the concentration of our solution in the tank initially?
The final concentration in the tank is 0.045 kg/L, which is the same as the concentration of the incoming solution.
To solve the problem, we can use the formula:
C1V1 + C2V2 = C3V3
where C1 is the initial concentration, V1 is the initial volume, C2 is the concentration of the incoming solution, V2 is the volume of the incoming solution, C3 is the final concentration, and V3 is the final volume.
We know that the initial volume of the tank is 1000 L and it contains 90 kg of salt. To find the initial concentration, we need to convert the mass of salt to concentration by dividing it by the total volume:
90 kg / 1000 L = 0.09 kg/L
This means that initially, the concentration of salt in the tank is 0.09 kg/L.
Next, we need to calculate how much salt enters and leaves the tank during a given time period. Since the incoming solution has a concentration of 0.045 kg/L and enters at a rate of 8 L/min, it brings in:
0.045 kg/L x 8 L/min = 0.36 kg/min
The outgoing solution has the same concentration as the final concentration in the tank, so we can use this formula to find it:
C1V1 + C2V2 = C3V3
(0.09 kg/L)(1000 L) + (0.045 kg/L)(8 L/min)(t min) = C3(1000 L + 8 L/min)(t min)
Simplifying and solving for C3, we get:
C3 = (0.09 kg/L)(1000 L) + (0.045 kg/L)(8 L/min)(t min) / (1000 L + 8 L/min)(t min)
At steady state, when the amount of salt entering and leaving the tank is equal, we can set the incoming and outgoing terms equal to each other:
0.36 kg/min = C3(8 L/min)
Solving for C3, we get:
C3 = 0.045 kg/L
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What is the answer with explanation?
The value of arc ABD is determined as 236⁰.
Option C.
What is the measure of arc ABD?The value of arc ABD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.
arc BA = 2 x 48⁰ (interior angles of intersecting secants)
arc BA = 96⁰
arc BD = 2 x 70⁰ (interior angles of intersecting secants)
arc BD = 140⁰
arc ABD = arc BA + arc BD
arc ABD = 96⁰ + 140⁰
arc ABD = 236⁰
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Consider the following algorithm that takes inputs a parameter 0
function integer X(p,n)The algorithm described simulates a random variable with a binomial distribution of parameters p and n.
The given algorithm involves generating random numbers and incrementing a variable X based on certain conditions. The variable X represents the number of successes or "1" outcomes in a sequence of n independent Bernoulli trials, where each trial has a probability of success equal to p.
In each iteration of the loop, the algorithm generates a random number between 0 and 1 (denoted as RND) and compares it to the probability parameter p. If the generated random number is less than or equal to p, the variable X is incremented by 1.
This process is repeated for a total of n trials, resulting in the count of successes, which follows a binomial distribution. The binomial distribution represents the number of successes in a fixed number of independent Bernoulli trials, where each trial has the same probability of success, given by parameter p. Therefore, the algorithm simulates a random variable with a binomial distribution of parameters p and n.
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Investigators performed a randomized experiment in which 411 juvenile delinquents were randomly assigned to either multisystemic therapy (MST) or just probation (control group). Of the 215 assigned to therapy, 87 had criminal convictions within 12 months. Of the 196 in the control group, 74 had criminal convictions within 12 months. Determine whether the therapy caused significantly fewer arrests at a 0.05 significance level. Start by comparing the sample percentages. Find and compare the sample percentages that were arrested for these two groups. The percentage of arrests for people who received MST was %.
The percentage of arrests for people who received Multisystemic Therapy (MST) can be calculated by dividing the number of individuals arrested in the MST group (87) by the total number of individuals.
Percentage of arrests for MST group = (87/215) * 100 ≈ 40.47%
To determine if therapy caused significantly fewer arrests at a 0.05 significance level, we need to compare this percentage with the percentage of arrests in the control group.
The percentage of arrests for the control group can be calculated in a similar manner by dividing the number of individuals arrested in the control group (74) by the total number of individuals in the control group (196), and multiplying by 100.
Percentage of arrests for control group = (74/196) * 100 ≈ 37.76%
Comparing the sample percentages, we find that the percentage of arrests for people who received MST (40.47%) is slightly higher than the percentage of arrests for the control group (37.76%).
To determine if this difference is statistically significant at a 0.05 significance level, we would need to perform a hypothesis test, such as a chi-square test, to compare the observed frequencies with the expected frequencies under the assumption that therapy has no effect on reducing arrests.
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Find the equation for the following parabola. Focus (3,4) Directrix y 2 A. (x-3)2-2 (y-2.5) B. (x-3)2 = 4(y-3) C. (x-3)2 = (y-4) D. (y-3)2-4 (x-3) Enter
To find the equation of a parabola given its focus and directrix, we use the standard form of the equation of a parabola which is:
[tex]\frac{(y-k)^2}{4a} = x-h[/tex]
Where (h,k) is the vertex of the parabola, and a is the distance between the vertex and the focus (or between the vertex and directrix, they're equal).
Therefore, the answer is option D, (y-3)²-4(x-3).
Using this formula, let's first find the vertex of the parabola. Since the directrix is a horizontal line, the vertex lies halfway between the focus and directrix on the y-axis. Thus, the vertex is at (3,3).
Since the focus is above the vertex, a is positive, and its value is the distance between the vertex and focus:
a = 4 - 3
= 1
Substituting these values into the standard form of the equation of a parabola gives:
[tex]\frac{(y-3)^2}{4(1)} = x - 3$$[/tex]
[tex]\frac{(y-3)^2}{4} = x - 3$$[/tex]
Multiplying both sides by 4 gives:
y - 3 = 2(x - 3)
y = 2x - 3
Therefore, the answer is option D, (y-3)²-4(x-3).
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A random sample of 50 home theater systems has a mean price of $115. Assume the population standard deviation is $19.50. Construct a 90% confidence interval for the population mean.
Based on a random sample of 50 home theater systems, the 90% confidence interval for the population mean price is approximately $110.81 to $119.19, assuming a population standard deviation of $19.50.
To construct a 90% confidence interval for the population mean of home theater systems, we can use the following formula
Confidence Interval = Sample Mean ± Margin of Error
The margin of error depends on the level of confidence and the standard deviation of the population. Given that the sample size is large (n = 50) and we know the population standard deviation is $19.50, we can use the z-distribution.
First, we need to find the critical value (z) for a 90% confidence level. Using a standard normal distribution table or calculator, the critical value for a 90% confidence level is approximately 1.645.
Next, we calculate the margin of error (E) using the formula:
Margin of Error (E) = z * (Population Standard Deviation / sqrt(n))
E = 1.645 * ($19.50 / √(50))
E ≈ $4.19
Now we can construct the confidence interval:
Confidence Interval = Sample Mean ± Margin of Error
Confidence Interval = $115 ± $4.19
Confidence Interval ≈ ($110.81, $119.19)
Therefore, we can say with 90% confidence that the population mean of home theater systems is between approximately $110.81 and $119.19.
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a new shopping mall records 150150150 total shoppers on their first day of business. each day after that, the number of shoppers is 15\, percent more than the number of shoppers the day before.
The number of shoppers on the first day is 150, and each subsequent day the number of shoppers increases by 15%.
Number of shoppers on the first day: The shopping mall recorded a total of 150 shoppers on their first day of business.
Increase in shoppers each day: Starting from the second day, the number of shoppers increases by 15% compared to the previous day.
To calculate the number of shoppers on each day, we can use the following steps:
Day 1: The number of shoppers on the first day is given as 150.
Day 2: To find the number of shoppers on the second day, we need to increase the number of shoppers from the previous day by 15%.
Number of shoppers on Day 2 = Number of shoppers on Day 1 + (15/100) * Number of shoppers on Day 1
Day 3: Similarly, to find the number of shoppers on the third day, we increase the number of shoppers from the second day by 15%.
Number of shoppers on Day 3 = Number of shoppers on Day 2 + (15/100) * Number of shoppers on Day 2
We can continue this process for each subsequent day, using the number of shoppers from the previous day to calculate the number of shoppers for the current day.
By following these steps, we can determine the number of shoppers on each day, starting from the first day and increasing by 15% each day compared to the previous day.
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41+98+0000000000000000000000000000000000000000000
139
ffsahshanjwjsjudke
Answer:
139 because zero is addition identityif 1-3(y+2)=-32 find the value of y/3
Answer:
7.6
Step-by-step explanation:
-3 multiple by y and -3 multiple by 2 resolve to 7.6....
4.) Select ALL equivalent expressions to 5x – 5.5. a) 5x -55 c) 5(x - 1.1) b) 2x - 3 + 3x - 2.5 ) 5.5(x - 1)
Answer:
1. (-125 a - 5.75) x + b c (605 x - 550 x^2) + 10.75
2. -125 a x + x (-550 b c x + 605 b c - 5.75) + 10.75
3. 0.25 (-500 a x - 220 b c (10 x - 11) x - 23 x + 43)
Step-by-step explanation:
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A grocery store collected sales data. It found that when customers buy less bread, they tend to purchase more rice. What can we conclude?
A. There is no correlation between amount of bread bought and amount of rice purchased.
B. There is a correlation between amount of bread bought and amount of rice purchased. However, there is no causation. This is because there is an increase in the amount of rice purchased with a decrease in the amount of bread bought.
C. There is a correlation between amount of bread bought and amount of rice purchased. There may or may not be causation. Further studies would have to be done to determine this.
Answer: C
Step-by-step explanation: C because there is obviously a correlation yet we cannot determine if there is causation or not.