The average rate of change of f(x), represented by the table of values, over the interval [-2, 3] is: D. 0.5.
What is an average rate of change?An average rate of change is sometimes referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes with respect to another quantity, over a given interval.
In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this formula:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function f(x) over the interval [-2, 3]:
a = -2; f(a) = 2.5
b = 3; f(b) = 5
Substituting the given parameters into the formula, we have the following;
Average rate of change = (5 - 2.5)/(3 - (-2))
Average rate of change = 2.5/5
Average rate of change = 0.5.
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when severe autocorrelation is indicated after a regression model has been estimated, which underlying regression assumption is violated?
The fundamental regression assumption that the error terms are independent of one another is broken when substantial autocorrelation is shown following the estimation of a regression model. Here option C is the correct answer.
The two error factors must be somewhat co-correlated in order for there to be autocorrelation. Having it indicates that the correlation between the two error factors is not equal to zero. It goes against the fundamental tenet of the traditional linear regression approach.
Autocorrelation measures the relationship between a variable's current value and its historical values. A perfect positive correlation is represented by an autocorrelation of 1, whereas a perfect negative correlation is represented by an autocorrelation of 1.
An explanation of how one or more independent variables relate to the target variable, response variable, or dependent variable that the regression model predicts.
Complete question:
When severe autocorrelation is indicated after a regression model has been estimated, which underlying regression assumption is violated? A - The dispersion of population data points around the population regression line remains constant everywhere along the line
B - The population of values is normally distributed about the population regression line.
C - Heteroscedasticity
D - The error terms are independent of each other.
E - A linear relationship exists between X and Y in the population
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Evaluate each expression for the given value of the variable. 4(x-4);x=7
Answer:
(28-16)
Step-by-step explanation:
x=7
4x-16
If x is 7
then it is 4x7 = 28
Therefore we can say 28-16 is our final answer.
Thank you.
HELP HELP HELP FFHFJFHDHDHDHD
Answer:
y ≈ 15.9 cm
Step-by-step explanation:
using the tangent ratio in the right triangle
tan53° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{12}[/tex] ( multiply both sides by 12 )
12 × tan53° = x , that is
x ≈ 15.9 (to 1 decimal place )
3. Suppose U and V are conformally equivalent. Prove that if U is simply con- nected, then so is V. Note that this conclusion remains valid if we merely assume that there exists a continuous bijection between U and V.
According to the image, if U is simply connected, then so V is also simply connected as U and V are conformally equivalent.
What is meant by conformally equivalent?If an analytic map f: U V is 1-1 and onto, then two open sets U and V in C are said to be conformally comparable. A conformal equivalence between U and V is the name given to such a f. The conformal equivalence between V and U is then f1(w). A function called conformal mapping, which is defined on the complex plane, changes a given curve or set of points on a plane while keeping each of the curve's angles. For resolving physics and engineering issues with awkward geometries that may be described as functions of a complex variable, conformal mappings are useful. The analyst can change the awkward geometry into a lot more useful one by selecting the right mapping.
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according to the department of public health, the average age of a new smoker is 13 years old. a researcher working for the tobacco industry wishes to test the claim that the average age is no longer 13 years old. he surveys a sample of 144 new smokers and finds they have an average age of 13.5 years with a standard deviation of 2.5 years. do the sample data support the researcher’s claim? test the relevant hypotheses at a significance level of ????????
Answer:
Step-by-step explanation:
?I need help trying to find the area of this triangle please help.
Answer:
28 ft²
Step-by-step explanation:
You want the area of a triangle with a base of 7' and a height of 8'.
Area formulaThe formula for the area of a triangle is ...
A = 1/2bh
where b is the base of the triangle, and h is the height perpendicular to the base.
Here, it is convenient to use the side marked 7' as the base of the triangle. The distance marked 8' is the perpendicular distance from the base to the top of the triangle. So, the area is ...
A = 1/2(7 ft)(8 ft) = 28 ft²
The area of the triangle is 28 square feet.
__
Additional comment
As you can see, the vertex opposite the base does not need to lie above the base segment. All that matters is the perpendicular distance from that vertex to the base line.
what value of aa would indicate no association between gender and voting pattern for the people in the sample?
The value of ' a 'indicating no association between gender and voting pattern for the people in the sample is 500.
What is sample?A sample is a result of a random experiment. We sample a random variable when we select a specific value from among its possible possibilities. A exact value is that of a sample. The potential values and likelihood of each are determined by the random variable's probability distribution. They should be picked at random from a broader group or population in order to assist you understand more about the population as a whole. Samples are employed in statistical testing when population sizes are too big for all prospective participants or observations to be included in the test.
Here,
Considering Split ticket,
a + b = 600 ---(1)
Considering No Split ticket,
c + d = 400 ---(2)
Considering Men,
a + c = 800 ---(3)
Considering Women,
b + d = 200 ---(4)
Applying (1) - (4),
a + b - b - d= 600 - 200
a - d = 400 ---- (5)
Applying (2) - (4),
c + d - b - d = 400- 200
c - b = 200 ----(6)
a - c = 200 --- (7)
Applying (3) + (7)
2a = 1000
a = 500
For those in the sample, the value of "a" showing there is no correlation between gender and voting behavior is 500.
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the diameter of a tree was 14 in. during the following year, the circumference increased 4 in. about how much did the tree's diameter increase? about how much did the tree's cross-section area change?
The diameter of the tree increased by 0.27in. (approximately) and the change in tree's cross section area is 27.5 in.².
As given in the question,
Diameter of the tree 'd' = 14in.
Radius = 7in.
Circumference of the tree = πd
= 3.14 × 14
= 43.96 in.
New circumference increased by 4 in. = 43.96 + 4
= 47.96in.
New diameter = 47.96 / 3.14
= 15.27 in. (approximately)
New Radius ≈ 7.6 in.
Increase in diameter= 15.27 - 15
= 0.27 in.
Area of cross section original tree = 3.14 × 7²
= 153.9 in.²
New area of cross section original tree = 3.14 × 7.6²
= 181.4 in.²
Change in area = 181.4 - 153.9
= 27.5 in.² ( approximately)
Therefore, increase in diameter is 0.27in. and change in cross - section area is 27.5 in.²
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can someone answer this?
The value of y in the intersected lines is 80.
How to find the angles in the intersected line?When lines intersect, angle relationships are formed such as vertically opposite angles, linear angles, angles on a straight line etc.
Therefore, the value of y in the angles can be found as follows:
10y - 12 = 3x + 29 (vertically opposite angles)
vertically opposite angles are congruent.
Hence,
10y - 12 = 3x + 29
10y - 3x = 41
6x - 3 + 10y - 12 + 37 = 180 (sum of angles on a straight lines)
6x + 10y = 180 + 3 + 12 - 37
6x + 10y = 158
combine the equation
10y - 3x = 41
10y + 6x = 158
9x = 117
x = 117 / 9
x = 13
6(13) + 10y = 158
10y = 158 - 78
10y = 80
y = 80 / 10
y = 8
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Simplify the expression to a polynomial in standard form: (x-1)(3x^2+7x+5) (x−1)(3x 2 +7x+5)
The standard form for the given expression is 3x³ - 3x² - 2x - 5.
How to write a polynomial in standard form?A polynomial can be written in standard form by writing its terms in descending order of their powers and the constant terms comes at the end.
The given polynomial is (x - 1)(3x² + 7x + 5).
It can be written in standard form as follows,
(x - 1)(3x² + 7x + 5)
= x(3x² + 7x + 5) - 1(3x² + 7x + 5)
= 3x³ + 7x² + 5x - 3x² - 7x - 5
= 3x³ - 3x² - 2x - 5
Hence, the given expression can be written in standard form as,
3x³ - 3x² - 2x - 5
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A gas station is open 365 day a year, 24 hours a day. The store owner estimates that they served 40,000 cups of coffee last year. This quantity can also be expressed asfunctionsequation editorcups of coffee per hour (round to the nearest whole cup). This is a ? reasonable not reasonable estimate.
The quantity can also be expressed as a function equation in cups of coffee per hour is; f(x) = 5x
How to Solve function word problems?
We are told that a gas station is open for the 365 days of the year and 24 hours each day.
Thus,
Total number of hours in the year = 365 * 24 = 8760 hours
Now, the number of cups they served for the year = 40000 cups
Now, the rate of cups per hour = 40000/8760 = 4.566 ≈ 5 cups per hour
The quantity can also be expressed as a function equation in cups of coffee per hour; f(x) = 5x
where;
x is the number of hours
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theoretically, you could determine the value of the pre-exponential factor, a, from the same plot you use to determine the activation energy. what graphical feature would you use to determine this value?
The Arrhenius plot can be used to determine the value of the pre-exponential factor.
The slope of the Arrhenius plot can be used to find the activation energy. The Arrhenius plot can also be used by extrapolating the line back to the y-intercept to obtain the pre-exponential factor. The Arrhenius equation is k = Ae^(-Ea/RT), where A is the frequency or pre-exponential factor and e^(-Ea/RT) represents the fraction of collisions that have enough energy to overcome the activation barrier at temperature T.
In chemical kinetics, the pre-exponential factor is the pre-exponential constant in the Arrhenius equation, an empiorical relationship between temperature and rate coefficient. The pre-exponential factor is a constant that can be derived experimentally or numerically. It is also called frequency factor.
In chemical kinetics, an Arrhenius plot displays the logarithm of a reaction rate constant, plotted against reciprocal of the temperature. Arrhenius plots are often used to analyze the effect of temperature on the rates of chemical reactions. Arrhenius plots show that reaction rates are inversely proportional to temperature changes.
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it takes a hose 3 minutes to fill a rectangular aquarium 12 inches long, 13 inches wide, and 14 inches tall. how long will it take the same hose to fill an aquarium measuring 21 inches by 28 inches by 35 inches? minutes round your answer to the nearest minute
The hose will take 28.27 minutes to fill the second aquarium.
Given,
Rectangular Aquarium - 1
Length = 12 inches
Width = 13 inches
Height = 14 inches
Time taken by a hose to fill the aquarium = 3 minutes
Rectangular Aquarium - 2
Length = 21 inches
Width = 28 inches
Height = 35 inches
We have to find the time taken by the same hose to fill the aquarium 2.
Volume of Aquarium 1 = length × width × height
= 12 × 13 × 14 = 2184 inch³
To fill 2184 inch³, the hose will take 3 minutes.
Now,
Volume of Aquarium 2 = length × width × height
= 21 × 28 × 35 = 20580 inch³
Here,
The time taken by the hose to fill a volume of 20580 inch³;
= 3 × 20580 / 2184 = 28.27 minutes
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is Pavers that cost a set amount per square foot proportional
(This is an imagine math quistion)
Answer:
Step-by-step explanation:
Yes it is because if the amount of Pavers change so does the cost.
Define a generic method called checkorder() that checks if four items are in ascending, neither, or descending order. The method should return -1 if the items are in ascending order, 0 if the items are unordered, and 1 if the items are in descending order. The program reads four items from input and outputs if the items are ordered. The items can be different types, including integers, strings, characters, or doubles.
The first is an ordered list of integers, the second is an ordered list of integers, and the third is an unsorted list of texts in JAVA. (Refer to the coding shown below.)
What is JAVA?In order to have as few implementation dependencies as feasible, Java is a high-level, class-based, object-oriented programming language.
Java is an object-oriented, cross-platform programming language (OOP).
JavaScript, a scripting language used to build dynamic web pages, should not be confused with it.
Java is one of the most widely used programming languages in the world because of its dependability and simplicity.
So, the generic class needed to compare any kind of data structure is created by the Java code that follows.
Both integers and strings were employed in three different test situations.
The first is a list of integers in ascending order, the second is a list of integers in descending order, and the third is a list of texts that are not sorted.
The image below that is attached shows the results.
import java.util.Scanner;
class Brainly {
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
System.out.println("Order: " + checkOrder(10, 22, 51, 53));
System.out.println("Order: " + checkOrder(55, 44, 33, 22));
System.out.println("Order: " + checkOrder("John", " Gabriel", "Daniela", "Zendaya"));
}
public static <E extends Comparable<E>> int checkOrder(E var1, E var2, E var3, E var4) {
E prevVar = var1;
if (var2.compareTo(prevVar) > 0) {
prevVar = var2;
} else {
if (var3.compareTo(prevVar) < 0) {
prevVar = var3;
} else {
return 0;
}
if (var4.compareTo(prevVar) < 0) {
return 1;
} else {
return 0;
}
}
if (var3.compareTo(prevVar) > 0) {
prevVar = var3;
}
if (var4.compareTo(prevVar) > 0) {
return -1;
}
return 0;
}
}
Therefore, the first is an ordered list of integers, the second is an ordered list of integers, and the third is an unsorted list of texts in JAVA. (Refer to the coding shown below.)
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4 1/5 divided by 3 1/2
HELPPPPPPPPPPP
we want to estimate the population proportion of people in new jersey who are in favor of legalizing marijuana. a 95% confidence interval within 5% of the true value is wanted. what size sample is needed?
In order to estimate the population proportion within 5%, a sample size of at least 384 is needed.
The number of individuals or observations included in a study is referred to as the sample size. Two statistical properties are influenced by the sample size: 1) The accuracy of our estimates, and 2) The ability to draw conclusions from the study.
This can be calculated using the formula:
n = (z^2 * p * (1-p)) / (e^2)
where z is the z-score corresponding to a 95% confidence level, p is the estimated proportion of people in favor of legalizing marijuana, and e is the margin of error (5%).
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Ingrid competed in a triathlon that requires her to run, swim and bike. If she swam at a rate of 3 mph for 1 and a half hour, biked at 12 mph for 3 hours and ran for 6 mph for 4 hours, find the distance of the triathlon.
The distance of the triathlon, given the time Ingrid spent swimming, biking, and running, is 61.5 miles
How to find the distance?To find the distance of the triathlon, find the distance of the individual events which are the running, swimming, and biking. Then sum these distances up to find the triathlon distance that Ingrid ran.
The distance for swimming:
= Rate x Number of hours
= 3 x 0.5 hours
= 1.5 miles
The distance for biking:
= 12 x 3
= 36 miles
The distance for running:
= 6 x 4
= 24 miles
The triathlon distance is:
= 1.5 + 36 + 24
= 61.5 miles
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3.
(07.04)
1 over 3b = 4 over 5 . Which of the following equals b in this equation? (4 points)
1 over 4
1 1 over 8
2 2 over 5
2 over 5
Answer:
c) 2 2 over 5 = 2 2/5
Step-by-step explanation:
Forming the equation,
→ (1/3)b = 4/5
Now the value of b will be,
→ (1/3)b = 4/5
→ b = (4/5) ÷ (1/3)
→ b = (4/5) × (3/1)
→ b = (4 × 3)/(5 × 1)
→ b = 12/5
→ [ b = 2 2/5 ]
Hence, value of b is 12/5.
Please Help!! Hurry!!!
Answer:
Step-by-step explanation:
(3, 12721) and (5,10835)
(10835 -12721) - (5-3)
-1886/2 = -943
Select the expression that have a value of 40 when x = 10.8.
The expression that has a value of 40 when x = 10.8. is (C) (x² ÷ 18) + 33.52
How to determine the expressions that fit the given category?The complete question is added at the end of this solution
From the question, we have the following expressions that can be used in our computation:
A 4,320 ÷ x
B 288/x + 16
C (x² ÷ 18) + 33.52
D (1,752 ÷ x) – 162/29
F x/12 + 36
The value of x is given as
x = 10.8
So, we evaluate the expressions at this value of x
Expression A: 4,320 ÷ x
4,320 ÷ 10.8 = 400 --- false
Expression B 288/x + 16:
288/10.8 + 16 = 42.7 --- false
Expression C (x² ÷ 18) + 33.52:
(10.8² ÷ 18) + 33.52 = 40 --- true
Expression D (1,752 ÷ x) – 162/29:
(1,752 ÷ 10.8) – 162/29 = 156.6 --- false
Expression F x/12 + 36:
10.8/12 + 36 = 36.9 --- false
Hence, the only expression is (x² ÷ 18) + 33.52
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Complete question
Select all the expressions that have a value of 40 when x = 10.8.
A 4,320 ÷ x
B 288/x + 16
C (x² ÷ 18) + 33.52
D (1,752 ÷ x) – 162/29
F x/12 + 36
Please answer this ASAP.
Answer:
y = 0.8x
Step-by-step explanation:
Parallel lines have the same slope but different y-intercepts
Bottom line slope can be found by noting that it passes through points
(0, -3.2) and (4,0)
Then find the difference in y values which is called the rise
Find the corresponding difference in x values called the run
rise/run = slope
For the bottom line
Rise = 0 - (-3.2) = 3.2
Run = 4 - 0 =4
So slope m = 3.2/4 = 0.8
Slope of top line is also 0.8
Since it passes through origin there is no y-intercept
So equation of top line is simply
y = 0.8x
according to a recent survey 85 percent of high school students own a personal media player. what is the probability that 6 out of 10 random highschool students own a personal media player
The probability is 0.04.
Define probability sampling.
The sampling probability of an element or member of the population in statistics, in the theory relating to sampling from finite populations, is its likelihood of being included in the sample during the drawing of a single sample.
Probability sampling refers to the selection of a sample from a population when this selection is based on the principle of randomization, that is, random selection or chance. When compared to non-probability sampling, probability sampling is more difficult, time-consuming, and typically more expensive.
Solution Explained:
Given,
x = 7, n = 10, p = 0.85 and q = 0.15
Using the formula,
P(X=6) = [tex]_{n}C_{x} (0.85)^{n} (0.15)^{x}[/tex]
= [tex]_{10}C_{6} (0.85)^{6} (0.15)^{4}[/tex]
= 210(0.377)(0.0005)
= 0.04
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a sample of 1600 computer chips revealed that 42% of the chips do not fail in the first 1000 hours of their use. the company's promotional literature claimed that above 39% do not fail in the first 1000 hours of their use. is there sufficient evidence at the 0.10 level to support the company's claim? state the null and alternative hypotheses for the above scenario.
Reject this null hypothesis because the p-value (0.0523) is lower than the significance level (0.10) in this case.
Explain the term Null hypothesis?The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data or measured phenomena for any given single observed variable.Let p represent the fraction of the population.
Taking into account the provided data, we have
Null hypothesis: H0 : p ≤ 0.35.
Alternative hypothesis: H1 : p > 0.35, the test is a right-tailed test since the alternative is right-tailed;
For the stated question-
n = 1000; p' = 0.42.
Test statistics for this sample proportion:
z = (p' - p) / √p(1 - p)/n
Put the values-
z = (0.42' - 0.39) / √0.39(1 - 0.39)/1000
z = 1.94
P-value for this right tailed test is;
P(z > 1.94) = 0.0523
Therefore reject this null hypothesis because the p-value (0.0523) is lower than the significance level (0.10) in this case.
We draw the conclusion that we have enough data to back up the company's claim at the 0.10 level.
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HELP ME PLEASE AS FAST AS POSIBLE
Answer:
243 inches to the 3 power
Step-by-step explanation:
In recent years, 64% of students at ACME University were women. Administrators wondered if this proportion has diminished. In a recent survey of 300 ACME University students, 178 were women. a. Check all assumptions for performing the binomial test for a population proportion. Are they satisfied?SRS
b. Write the null and alternative hypotheses. Null- true proportion= 0.64Alternative- the true proportion= <0.64
c. Carry out the binomial test at the α = 7% significance level. Calculate the p-value, and state your conclusion in a complete sentence.
p-value= 0.05309if the null hypothesis is true, there is a 5.3% chance of getting a small sample proportion. We should reject the null if favor of the alternative if a=7
d. How would your conclusion in part c. change if the significance level α was changed to 5%? Explain. We would fail to reject the null hypothesis
As per the question, the following presumptions need to be true in order to run the binomial test for a population proportion:
a) A simple random sample (SRS) drawn from the population of interest must be used to gather the data. The sample's observations must be unrelated to one another. A binary answer variable is required (i.e., it can only take on two possible values, such as "success" and "failure").
The Central Limit Theorem must be applicable, hence the sample size must be sufficient (i.e., np and nq must both be greater than 5, where p is the proportion of successes in the population and q is the proportion of failures in the population).
From the facts given, it is unclear whether these presumptions are true. In example, it is unclear whether the observations are independent or whether the data was gathered from a straightforward random sample.
b) For this test, the following alternative and null hypotheses are presented:
The actual percentage of female students at ACME University is 0.64, which is null. Alternately, the actual percentage of female students at ACME University is less than 0.64.
c) The p-value must be determined before the binomial test can be run at the = 7% significance level. A statistical software program or a binomial test calculator can be used for this.
The p-value for this test is 0.05309 assuming the binomial test assumptions are met. This suggests that there is a 5.3% chance of generating a sample proportion as little as or smaller than the one seen in the survey if the null hypothesis is true (i.e., the true proportion of women among ACME University students is 0.64).
We can reject the null hypothesis in favor of the alternative hypothesis because the p-value is smaller than the significant level (0.05309 0.07). In other words, we can infer that the actual percentage of female students at ACME University is less than 0.64.
d) Our findings would remain unchanged if the significance criterion was raised to 5%. Because the p-value is still below the significance level (0.05309 0.05), the alternative hypothesis would still be accepted instead of the null hypothesis.
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The letters that form the word
MATHEMATICS are placed in a bowl. Are the
odds favorable or unfavorable that he will
choose a letter that is a vowel followed by a
"T"?
Answer:
Step-by-step explanation:
The odds arent favorable its a 2/11 chance of happening
Which of the following options have the same value as 60% and 94?
A: 0.06⋅94
B: 0.6⋅94
C: 5/3⋅94
D: 60⋅94
E: 60/100⋅94
Answer:
0.6 x 94
Step-by-step explanation:
You can convert 60% into a decimal, by moving the decimal place twice to the left, and it will still be the same. So, we have 0.60. Then, usually the term "and" means addition, but that is not in one of the answers, so I suppose they mean multiplication. So, we can set up this equation:
0.6 x 94
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6. 112 how big is the tip percentage at a restaurant? use technology and the restauranttips dataset to find a 95% confidence interval for the mean tip percentage (pcttip) at the restaurant. Interpret the answer in context
The 95% confidence interval for the mean tip percentage is (3.49, 4.22)
How to find confidence interval?Confidence interval is the two-sided limit consisting of the lower limit and the upper limit and the value between the two limits is the parameter value.
For this question, we have given a graph of the data, so we only need to see the data and interpret that to answer the question.
First, since confidence interval is 95% so we must see 2.5% limit for two side or equal to 0.025.
For the lower limit, see upper value of dot plot then see separate lowest 0.025 of data is 3.491 or 3.49.
For the upper limit, see lower value of dot plot then see separate highest 0.025 of data is 4.224 or 4.22.
Thus, the 95% confidence interval is (3.49, 4.22) for the mean tip percentage.
Your question is incomplete, but most probably your full question was (image attached)
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Which fraction is equivalent ?
Answer:
Option A
Step-by-step explanation:
→ Simplify all the options
a. 5/6 and b is 2/3