1) A liquor store owner wants to re-order their store to put the more expensive wines near the front. The owner samples 40 bottles of red and 40 bottles of white wine to find out which is more expensive. The owner finds the average price of white is $19.33, while the average price of red is $20.87 (standard deviation of $2.88 for white and $3.05 for red).
1a) What is the point estimate of the population price difference between red and white wines?
1b) What is the margin of error for alpha=0.01?
1c) What is the confidence interval for the difference between the two population means? Use alpha=0.05.
Answers
Answer:
Bellow
Step-by-step explanation:
1a) The point estimate of the population price difference between red and white wines is given by:
$$\bar{x}_1 - \bar{x}_2 = 20.87 - 19.33 = 1.54$$
Therefore, the point estimate of the population price difference between red and white wines is $1.54.
1b) The margin of error for alpha=0.01 can be calculated using the following formula:
$$ME = z_{\alpha/2}\cdot\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$$
where $z_{\alpha/2}$ is the critical value of the standard normal distribution for the given level of significance, $s_1$ and $s_2$ are the sample standard deviations, and $n_1$ and $n_2$ are the sample sizes for the two populations.
For alpha=0.01, the critical value of the standard normal distribution is $z_{\alpha/2}=2.58$. Substituting the given values, we get:
$$ME = 2.58\cdot\sqrt{\frac{2.88^2}{40} + \frac{3.05^2}{40}} \approx 1.01$$
Therefore, the margin of error for alpha=0.01 is approximately $1.01.
1c) The confidence interval for the difference between the two population means can be calculated using the following formula:
$$(\bar{x}_1 - \bar{x}_2) \pm z_{\alpha/2}\cdot\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$$
For alpha=0.05, the critical value of the standard normal distribution is $z_{\alpha/2}=1.96$. Substituting the given values, we get:
$$(20.87 - 19.33) \pm 1.96\cdot\sqrt{\frac{2.88^2}{40} + \frac{3.05^2}{40}}$$
Simplifying this expression, we get:
$$(1.54) \pm 1.11$$
Therefore, the 95% confidence interval for the difference between the two population means is approximately $(0.43, 2.65)$.
Related Questions
solve the rational equation 4 divided by x equals quantity 3 times x plus 2 end quantity divided by x squared, and check for extraneous solutions. x
Answers
The solution x = 2 is valid for the original equation.
To solve the rational equation (4/x) = (3x + 2)/x², we can start by multiplying both sides of the equation by x² to eliminate the denominators:
x² * (4/x) = x² * [(3x + 2)/x²]
Simplifying:
4x = 3x + 2
Next, we can isolate the x term by subtracting 3x from both sides:
4x - 3x = 3x + 2 - 3x
x = 2
So, the solution to the rational equation is x = 2.
Now, let's check for extraneous solutions by substituting x = 2 back into the original equation:
(4/2) = (3(2) + 2)/(2²)
2 = (6 + 2)/4
2 = 8/4
2 = 2
Since the equation is true when x = 2, there are no extraneous solutions.
Therefore, for the initial equation, x = 2 is a viable answer.
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Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answers
Answer:
1/2 is the correct answer
a) Set-up an integral for the area of the surface obtained by rotating the curve y=tanx,0≤x≤π3about the x-axisb) Set-up an integral for the area of the surface obtained by rotating the curve y=tanx,0≤x≤π3about the y-axis
Answers
The area of the surface obtained by the curve rotated along the x-axis is \(S_1=\int\limits_0^{\pi/3}2\pi (\tan x)\sqrt{1+\sec^4x}\;dx\). The area of the surface obtained by the curve rotated along the y-axis is \(S_2=\int\limits_0^{\sqrt{3}}2\pi (\tan^{-1}y)\sqrt{1+\left(\frac{1}{1+y^2}\right)^2}\;dy\).
A surface type that results from rotating a curve around a specific axis is the area of the surface of revolution. The formula for the area around the x-axis is given by, \(S_1=\int\limits_a^b2\pi f(x)\sqrt{1+(f'(x))^2}\;dx\) and around the y-axis is \(S_2=\int\limits_a^b2\pi g(y)\sqrt{1+(g'(y))^2}\;dy\).
a) Given the expression is rotated about the x-axis. Let,
\(\begin{aligned}f(x)&=y\\&=\tan x \in \left[0,\frac{\pi}{3}\right] \end{aligned}\)
Then,
\(f'(x)=\sec^2x.\)
Substitute f(x) and f'(x) value in the S₁ formula, we get,
\(S_1=\int\limits_0^{\pi/3}2\pi (\tan x)\sqrt{1+\sec^4x}\;dx\)
b) Given the expression is rotated about the y-axis. Let,
\(\begin{aligned}x&=g(y)\\&=\tan^{-1}y \in \left[0, \sqrt{3}\right] \end{aligned}\)
Then,
\(g'(y)=\frac{1}{(1+y^2)}\)
Substitute g(y) and g'(y) value in the S₂ formula,
\(S_2=\int\limits_0^{\sqrt{3}}2\pi (\tan^{-1}y)\sqrt{1+\left(\frac{1}{1+y^2}\right)^2}\;dy\)
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The complete question is -
a) Set up an integral for the area of the surface obtained by rotating the curve y=tanx,0≤x≤π/3 about the x-axis.
b) Set up an integral for the area of the surface obtained by rotating the curve y=tanx,0≤x≤π/3 about the y-axis.
2x + 8 = -4 I NEED ALL PLS
Answers
Answer:
Answer down below!
Step-by-step explanation:
Let's write out the equation!
2x + 8 = -4
To solve this, you have to subtract the 8 and bring it over to -4
That would look something like:
2x -(+8) = -4 -8
That leaves you with 2x = -12
Now you divide 2 and -12 which will give you
-6
Answer:X= - 6
Step-by-step explanation:
MOVE +8 to the right which would make it negative so -8-4.You would add both numbers which would be -12 and then u divide -12 with 2 so
-12/2 is -6
based off of this information, what conclusions can be made about the mean value theorem? this contradicts the mean value theorem since f satisfies the hypotheses on the given interval but there does not exist any c on (1, 4) such that f '(c)
Answers
The correct option is; 4: this contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) (7 − 1) , but f is not continuous at x = 3.
Explain the term Mean Value Theorem?The Mean Value Theorem says that there occurs a point c in the interval (a,b) so that f'(c) equals the function's average rate of change throughout [a,b] if a function f is continuous just on closed interval [a,b] as well as differentiable just on open interval (a,b).The function being used is;
f(x) = (x - 3)⁻²
If we separate this function according to x, we obtain;
f'(x) = -2/(x - 3)³
Finding all c values f(7) − f(1) = f '(c)(7 − 1).is our goal.
This suggests that;
0.06 - 0.25 = -2/(c - 3)³ x 6
-0.19 = -12/(c - 3)³
(c - 3)³ = 63.157
c = 6.98
If the Mean Value Theorem holds for this function, then f must be continuous on [1,7] and differentiable on (1,7).
But when x = 3, f is not continuous, hence the Mean Value Theorem's prediction is false.
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The complete question is-
Let f(x) = (x − 3)−2. Find all values of c in (1, 7) such that f(7) − f(1) = f '(c)(7 − 1). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) c = Based off of this information, what conclusions can be made about the Mean Value Theorem?
This contradicts the Mean Value Theorem since f satisfies the hypotheses on the given interval but there does not exist any c on (1, 7) such that f '(c) = f(7) − f(1) 7 − 1 . This does not contradict the Mean Value Theorem since f is not continuous at x = 3. This does not contradict the Mean Value Theorem since f is continuous on (1, 7), and there exists a c on (1, 7) such that f '(c) = f(7) − f(1) 7 − 1 . This contradicts the Mean Value Theorem since there exists a c on (1, 7) such that f '(c) = f(7) − f(1) 7 − 1 , but f is not continuous at x = 3. Nothing can be concluded.an ecology center wants to set up an experimental garden in the shape of a rectangle. the length of the rectangle is 4 yards longer than the width. what are the dimensions of the garden if the enclosed area is 21 square yards. state units.
Answers
Let’s assume that the width of the rectangle is x.
Since the length is 4 yards longer, we can write the length as x + 4.
The area of a rectangle is length * width, and the area is already given to us as 21 square yards.
So length * width = area, meaning x * x + 4 = 21
So x^2 + 4 = 21
= x^2 = 21 - 4
= x^2 = 17
= x = root of 17
= 4.12 yards
We’ve found out that the width is 4.12 yards, so the length must by 4.12 + 4
= 8.12 yards.
So, the dimensions of the garden are 8.12 * 4.12 yards*
*This answer is rounded, so it won’t be exact.
Another, more exact value is root 17 * root 17 + 4
Find two numbers whose difference is 92 and whose product is a minimum.
Answers
Step-by-step explanation:
x -y = 92 x = 92+y
xy = minumum
(92+y) * y = minumum
y^2 + 92y = minumum this quadratic has a minimum at
y = -b/2a = - 92/(2*1) = - 46
x - -46 = 92 shows x = +46 minimum is then - 2116
What was his mistake????
Answers
Helena can buy 2 shirts for $25 or 3 shirts for $36. do these quantities have a proportional relationship? explain. yes; the ratio of cost to shirts is equivalent. yes; the constant of proportionality is 12. yes; the constant of proportionality is 12.5. no; the ratio of cost to shirts is not equivalent.
Answers
The quantities do not have a proportional relationship because the ratio of the cost to shirts is not equivalent.
Are the quantities proportional?The two quantities would have a proportional relationship if the constant of proportionality are equal. The constant of proportionality would be equivalent to the cost of one shirt.
The equation that can be used to determine the constant of proportionality is:
k = y / x
Where:
y = total cost of the shirts x = number of shirts boughtk = 25 / 2
k = 12.60
k = $36 / 3
k = $12
The quantities are not proportional because the constant of proportionality are different.
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Find the inequality represented by the graph
Answers
Answer:
y<or equal to 5/2x + 5
Step-by-step explanation:
when graphing inequalities, the line is solid when the inequality is also "or equal to". also, the less than sign indicates that the area below the line will be shaded. the y intercept is the y value when x is 0, so + 5. the slope, calculated with rise over run, is 5/2x
Which get the tens digit of x. Ex: If x = 693, which yields 9?
a. x % 10
b. x % 100
c. (x / 10) % 10
Answers
The correct answer is (c) x's tens digit. , if x = 693, that yield 9 is (x / 10) % 10
Here's how we have to evaluate the expression:
Substitute x = 693 into the expression to get:
(693 / 10) % 10
Perform the division first:
693 / 10 = 69 with a remainder of 3.
Substitute the result of the division into the expression:
(69 % 10)
To Evaluate the remainder use the modulo operator (%):
69 % 10 = 9
The result, 9, is the tens digit of 693.
=(x / 10) % 10.
The tens digit of a number refers to the digit in the second place from the right, or the digit that represents the multiple of 10. For example, in the number 365, the tens digit is 6 because it represents 6 tens or 60.
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A figure was moved 5 units to the right, then a
mirror image was made. Which transformations were used? Rotation, dilation, reflection, translation
Answers
Answer:
Step-by-step explanation:
First a translation then a reflection.
The perimeter P of a rectangle is P = 21 + 2w, where I and w are the rectangle's length and
width, respectively.
(A) Rewrite the formula to find the length given perimeter and width. Justify each step in your solution with the property used. (B) compite the length of a rectangle with a perimeter 40.2in and width of 6.7in.
Answers
Answer:
see below
Step-by-step explanation:
P = 2l + 2w
Subtract 2w using the subtraction property of equality
P -2w = 2l+2w-2w
P -2w = 2l
Divide each side by 2, using the division property of equality
P/2 -2w/2 = 2l/2
1/2 P -w = l
Now we have P =40.2 and w = 6.7
l =1/2 (40.2) - 6.7
l =20.1-6.7
=13.4
Derive expressions for the means and variances of the following linear combinations in terms of the means and covariances of the random variables X1, X2, and X3. (a) X1 - 2X2 (b) X1 + 2X2 - 3 (C) 3X1 - 4X2 if X1 and X, are independent (So, 012 = 0).
Answers
Means and Variances of Linear Combinations:
(a) X1 - 2X2
Mean: μa = μ1 - 2μ2
Variance: σa2 = σ12 + 4σ22 + 4σ122
(b) X1 + 2X2 - 3
Mean: μb = μ1 + 2μ2 - 3
Variance: σb2 = σ12 + 4σ22 + 4σ122
(c) 3X1 - 4X2
Mean: μc = 3μ1 - 4μ2
Variance: σc2 = 9σ12 + 16σ22
In the case that X1 and X2 are independent, then σ122 = 0, so:
(a) X1 - 2X2
Mean: μa = μ1 - 2μ2
Variance: σa2 = σ12 + 4σ22
(b) X1 + 2X2 - 3
Mean: μb = μ1 + 2μ2 - 3
Variance: σb2 = σ12 + 4σ22
(c) 3X1 - 4X2
Mean: μc = 3μ1 - 4μ2
Variance: σc2 = 9σ12 + 16σ22
Plz help me:)!!!✌︎('ω')✌︎
Answers
A locker combination has three nonzero digits, with no repeated digits. If the first digit is a 2, what is the probability the second digit is also even?
A. 1/2
B. 1/3
C. 3/7
D. 3/8
Answers
Justin and Tyson are beginning an exercise program to train for football season and want to build muscle. Justin weighs 150 pounds and hopes to gain 2 pound per week. Tyson weighs 160 pounds and hopes to gain 1 pound per week. After how many weeks will they weigh the same amount?
Answers
Answer:
At 15 weeks they will both weigh 180
Step-by-step explanation:
150 + 2w = 195 - w
2w + w = 195 - 150
3w = 45
w = 45/3
w = 15 <=== they will weigh the same at 15 weeks
150 + 2(15) = 150 + 30 = 180...and they will both weigh 180 lbs
I hope this helps you :)
Choose the best estimate for the weight of a cantaloupe. Responses A 2 decigrams2 decigrams B 2 kilograms2 kilograms C 2 grams2 grams D 2 milligrams
Answers
The best estimate for the weight of a cantaloupe is 2 kilograms (B).
A decigram is 1/10th of a gram, which would be too small of weight for a cantaloupe. 2 grams (C) is also too small for a cantaloupe as it would only be the weight of a few small seeds. 2 milligrams (D) is an extremely small weight, only suitable for a single grain of salt or a tiny insect.
Therefore, 2 kilograms (B) is the most reasonable estimate for the weight of a cantaloupe as it falls within the typical range of cantaloupe weights.
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Complete Question:
Choose the best estimate for the weight of a cantaloupe. Responses
A 2 decigrams
B 2 kilograms
C 2 grams
D 2 milligrams
The length of a rectangle is equal to triple the width. what is its width and length if its perimeter is 88 centimeters.
Answers
Answer:
56fifjjfiggitrireieisixii3eiirr
Answer:
Length = 33 cm
width = 11 cm
Step-by-step explanation:
a = 3w ⇒ eq. 1
88 = 2(a+w) ⇒ eq. 2
a = length
w = width
then:
replacing the value of the eq. 1 on the eq. 2
88 = 2(3w + w)
88/2 = 4w
44 = 4w
w = 44/4
w = 11 cm
from the eq. 1
a = 3w
a = 3*11
a = 33cm
Check:
perimeter = 88 = 2(a+w)
88 = 2(33+11)
88 = 2*44
The five values for a data set are: minimum = 0 lower quartile = 2 median = 3. 5 upper quartile = 5 maximum = 10 Bruno created the box plot using the five values. What error did he make? The right whisker should go from 3. 5 to 10. The left whisker should go from 0 to 2. The box should go from 2 to 3. 5. The box should go from 3. 5 to 5
Answers
The five values for a data set are: minimum = 0 lower quartile = 2 median = 3. 5 upper quartile = 5 maximum = 10 Bruno created the box plot using the five values. Bruno made error. The left whisker should go from 0 to 2.
About quartileQuartiles is a type of quartile that divides data into four parts with approximately the same number. The first quartile or lower quartile (Q1) is the middle value between the smallest value and the median of the data group. The first quartile is a marker that the data in that quartile is 25% below the data group.
The second quartile (Q2) is the median data which marks 50% of the data (dividing the data in half). The third or upper quartile (Q3) is the middle value between the median and the highest value of the data set. The third quartile is a marker that the data in that quartile is 75% below the data group. Quartiles are a form of an ordered statistic because to determine quartiles, data needs to be sorted from smallest to largest value first.
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−9+12×(−13)+2÷19 i need help on how do this and how you do it
Answers
Find the distance between the points (0, 0) and (4, 0).
02
04
O √8
Answers
Answer:
4 units
Step-by-step explanation:
(0, 0 ) and (4, 0 )
since the y- coordinates are equal then the distance between the points is the difference of the x- coordinates, that is
| 4 - 0 | = | 4 | = 4 or
| 0 - 4 | = | - 4 | = | 4 | = 4
Please help thank you
Answers
Answer: D (4,1)
Step-by-step explanation:
2x + 3(x-3) = 11
2x + 3x - 9 = 11
5x = 11 + 9
x = 20/5 = 4
y = x-3
= 4-3 = 1
Jennifer is saving money to buy a bike. The bike costs $239. She has $127 saved, and each week she adds
$16 to her savings.
How long will it take her to save enough money to buy the bike?
It will take her
weeks to save for the bike.
Answers
Answer: 7 weeks
Step-by-step explanation:
16X + 127 = 239
16X = 239 - 127
16X = 112
X = 112/16
X = 7
help me !!!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
The MAD is 2.
Customers at a fast food restaurant were invited to complete a brief survey to rate their experiences at the restaurant. One day,48 customers chose to complete the survey. Which statement best explains why this was probably NOT a representative sample?
Answers
Answer:
The sample included only those people who chose to complete the survey.
Step-by-step explanation:
In the notation "s(x) = ...," what does "s(x)" represent? A. The value found when s is multiplied by the value x. B. There is not enough information to answer this question. C. The value of s(x) depends on the value of x, since s is a function of x. D. The value of x depends on the value of s(x), since x is a function of s.
Answers
s(x) represents the value of s(x) depending on the value of x since s is a function of x.
The first thing you should be aware of in this situation is that the following is contained in the provided expression:
S: stands for a function whose value we are interested in.
In order to understand the function s, we must use the term (numerical value) represented by x.
S is therefore dependent on X.
So, we have:
As s is a function of x, its value depends on the value of x.
As s is a function of x, the value of s (x) depends on the value of x.
Consider the provided notation.
Since s is a function of x. The s(x) value depends on the x value.
For any function f(x); The independent variable is x.
i.e. it depends on the variable x.
Similarly, here s(x) is the dependent variable. which is defined for the corresponding variable x.
Hence, s(x) represents the value of s(x) depending on the value of x, since s is a function of x.
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Match each phrase with the algebraic expression it describes
Answers
Answer:
Step-by-step explanation:
This is all about the symbols and how they are pronounced; it's also about what they mean in less formal language.
h is less than 21: h < 21
h is greater than or equal to 21: \(h \ge 21\) (notice the half-an-equal sign under the greater than sign)
h is less than or equal to 21: \(h \le 21\)
h is equal to 21: h = 21
h is greater than 21: h > 21
Learn these well, and they'll be your friends for life!
How do you solve (2k – 1)^2= 9
Answers
Answer: MathPapa
Step-by-step explanation:
Just put it there. Since the square is there, you put two of those side by side and then multiply all the numbers. Then you solve normally. (2k-1)(2k-1)=9
What is the slope of y = x +5?
Answers
1
Step-by-step explanation:
Hi there!
»»————- ★ ————-««
I believe your answer is:
m = 1
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
\(\boxed{\text{General Slope-Intercept Form:}}\\\\y = mx + b\\\rule{150}{0.5}\\\text{m - slope}\\\text{b - Y-intercept}\)
⸻⸻⸻⸻
The slope is '1'. Unusually, the 1 is not written in equations. Since '1' would take m's place, the slope of the given equation is 1.
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.