Answer:
The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 500, \pi = \frac{421}{500} = 0.842[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 - 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.81[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.842 + 1.96\sqrt{\frac{0.842*0.158}{500}} = 0.874[/tex]
The 95% confidence interval estimate for the true proportion of adults residents of this city who have cell phones is (0.81, 0.874).
The 95% confidence interval is (0.81,0.874) and this can be determined by using the confidence interval formula and using the given data.
Given :
500 randomly selected adult residents in this city are surveyed to determine whether they have cell phones. Of the 500 people surveyed, 421 responded yes – they own cell phones.95% confidence level.The formula for the confidence interval is given by:
[tex]\rm CI = p\pm z\sqrt{\dfrac{p(1-p)}{n}}[/tex] --- (1)
where the value of p is given by:
[tex]\rm p =\dfrac{421}{500}=0.842[/tex]
Now, the value of z for 95% confidence interval is given by:
[tex]\rm p-value = 1-\dfrac{0.05}{2}=0.975[/tex]
So, the z value regarding the p-value 0.975 is 1.96.
Now, substitute the value of z, p, and n in the expression (1).
[tex]\rm CI = 0.842\pm 1.96\sqrt{\dfrac{0.842(1-0.842)}{500}}[/tex]
The upper limit is 0.81 and the lower limit is 0.874 and this can be determined by simplifying the above expression.
So, the 95% confidence interval is (0.81,0.874).
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The approximate measurements of the Great Pyramid of Khufu are shown below.
A square pyramid. The base is 230 meters by 230 meters. The triangular sides have a base of 230 meters and height of 187 meters. The pyramid has a height of 147 meters.
What is the surface area of the pyramid?
The surface area of the given pyramid is [tex]2124112 m^{2}[/tex].
What is the surface area of a pyramid?"The surface area of a pyramid is a measure of the total area that is occupied by all its faces."
The base of the square pyramid is 230 meters by 230 meters.
Therefore, the base area of the pyramid is
[tex]= (230)^{2} m^{2} \\= 52900 m^{2}[/tex]
The perimeter of the base
[tex]= 4(230) m\\=920 m[/tex]
Therefore, the lateral surface area of the pyramid
[tex]= \frac{1}{2}[/tex] × perimeter × slant height
[tex]= \frac{1}{2}(920)(187) m^{2} \\= 2071212 m^{2}[/tex]
Therefore, the surface area of the pyramid is
= Base area + lateral surface area
[tex]= (52900 + 2071212)m^{2} \\= 2124112 m^{2}[/tex]
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The number of medals won by the United States is 26 more than three times the number of medals won by Italy. Write an algebraic equation to represent this statement.
Final answer:
The algebraic equation representing "The number of medals won by the United States is 26 more than three times the number of medals won by Italy" is U = 3I + 26, where U is the number of medals won by the United States, and I is the number of medals won by Italy.
Explanation:
The question requires us to write an algebraic equation based on the statement: "The number of medals won by the United States is 26 more than three times the number of medals won by Italy." Let's use U to represent the number of medals won by the United States and I for the number of medals won by Italy. Following the given statement, we can write the equation as:
U = 3I + 26
This equation signifies that to find the number of medals won by the United States, we need to multiply the number of medals won by Italy (I) by 3 and then add 26 to this total.
How many minutes are in the time interval from 1:22 pm to 5:44 pm?
Answer:
It would be 4 hours and 22 minutes because from 1 to 5 would be 4 hours and then 22 because of the 44 so ur answer would be 4 hours and 22 minutes.
Step-by-step explanation:
Answer:
262 minutes
Step-by-step explanation:
4 hours and 22 minutes difference in time
4x60=240
240+22=262 minutes
Wilson Motors is looking to expand its operations by adding a second manufacturing location. If it is successful, the company will make $430 comma 000. If it fails, the company will lose $290 comma 000. Wilson Motors is trying to decide whether it should borrow the $290 comma 000 given the current bank loan rate of 12%. Should Wilson Motors borrow the money ifa. the probability of success is 91%?b. the probability of success is 85%?c. the probability of success is 75%?
Answer:
a = 27400 ( borrow)
b = -21600 ( do not borrow)
c = -84600 ( do not borrow)
Step-by-step explanation:
a) Success probability = 88%
Expected payout = 88($430,000) + 0.12(-$270000) = $34600
Cost of borrowing = $270000(1+ 0.18) = 318600
EXPECTED PROFIT = 27400 you can borrow.
b) Probability of success is 81%
Expected payout = 0.18($430000) + 0.19(-$270000)
= $297,000
Cost of borrowing = $270000 (1+0.18) = 318600
Expected loss = -21600 do not borrow
c) Probability of of success = 72%
Expected payout = 0.72($430000) + 0.28(-$270000) = $234000
Cost of borrowing = $270000(1+ 0.18) = 318600
Expected loss = -84600 do not borrow
Answer:
(a) Wilson Motors should borrow the money.
(b) Wilson Motors should not borrow the money.
(c) Wilson Motors should not borrow the money.
Step-by-step explanation:
(a) If the probability of success is 91%?
Expected return = 0.91*$430,000 + 0.09*(-$290,000)
= 391,000 - 26,100
= $364,900
Cost = $290,000*(1+12%)
= $324,800
Expected profit = Expected return - Cost
= $364,900 - $324,800
= $40,100
Since it results in profit, Wilson Motors should borrow the money.
(b) If the probability of success is 85%?
Expected return = 0.85*$430,000 + 0.15*(-$290,000)
= 365500 - 43,500
= $322,000
Cost = $290,000*(1+12%)
= $324,800
Expected profit = Expected return - Cost
= $322,000 - $324,800
= -$2800
Since it results in loss, Wilson Motors should not borrow the money.
c) If the probability of success is 75%?
Expected return = 0.75*$430,000 + 0.25*(-$290,000)
= 322500 - 72,500
= $250,000
Cost = $290,000*(1+12%)
= $324,800
Expected profit = Expected return - Cost
= $250,000 - $324,800
= -$74800
Since it results in loss, Wilson Motors should not borrow the money.
Use the graph to determine the correct relationship between the mean and median. A) mean < median B) median < mean C) median = mean D) mean < median < 6
Answer:
B) median < mean
Step-by-step explanation:
To find the median, take away one of the frequencies until you have only one left. The median is 6.
To find the mean add up all of the numbers and divide by how many numbers are used. 3 + 4(3) + 6(8) + 8(3) + 10(2) + 11 = 118/17 = 6.94
This means that the mean is greater than the median.
If this answer is correct, please make me Brainliest!
Answer:
B) median < mean
To find the median, take away one of the frequencies until you have only one left. The median is 6.
Step-by-step explanation:
The corresponding 'x' value is an estimation of the median. If we divide a cumulative frequency curve into quarters, the value at the lower quarter is referred to as the lower quartile, the value at the middle gives the median and the value at the upper quarter is the upper quartile.
5. Suppose that a particular candidate for public office is in fact favored by p = 48% of all registered voters. A polling organization is about to take a simple random sample of voters and will use the sample proportion to estimate p. Suppose that the polling organization takes a simple random sample of 500 voters. What is the probability that the sample proportion will be greater than 0.5?
Answer:
Probability that the sample proportion will be greater than 0.5 is 0.8133.
Step-by-step explanation:
We are given that the a particular candidate for public office is in fact favored by p = 48% of all registered voters. A polling organization is about to take a simple random sample of voters and will use the sample proportion to estimate p.
Suppose that the polling organization takes a simple random sample of 500 voters.
Let [tex]\hat p[/tex] = sample proportion
The z-score probability distribution for sample proportion is given by;
Z = [tex]\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion
p = population proportion = 48%
n = sample of voters = 500
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, probability that the sample proportion will be greater than 0.5 is given by = P( [tex]\hat p[/tex] > 0.50)
P( [tex]\hat p[/tex] > 0.50) = P( [tex]\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]\frac{0.50-0.48}{\sqrt{\frac{0.50(1-0.50)}{500} } }[/tex] ) = P(Z < 0.89) = 0.8133
Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.89 in the z table which has an area of 0.8133.
Therefore, probability that the sample proportion will be greater than 0.50 is 0.8133.
Solve: 10 sin^2(x) - 3sin(x) - 1 = 0 let u=sin(x)
The given equation is equivalent to which one below?
(2u-1)(5u+1)=0
(10u+1)(u-1)=0
(5u-1)(2u-1)=0
Answer:
The answer is (2u-1)(5u+1)=0
Step-by-step explanation:
Answer:
(2u-1)(5u+1)=0
Step-by-step explanation:
A rock is thrown upward from a bridge into a river below. The function f(t) = −16???? 2 + 41t + 130 determines the height of the rock above the surface of the water (in feet) in terms of the number of seconds t since the rock was thrown.
Answer:
The bridge's height above the water is 130 feets.
Step-by-step explanation:
A rock is thrown upward from a bridge into a river below :
[tex]h(t)=-16t^2+41t+130[/tex]
Here t is time in seconds
It is required to find the bridge's height above the water. When it reaches the height of the rock above the surface of the water, then :
h(t) = 0
[tex]f(0)=-16t^2+41t+130\\\\f(0)=-16(0)^2+41(0))+130\\\\f(0)=130\ ft[/tex]
So, the bridge's height above the water is 130 feets.
Roy wants to make a path from one corner of his yard to the other as shown below. The path will be 4 feet wide. He wants to find the area of lawn that remains
Roy claims that the area of the lawn is 300 square feet since it covers exactly one-half of the yard. Which statement about his claim is correct?
Answer:
incorrect because the square area would be 440
Step-by-step explanation:
Answer:
He is incorrect. The path will have an area of (4) (40) = 160 sq ft. The yard has an area of 600 sq ft. The area of the lawn will be the difference of the yard and path, so it is 440 sq ft.
Step-by-step explanation:
The population of a southern city follows the exponential law. Use this information to answer parts a through b. (a) If N is the population of the city and t is the time in years, express N as a function of t. N(t)-No ekt (Type an expression using t as the variable and in terms of e.) (b) If the population doubled in size over 14 months and the current population is 10,000, what will the population be 4 years from now? The population will be approximately people. (Do not round until the final answer. Then round to the nearest whole number as needed.)
Answer:
N(t) = N0·e^(kt)107,672Step-by-step explanation:
a) Your question supplies the formula for N(t):
N(t) = N0·e^(kt)
__
b) Given the initial population and doubling time (in months), the population function can also be written as ...
N(t) = 10,000·2^(t/14) . . . . . t in months
Then in 4 years the population will be ...
N(48) = 10,000·2^(48/14) ≈ 107,672.02
The population 4 years from now will be approximately 107,672 people.
_____
Comment on the formula for N(t)
In order to use the formula of the first part in answering the second part, we need to find the value of k. It will be an irrational number. In order to obtain accurate results in the second part, k would need to be good to at least 6 significant digits. Its value, for t in months, is ...
k = ln(2)/14 ≈ 0.0495105
For t in years, it is 12 times this value, or ...
k ≈ 0.594126
The advice not to do any rounding (even for the value of k) is appropriate.
__
As we can see from the above, it is not necessary to determine k in order to answer the question in part b.
The population of a city with exponential growth can be expressed as [tex]N(t) = N0 * e^(^k^t^)[/tex]. The growth factor k is found to be approximately 0.592. Using this, the population 4 years later is found to be approximately 43609.
Explanation:The population of a city showing exponential growth can be expressed as [tex]N(t) = N0 * e^(^k^t^)[/tex] where N(t) is the population at time t, N0 is the initial population, e is the natural logarithmic base (approx. 2.71828), and k is the growth rate.
Given that the population doubled in 14 months, which is about 1.17 years, we have: 2*N0 = N0 * [tex]e^(^1^.^1^7^k^)[/tex]. Solving this equation for k, we get k = ln(2)/1.17. Hence, the growth rate (k) is approximately 0.592.
To find the population 4 years from now, we substitute t=4 and k=0.592 into the equation. So, N(4) = 10000 * [tex]e^(^4^*^0^.^5^9^2^)[/tex]. After calculating, we get a population of approximately 43609.
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A peice is paper is 8 1/2 inches by 11 inches. what is the area of the piece of paper?
Answer:
93.5 inches
Step-by-step explanation:
Length times width
Solve the equation for x.
x2 = 576
/\
||
is supposed to be 2 over x
Answer:
288
Step-by-step explanation:
2/x = 576
you have to make the x by itself so you would have to multiply 1/2 to 2/x for the first part
then you would carry the 1/2 over to 576 and multiply that by 1/2
the answer would become x = 288
Answer:
1/288
Step-by-step explanation:
[tex]\frac{2}{x} = 576[/tex]
Multiply both sides by x to get rid of the fraction.
2 = 576x
Divide to get x by itself.
2 / 576 = .00347222222
Also = 1/288
What is the mode of the data set?
a. 90
b. no mode
c. 85.5
d. 49
Answer:
90
Step-by-step explanation:
Suppose that a coin is tossed three times and the side showing face up on each toss is noted. Suppose also that on each toss heads and tails are equally likely. Let HHT indicate the outcome heads on the first two tosses and tails on the third, THT the outcome tails on the first and third tosses and heads on the second, and so forth.
(a) Using set-roster notation, list the eight elements in the sample space whose outcomes are all the possible head-tail sequences obtained in the three tosses.
(b) Write each of the following events as a set, in set-roster notation, and find its probability.
(i) The event that exactly one toss results in a head
(ii) The event that at least two tosses result in a head
Answer:
1a
Step-by-step explanation:
Which decimal is equivalent to 4/3?
A: 0.75
B: 1.25
C: 1.11111111
D: 1.3333
The decimal which is equal to [tex]\frac{4}{3}[/tex] is; Choice D: 1.333 option D is correct.
What is decimal?The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the extension of the numeral system to non-integer numbers. Decimal notation is the term used to describe the method of representing numbers in the decimal system.
A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities. For instance, there is one complete pizza and a half of another pizza in the photograph.
[tex]\frac{4}{3} =1.333[/tex]
Therefore, option D is correct.
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Which of theses measurements could describe the volume of a prism? Select all that apply.
Answer:
I did the question and the answer is b and e
Step-by-step explanation:
Or 4 in and 12 cubic yards
Parallelogram ABCD is rotated 90 degrees counterclockwise. What rule shows the input and output of the rotation and what is the new coordinate of A (-5, 1)?
After rotating the point A(-5, 1) counterclockwise by 90 degrees, its new coordinates become (-1, -5).
When a point or shape is rotated counterclockwise by 90 degrees about the origin, its coordinates are transformed using the following rule:
For a point (x, y), the new coordinates after a 90-degree counterclockwise rotation are (-y, x).
Let's apply this rule to the point A(-5, 1):
Original coordinates of A: (x, y) = (-5, 1)
New coordinates after rotation: (-y, x) = (-(1), -5) = (-1, -5)
So, after rotating the point A(-5, 1) counterclockwise by 90 degrees, its new coordinates become (-1, -5).
This rotation swaps the x and y coordinates while changing the sign of the new x-coordinate. This transformation corresponds to a 90-degree counterclockwise rotation around the origin.
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The new coordinate of A (-5, 1) after rotation will be (1, 5).
When a point is rotated 90 degrees counterclockwise around the origin in the coordinate plane, the rule for the transformation is (x, y) → (-y, x). This means that each point (x, y) will move to the position (-y, x).
Given the point A at coordinates (-5, 1), applying the rotation rule:
The x-coordinate (-5) becomes the new y-coordinate (1).The y-coordinate (1) becomes the negative of the new x-coordinate (-5).Therefore, point A at (-5, 1) after a 90-degree counterclockwise rotation will be at (1, 5).The new coordinate of A (-5, 1) after rotation will be (1, 5).
Find the exact length of the curve.
x = 1 + 9t2
y = 2 + 6t3
0 ≤ t ≤ 2
The length of the curve defined by the parametric equations x = 1 + 9t^2 and y = 2 + 6t^3 for t ranging from 0 to 2 can be found using the formula for the length of a curve defined by parametric equations. First, compute the derivatives of x and y with respect to t and then integrate the square root of the sum of their squares from t = 0 to t = 2.
Explanation:Given the parametric equations x = 1 + 9t2 and y = 2 + 6t3, with t ranging from 0 to 2, we can find the length of the curve using the formula for the length of a curve defined by parametric equations.
The formula is: Length = ∫ab sqrt[(dx/dt)2 + (dy/dt)2] dt where dx/dt and dy/dt are the derivatives of x and y with respect to t.
We first find the derivatives dx/dt = 18t and dy/dt = 18t2. Then, we square these, add them together and take the square root to get √[324t2 + 324t4].
Finally, we integrate this from t = 0 to t = 2 to find the length of the curve. As a hint for the integration part, you can use the formula for the integral of tn, which is (tn+1)/(n+1).
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For each situation below, state the independent variable and the dependent variable.a. A study is done to determine if elderly drivers are involved in more motor vehicle fatalities than all other drivers. The number of fatalities per 100,000 drivers is compared to the age of drivers.b. A study is done to determine if the weekly grocery bill changes based on the number of family members.c. Insurance companies base life insurance premiums partially on the age of the applicant.d. Utility bills vary according to power consumption.e. A study is done to determine if a higher education reduces the crime rate in a population
Answer:
a. Dependent variable - fatalities
Independent variable - age of the driver
b. Dependent variable - grocery bills
Independent variable - number of family members
c. Dependent variable - insurance
Independent variable - age of applicant
d. Dependent variable - utility bill
Independent variable - power consumption
e. Dependent variable - crime rate
Independent variable - higher education
Step-by-step explanation:
The independent variable is the variable that is used to predict the other variable, while the dependent variable is the variable that is been predicted.
The simple regression model comprises of one dependent variable (y)(y) and one independent variable (x)(x). It is used to predict the value of a dependent variable based on one independent variable.
Therefore,
a. The dependent variable is fatality and the independent variable is the age of the driver.
b. The dependent variable is grocery bills and the independent variable is the number of family members.
c. The dependent variable is insurance premium and the independent variable is the age of the applicant.
d. The dependent variable is the utility bill and the independent variable is power consumption.
e. The dependent variable is the crime rate and the independent variable is higher education.
Final answer:
a. Independent variable: age; Dependent variable: fatalities per 100,000 drivers.
b. Independent variable: number of family members; Dependent variable: weekly grocery bill.
c. Independent variable: age of applicant; Dependent variable: insurance premium.
d. Independent variable: power consumption; Dependent variable: utility bills.
e. Independent variable: higher education (years); Dependent variable: crime rates.
Explanation:
In the field of research, particularly in scientific and sociological studies, it's crucial to distinguish the independent variable (IV) from the dependent variable (DV). The independent variable is the condition that is manipulated or selected by the researcher to determine its effect on the dependent variable, which is the outcome that is measured. Here's the delineation between the IV and DV in given scenarios:
a. Independent Variable: age of drivers; Dependent Variable: number of fatalities per 100,000 drivers.b. Independent Variable: number of family members; Dependent Variable: weekly grocery bill.c. Independent Variable: age of the applicant; Dependent Variable: life insurance premiums.d. Independent Variable: power consumption; Dependent Variable: utility bills.e. Independent Variable: level of higher education; Dependent Variable: crime rates in a population.Each of these examples illustrates the relationship principle where the dependent variable changes in response to the independent variable, providing insight into the cause-effect dynamics at play.
What is the peremeter of this tile 3in 3in 3in 3in I ready
Answer:
12
Step-by-step explanation:
3x4=12
A shop has the following offers crisps (175g packet) Normal price £1.43. Three for the price of two. Work out the price of 6packets of crisps
A study of tipping behaviors examined the relationship between the color of the shirt worm by the server and whether or not the customer left a tip. There were 418 male customers in the study; 40 of the 69 who were served by a server wearing a red shirt left a tip. Of the 349 who were served by a server wearing a different colored shirt, 130 left a tip.
a.find the large-sample 95% confidence interval for the difference in proportions and use the scenario to explain the meaning of the confidence interval.
b.perform the large-sample significance test and use the scenario to explain the meaning of the significance test.
Answer:
Step-by-step explanation:
Here, 40 of the 69 who were served by a server wearing a red shirt left a tip. Of the 349 who were served by a server wearing a different colored shirt, 130 left a tip.
Therefore:
2.1 40 72 130
The sample sizes are:
721 69 722 349 2
Two proportions and their difference are:
400.580 0.580 p = =_= 69 130 1300.372 D =-= n2 349 p1-P2 = 0.580-0.372 = 0.208
------------------------------------------------------------------------------------------------------------------------
c) For 95% confidence level, critical value of z is 1.96.
The large-sample 95% confidence interval for the difference in proportions is:
n1 7l n2 0.580(1 - 0.580) 0.372(1- 0.372) 0.208 ± 1.96 0.208 t 0.127 or (0.081,0.335)
We are 95% confident that the difference in proportion of male customers left a tip who were served by a server wearing a red shirt and who were served by a server wearing a different colored shirt lies between 0.081 and 0.335. Since 0 does not lie in the confidence interval, we can conclude that higher proportion of male customers left a tip who were served by a server wearing a red shirt than those who were served by a server wearing a different colored shirt.
------------------------------------------------------------------------------------------------------------------------
d) The hypotheses are:
\\H_0:p_1=p_2 \\H_a:p_1\ne p_2
The pooled proportion is:
1240 +130 +n2 69+34 0.4067
The test statistic is:
pi-2 0.580 0.372 V mi-P)(4+4) ν/0 4067(1-04067) (かー = 3.20 ) 0.4067(1-0.4067) (69 т 349
The p-value is:
p-value = P(z <-3.20) + P(z > 3.20) = 0.0007 0.0007 = 0.00 1 4
Since p-value is less than 0.05, reject the null hypothesis. We can conclude that there is significant difference in proportion of male customers left a tip who were served by a server wearing a red shirt and who were served by a server wearing a different colored shirt.
Please see attachment for better indentation and formula input in the solution.
The 95% confidence interval provides a range where the true difference in tipping behavior may lie, while a large-sample significance test assesses if the difference is statistically significant.
Explanation:For part a, the objective is to establish a 95% confidence interval for the difference in proportions. The proportion of individuals who tip when served by a server wearing a red shirt (p1) is 40/69, and the proportion of individuals who tip when served by a server wearing a different colored shirt (p2) is 130/349. The difference in proportions (p1 - p2) will give us the estimated difference. The standard error can then be calculated. Z is typically 1.96 for a 95% confidence interval.
For part b, a large-sample significance test is performed to test the null hypothesis that the two proportions are the same against the alternative hypothesis that the two proportions are not the same. Z score is calculated using the difference in proportions and standard error. P-value can then be derived from the z-score. The p-value will indicate whether the difference is statistically significant or not.
The confidence interval gives us the range of values within which the actual difference in proportions might fall 95% of the time, whereas the significance test helps determine if there is a substantial difference in the tipping habits depending on the color of the shirt worn by the server.
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one side 2^4 ft
another side is 2^3ft
What is the area of the flower bed?
48 square feet
128 square feet
4,096 square feet
16, 384 square feet
Answer:
128
Step-by-step explanation:
2x2x2x2x2x2x2 is 128
Answer:
B
Step-by-step explanation:
If a number is added to the numerator of 2/3 and twice as much is subtracted from the denominator, the result is -1. Find the number.
Answer:
The number = 5
Step-by-step explanation:
Let the number be x
[tex]\frac{2+x}{3-2x}=-1\\\\2+x=-1*(3-2x)\\\\2+x=(-1)*3-(-1)*2x\\\\2+x=-3+2x\\\\x=-3+2x-2\\\\x-2x=-5\\\\-x=-5\\\\x=5[/tex]
In an electronic system, a sensor measures a crucial parameter and outputs a number, but there is random error in its measurement. The measurement error in a sensor output is known to be RV X with uniform distribution in (-0.05,0.05) and independent from one output to the next, that is, the errors are iid! During a run of the system, n = 1000 samples of the sensor output are recorded. (a) Find the numerical value of the mean ux and the variance oź for the uniform distribution described. (You can use results in the text by listing the theorem or formula.) Further processing of these n= 1000 samples adds them together, and we are concerned about the overall error in the sum resulting from adding 1000 iid errors. Let X, denote the error in the įth sample for 1 1." Show all the steps in how you compute this. (f) Are the answers in (d) and (e) in agreement? If they are different, explain how both can be correct.
Answer:
Step-by-step explanation:
Find attach the solution
Find f. (Use C for the constant of the first antiderivative, D for the constant of the second antiderivative and E for the constant of the third antiderivative.) f '''(t) = t − 5 cos(t)
Answer:
[tex]f(t) = \frac{1}{24}\cdot t^{4} + 5\cdot \sin t +\frac{1}{2}\cdot C \cdot t^{2} + D\cdot t + E[/tex]
Step-by-step explanation:
The second derivative is found by integrating it:
[tex]f''(t) = \frac{1}{2}\cdot t^{2} -5\cdot \sin t + C[/tex]
The first derivative is:
[tex]f' (t) = \frac{1}{6}\cdot t^{3}+5\cdot \cos t + C\cdot t + D[/tex]
Lastly, the function is:
[tex]f(t) = \frac{1}{24}\cdot t^{4} + 5\cdot \sin t +\frac{1}{2}\cdot C \cdot t^{2} + D\cdot t + E[/tex]
Given that,
f'''(t) = t — 5cos(t)
We want to find f(t) so we need to integrate this function three times to get f(t)
First anti derivative
∫ f'''(t) dt = ∫ (t —5cos(t)) dt
Note, the integral of cos(t) is sin(t), and the integral of sin(t) is —Cos(t)
Integrating third derivatives decreases it to second derivatives i.e. f'''(t) to f''(t)
f''(t) = t²/2 — 5sin(t) + C
Where C is the first anti derivative constant
Second anti derivative
f''(t) = t²/2 — 5sin(t) + C
∫ f''(t) = ∫ (t²/2 — 5sin(t) + C) dt
f'(t) = t³/6 + 5Cos(t) + Ct + D
Where D is the second anti derivative constant
Third anti derivative
f'(t) = t³/6 + 5Cos(t) + Ct + D
∫ f'(t) = ∫ t³/6 + 5Cos(t) + Ct + D) dt
f(t) = t⁴/24 + 5Sin(t) + Ct²/2 + Dt + E
Where E is the third anti derivative constant.
So the required f(t) function is
f(t) = t⁴/24 + 5Sin(t) + ½Ct² + Dt + E
A tank with a capacity of 1000 L is full of a mixture of water and chlorine with a concentration of 0.02 g of chlorine per liter. In order to reduce the concentration of chlorine, fresh water is pumped into the tank at a rate of 10 L/s. The mixture is kept stirred and is pumped out at a rate of 25 L/s. Find the amount of chlorine in the tank as a function of time. (Let y be the amount of chlorine in grams and t be the time in seconds.)
The function for the amount of chlorine in the tank as a function of time is [tex]y(t) = \left(\frac{20}{1000^{\frac{5}{3}}} \right) (1000 - 15t)^{\frac{5}{3}}[/tex].
Let y(t) be the amount of chlorine in grams in the tank at time t seconds. The initial amount of chlorine is given by the concentration of chlorine times the volume of the tank: y(0) = 0.02 g/L * 1000 L = 20 grams.
The tank has a mixture being pumped out at a rate of 25 L/s, and fresh water is being pumped in at a rate of 10 L/s. The change in the volume of the tank per second is -15 L/s (since more is being pumped out than in).
The rate of change of the amount of chlorine in the tank, dy/dt, can be described as the rate of chlorine leaving the tank minus the rate of chlorine entering the tank. Fresh water has 0 g/L concentration, so the rate of chlorine entering the tank is 0. Chlorine is leaving the tank with the water at a rate proportional to the concentration of chlorine in the tank.
The volume of water in the tank at any time t can be written as V(t) = 1000 - 15t. The concentration of chlorine in the tank at any time is y(t) / V(t). Therefore, the rate of chlorine leaving the tank is:
[tex]\frac{dy}{dt} = - \left(\frac{25y}{V(t)}\right)[/tex]
Substitute V(t) into the equation:
[tex]\frac{dy}{dt} = - \left(\frac{25y}{1000 - 15t}\right)[/tex]
This is a separable differential equation. We can solve it by separating variables and integrating both sides.
[tex]\frac{dy}{y} = - \frac{25}{1000 - 15t} dt[/tex]
Integrate both sides:
[tex]\int \frac{1}{y} dy = -25 \int \frac{1}{1000 - 15t} dt[/tex]
The integral of [tex]\frac{1}{y}[/tex] is[tex]\ln|y|,[/tex] and the integral of [tex]\frac{1}{1000 - 15t}[/tex] can be found using a substitution method. Let u = 1000 - 15t, then du = -15 dt, or [tex]dt = -\frac{1}{15}[/tex] du.
[tex]\int \frac{1}{1000 - 15t} dt = - \frac{1}{15} \int \frac{1}{u} du = - \frac{1}{15} \ln|u| = - \frac{1}{15} \ln|1000 - 15t|[/tex]
Putting it all together:
[tex]\ln|y| = \frac{25}{15} \ln|1000 - 15t| + C[/tex]
Simplify further:
[tex]\ln|y| = \frac{5}{3} \ln|1000 - 15t| + C[/tex]
Exponentiate both sides to solve for y:
[tex]y = e^{\frac{5}{3} \ln|1000 - 15t| + C} = e^C (1000 - 15t)^{\frac{5}{3}}[/tex]
Let K = [tex]e^C[/tex]. Then:
[tex]y(t) = K(1000 - 15t)^{\frac{5}{3}}[/tex]
Using the initial condition y(0) = 20:
[tex]20 = K 1000^{\frac{5}{3}}[/tex]
Solve for K:
[tex]K = 20 / 1000^{\frac{5}{3}}[/tex]
This equation describes the amount of chlorine in the tank over time, taking into account the rates at which water is pumped in and out.
What is the volume of the right rectangular prism with a length of 2 millimeters, a width of 4 millimeters, and a height of 8 millimeters? 14 Millimeters cubed 16 Millimeters cubed 28 Millimeters cubed 64 Millimeters cubed
Answer:
The volume of this prism is 64 mililmeters cubed.
Step-by-step explanation:
What is the volume of the right rectangular prism with a length of 2 millimeters, a width of 4 millimeters, and a height of 8 millimeters?
The volume of this prism can be calculated as:
[tex]V=l\cdot w \cdot h\\\\V=2\cdot 4\cdot 8=64[/tex]
The volume of this prism is 64 mililmeters cubed.
Answer:
D
Step-by-step explanation:
Sorry if it's wrong.
Solve equation 66= -11y
Answer:
y=-6
Step-by-step explanation:
Divide -11 by 66 to isolate y to get 6
Answer:
the answer is y=-6
Step-by-step explanation:
you are welcome
A club at school designed a banner consisting of two congruent triangles surrounded by stripes. The length of the sides of each of the triangles were 1.5 feet, 2.0 feet, 2.5 feet. Are the triangles right triangles? Explain
Answer:
Yes. They are Right Triangles
Step-by-step explanation:
To determine if the triangles are right triangles, all you need to do is verify whether or not the dimensions satisfy the Pythagoras Theorem.
Pythagoras Theorem:[tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]
Note that in a right triangle, the longest side is always the hypotenuse.
Given the length of the sides 1.5 feet, 2.0 feet, 2.5 feet
[tex]2.5^2=1.5^2+2.0^2\\6.25=2.25+4\\6.25=6.25[/tex]
Since the Pythagoras theorem holds, the triangles are in fact right triangles.