Answer:
a) The observed proportion of wallets that were returned
p = 0.45625
b) 95% of confidence intervals for Population proportion
0.40168 , 0.51082)
c) The lower bound of the 95% confidence interval = 0.40168
d) The upper bound of the 95% confidence interval = 0.51082
Step-by-step explanation:
Step(i):-
a)
Given data the researchers left a total of 320 wallets around Edinburgh, as though the wallets were lost. Each contained contact information including an address. Of the wallets, 146 were returned by the people who found them
Given sample size 'n' = 320
Given data 'x ' = 146
Sample proportion
[tex]p = \frac{x}{n}[/tex]
[tex]p = \frac{x}{n} = \frac{146}{320} = 0.45625[/tex]
Step(ii):-
b) 95% of confidence intervals for Population proportion
Level of significance = 95% or 0.05%
[tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96[/tex]
95% of confidence intervals for Population proportion are determined by
[tex](p - Z_{0.025} \frac{\sqrt{p(1-p)} }{\sqrt{n} } , p + Z_{0.025} \frac{\sqrt{p(1-p)} }{\sqrt{n} })[/tex]
[tex](0.45625 - 1.96\frac{\sqrt{0.45625(1-0.45625)} }{\sqrt{320} } , 0.45625 + 1.96\frac{\sqrt{0.45625(1-0.45625)} }{\sqrt{320} })[/tex]
(0.45625 - 0.05457 , 0.45625 + 0.05457)
( 0.40168 , 0.51082)
c) The lower bound of the 95% confidence interval = 0.40168
d) The upper bound of the 95% confidence interval = 0.51082
How much pure acid is in 780 milliliters of a 12% solution?
Answer:
93.6 ml
Step-by-step explanation:
12% of that 780 ml is pure acid: 0.12(780 ml) = 93.6 ml
The amount of pure acid is 93.6 ml.
What is proportion?Proportion is explained majorly based on ratio and fractions. A fraction, represented in the form of a/b, while ratio a:b, then a proportion states that two ratios are equal. Here, a and b are any two integers. The ratio and proportion are key foundations to understand the various concepts in mathematics as well as in science.
The direct proportion formula says if the quantity y is in direct proportion to quantity x, then we can say y = kx, for a constant k. y = kx is also the general form of the direct proportion equation.
Given:
You have 780 ml of a 12% solution
So,
780 ml represents 100%,
x ml represents 12%.
Using proportion:
780/x= 100/12
780*12/100=x
93.6 ml = x
Learn more about this concept here:
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A researcher finds that of 1000 people who said that they attend a religious service at least once a week, A stopped to help a person with car trouble. Of 1200 people interviewed who had not attended a religious service at least once a month, B stopped to help a person with car trouble. At the 0.05 significance level, test the claim that the two proportions are equal.
Answer:
There is enough evidence to support the claim that the proportions are not equal. (P-value: 0.048).
Step-by-step explanation:
The question is incomplete:
"A researcher finds that of 1000 people who said that they attend a religious service at least once a week, 31 stopped to help a person with car trouble. Of 1200 people interviewed who had not attended a religious service at least once a month, 22 stopped to help a person with car trouble. At the 0.05 significance level, test the claim that the two proportions are different."
This is a hypothesis test for the difference between proportions.
The claim is that the proportions are not equal.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
The significance level is 0.05.
The sample 1, of size n1=1000 has a proportion of p1=0.031.
[tex]p_1=X_1/n_1=31/1000=0.031[/tex]
The sample 2, of size n2=1200 has a proportion of p2=0.018.
[tex]p_2=X_2/n_2=22/1200=0.018[/tex]
The difference between proportions is (p1-p2)=0.013.
[tex]p_d=p_1-p_2=0.031-0.018=0.013[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{31+22}{1000+1200}=\dfrac{53}{2200}=0.024[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.024*0.976}{1000}+\dfrac{0.024*0.976}{1200}}\\\\\\s_{p1-p2}=\sqrt{0+0}=\sqrt{0}=0.007[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.013-0}{0.007}=\dfrac{0.013}{0.007}=1.98[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]P-value=2\cdot P(z>1.98)=0.048[/tex]
As the P-value (0.048) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportions are not equal.
Which describes something that is an obligation that must be paid?
A. Liability
O B. Bond
C. Liquid asset
Answer:
Liability
Step-by-step explanation:
Ap3x
Express this decimal as a fraction.
0.8 repeating decimal
Select the correct answer.
Circle O is represented by the equation (x + 7)2 + (x + 7)2 = 16. What is the length of the radius of circle O?
A. 3
B. 4
C. 7
D. 9
E. 16
Answer:
4
Step-by-step explanation:
because r2=16 so you have to find the square root of 16 to get r
Which number is the additive inverse of -5?
1
О-5
ОО
ch.
O5
Answer:
5
Step-by-step explanation:
Additive inverses are two numbers that add to 0.
Since -5 + 5 = 0, then the additive inverse of -5 is 5.
Answer: 5
Answer:
It would just be the opposite -5 the inverse is 5.
Step-by-step explanation:
Hope my answer has helped you in anyway and if not I am sorry.
Find the area of a trapezoid with base lengths 3 and 5 and heigh of 9
A trapezoid is a quadrilateral with exactly one pair of parallel sides.
Formula for area: [tex]A = \frac{1}{2}(^{b}1 + ^{b}2)(h)[/tex]
In this formula, the bases are the parallel sides.
Now plug the information into the formula.
[tex]A = \frac{1}{2} (3 + 5)(9)[/tex].
Follow your order of operations, simplify inside the parentheses first.
[tex]A = \frac{1}{2}(8)(9)[/tex].
(1/2)(8) is 4 so we have (4)(9) which is 36.
So the area of the trapezoid is 36.
In a certain city, the monthly cost of telephone service is given the function C = 0.10n + 18, where n is the number of calls, 10 cents is the cost per call, and $14 is a fixed charge. Find the cost of making 60 calls a month.
Answer:
The cost of making 60 calls a month is $20.
Step-by-step explanation:
There was a small typing mistake there. If the fixed charge is $14, the cost of n calls is given by the following equation:
[tex]C(n) = 0.1n + 14[/tex]
Find the cost of making 60 calls a month.
This is C(60), that is, C when n = 60. So
[tex]C(n) = 0.1n + 14[/tex]
[tex]C(60) = 0.1*60 + 14 = 20[/tex]
The cost of making 60 calls a month is $20.
Evaluate the following Integrals ∫sin
Answer:
[tex]\displaystyle \int {xsinx} \, dx = -xcosx + sinx + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Integration
IntegralsIndefinite IntegralsIntegration Constant CIntegration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration by Parts: [tex]\displaystyle \int {u} \, dv = uv - \int {v} \, du[/tex]
[IBP] LIPET: Logs, inverses, Polynomials, Exponentials, TrigStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {xsinx} \, dx[/tex]
Step 2: Integrate Pt. 1
Identify variables for integration by parts using LIPET.
Set u: [tex]\displaystyle u = x[/tex][u] Differentiate [Basic Power Rule]: [tex]\displaystyle du = dx[/tex][dv] Trigonometric Integration: [tex]\displaystyle v = -cosx[/tex]Set dv: [tex]\displaystyle dv = sinx \ dx[/tex]Step 3: Integrate Pt. 2
[Integral] Integration by Parts: [tex]\displaystyle \int {xsinx} \, dx = -xcosx - \int {-cosx} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {xsinx} \, dx = -xcosx + \int {cosx} \, dx[/tex][Integral] Trigonometric Integration: [tex]\displaystyle \int {xsinx} \, dx = -xcosx + sinx + C[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
Book: College Calculus 10e
Five crates weigh 200 pounds. One crate weighs 20 pounds but each of the other four crates weigh the same amount. What is the weight of the other 4 crates?
Subtract 20 from the total weight and divide by 4:
200 - 20 = 180
180/4 = 45
Each other crate weighs 45 pounds each.
Evaluate-2+7x^2-2x^3-8x+7x^4 at x=5
Answer:
4262
Step-by-step explanation:
2 + 7x^2- 2x^3-8x +7x^4 at x = 5
= 2 + 7*(5)^2 - 2*(5)^3-8*5 +7*(5)^4
=2+175-250-40+4375
=4552-290
=4262
How much do you need to invest every month in an annuity to
reach a goal of $25,000 at the end of 5 years, if compounding is
done every month and the annual interest rate is 4%. Round up
to the next penny.
Answer:
A=25000 is the future value. P the value that we need to invest. r= 0.04 represent the interest rate in fraction. n = 12 represent the number of times that the rate is compounded in a year. t = 5 years.
If we solve for the value of P we got:
[tex] P= \frac{A}{(1+ \frac{r}{n})^{nt}}[/tex]
And replacing we got:
[tex] P= \frac{25000}{(1+ \frac{0.04}{12})^{12*5}} =20475.078[/tex]
And rounded to the nesrest penny we need to invest $20475.08 in order to have after 5 years $25000
Step-by-step explanation:
For this case we can use the future value with compound interest given by:
[tex] A = P (1+ \frac{r}{n})^{nt}[/tex]
Where:
A=25000 is the future value. P the value that we need to invest. r= 0.04 represent the interest rate in fraction. n = 12 represent the number of times that the rate is compounded in a year. t = 5 years.
If we solve for the value of P we got:
[tex] P= \frac{A}{(1+ \frac{r}{n})^{nt}}[/tex]
And replacing we got:
[tex] P= \frac{25000}{(1+ \frac{0.04}{12})^{12*5}} =20475.078[/tex]
And rounded to the nesrest penny we need to invest $20475.08 in order to have after 5 years $25000
Two numbers are in the ratio of 3:4. If they sum of the numbers is 63, find the numbers
Answer:
27 and 36
Step-by-step explanation:
Let's call the two numbers x and y.
[tex]3x=4y \\\\x+y=63[/tex]
If you subtract y from both sides of the second equation, you can isolate x and substitute it into the first equation:
[tex]x=63-y \\\\3(63-y)=4y\\\\189-3y=4y\\\\189=7y\\\\y=27\\\\x=63-27=36[/tex]
Hope this helps!
Please answer this correctly
Answer
51
Explanation
85/15=y/9
765=15y
51
Answer:
y = 51
Step-by-step explanation:
These triangles are similar, so you can set up a proportion to solve for y:
[tex]\frac{85}{15} =\frac{y}{9}[/tex]
Cross multiply:
[tex]\frac{765}{15y}[/tex]
Divide 765 by 15:
y = 51
an employee of a grocery store is placing an order for soda. there are 8 varieties of soda and they are sold in cases. each case contains all the same variety of soda. the store will order 50 cases total. how many ways are there to place the order
Answer:
There are 536,878,650 ways to place the order.
Step-by-step explanation:
The order in which the cases are put is not important. So we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
8 varieties from a set of 50. So
[tex]C_{50,8} = \frac{50!}{8!(50-8)!} = 536878650[/tex]
There are 536,878,650 ways to place the order.
___, ___, 17, ___, ___, 29 Work out the missing terms. Work out the nth term
Answer:
The sequence is of the form
9 , 13 , 17 , 21 , 25 ,29
Step-by-step explanation:
Explanation:-
Step(i):-
Given sequence , ___, __17_ ,___,___ 29
The third term = 17
a + (3-1)d = 17
a + 2 d = 17 ...(i)
The sixth term = 29
a + (6-1)d =29
a + 5 d = 29 ...(ii)
solving (i) and (ii) equations
Subtracting (i) and (ii) equations , we get
a + 2 d -a -5 d = 17 -29
- 3 d = - 12
d =4
Substitute 'd' =4 in equation (i)
a + 2 d = 17
a + 2(4) =17
a = 17 -8 = 9
Step(ii):-
The arithmetic sequence
a , a+d , a+2 d , a+ 3 d , a+ 4 d , a+5 d
9 , 9 + 4, 9 +2 (4) , 9+3(4) , 9 +4(4) , 9+5(4)
9 , 13 , 17 , 21 , 25 ,29
Conclusion:-
The sequence is of the form
9 , 13 , 17 , 21 , 25 ,29
9, 13, 17, 21, 25, 29
Determine whether the following sampling is dependent or independent. Indicate whether the response variable is qualitative or quantitative.
A researcher wishes to compare mental health of married lawyers and their spouses. She obtains a random sample of 406 such couples who take a mental health inventory and determines each spouses mental health.
1. Is this dependent or independent? Is it because one sample does or does not dictate the individual to be used in the second sample?
2. Is it quantitative or qualitative? And is that because it is an attribute classification or numerical measure?
Answer:1. Dependent
2.Qualitative Variable
Step-by-step explanation:
Step 1--- Dependent
Reason-- The researcher considers a couple as a whole and The sampling is dependent because a spouce selected for one sample dictates or determines which individual to be in the second sample.
Step 2----Qualitative variable
Reason--- it classifies the individual spouce mental health based on mental health inventory of the couple
Because Qualitative variables are variables which can be placed according to characteristic or attribute, here the characteristics is mental health.
Answer:
1) Dependent. It is becasue one sample indicates the individual to be used in another sample.
2) Quantitative. Attribute classification is numerical measure
Step-by-step explanation:
Mental health of Married lawyer and their spouses are to be compared. A married lawyers mental health is to be compared with his/her spouse only
Here attribute is mental health inventory which is quantitative.
Can someone plz help me solved this problem I need help plz help me! Will mark you as brainiest!
Answer:
11
4
Step-by-step explanation:
3 hrs to travel 45 miles downstream
4 hrs to travel 28 miles upstream
speed of boat in still water= s
speed of the current= c
s+c= 45/3= 15s-c= 28/4=7added up the 2 equations, we get:
2s= 22s= 11 mphc= 4 mphHow many lbs to a kg?
Answer:
The answer would be, 0.454
Step-by-step explanation:
1 pound= 0.454 kilogram
Answer:
1kg = 2.20462262 rounded 2.20
Researchers suspect that myopia, or nearsightedness, is becoming more common over time. A study from the year 2010 showed 123 cases of myopia in 400 randomly selected people. Another study from the year 2019 showed 228 cases in 600 randomly selected people. We are going to do a hypothesis test to see if p1 = the proportion of people who have myopia in 2019 is equal to p2 = proportion of people who have myopia in 2010 at the 0.05 significance level.
null and alternative hypothesis ?
a. H0:P1=P2; Ha：P1≥P2
b. H0:P1=P2; Ha：P1≠P2
c. H0:P1≠P2; Ha：P1=P2
d. H0:P1≥P2; Ha：P1≠P2
Answer:
We want to test if the if p1 = the proportion of people who have myopia in 2019 is equal to p2 = proportion of people who have myopia in 2010 (alternative hypothesis) , then the system of hypothesis are:
Null hypothesis: [tex]p_1 = p_2[/tex]
Alternative hypothesis: [tex] p_1 = p_2[/tex]
And the best option would be:
b. H0:P1=P2; Ha：P1≠P2
Step-by-step explanation:
For this case we have the following info given:
[tex]X_1 = 228 [/tex] the myopia cases in 2019
[tex] n_1= 600[/tex] the sample size in 2019
[tex] \hat p_1= \frac{228}{600}= 0.38[/tex] estimated proportion of myopia cases in 2019
[tex]X_2 = 123 [/tex] the myopia cases in 2010
[tex] n_2= 400[/tex] the sample size in 2010
[tex] \hat p_2= \frac{123}{400}= 0.3075[/tex] estimated proportion of myopia cases in 2010
And we want to test if the if p1 = the proportion of people who have myopia in 2019 is equal to p2 = proportion of people who have myopia in 2010 (alternative hypothesis) , then the system of hypothesis are:
Null hypothesis: [tex]p_1 = p_2[/tex]
Alternative hypothesis: [tex] p_1 = p_2[/tex]
And the best option would be:
b. H0:P1=P2; Ha：P1≠P2
And we can conduct a two sample z proportion test in order to verify the hypothesis.
Answer:
< 0.5 \leqslant pvalue < 0.10[/tex]answer C on khan academyIvan and Tanya share £150 in the ratio 4:1
Work out how much more Ivan gets compared to Tanya.
Answer:
Ivan gets £90 more than Tanya.
Step-by-step explanation:
£150÷5=£30
Every 1 part of the ratio is £30
Ivan : Tanya
£120: £30
Ivan gets £90 more than Tanya.
a number cube is rolled 2 times in a row. What is the probability of rolling a number greater than 2 both times?
Answer:
70%
Step-by-step explanation:
Answer:
The probability of rolling a number greater than 2 two times in a row is arond 0.44
Step-by-step explanation:
Divide the number of events by the number of possible outcomes. This will give us the probability of a single event occurring. In the case of rolling a 3 on a die, the number of events is 1 (there's only a single 3 on each die), and the number of outcomes is 6.
Probability formula is the ratio of number of favorable outcomes to the total number of possible outcomes. Measures the likelihood of an event in the following way: - If P(A) > P(B) then event A is more likely to occur than event B. - If P(A) = P(B) then events A and B are equally likely to occur.
For each of the following research scenarios, decide whether the design uses a related sample. If the design uses a related sample, identify whether it uses matched subjects or repeated measures. (Note: Researchers can match subjects by matching particular characteristics, or, in some cases, matched subjects are naturally paired, such as siblings or married couples.)John Caccioppo was interested in possible mechanisms by which loneliness may have deterious effects of health. He compared the sleep quality of a random sample to lonely people to the sleep quality of a random sample of nonlonely people.
The design described ______a, b, or c_________________________.
a. does not use a related sample
b. uses a related sample (repeated measures)
c. uses a related sample (matched subjects)
Answer:
The correct option is (a).
Step-by-step explanation:
The dependent t-test (also known as the paired t-test or matched-samples t-test) compares the two means associated groups to conclude if there is a statistically significant difference amid these two means.
We use the paired t-test if we have two measurements on the same item, person or thing. We should also use this test if we have two items that are being measured with a unique condition.
For instance, an experimenter tests the effect of a medicine on a group of patients before and after giving the doses.
In this case the researcher selected a random sample of the sleep quality of lonely people and the random sample of the sleep quality of non-lonely people.
Both the sample in this case are selected from two very different population.
This clearly indicates that the study design is for non-related samples.
Thus, the correct option is (a).
are all parallelograms quidrilaterals
Answer:
yes
Step-by-step explanation:
All four sides of a rhombus are congruent. Its properties include that each pair of opposite sides is parallel, also making it a parallelogram. ... All rectangles are parallelograms, but not all parallelograms are rectangles. And all of these shapes are quadrilaterals.
are the values of the expressions 2m−13 and m+3 equal?
Answer:
The correct answer is m=8
Compute the sample mean and sample standard deviation for private and public colleges. Round your answers to two decimal places. S1 = S2 = b. What is the point estimate of the difference between the two population means? Round your answer to one decimal place. Interpret this value in terms of the annual cost of attending private and public colleges. $ c. Develop a 95% confidence interval of the difference between the annual cost of attending private and pubic colleges. 95% confidence interval, private colleges have a population mean annual cost $ to $ more expensive than public colleges. Check My Work Icon Key Previous Question 4 of 9 NextExercise 10.13
Answer:
(1) The sample mean is = 6.98, the standard deviation is = 4.53 (2) The pint estimate difference is = 20.2 (3) The confidence interval limits are $ 15943.6 and $24456.4
Step-by-step explanation:
Solution
(A) The first step is to compute the mean sample and the standard deviation for private and public colleges.
Thus,
The mean and private colleges is computed as follows:
The mean and private colleges = The sum of derivation/The total number of observation
x= 42.5
The standard deviation is S₁ = 6.9806 = √∈ (xi - x)²/n-1
The mean of public colleges y =22.3
Standard deviation S₂ = 4.5323 = √∈ (yi - y)²/n-1
Thus,
S₁ = 6.98
S₂ =4.53
(b) We find the point estimate of the difference between two population means
Thus,
x -y = 42.5 -22.3
=20.2
Therefore, the annual cost is =$20,200
Note: Kindly find an attached copy of the option c and the complete question stated above.
What is the vertex of the graph of y+2x+3=-(x+2)^2+1
Answer:
(-3, 3)
Step-by-step explanation:
HELP.
The number of reports of a certain virus has increased exponentially since 1960. The current number of cases can be approximated using the function r(t) = 207 e ^ 0.005t, where t is the number of years since 1960. Estimate the number of cases in the year 2010.
Answer:
The number of cases in the year 2010 is 266.
Step-by-step explanation:
An exponential function is one that the independent variable x appears in the exponent and has a constant a as its base. Its expression is:
f(x)=aˣ
being a positive real, a> 0, and different from 1, a ≠ 1.
In this case:
[tex]r(t) = 207*e^{0.005*t}[/tex]
where t is the number of years since 1960 and e is an irrational number of which it is not possible to know its exact value because it has infinite decimal places. The first figures are 2,7182818284590452353602874713527 and is often called the Euler's number. e is the base of natural logarithms.
In this case, you want to know the number of cases r (t) in 2010. So, to know t you must know how many years have passed since 1960. For that, you can simply do the following subtraction: 2010-1960 and you get as a result : 50.
Replacing in the exponential expression r (t):
[tex]r(t) = 207*e^{0.005*50}[/tex]
Solving:
r(t)=265.79 ≅ 266
The number of cases in the year 2010 is 266.
Answer the question and do it correctly!
Answer:
2.4Step-by-step explanation:
PEMDAS(Parentheses) 6 + -5.8 = 0.2
(Multiplication) 3.4 - 5 x 0.2
(Subtraction) 3.4 - 1 = 2.4
2.4
I'm always happy to help :)
Mr. Lim and Mr. Tay had $31 090 at first.Mr. Lim donated $2390 of his money and Mr. Tay spent half of his money on a holiday trip. As a result, Mr. Lim had 3 times as much money as Mr. Tay. How much money did Mr. Lim have at first?
Answer:
Mr.Lim had 19610 dollars, and Mr.Tay had 11480 dollars at first.
Step-by-step explanation:
Mr. Lim had 19610 dollars at first.
To find how much did Mr. Lim had at first.Given:
Mr. Lim and Mr. Tay had $31 090 at first.
Mr. Lim donated $2390 of his money and
Mr. Tay spent half of his money on a holiday trip.
Mr. Lim had 3 times as much money as Mr. Tay.
Step 1:
Let Mr. Tay had x
Let Mr. Lim had y
x + y=31090………..(1)
Step 2:
Mr. Tay spent on holiday = x + 2390/2
Money left with Mr. Lim = y - 2390
Given,
y - 2390 = 3(x + 2390/2) .............(2)
Step 3:
Equating equation (1) and (2)
we get,
x = 11480
y = 19610
Hence, Mr. Lim has $19610, and Mr. Tay had $11480 dollars at first.
To learn how to calculate the amount spent, refer,
https://brainly.com/question/2263981#SPJ2
