Answer:= (504, 516)
Therefore, the 90% confidence interval (a,b) = ( 504, 516)
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean gain x = 510
Standard deviation r = 37
Number of samples n = 95
Confidence interval = 90%
z(at 90% confidence) = 1.645
Substituting the values we have;
510+/-1.645(37/√95)
510+/-1.645(3.796)
510+/-6.24
510+/-6
= (504, 516)
Therefore at 90% confidence interval (a,b) = ( 504, 516)
Use Demoivres Theorem to find (1 + i) 20.
a. 1024i
b. -1024
C.-1024
D.1024
Answer:
-1024
Step-by-step explanation:
Moivre's theorem allows to easily obtain trigonometric formulas that express the sine and cosine of a multiple angle as a function of the sine and cosine of a simple angle.
De Moivre's theorem can be applied to any complex number [tex]z[/tex]
Where:
[tex]z\in Z[/tex]
Let:
[tex](1+i)=z\\n=20[/tex]
According to Demoivres Theorem, If:
[tex]z=||z||(cos(\theta)+isin(\theta))[/tex]
Then:
[tex]z^n=||z||^n(cos(n\theta)+isin(n\theta))[/tex]
For a complex number [tex]z[/tex]:
[tex]z=a+bi[/tex]
Its magnitude and angle are given by:
[tex]||z||=\sqrt{a^2+b^2} \\\\\theta=arctan(\frac{b}{a} )[/tex]
So:
[tex]||z||=\sqrt{1^2+1^2} =\sqrt{2}[/tex]
[tex]\theta=arctan(\frac{1}{1} )=45^{\circ}[/tex]
Therefore, using De Moivre's theorem:
[tex]z^n=(\sqrt{2} )^{20}(cos(20*45)+isin(20*45))\\\\z^n=(\sqrt{2} )^{20}(cos(900)+isin(900))\\\\z^n=1024(-1+i(0))\\\\z^n=1024(-1)\\\\z^n=(1+i)^{20}=-1024[/tex]
C on e2020
i did it *dab*
You would like to determine if there is a higher incidence of smoking among women than among men in a neighborhood. Let women and men be represented by populations 1 and 2, respectively. The relevant hypotheses are constructed as ____________.
H0: Mue1-Mue2 less than or equal 0.
Ha: Mue1-Mue2>0
H0: Mue1-Mue greater or equal 0.
Ha: Mue1-Mue<0
H0: P1-P2 less than or equal 0
Ha: P1-P2>0
H0: P1-P2 greater than or 0
Ha: P1-P2<0
Answer:
H₀: p₁ - p₂ < 0.
Hₐ: p₁ - p₂ > 0.
Step-by-step explanation:
In this case, we need to determine if there is a higher incidence of smoking among women than among men in a neighborhood.
An experiment can be performed involving collecting two samples of men and women and computing the proportion of men and women smokers in the neighborhood. Then these two sample proportions can be used to determine which proportion is higher.
We are computing proportions of men and women smokers instead of the mean number of men and women smokers because the we need to determine the incidence of smoking among men and women, i.e. the occurrence or frequency or rate of men and women smokers.
So, a two proportion test can be applied to determine whether the proportion of women smokers is higher than men.
The population proportion of women in the neighborhood is represented by p₁ and the population proportion of men in the neighborhood is represented by p₂.
The hypothesis can be defined as:
H₀: The proportion of women smokers is not higher than men, i.e. p₁ - p₂ < 0.
Hₐ: The proportion of women smokers is higher than men, i.e. p₁ - p₂ > 0.
Final answer:
The null hypothesis (H0) should be P1 - P2 ≥ 0, indicating no higher incidence of smoking among women, and the alternative hypothesis (Ha) should be P1 - P2 < 0, suggesting a higher incidence of smoking among women.
Explanation:
When conducting a hypothesis test to determine if there's a higher incidence of smoking among women than among men in a neighborhood, you would use two hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha). Since we are looking to find if the incidence is higher in women, the null hypothesis should reflect there is no difference or that the incidence in women is less than or equal to the incidence in men. Therefore, the correct setup using population proportions (P1 for men and P2 for women) would be:
H0: P1 - P2 ≥ 0 (there is no higher incidence of smoking among women compared to men)Ha: P1 - P2 < 0 (there is a higher incidence of smoking among women compared to men)The null hypothesis statement is that the proportion of women who smoke is less than or equal to the proportion of men who smoke. The alternative hypothesis is what you intend to prove, which is that more women smoke than men in the neighborhood, hence P1 - P2 < 0. This would be considered a left-tailed test.
The mean monthly food budget for 39 residents of the local apartment complex is $419. What is the best point estimate for the mean monthly food budget for all residents of the local apartment complex?
Answer:
The best point estimate for the mean monthly food budget for all residents of the local apartment complex is $419.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem:
The mean of the sample is $419.
What is the best point estimate for the mean monthly food budget for all residents of the local apartment complex?
By the Central Limit Theorem(inverse, that is, sample to the population), $419.
The best point estimate for the mean monthly food budget for all residents of the local apartment complex is $419.
A total of 1 232 students have taken a course in Spanish, 879 have taken a course in French, and 114 have taken a course in Russian. Further, 103 have taken courses in both Spanish and French, 23 have taken courses in both Spanish and Russian, and 14 have taken courses in both French and Russian. If 2 092 students have taken at least one of Spanish, French, and Russian, how many students have taken a course in all three languages
Answer:
[tex]n(S\cap F \cap R)=7[/tex]
Step-by-step explanation:
The Universal Set, n(U)=2092
[tex]n(S)=1232\\n(F)=879\\n(R)=114[/tex]
[tex]n(S\cap R)=23\\n(S\cap F)=103\\n(F\cap R)=14[/tex]
Let the number who take all three subjects, [tex]n(S\cap F \cap R)=x[/tex]
Note that in the Venn Diagram, we have subtracted [tex]n(S\cap F \cap R)=x[/tex] from each of the intersection of two sets.
The next step is to determine the number of students who study only each of the courses.
[tex]n(S\:only)=1232-[103-x+x+23-x]=1106+x\\n(F\: only)=879-[103-x+x+14-x]=762+x\\n(R\:only)=114-[23-x+x+14-x]=77+x[/tex]
These values are substituted in the second Venn diagram
Adding up all the values
2092=[1106+x]+[103-x]+x+[23-x]+[762+x]+[14-x]+[77+x]
2092=2085+x
x=2092-2085
x=7
The number of students who have taken courses in all three subjects, [tex]n(S\cap F \cap R)=7[/tex]
Using the principle of Inclusion-Exclusion, we find that 7 students have taken courses in all three languages: Spanish, French, and Russian.
Finding the Number of Students Taking All Three Language Courses
We can solve this problem using the principle of Inclusion-Exclusion. Let:
S = number of students taking Spanish
F = number of students taking French
R = number of students taking Russian
SF = number of students taking both Spanish and French
SR = number of students taking both Spanish and Russian
FR = number of students taking both French and Russian
SFR = number of students taking all three languages.
From the given data:
S = 1232F = 879R = 114SF = 103SR = 23FR = 14Total students taking at least one language = 2092The principle of Inclusion-Exclusion states:
Total = S + F + R - SF - SR - FR + SFR
2092 = 1232 + 879 + 114 - 103 - 23 - 14 + SFR
Solving for SFR:
2092 = 2085 + SFR
Thus, SFR = 2092 - 2085 = 7
Therefore, 7 students have taken courses in all three languages: Spanish, French, and Russian.
As Saturn revolves around the sun, it travels at a speed of approximately 6 miles per second. Convert this speed to miles per minute. At this speed, how many miles will Saturn travel in 3 minutes?
Answer:360 miles per minute , and 1080 in 3 minutes
Step-by-step explanation:
Simplify the following equation as best as you can.
-6.4m + 4(0.5m - 0.8)
Answer:
-4.4m-3.2
Step-by-step explanation:
-6.4m+4(0.5m-0.8)
-6.4m+4*0.5+4*0.8
-6.4m+2m-3.2
-4.4m-3.2
Answer:
-4.4m-3.2
Step-by-step explanation:
multiply everything in the parentheses by 4 and then add.
Samuel bought 32 and 1/2 ft of window trim at a hardware store the trim cost $1.75 per foot including sales tax if Samuel paid with a $100 bill how much change should he have received
Answer:
The amount of change he should received is
$100 - $56.875
= $43.125
= $43.13
Step-by-step explanation:
Length of window trim = 32 and 1/2 ft
Cost per foot = $1.75
Amount paid = $100
Total cost of window trim = 32.5×1.75 = $56.875
The amount of change he should received is
$100 - $56.875
= $43.125
= $43.13
represent the times necessary to perform three successive repair tasks at a service facility. Suppose they are normal random variables with means of 50 minutes, 60 minutes, and 40 minutes, respectively. The standard deviations are 15 minutes, 20 minutes, and 10 minutes, respectively
Question: The question is incomplete. What need to be calculated is not included in the question. Below is the question requirement and the answer.
a) Suppose X1, X2, and X3 are independent. All three repairs must be completed on a given object. What is the mean and variance of the total repair time for this object?
Answer:
Mean = 50 minutes
Variance = 725 minutes
Step-by-step explanation:
X₁ = 50
X₂ = 60
X₃ = 40
σ₁ = 15
σ₂ = 20
σ₃ = 10
Calculating the mean E(Y) using the formula;
E(Y) = E(X₁ +X₂ +X₃)/3
= (EX₁ + EX₂ + EX₃)/3
= (50 + 60 + 40)/3
= 50 minutes
Therefore, the mean of the total repair time for this object is 50 minutes
Calculating the variance V(Y) using the formula;
V(Y) = V(X₁ +X₂ +X₃)
= E(X₁) +E(X₂) + E(X₃)
= σ₁² + σ₂² + σ₃²
= 15² + 20² + 10²
= 225 + 400 + 100
= 725 minutes
Therefore, the variance of the total repair time for this object is 725 minutes
Which equation represents the magnitude of an
earthquake that is 100 times more intense than a
standard earthquake?
Answer:
m=log 100s/S
Step-by-step explanation:
howdy!
answer is in the attachment below :)
jerome filled bags with trail mix. the weights of the bags are
a snack mix recipe calls for 1 1/4 cups of dip and 1/2 cups of veggies. Parkers want to make the same recipe using 1 cup of veggies. How many cups of dip will parker need?
Answer:
2 1/2 cups
Step-by-step explanation:
You are doubling your recipe. You would do 1 1/4 × 2. First, 1 × 2 = 2 and then 1/4 × 2 = 1/2. Put them together for your answer. I hope this helped.
Final answer:
Parker will need 2 1/2 cups of dip.
Explanation:
To find out how many cups of dip Parker will need, we can set up a proportion using the given information.
The snack mix recipe calls for 1 1/4 cups of dip and 1/2 cups of veggies.
Let's call the number of cups of dip Parker needs x.
The proportion will be: 1 1/4 cups / 1/2 cups = x cups / 1 cup.
To solve for x, we can cross multiply and then divide: (1 1/4) * 1 = (1/2) * x.
Simplifying both sides gives us 5/4 = 1/2 * x.
To isolate x, we can multiply both sides by the reciprocal of 1/2, which is 2/1: (5/4) * (2/1) = x.
Multiplying gives us x = 10/4, which simplifies to x = 2 1/2 cups.
Suppose that E and F are two events and that Upper P (Upper E and Upper F )equals0.3 and Upper P (Upper E )equals0.5. What is Upper P (F|E )? Upper P (F|E )equals nothing (Type an integer or a decimal.)
Answer:
[tex]P(\frac{F}{E}) =\frac{0.3}{0.5} =0.6[/tex]
Step-by-step explanation:
Step 1:-
Suppose that E and F are two events and that P(E n F) = 0.3
also given P(E) =0.5
Conditional probability:-
if E₁ and E₂ are two events in a Sample S and P(E₁)≠ 0, then the probability of E₂ , after the event E₁ has occurred, is called the Conditional probability
of the event E₂ given E₁ and is denoted by
[tex]P(\frac{F}{E}) = \frac{P(EnF)}{P(E)}[/tex]
[tex]P(\frac{F}{E}) =\frac{0.3}{0.5} =0.6[/tex]
what is the slope intercept form of 2x-3y=9
Answer:
-3y=-2x+9
Step-by-step explanation:
flip the value
when flipping a value remember to invert its sign
What is the first step in solving 2x=y X+y=30
Answer: x = 10 y=20
Step-by-step explanation:
You can answer this question by plugging in each equation:
2x=y, x+y=30. Let us plug y as 2x in the second equation x+y=30
x+2x= 30
3x= 30
x=10
After we found x we can then find y by plugging the 10 for x.
2(10) = y
y =20
or you could plug in the other equation
10+y=30
subtract 10 from 30 and we get 20
to double check we can plug in both numbers
2(10) = 20 which is correct
and 10 + 20 = 30 which is correct
A student has a monthly budget of $800. She can spend her budget on two items, X and Y. Each unit of X costs $20 and each unit of Y costs $10. If the student has a utility function of U = 348X + 100Y + 6X2 + 4Y2 + 2XY, what is the optimal amount of X and Y for her to consume to have the maximum utility? What is this total utility? What is the value of lambda and what does this mean?
Answer:
Check the explanation
Step-by-step explanation:
Total utility is the overall satisfaction that a particular consumer received from consuming a given overall quantity of a good or service, To calculate the value of total utility economists utilize the following basic total utility formula: TU = U1 + MU2 + MU3
Kindly check the attached image below to see the step by step explanation to the question above.
A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 90% confidence interval for the mean score of all such subjects.Immersive Reader
Answer:
The 90% confidence interval for the mean score of all such subjects is between 39.7 and 112.7
Step-by-step explanation:
We have the standard deviation of the sample, so we use the t-distribution to build the confidence interval.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 27 - 1 = 26
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 26 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95([tex]t_{95}[/tex]). So we have T = 1.7056
The margin of error is:
M = T*s = 1.7056*21.4 = 36.50.
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 76.2 - 36.5 = 39.7
The upper end of the interval is the sample mean added to M. So it is 76.2 + 36.5 = 112.7
The 90% confidence interval for the mean score of all such subjects is between 39.7 and 112.7
Which point has coordinates of (2, 0)?
Answer:
J
Step-by-step explanation:
What is the constant proportionality
Answer:
The relationship between price and the number of empanadas is PROPORTIONAL.
1 Empanada = 50 cent = $0.5
Constant of PROPORTIONALITY = ½
Step-by-step explanation:
From the given table:
2 Empanadas = $1
6 Empanadas = $3
We see that, as the number of Empanadas increases, the amount in Dollars also increases. Such that:
Let E = Empanadas
$ = dollar
~ = sign of PROPORTIONALITY.
Therefore:
$ ~ E
$ = KE
Where K = constant of proportionality.
When E = 4; $ = 2
$2 = K4
K= 2/4
K = ½
$ = ½E (Binding formula)
This applies for all the number of Empanadas bought.
Answer:
.50
Step-by-step explanation:
I ready
Uta invests an amount into a compound interest investment account that pays 6% a year. After six years she withdraws her total balance of $500. Using the formula A=p(1+r)t how much money did Uta initially invest?
Uta initially invest $353, if she withdraws $500 after six years with compound interest of 6% a year.
Step-by-step explanation:
The given is,
After six years she withdraws her total balance of $500
Interest rate 6 % a year ( compounded )
Step:1
Formula to calculate the future amount with an compound interest rate,
[tex]F=P(1+r)^{t}[/tex].............................(1)
Where, F - Future worth amount
P - Initial investment
r - Rate of interest
t - No. of years
Step:2
From the given,
F = $500
r = 6%
t = 6 years
Equation (1) becomes,
[tex]500 = P(1+0.06)^{6}[/tex]
= [tex]P(1.06)^{6}[/tex]
= P (1.41852)
[tex]P= \frac{500}{1.41852}[/tex]
= 352.48
≅ 353
P = $353
Result:
Uta initially invest $353, if she withdraws $500 after six years with compound interest of 6% a year.
Answer:
C- $352.48
Step-by-step explanation:
Just took test :]
8/12 - 2/12 =
THIS IS WORTH 100pts the only question pleaseeeeee
Answer:
1/2
Step-by-step explanation:
Since they have the same denominator, you can just subtract the numerators. So, 8-2=6.
6/12 can be simplified to 1/2.
Answer:
the answer is 1/2 or 0.5
Step-by-step explanation:
hope this helps!
Rebekah wants to read a certain number of pages each day during summer vacation.
Today, she read 204 pages, which is 136% of her goal.
How many pages does Rebekah want to read each day?
A. 75 pages
B. 130 pages
C. 150 pages
D. 560 pages
Answer:
C. 150 pages
Step-by-step explanation:
204 divided by 136 = 1.5
1.5 * 100 = 150
Hope it helps! :)
A cable runs along the wall from C to P at a cost of $4 per meter, and straight from P to M at a cost of $5 per meter. If M is 9 meters from the nearest point A on the wall where P lies, and A is 33 meters from C, find the distance from C to P such that the cost of installing the cable is minimized and find this cost.
Answer:
The minimum cost of installing the cable is $156.
Step-by-step explanation:
We have an optimization problem.
We have to minimize the cost of the cable.
We will use the variable x to express the the length of cable CP and PM, accordingly to the attache picture.
The length of the cable that goes from C to P (let's call it CP) is x.
[tex]\bar{CP}=x[/tex]
Then, the length of the cable that goes from P to M (PM) can be calcualted usign the Pithagorean theorem:
[tex]\bar{PM}=\sqrt{(33-x)^2+9^2}[/tex]
The cost function Y is:
[tex]Y=4*\bar{CP}+5*\bar{PM}=4x+5\sqrt{(33-x)^2+9^2}[/tex]
To optimize this cost funtion we have to derive and equal to 0:
[tex]\dfrac{dY}{dx}=0\\\\\\\dfrac{dY}{dx}=4+5(\dfrac{1}{2})((33-x)^2+9^2)^{-1/2} *(-2)(33-x)\\\\\\\dfrac{dY}{dx}=4+5\dfrac{x-33}{\sqrt{(33-x)^2+81}}=0\\\\\\\dfrac{x-33}{\sqrt{(33-x)^2+81}}=-\dfrac{4}{5}\\\\\\(x-33)=-\dfrac{4}{5}\sqrt{(33-x)^2+81}\\\\\\(x-33)^2=(-\dfrac{4}{5})^2[(x-33)^2+81]\\\\\\(x-33)^2=\dfrac{16}{25}(x-33)^2+\dfrac{1296}{25}\\\\\\\dfrac{25-16}{25} (x-33)^2=\dfrac{1296}{25}\\\\\\9(x-33)^2=1296\\\\\\x-33=\sqrt{\dfrac{1296}{9}}=\sqrt{144}=\pm12\\\\\\x=33\pm12\\\\\\x_1=33-12=21\\\\x_2=33+12=45[/tex]
The valid solution is x=21, as x can not phisically larger than 33.
The cost then becomes:
[tex]Y=4*\bar{CP}+5*\bar{PM}=4x+5\sqrt{(33-x)^2+9^2}\\\\\\Y=4*21+5\sqrt{(33-21)^2+81}\\\\Y=81+5\sqrt{144+81}\\\\Y=81+5\sqrt{225}\\\\Y=81+5*15\\\\Y=81+75\\\\Y=156[/tex]
This optimization problem in calculus can be solved by setting up a cost function for the total cable installation, taking its derivative, setting it equal to 0 to find the critical points, which will give you the distance from C to P that minimizes cost, check this point for being minimal and calculating the minimal cost by substituting the found distance into the originally defined cost function.
Explanation:The problem can be solved using the calculus principle of optimization. The situation described in your question makes a right triangle AMP. In this triangle, the vertical side (AP) measures 9 meters, and the hypotenuse (PM) represents cable installation that costs $5 per meter. The distance PC along the wall is $4 per meter. The cost of total cable installation from C -> P -> M is given as follows:
Cost = 4 * length CP + 5 * length PM
By the Pythagorean theorem, we know that [tex]PM = \sqrt{AP^2 + (33 - CP)^2}[/tex] Substituting PM into the equation, we get[tex]\text{Cost} = 4CP + 5 \cdot \sqrt{9^2 + (33-CP)^2}[/tex]
To minimize the cost, we take the derivative of the cost function and set it equal to 0 to find the critical points. Solving this equation will give you the value of CP that minimizes cost. Hence, by substituting found CP back to the original cost formula, we can find the minimal cost of installing the cable.
Learn more about Calculus Optimization here:https://brainly.com/question/35182200
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Given the following information about a hypothesis test of the difference between two means based on independent random samples, which one of the following is the correct rejection region at a significance level of .05? Assume that the samples are obtained from normally distributed populations having equal variances.HA: μA > μB, = 12, = 9, s1 = 5, s2 = 3, n1 = 13, n2 = 10.A. Reject H0 if Z > 1.96B. Reject H0 if Z > 1.645C. Reject H0 if t > 2.08D. Reject H0 if t > 1.782E. Reject H0 if t > 1.721
Answer:
Null hypothesis:[tex]\mu_{A} \leq \mu_{B}[/tex]
Alternative hypothesis:[tex]\mu_{A} > \mu_{B}[/tex]
Since we dpn't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:
[tex]t=\frac{\bar X_{A}-\bar X_{B}}{\sqrt{\frac{\sigma^2_{A}}{n_{A}}+\frac{\sigma^2_{B}}{n_{B}}}}[/tex] (1)
Now we need to find the degrees of freedom given by:
[tex] df = n_A + n_B -2= 13+10-2=21[/tex]
And now since we are conducting a right tailed test we are looking ofr a value who accumulates 0.05 of the are on the right tail fo the t distribution with df =21 and we got:
[tex] t_{cric}= 1.721[/tex]
And for this case the rejection zone would be:
E. Reject H0 if t > 1.721
Step-by-step explanation:
Data given and notation
[tex]\bar X_{A}=12[/tex] represent the mean for 1
[tex]\bar X_{B}=9[/tex] represent the mean for 2
[tex]s_{A}=5[/tex] represent the sample standard deviation for 1
[tex]s_{2}=3[/tex] represent the sample standard deviation for 2
[tex]n_{1}=13[/tex] sample size for the group 1
[tex]n_{2}=10[/tex] sample size for the group 2
t would represent the statistic (variable of interest)
[tex]\alpha=0.05[/tex] significance level provided
Develop the null and alternative hypotheses for this study
We need to conduct a hypothesis in order to check if the mean for group A is higher than the mean for B:
Null hypothesis:[tex]\mu_{A} \leq \mu_{B}[/tex]
Alternative hypothesis:[tex]\mu_{A} > \mu_{B}[/tex]
Since we dpn't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:
[tex]t=\frac{\bar X_{A}-\bar X_{B}}{\sqrt{\frac{\sigma^2_{A}}{n_{A}}+\frac{\sigma^2_{B}}{n_{B}}}}[/tex] (1)
Now we need to find the degrees of freedom given by:
[tex] df = n_A + n_B -2= 13+10-2=21[/tex]
And now since we are conducting a right tailed test we are looking ofr a value who accumulates 0.05 of the are on the right tail fo the t distribution with df =21 and we got:
[tex] t_{cric}= 1.721[/tex]
And for this case the rejection zone would be:
E. Reject H0 if t > 1.721
What is the product of (3y+4)2
Answer:
6y+8
Step-by-step explanation:
You should apply distributive property of the product, and multiply 2 by 3y and then add to that result the product of 2 times 4: [tex](3y+4)\times2= 2\times3y+2\times4=6y+8[/tex].
The endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).
The center of the circle is at the point , and its radius is units. The equation of this circle in standard form is .
Answer:
Read the explanation for the answers
Step-by-step explanation:
To find the midpoint, you simply need to find the average of the two endpoints. The average of 10.5 and 5.5 is 8, and the average of 4 and 4 is 4. Therefore, the center of the circle is at (4,8). The radius is the distance from the center to either of these points, or 8-5.5=2.5 units. And finally, the formula for the circle in standard form is [tex](y-8)^2+(x-4)^2=6.25[/tex]. Hope this helps!
solve x+3<9
[tex]x + 3 < 9[/tex]
X + 3 < 9
Subtract 3 from both sides:
X < 6
The answer is x < 6
Suppose parts (a) through (d) below provide results for a study on the role of calcium in reducing the symptoms of PMS. For each of the parts, compute an approximate 95% confidence interval for the difference in mean symptom scores between the placebo and calcium-treated conditions for the symptom listed. In each case, the results given are mean ± standard deviation. Suppose there were 228 participants in the placebo group and 212 in the calcium-treated group. (Round your answers to two decimal places.)
(a) mood swings: placebo = 0.70 ± 0.78; calcium = 0.50 ± 0.53
(b) crying spells: placebo = 0.39 + 0.57; calcium = 0.21 + 0.40
(c) aches and pains: placebo = 0.45 + 0.60; calcium = 0.37 + 0.45
(d) craving sweets or salts: placebo = 0.60 + 0.75; calcium = 0.44 + 0.61
Answer:
Step-by-step explanation:
Hello!
To test if calcium reduces the symptoms of PMS two independent groups of individuals are compared, the first group, control, is treated with the placebo, and the second group is treated with calcium.
The parameter to be estimated is the difference between the mean symptom scores of the placebo and calcium groups, symbolically: μ₁ - μ₂
There is no information about the distribution of both populations X₁~? and X₂~? but since both samples are big enough, n₁= 228 and n₂= 212, you can apply the central limit theorem and approximate the sampling distribution to normal X[bar]₁≈N(μ₁;δ₁²/n) and X[bar]₂≈N(μ₂;δ₂²/n)
The formula for the CI is:
[(X[bar]₁-X[bar]₂) ± [tex]Z_{1-\alpha /2}[/tex] * [tex]\sqrt{\frac{S^2_1}{n_1} +\frac{S^2_2}{n_2} }[/tex]]
95% confidence level [tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]
(a) mood swings: placebo = 0.70 ± 0.78; calcium = 0.50 ± 0.53
X₁: Mood swings score of a participant of the placebo group.
X₂: Mood swings score of a participant of the calcium group.
[(0.70-0.50) ± 1.96 * [tex]\sqrt{\frac{0.78^2}{228} +\frac{0.53^2}{212} }[/tex]]
[0.076; 0.324]
(b) crying spells: placebo = 0.39 + 0.57; calcium = 0.21 + 0.40
X₁: Crying spells score of a participant of the placebo group.
X₂: Crying spells score of a participant of the calcium group.
[(0.39-0.21) ± 1.96 * [tex]\sqrt{\frac{0.57^2}{228} +\frac{0.40^2}{212} }[/tex]]
[0.088; 0.272]
(c) aches and pains: placebo = 0.45 + 0.60; calcium = 0.37 + 0.45
X₁: Aches and pains score of a participant of the placebo group.
X₂: Aches and pains score of a participant of the calcium group.
[(0.45-0.37) ± 1.96 * [tex]\sqrt{\frac{0.60^2}{228} +\frac{0.45^2}{212} }[/tex]]
[-0.019; 0.179]
(d) craving sweets or salts: placebo = 0.60 + 0.75; calcium = 0.44 + 0.61
X₁: Craving for sweets or salts score of a participant of the placebo group.
X₂: Craving for sweets or salts score of a participant of the calcium group.
[(0.60-0.44) ± 1.96 * [tex]\sqrt{\frac{0.75^2}{228} +\frac{0.61^2}{212} }[/tex]]
[0.032; 0.287]
I hope this helps!
Using the z-distribution, the 95% confidence intervals are:
a) (0.08, 0.32).
b) (0.09, 0.27).
c) (-0.02, 0.18).
d) (0.03, 0.29).
We have to find the critical value, which is z with a p-value of [tex]\frac{1 + \alpha}{2}[/tex], in which [tex]\alpha[/tex] is the confidence level.
In this problem, [tex]\alpha = 0.95[/tex], thus, z with a p-value of [tex]\frac{1 + 0.95}{2} = 0.975[/tex], which means that it is z = 1.96.
Item a:
The standard errors are:
[tex]s_P = \frac{0.78}{\sqrt{228}} = 0.0517[/tex]
[tex]s_C = \frac{0.53}{\sqrt{212}} = 0.0364[/tex]
For the distribution of the differences, we have that:
[tex]\overline{x} = \mu_P - \mu_C = 0.7 - 0.5 = 0.2[/tex]
[tex]s = \sqrt{s_P^2 + s_C^2} = \sqrt{0.0517^2 + 0.0364^2} = 0.0632[/tex]
The interval is:
[tex]\overline{x} \pm zs[/tex]
Hence:
[tex]\overline{x} - zs = 0.2 - 1.96(0.0632) = 0.08[/tex]
[tex]\overline{x} + zs = 0.2 + 1.96(0.0632) = 0.32[/tex]
The interval is (0.08, 0.32).
Item b:
The standard errors are:
[tex]s_P = \frac{0.57}{\sqrt{228}} = 0.03775[/tex]
[tex]s_C = \frac{0.4}{\sqrt{212}} = 0.02747[/tex]
For the distribution of the differences, we have that:
[tex]\overline{x} = \mu_P - \mu_C = 0.39 - 0.21 = 0.18[/tex]
[tex]s = \sqrt{s_P^2 + s_C^2} = \sqrt{0.03775^2 + 0.02747^2} = 0.0467[/tex]
Hence:
[tex]\overline{x} - zs = 0.18 - 1.96(0.0467) = 0.09[/tex]
[tex]\overline{x} + zs = 0.18 + 1.96(0.0467) = 0.27[/tex]
The interval is (0.09, 0.27).
Item c:
The standard errors are:
[tex]s_P = \frac{0.6}{\sqrt{228}} = 0.0397[/tex]
[tex]s_C = \frac{0.45}{\sqrt{212}} = 0.0309[/tex]
For the distribution of the differences, we have that:
[tex]\overline{x} = \mu_P - \mu_C = 0.45 - 0.37 = 0.08[/tex]
[tex]s = \sqrt{s_P^2 + s_C^2} = \sqrt{0.0397^2 + 0.0309^2} = 0.0503[/tex]
Hence:
[tex]\overline{x} - zs = 0.08 - 1.96(0.0503) = -0.02[/tex]
[tex]\overline{x} + zs = 0.08 + 1.96(0.0503) = 0.18[/tex]
The interval is (-0.02, 0.18).
Item d:
The standard errors are:
[tex]s_P = \frac{0.75}{\sqrt{228}} = 0.0497[/tex]
[tex]s_C = \frac{0.61}{\sqrt{212}} = 0.0419[/tex]
For the distribution of the differences, we have that:
[tex]\overline{x} = \mu_P - \mu_C = 0.60 - 0.44 = 0.16[/tex]
[tex]s = \sqrt{s_P^2 + s_C^2} = \sqrt{0.0497^2 + 0.0419^2} = 0.065[/tex]
Hence:
[tex]\overline{x} - zs = 0.16 - 1.96(0.065) = 0.03[/tex]
[tex]\overline{x} + zs = 0.16 + 1.96(0.065) = 0.29[/tex]
The interval is (0.03, 0.29).
A similar problem is given at https://brainly.com/question/15297663
PLEASE HELP ASAP!! Major question points!! geometry
Answer:
A
Step-by-step explanation:
If you plug in the numbers to the formula, A is the correct answer.
Which of the following are true about regression with one predictor variable (often called "simple regression")? Check all that apply.
A. The slope describes the amount of change in Y for a one-unit increase in X
B. The regression equation is the line that best fits a set of data as determined by having the least squared error
C. The slope, b, of the regression equation has the same value as r, the estimated correlation
Answer:
A. The slope describes the amount of change in Y for a one-unit increase in X .B. The regression equation is the line that best fits a set of data as determined by having the least squared error.Step-by-step explanation:
In statistics, linear regression is a analysis we do to describe the relationship between two variables. With this study, we pretend to know if there's a positive or negative correlation between those variables, if that correlation is strong or weak.
In a linear regression analysis, we modeled the data set using a regression equation, which is basically the line that best fits to the data set, this line is like the average where the majority of data falls. That means choice A is right.
When we use linear equations, we need to know its characteristics, and the most important one is the slope, which is the ratio between the dependent variable and the independent variable. Basically, the slope states the unit rate between Y and X, in other words, it states the amount of Y per unit of X. That means choice B is correct.
Therefore, the correct answers are A and B.
The options that are true about regression with one predictor variable include:
A. The slope describes the amount of change in Y for a one-unit increase in XB. The regression equation is the line that best fits a set of data as determined by having the least squared error.Regression simply refers to a statistical measurement which attempts to determine the strength that exists between a dependent variable and the independent variables.
It should be noted that in one predictor variable, the slope describes the amount of change in Y for a one-unit increase in X and the regression equation is the line that best fits a set of data as determined by having the least squared error.
Read related link on:
https://brainly.com/question/11503532
A marketing consultant was hired to visit a random sample of five sporting goods stores across the state of California. Each store was part of a large franchise of sporting goods stores. The consultant taught the managers of each store better ways to advertise and display their goods.
The net sales for 1 month before and 1 month after the consultant's visit were recorded as follows for each store (in thousands of dollars):
Before visit: 57.1 94.6 49.2 77.4 43.2
After visit: 63.5 101.8 57.8 81.2 41.9
Do the data indicate that the average net sales improved? (Use a= 0.05)
Answer:
[tex]t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{4.94 -0}{\frac{3.901}{\sqrt{5}}}=2.832[/tex]
[tex]df=n-1=5-1=4[/tex]
[tex]p_v =P(t_{(4)}>2.832) =0.0236[/tex]
We see that the p value is lower than the significance level of 0.05 so then we have enough evidence to reject the null hypothesis and we can conclude that the average net sales improved
Step-by-step explanation:
Let put some notation
x=test value before , y = test value after
x: 57.1 94.6 49.2 77.4 43.2
y: 63.5 101.8 57.8 81.2 41.9
The system of hypothesis for this case are:
Null hypothesis: [tex]\mu_y- \mu_x \leq 0[/tex]
Alternative hypothesis: [tex]\mu_y -\mu_x >0[/tex]
The first step is calculate the difference [tex]d_i=y_i-x_i[/tex] and we obtain this:
d: 6.4, 7.2, 8.6, 3.8, -1.3
The second step is calculate the mean difference
[tex]\bar d= \frac{\sum_{i=1}^n d_i}{n}=4.94[/tex]
The third step would be calculate the standard deviation for the differences, and we got:
[tex]s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =3.901[/tex]
The next step is calculate the statistic given by :
[tex]t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{4.94 -0}{\frac{3.901}{\sqrt{5}}}=2.832[/tex]
The next step is calculate the degrees of freedom given by:
[tex]df=n-1=5-1=4[/tex]
Now we can calculate the p value, since we have a right tailed test the p value is given by:
[tex]p_v =P(t_{(4)}>2.832) =0.0236[/tex]
We see that the p value is lower than the significance level of 0.05 so then we have enough evidence to reject the null hypothesis and we can conclude that the average net sales improved