Answer:
θ [tex]0.75\pi[/tex] [tex]1.75\pi[/tex]
r 10.551 244.151
Step-by-step explanation:
The maximum value for [tex]\theta[/tex] is:
[tex]\theta_{max} = \ln r[/tex]
[tex]\theta_{max} = 2.199\pi\,rad[/tex]
The formula for the slope of the tangent line in polar coordinates is:
[tex]m = \frac{r'\cdot \sin \theta + r \cdot \cos \theta}{r' \cdot \cos \theta - r \cdot \cos \theta}[/tex]
Horizontal tangent lines have a slope of zero. So, the following relation must be satisfied:
[tex]r'\cdot \sin \theta + r \cdot \cos \theta = 0[/tex]
[tex]r'\cdot \sin \theta = - r \cdot \cos \theta[/tex]
[tex]\tan \theta = - \frac{r}{r'}[/tex]
[tex]\tan \theta = -\frac{e^{\theta}}{e^{\theta}}[/tex]
[tex]\tan \theta = -1[/tex]
[tex]\theta = \tan^{-1}(-1)[/tex]
[tex]\theta = \frac{3}{4}\pi + i\cdot \pi[/tex], for all [tex]i \in \mathbb{N}_{O}[/tex].
The maximum value of i is:
[tex]i = \frac{\theta_{max}-\frac{3}{4}\pi }{\pi}[/tex]
[tex]i = \frac{2.199-0.75}{1}[/tex]
[tex]i = 1.449[/tex] ([tex]i_{max} = 1[/tex]).
Then, values are listed below:
θ [tex]0.75\pi[/tex] [tex]1.75\pi[/tex]
r 10.551 244.151
Answer:
{ ( 2.193 , π / 4) , ( 10.551 , 3π / 4) , ( 50.754 , 5π / 4) , ( 244.151 , 7π / 4) }
Step-by-step explanation:
Given:-
- The polar curve has the equation:
r = e^θ
- list the points starting with the smallest value of r such that:
1 ≤ r ≤ 1000 , 0 ≤ θ < 2π.
Find:-
List all of the points (r,θ) where the tangent line is horizontal
Solution:-
- We will first transform the polar curve to cartesian coordinate system using the parametric relations:
x = r*cos (θ)
y = r*sin (θ)
- The tangent line is horizontal when the " dy / dθ " = 0 and " dx / dθ " = 0, so:
x = e^θ*cos (θ) , y = e^θ*sin (θ)
dx / dθ = e^θ*cos (θ) - e^θ*sin(θ)
= e^θ*[cos (θ) - sin(θ)]
dx / dθ = e^θ*[cos (θ) - sin(θ)] = 0,
e^θ = 0 , [cos (θ) - sin(θ)] = 0
e^θ ≠ 0 for the given interval 0 ≤ θ< 2π
cos (θ) - sin(θ) = 0 , tan ( θ ) = 1 - (1st quad and 3rd quad)
θ = { π / 4 , 5π / 4 } , 0 ≤ θ< 2π
- Similarly, evaluate dy/dθ = 0;
dy/dθ = e^θ*cos (θ) + e^θ*sin(θ)
= e^θ*[cos (θ) + sin(θ)]
dy / dθ = e^θ*[cos (θ) + sin(θ)] = 0,
e^θ = 0 , [cos (θ) + sin(θ)] = 0
e^θ ≠ 0 for the given interval 0 ≤ θ< 2π
cos (θ) + sin(θ) = 0 , tan ( θ ) = -1 , (2nd quad and 4th quad)
θ = { 3π / 4 , 7π / 4 } , 0 ≤ θ< 2π
- All possibilities of " θ " over the interval satisfying the a horizontal tangent line to the given polar curve:
θ = { π / 4, 3π / 4 , 5π / 4 , 7π / 4 } , 0 ≤ θ < 2π
- We will plug the evaluated list of values of "θ " in the given polar curve and determine the corresponding values of "r":
r = e^θ
θ = π / 4 , r = e^(π / 4) = 2.193
1: ( r , θ ) = ( 2.193 , π / 4)
θ = 3π / 4 , r = e^(3π / 4) = 10.55072
2: ( r , θ ) = ( 10.551 , 3π / 4)
θ = 5π / 4 , r = e^(5π / 4) = 50.754
3: ( r , θ ) = ( 50.754 , 5π / 4)
θ = 7π / 4 , r = e^(7π / 4) = 244.151
4: ( r , θ ) = ( 244.151 , 7π / 4)
Write an algebraic equation for the situation:
Daniel is six inches shorter than Ernie, how y’all is Daniel
Answer:
ernie=X so Daniel = X-6
Step-by-step explanation:
The variable, the number of hours Daniel worked, is modeled by an orange x tile. Working 3 times as many hours is modeled with 3 orange x tiles. The multiplication expression that represents the situation is 3x.y-
100 POINTS!!
PLEASE PROVIDE STEPS
THANK YOU
Step-by-step explanation:
R'(x) = 5x³ − 60x²
A) R"(x) = 15x² − 120x
0 = 15x² − 120x
0 = 15x (x − 8)
x = 0 or 8
B) R"(-1) = 135
R"(1) = -105
R"(x) changes signs around x = 0, so x = 0 is an inflection point.
R"(7) = -105
R"(9) = 135
R"(x) changes signs around x = 8, so x = 8 is an inflection point.
The amount of coffee that people drink per day is normally distributed with a mean of 15 ounces and a standard deviation of 4.5 ounces. 10 randomly selected people are surveyed. Round all answers to 4 decimal places where possible. What is the distribution of X ? X ~ N( 15 , 4.5 ) What is the distribution of ¯ x ? ¯ x ~ N( 15 , ) What is the probability that one randomly selected person drinks between 14.5 and 16.5 ounces of coffee per day? For the 10 people, find the probability that the average coffee consumption is between 14.5 and 16.5 ounces of coffee per day. For part d), is the assumption that the distribution is normal necessary? YesNo Find the IQR for the average of 10 coffee drinkers. Q1 = ounces Q3 = ounces IQR: ounces
Answer:
Step-by-step explanation:
Hello!
The variable of interest is
X: the amount of coffee a person drinks per day. (ounces)
This variable has a normal distribution with μ= 15 ounces and σ=4.5 ounces.
10 randomly selected persons where surveyed.
a) X~N(μ;σ²) ⇒ X~N(15;20.25)
b) The sample means has the same distribution as the original variable except that the population variance is affected by the sample size:
X[bar]~N(μ;σ²/n) ⇒ X[bar]~N(15;20.25/10) ⇒ X[bar]~N(15;2.025)
c)
You need to find the probability that one random person drinks between 14.5 and 16.5 ounces of coffee per day, symbolically:
P(14.5 ≤ X ≤ 16.5)
For this part, since you need to calculate the probability that one person drinks between 14.5 and 16.5 ounces of coffee daily out of the whole population of people that drink coffee, you have to work using the distribution of the variable:
X~N(15;20.25)
To reach the correspondent probability you have to first standardize both bonds of the interval using Z=(X-μ)/δ~N(0;1):
P(14.5 ≤ X ≤ 16.5)
P(X ≤ 16.5) - P(X ≤ 14.5)
P(Z≤ (16.5-15)/4.5) - P(Z≤ (14.5-15)/4.5)
P(Z≤ 0.33) - P(Z≤ -0.11)= 0.62930 - 0.45620= 0.1731
d)
In this item, you need to calculate the probability that one out of the ten people surveyed drinks on average between 14.5 and 16.5 ounces of coffee.
P(14.5 ≤ X[bar] ≤ 16.5)
To calculate the correspondent probability you have to work using the distribution od the sample mean: X[bar]~N(15;2.025) and the standard normal: Z=(X[bar]-μ)/(δ/√n)~N(0;1)
P(X[bar] ≤ 16.5) - P(X[bar] ≤ 14.5)
P(Z≤ (16.5-15)/1.42) - P(Z≤ (14.5-15)/1.42)
P(Z≤ 1.06) - P(Z≤ -0.35)= 0.85543 - 0.36317= 0.49226
e)
Yes. Without the assumption that the variable had a normal distribution, you wouldn't be able to use the standard normal distribution to calculate the asked probabilities.
There is a possibility to apply the Central Limit Theorem to approximate the sampling distribution to normal if the sample was large enough (n ≥30) which is not the case.
f)
You need to find the IQR for the average consumption of coffee for a sample of 10 persons.
For this, you have to work using the distribution of the sample mean X[bar]~N(15;2.025)
The 1st quartile is the value that divides the bottom 25% of the distribution from the top 75%, symbolically:
P(X[bar]≤x[bar]₀)= 0.25
First, you have to determine the value of Z that accumulates 0.25 of probability:
P(Z≤z₀)= 0.25
z₀= -0.674
Now using the formula Z=(X[bar]-μ)/(δ/√n), you have to "reverse" the standardization, i.e. clear the value of X[bar]:
z₀=(x[bar]₀-μ)/(δ/√n)
-0.674=(x[bar]₀-15)/1.42
-0.674*1.42= (x[bar]₀-15)
x[bar]₀= (-0.674*1.42)+15
1st Quartile x[bar]₀= 14.0429 ounces
The third quartile is the value that divides the bottom 75% of the distribution from the top 25% of it:
P(X[bar]≤x[bar]₀)= 0.75
As before, the first step is to determine the corresponding value of Z:
P(Z≤z₀)= 0.75
z₀= 0.674
z₀=(x[bar]₀-μ)/(δ/√n)
0.674= (x[bar]₀-15)/1.42
0.674*1.42= x[bar]₀-15
x[bar]₀= (0.674*1.42)+15
3rd Quartile x[bar]₀= 15.9571
The IQR is the difference between Q3 and Q1:
IQR= 15.9571 - 14.0429= 1.9142
I hope this helps!
The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have thelr weddings in the Caribbean. A Caribbean vacation resort recently advertised In Bride Magazine that the cost of a Caribbean wedding was less than $30,000. Listed below is a total cost in $000 for a sample of 8 Caribbean weddings. At the 0.05 significance level, is it reasonable to conclude the mean wedding cost is less than $30,000 as advertised? 29.7 29.4 31.7 29.0 29.1 30.5 29.1 29.8 Excel Data a. State the null hypothesis and the alternate hypothesis. (Enter your answers in thousands of dollars.) b. State the decision rule for 0.05 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) H0 if t c. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) of the test statistic d. What is the conclusion regarding the null hypothesis? o not reject cost is not less n $30 Reference links for lation Mean ulation Sta
Answer:
Step-by-step explanation:
The mean of the set of data given is
Mean = (29.7 + 29.4 + 31.7 + 29.0 + 29.1 + 30.5 + 29.1 + 29.8)/8 = 29.788 = $29788
Standard deviation = √(summation(x - mean)/n
n = 8
Summation(x - mean) = (29700 - 29788)^2 + (29400 - 29788)^2 + (31700 - 29788)^2 + (29000 - 29788)^2 + (29100 - 29788)^2 + (30500 - 29788)^2 + (29100 - 29788)^2 + (29800 - 29788)^2 = 5888752
Standard deviation = √(5888752/8) = 857.96
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ < 30000
For the alternative hypothesis,
µ > 30000
It is a right tailed test
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 8,
Degrees of freedom, df = n - 1 = 8 - 1 = 7
t = (x - µ)/(s/√n)
Where
x = sample mean = 29788
µ = population mean = 30000
s = samples standard deviation = 857.96
t = (29788 - 30000)/(857.96/√8) = - 0.7
We would determine the p value using the t test calculator. It becomes
p = 0.253
Since alpha, 0.05 < than the p value, 0.253, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, the sample data did not show evidence that the mean wedding cost is not less than $30,000 as advertised
Which two figures have the same number of lateral faces?
Answer:
Cube and cuboid
Both have 6 faces
Answer:
Cube and cuboid
Both have 6 faces
7/15+(-5/6)
What is the answer and how do I get it?
Answer:
-0.36666666666...
Step-by-step explanation:
not sure how to explain, that's a repeating number.
The problem I need to solve is rt=w and I need to solve for r I need help
Answer:
r = w/t
Step-by-step explanation:
To solve this problem, we need to isolate the variable r, or get it alone by itself on the left side of the equation. To do this, we must get rid of the t. Since the r and t are multiplied together, we must divide by t to get the r alone. This is modeled below:
rt = w
rt/t = w/t
r = w/t
Hope this helps!
Given: g ∥ h and ∠2 ≅ ∠3
Prove: e ∥ f
Horizontal and parallel lines e and f are intersected by diagonal and parallel lines g and h. At the intersection of lines g and e, the bottom right angle is angle 2. At the intersection of lines h and e, the bottom right angle is angle 1. At the intersection of lines f and h, the top left angle is angle 3.
Statements Reasons
1. g || h 1. given
2. ∠1 ≅ ∠2 2. corresponding angles theorm
3. ∠2 ≅ ∠3 3. given
4. ∠1 ≅ ∠3 4. transitive property
5. e || f 5. ?
What is the missing reason in the proof?
vertical angles theorem
alternate exterior angles theorem
converse corresponding angles theorem
converse alternate interior angles theorem
Answer:
In the image, you can observe a diagram representing this problem.
We know by given that [tex]g \parallel h[/tex] and [tex]\angle 2 \cong \angle 3[/tex].
From the parallelism between line g and line h, we deduct several congruence between angles.
[tex]\angle 2 \cong \angle 1[/tex], by corresponding angles (same side of the transversal, one interior, the other exterior to parallels).
Now, to demonstrate [tex]e \parallel f[/tex], we must demonstrate a congruence between angle 2 and an angle on the intersection between line g and line f.
In the parallelogram formed, we know
[tex]\angle 2 + \angle 3+ 180-\angle 1 + x =360[/tex]
Where [tex]x[/tex] is the angle at the intersection line g and line f.
But, we know [tex]\angle 2 \cong \angle 3[/tex] and [tex]\angle 2 \cong \angle 1[/tex], so
[tex]\angle 2 + \angle 2 +180 - \angle 2 +x=360\\\angle 2 + x=180[/tex]
Notice that we don't have a congruence, however there's theorem which states that the same-side interior angles of parallels are supplementary.
In this case, we use the corolary of that theorem, which states if two same-side interior angles are supplementary, then the lines are parallels.
[tex]\therefore e \parallel f[/tex]
However, according to the choices of the problem, the missin proof is "converse alternate interior angles theorem", because the problem was demonstrate using transitive property, to show that angles 1 and 3 are congruent, there by converse alternate interior angles theorem, lines e and f are parallels.
This is the same case we used, but using converse alternate interior angles theorem.
Answer:
the answer is c-
Step-by-step explanation:
converse alternate interior angles theorem
hope this is helpful
give brainliest to the other dude
Which economic indicator measures the change in prices of specific goods and services over time?
A.
Price Change Rate
B.
Consumer Price Schedule
C.
Consumer Price Index
Answer:
C. Consumer Price Index
Step-by-step explanation:
The Consumer Price Index is based on the cost of a specific shopping list of goods. It is published monthly by the US Bureau of Labor Statistics.
Round 7.6378 to the nearest 0.1
Answer:
7.64
Step-by-step explanation:
company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 26 miles per gallon. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 25.02 mpg and a standard deviation of 4.83 mpg. Is this strong evidence that they have failed to attain their fuel economy goal
Answer:
[tex]t=\frac{25.02-26}{\frac{4.83}{\sqrt{50}}}=-1.435[/tex]
[tex]p_v =P(t_{(49)}<-1.435)=0.0788[/tex]
If we compare the p value and the significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant lower than 26 so then the specification is satisfied.
Step-by-step explanation:
Data given and notation
[tex]\bar X=25.02[/tex] represent the sample mean
[tex]s=4.83[/tex] represent the sample standard deviation
[tex]n=50[/tex] sample size
[tex]\mu_o =26[/tex] represent the value that we want to test
[tex]\alpha[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is at least 26 mpg, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 26[/tex]
Alternative hypothesis:[tex]\mu < 26[/tex]
If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
[tex]t=\frac{25.02-26}{\frac{4.83}{\sqrt{50}}}=-1.435[/tex]
P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n-1=50-1=49[/tex]
Since is a one sided test the p value would be:
[tex]p_v =P(t_{(49)}<-1.435)=0.0788[/tex]
Conclusion
If we compare the p value and the significance level assumed [tex]\alpha=0.05[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its significant lower than 26 so then the specification is satisfied.
Using the t-distribution, it is found that since the test statistic is more than the critical value for the left-tailed test, this is not strong evidence that they have failed to attain their fuel economy goal.
At the null hypothesis, it is tested if the fleet average is of at least 26 miles per gallon, that is:
[tex]H_0: \mu \geq 26[/tex]
At the alternative hypothesis, it is tested if it is less, that is:
[tex]H_1: \mu < 26[/tex]
We have the standard deviation for the sample, hence, the t-distribution is used to solve this question.
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are: [tex]\overline{X} = 25.02, \mu = 26, s = 4.83, n = 50[/tex].
Hence, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{25.02 - 26}{\frac{4.83}{\sqrt{50}}}[/tex]
[tex]t = -1.43[/tex]
The critical value for a left-tailed test, as we are testing if the mean is less than a value, with a significance level of 0.05 and 50 - 1 = 49 df is of [tex]t^{\ast} = -1.677[/tex]
Since the test statistic is more than the critical value for the left-tailed test, this is not strong evidence that they have failed to attain their fuel economy goal.
To learn more about the t-distribution, you can take a look at https://brainly.com/question/13873630
B / 3 - 6 equals 9.
Answer:
B = 45
Step-by-step explanation:
B/3 - 6 = 9
B/3 = 15
B = 45
Tell me if I am wrong.
Can I get brainliest
(I need help ASAP)
- Which name doesn’t apply to the figure?
A. square
B. rhombus
C. parallelogram
D. quadrilateral
Answer:
A- square
Step-by-step explanation:
A square should have 4 right angles.
Round 67.62 to
the nearest whole
number.
what is two plus two
Answer:
4
Step-by-step explanation:
Question- what is two plus two
Answer- 2+2=4
Light travels at a speed of about 186,000 miles per second. How far does light travel in 5 second? Use repeated addition to solve.
Answer:
Step-by-step explanation:
The speed of light in a vacuum is 186,282 miles per second (299,792 kilometres per second), and in theory nothing can travel faster than light. In miles per hour, light speed is, well, a lot: about 670,616,629 mph. If you could travel at the speed of light, you could go around the Earth 7.5 times in one second.
186 ,282 x 5 = 931 , 410 for 5 seconds
3 friends are sharing 1/2 of a blueberry ....how much pie would each friend get
Answer:
each friend would get 1/6 when you divide 1/2 by 3
Step-by-step explanation:
Each friend receives 1/6 of the pie.
The student asked how much pie each of three friends would get if they share 1/2 of a blueberry pie. To find the answer, you simply divide the half of the pie by three, since there are three friends sharing it. That is, 1/2 ÷ 3.
You can think of this division as splitting the 1/2 of the pie into three equal parts. Each friend would get 1/6 of the pie, because 1/2 ÷ 3 = 1/6. This intuitively makes sense because if a pie is cut into six equal slices, three slices (which is half the pie) can be shared by three friends, giving each one slice.
A teacher interested in determining the effect of a new computer program on learning to read conducted a study. One hundred students were randomly assigned to one of two groups. The first group used the computer program while the second group did not. Both groups were tested to determine how much their reading levels improved. The results for the two groups were compared. What kind of study is this?
1.This is an experiment because a treatment was applied to a group.
2.This is an experiment because students were able to choose which group to join.
3.This is a survey because students were randomly assigned to groups.
4.This is a survey because a treatment was applied to both groups
Answer:
c
Step-by-step explanation:
Which of the following is not an example of primary data?
A. Financial data tapes that contain data compiled from the New York Stock Exchange
B. Data published by the New York Stock Exchange
C. Data published by the U.S. Census Bureau
D. Data published by Statistics Canada
Answer:
A. Financial data tapes that contain data compiled from the New York Stock
Step-by-step explanation:
Primary data is data that is collected by a researcher from first-hand sources. Data published by the New York Stock Exchange is primary data, which inherently makes the data tapes secondary data, because they contain the data from a source other than original source.
write p-20=-30 as an addition problem
The equation p-20=-30 can be rewritten as an addition problem by adding 20 to both sides of the equation. The resulting addition equation is p = -30 + 20.
Explanation:The equation p-20=-30 can be written as an addition problem by moving -20 to the other side of the equation. This is done by adding 20 to both sides of the equation, which results in the equation p = -30 + 20. In other words, you can add -30 and 20 together to find the value of p. This is how you write the equation p-20=-30 as an addition problem. So the equation becomes p= -30+20
Learn more about Equation Transformation here:https://brainly.com/question/28327649
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A circle has a diameter that measures 8 inches What is the area of the circle to the nearest 10th use 3.14 for pi
The area of a circle can be calculated by formula πr^2...
radius(r)=4inches
therefore,
Area(A)=3.14×4
=12.56
Final answer:
To calculate the area of a circle with an 8-inch diameter using 3.14 for π, the formula A = πr² gives us 50.24 square inches, which rounds to 50.2 square inches to the nearest tenth.
Explanation:
The student is asking for the area of a circle with a diameter of 8 inches using 3.14 for π (Pi). The area of a circle is given by the formula A = πr², where 'r' is the radius of the circle. Since the diameter is twice the radius, we have that the radius 'r' is 4 inches (half of 8 inches). Plugging this into the formula we get A = 3.14 × 4².
To find the area to the nearest tenth, we perform the calculation: A = 3.14 × 16 = 50.24. Therefore, the area of the circle is 50.2 square inches when rounded to the nearest tenth.
A 4.5 pound bag of apples cost $22.50. What is the unit price?
Answer:
The unit price is $5.
Answer:
$5.00.
Step-by-step explanation:
This is 22.5 / 4.5
= $5.00
Prove that the diagonals of a parallelogram bisect each other.
Name the coordinates for point C.
A: (2a, 2b + 2c)
B: (2a, 2b)
C: (2a, 2c)
D: (2a + 2b, 2c)
Answer:2a + 2b, 2c
Step-by-step explanation:
you work in the HR department at a large franchise. you want to test whether you have set your employee monthly allowances correctly. the population standard deviation is 150. You want to test if the monthly allowances should be increased. A random sample of 40 employees yielded a mean monthly claim of $640.
1- at the 1% significance level, test if the average monthly allowances should be greater than 500(use the 5 steps hypothesis testing procedure)
2- Confirm your answer by the p value approach.
Answer:
1) Null hypothesis:[tex]\mu \leq 500[/tex]
Alternative hypothesis:[tex]\mu > 500[/tex]
[tex]z=\frac{640-500}{\frac{150}{\sqrt{40}}}=5.90[/tex]
For this case since we are conducting a right tailed test we need to find a critical value in the normal standard distribution who accumulates 0.01 of the area in the right and we got:
[tex]z_{crit}= 2.33[/tex]
For this case we see that the calculated value is higher than the critical value
Since the calculated value is higher than the critical value we have enugh evidence to reject the null hypothesis at 1% of significance level
2) Since is a right tailed test the p value would be:
[tex]p_v =P(z>5.90)=1.82x10^{-9}[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, same conclusion for part 1
Step-by-step explanation:
Part 1
Data given
[tex]\bar X=640[/tex] represent the sample mean
[tex]\sigma=150[/tex] represent the population standard deviation
[tex]n=40[/tex] sample size
[tex]\mu_o =500[/tex] represent the value that we want to test
[tex]\alpha=0.01[/tex] represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
Step1:State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean is higher than 500, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 500[/tex]
Alternative hypothesis:[tex]\mu > 500[/tex]
Step 2: Calculate the statistic
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
We can replace in formula (1) the info given like this:
[tex]z=\frac{640-500}{\frac{150}{\sqrt{40}}}=5.90[/tex]
Step 3: Calculate the critical value
For this case since we are conducting a right tailed test we need to find a critical value in the normal standard distribution who accumulates 0.01 of the area in the right and we got:
[tex]z_{crit}= 2.33[/tex]
Step 4: Compare the statistic with the critical value
For this case we see that the calculated value is higher than the critical value
Step 5: Decision
Since the calculated value is higher than the critical value we have enugh evidence to reject the null hypothesis at 1% of significance level
Part 2
P-value
Since is a right tailed test the p value would be:
[tex]p_v =P(z>5.90)=1.82x10^{-9}[/tex]
If we compare the p value and the significance level given [tex]\alpha=0.01[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, same conclusion for part 1
A procurement specialist has purchased 23 resistors from vendor 1 and 30 resistors from vendor 2. Let represent the vendor 1 observed resistances, which are assumed to be normally and independently distributed with mean 120 ohms and standard deviation 1.7 ohms. Similarly, let represent the vendor 2 observed resistances, which are assumed to be normally and independently distributed with mean 125 ohms and standard deviation of 2.0 ohms. What is the sampling distribution of ? What is the standard error of ? The sampling distribution of is What is thesampling distribution of X1 − X2? What is the standard errorof X1 − X2?
Answer:
The standard error( X1 − X2 ) = 0.547
Step-by-step explanation:
Step:-(1)
Given a procurement specialist has purchased 23 resistors
Given normally and independently distributed with mean 120 ohms and standard deviation 1.7
mean of the Population of the vendor 1 is μ₁ = 120 ohms
Standard deviation of the Population the vendor 1 is σ₁ = 1.7 ohms
similarly represent the vendor 2 observed resistances, which are assumed to be normally and independently distributed with mean 125 ohms and standard deviation of 2.0
mean of the Population of the vendor 2 is μ₂ = 120 ohms
Standard deviation of the Population the vendor 2 is σ₂ = 1.7 ohms
The standard error of the difference of two means
Se( X1 − X2) = [tex]\sqrt{\frac{σ^2_{1} }{n_{1} } +\frac{σ^2_{2} }{n_{1} } }[/tex]
Here σ₁ = 1.7 ohms and σ₂ = 2 ohms and n₁=n₂ =n = 23 resistors
se(X1 − X2) = [tex]\sqrt{\frac{1.7^2}{23 } +\frac{2^2 }{23} }[/tex]
se(X1 − X2) = √0.2995
= 0.547
Conclusion:-
The standard error of X1 − X2 = 0.547
Final answer:
Explains the standard error of sample means for two vendors and the distribution of sample means.
Explanation:
The standard error of the sample mean in this scenario, rounded to two decimal places, is calculated as follows:
For vendor 1: standard error = 1.7 / sqrt(23)
For vendor 2: standard error = 2.0 / sqrt(30)
The distribution of the sample mean X: Since the sample means are normally distributed, the sampling distribution of X is approximately normal.
The standard error of X1 − X2: The standard error of the difference between sample means X1 and X2 is calculated using the formula for the standard error of the difference between two independent sample means.
The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The resistance R is slowly increasing as the resistor heats up. Use Ohm's Law, V = IR, to find how the current I is changing at the moment when R = 337Ω, I = 0.01A, dV/dt = -0.07V/s, and dR/dt = 0.06Ω/s. (Round your answer to six decimal places.)
Answer:
The current is decreasing at a rate 0.000209 ampere per second.
Step-by-step explanation:
We are given the following in the question:
[tex]R = 337\Omega\\I = 0.01 A\\\\\dfrac{dV}{dt} = -0.07\text{ V/s}\\\\\dfrac{dR}{dt} = 0.06\text{ ohm/s}[/tex]
According to the Ohm's Law:
V = IR
Differentiating we get,
[tex]\dfrac{dV}{dt} = I\dfrac{dR}{dt} + R\dfrac{dI}{dt}[/tex]
Putting values, we get,
[tex]-0.07 = (0.01)(0.06)+ (337)\dfrac{dI}{dt}\\\\(337)\dfrac{dI}{dt} = -0.07-(0.01)(0.06) =-0.0706\\\\\dfrac{dI}{dt} = \dfrac{-0.0706}{337} = -0.000209\text{ A/s}[/tex]
Thus, the current is decreasing at a rate 0.000209 ampere per second.
A Starbucks coffee costs $4.50. What is the total price if the sales tax rate is 7%?
Answer:
$4.815
Step-by-step explanation:
4.50 x 7/100=0.315
then add 4.50+0.315=4.815
Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 10 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: SST = 10,800. SSTR = 4560. Set up the ANOVA table for this problem. Using alpha = .05. test for any significant difference in the means for the three assembly methods.
Answer:
During the test for any significant difference in the means for the three assembly methods, there is significant evidence to reject the claim of equal population means
Step-by-step explanation:
Let;
SS be sum of square
MS be Mean Square
d.f be degree of freedom
trt be treatment
w be workers
Pls see attached files for detail step by step solutions as typing the explanation is not possible because of tables involved.
Using a one-way ANOVA test, it is determined that at least one of the assembly methods differs significantly from the others in terms of units assembled correctly by the randomly assigned workers.
Explanation:The question involves the use of a one-way Analysis of Variance (ANOVA) to explore any significant difference in the means of the three proposed assembly methods. The given data are: SST (Total Sum of Squares) = 10800, SSTR (Sum of Squares between groups) = 4560. We can calculate SSE (Sum of Squares within groups) using the formula: SSE = SST - SSTR, which gives 10800 - 4560 = 6240.
The degrees of freedom (df) for between groups is k - 1 = 3 - 1 = 2 (where k is the number of groups). Similarly, the total degrees of freedom is n - 1 = 30 - 1 = 29 (where n is the total number of observations). The within groups degrees of freedom is df(total) - df(between) = 29 - 2 = 27.
Next, calculate Mean Square Between (MSB) = SSTR/df(between) = 4560/2 = 2280 and Mean Square Error (MSE) = SSE/df(within) = 6240/27 = 231.112. The F-statistic is given by F = MSB/MSE = 2280/231.112 = 9.869.
For a one-way ANOVA test at alpha = .05 with df(between) = 2 and df(within) = 27, checking an F distribution table, the critical value of F is approximately 3.354. Since our calculated F(9.869) > F critical(3.354), there is evidence to reject the null hypothesis. This indicates that at least one assembly method has a significantly different mean than the others.
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shareholdings in Tazon Insurance by Country ( As of April in Year 1) Total number of shares: 45 million. Germany 15% France 10% Switzerland 8% Other 14% Treasury Stock 5% IS 30% UK 18% if each share had a market value of $30 in April year 1, what was the total value of the German shareholding?
The total value of the German shareholding is 202500 million dollars.
Given that, the total number of shares is 45 million.
We need to find the total value of the German shareholding.
How to calculate the total value of share holding?Determine the company's earnings per share.Add the company's stock price to its EPS to determine your shareholder value on a per-share basis.Multiply the per-share shareholder value by the number of shares in the company you own.Germany holds 15% of the shares, which is 15% of 45 million
=15/100×45000000=67,50,000
Number of shares Germany holds=67,50,000
Now, the total value of the German shares=67,50,000×30=$20,25,00,000
Therefore, the total value of the German shareholding is 202500 million dollars.
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Final answer:
The total value of the German shareholding in Tazon Insurance is $202.5 million as of April in Year 1.
Explanation:
The student is asking for the calculation of the total value of German shareholdings in Tazon Insurance when each share is valued at $30. To find this, we need to calculate the number of shares held by Germany and then multiply by the share price.
Calculate the number of shares held by Germany: 45 million shares * 15% = 6.75 million shares.Multiply the number of shares by the market value: 6.75 million shares * $30/share = $202.5 million.Therefore, the total value of the German shareholding in Tazon Insurance is $202.5 million as of April in Year 1.
You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately σ = 79.5 σ=79.5 dollars. You would like to be 90% confident that your estimate is within 4 dollar(s) of average spending on the birthday parties. How many parents do you have to sample?
Answer:
We need to sample at least 1069 parents.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
How many parents do you have to sample?
We need to sample at least n parents.
n is found when [tex]M = 4, \sigma = 79.5[/tex]. So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]4 = 1.645*\frac{79.5}{\sqrt{n}}[/tex]
[tex]4\sqrt{n} = 1.645*79.5[/tex]
[tex]\sqrt{n} = \frac{1.645*79.5}{4}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.645*79.5}{4})^{2}[/tex]
[tex]n = 1068.92[/tex]
Rounding up
We need to sample at least 1069 parents.
Answer:
[tex]n=(\frac{1.64(79.5)}{4})^2 =1062.43 \approx 1063[/tex]
So the answer for this case would be n=1063 rounded up to the nearest integer
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=79.5[/tex] represent the population standard deviation
n represent the sample size
Solution to the problem
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =4 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 90% of confidence interval now can be founded using the normal distribution. And in excel we can use this formula to find it:"=-NORM.INV(0.05;0;1)", and we got [tex]z_{\alpha/2}=1.64[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.64(79.5)}{4})^2 =1062.43 \approx 1063[/tex]
So the answer for this case would be n=1063 rounded up to the nearest integer