Answer:
[tex]\cos'(z) = -\sin(z)[/tex]
Step-by-step explanation:
According to the information given by the problem
[tex]\sin(z) = {\displaystyle \frac{e^{iz} - e^{-iz} }{2i} }[/tex]
[tex]\cos(z) = {\displaystyle \frac{e^{iz} + e^{-iz} }{2} }[/tex]
Now, if you compute the derivative of [tex]\cos[/tex] you get that
[tex]\cos'(z) = {\displaystyle \frac{ ie^{iz}-i e^{iz} }{2} } = {\displaystyle \frac{ i ( e^{iz}- e^{iz} )}{2} }\\\\= {\displaystyle \frac{ i ( e^{iz}- e^{iz} )}{2} } *\frac{i}{i} }\\\\= {\displaystyle - \frac{ e^{iz}- e^{iz} }{2i} } = -\sin(z)[/tex]
Help me not big brained
Answer:
33 yd
Step-by-step explanation:
To find the area of a triangle, you can follow the formula:
(base x height) / 2
By putting this formula into context, you can substitute the values of the terms with the information provided in the problem:
(base x height) / 2
(11 yd x 6 yd) / 2
66 yd / 2
33 yd
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W. The appropriate hypotheses to determine if the manufacturer's claim appears reasonable are
Answer:
Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 250 W
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 250 W
Step-by-step explanation:
We are given that an appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W.
They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Let [tex]\mu[/tex] = mean power consumption of microwave ovens.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 250 W
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 250 W
Here, null hypothesis states that the mean power consumption of microwave ovens is no more than 250 W.
On the other hand, alternate hypothesis sates that the mean power consumption of microwave ovens is more than 250 W.
The test statistics that would be used here is One-sample z test statistics as we know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
Hence, this would be the appropriate hypotheses to determine if the manufacturer's claim appears reasonable.
The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught.
Step 2 of 2 : Suppose a sample of 1390 suspected criminals is drawn. Of these people, 514 were captured. Using the data, construct the 98% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list. Round your answers to three decimal places.
Answer:
Step-by-step explanation:
Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 1390
x = 514
p = 514/1390 = 0.37
q = 1 - 0.37 = 0.63
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.01 = 0.99
The z score corresponding to the area on the z table is 2.33. Thus, confidence level of 98% is 2.33
Therefore, the 98% confidence interval is
0.37 ± 2.33√(0.37)(0.63)/1390
Confidence interval = 0.37 ± 0.0302
I’m on a roll ᕕ( ᐛ )ᕗ
Answer:
Yessirrr you are!!!
Step-by-step explanation:
Assume that when adults with smartphones are randomly selected, 42% use them in meetings or classes. If 30 adult smartphone users are randomly selected, find the probability that exactly 24 of them use their smartphones in meetings or classes.
Answer:
0.00205%
Step-by-step explanation:
Use binomial probability:
P = nCr p^r q^(n-r)
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1-p).
n = 30, r = 24, p = 0.42, and q = 0.58.
P = ₃₀C₂₄ (0.42)²⁴ (0.58)³⁰⁻²⁴
P ≈ 0.00205%
A Statistics class is estimating the mean height of all female students at their college. They collect a random sample of 36 female students and measure their heights. The mean of the sample is 65.3 inches. The standard deviation is 5.2 inches. Use the T-distribution Inverse Calculator applet to answer the following question. What is the 90% confidence interval for the mean height of all female students in their school? Group of answer choices (56.5, 74.1) (63.6, 67.0) (63.8, 66.8) (63.9, 66.7)
Answer: = ( 63.9, 66.7)
Therefore at 90% confidence interval (a,b)= ( 63.9, 66.7)
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 x = 65.3
Standard deviation r = 5.2
Number of samples n = 36
Confidence interval = 90%
z(at 90% confidence) = 1.645
Substituting the values we have;
65.3 +/-1.645(5.2/√36)
65.3 +/-1.645(0.86667)
65.3+/- 1.4257
65.3+/- 1.4
= ( 63.9, 66.7)
Therefore at 90% confidence interval (a,b)= ( 63.9, 66.7)
Two different samples will be taken from the same population of test scores where the population mean and standard deviation are unknown. The first sample will have 25 data values, and the second sample will have 64 data values. A 95% confidence interval will be constructed for each sample to estimate the population mean. Which confidence interval would you expect to have greater precision (a smaller width) for estimating the population mean?
Answer:
The sample consisting of 64 data values would give a greater precision.
Step-by-step explanation:
The width of a (1 - α)% confidence interval for population mean μ is:
[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}[/tex]
So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (n).
That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.
Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.
The two sample sizes are:
n₁ = 25
n₂ = 64
The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.
Width for n = 25:
[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\cdot [2\cdot z_{\alpha/2}\cdot \sigma][/tex]
Width for n = 64:
[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\cdot [2\cdot z_{\alpha/2}\cdot \sigma][/tex]
Thus, the sample consisting of 64 data values would give a greater precision
Answer:
Confidence Interval with sample size 25 = Broader, less precision; Confidence Interval with sample size 64 = Narrower, more precision
Step-by-step explanation:
Confidence Interval is the range around sample statistic, which contains the actual population parameter. Confidence level is the percentage probability, with which the population parameter is expected to be in confidence interval.
When sample size increases : the margin of error, ie sampling error between population parameter & sample statistic decreases. The reduced margin of error increases the level of confidence & precision in confidence interval range. So, the confidence interval range becomes narrower.
Hence, confidence interval becomes narrower & has more precision, when sample size increases from sample number = 25 to sample number = 64.
SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school are given below. 380 520 480 510 560 630 670 490 500 550 400 350 440 490 620 660 700 730 740 560 Test if the standard deviation of the reading and writing section SAT score of the students in this school is higher than 100. What is the value of the test statistic (round off to the nearest integer)
Answer:
The value of test statistics is 25.
Step-by-step explanation:
We are given below the SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school;
380, 520, 480, 510, 560, 630, 670, 490, 500, 550, 400, 350, 440, 490, 620, 660, 700, 730, 740, 560
Let [tex]\sigma[/tex] = population standard of the reading and writing section SAT score of the students in this school
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\sigma \leq[/tex] 100 {means that the reading and writing section SAT score of the students in this school is lesser than or equal to 100}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\sigma[/tex] > 100 {means that the reading and writing section SAT score of the students in this school is higher than 100}
The test statistics that would be used here is One-sample Chi-square test statistics;
T.S. = [tex]\frac{(n-1)s^{2} }{\sigma^{2} }[/tex] ~ [tex]\chi^{2} __n_-_1[/tex]
where, [tex]s^{2}[/tex] = sample variance = [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex] = 13135.8
n = sample of 11th-grade students = 20
So, the test statistics = [tex]\frac{(20-1)\times 13135.8^{2} }{100^{2} }[/tex]
= 24.96 ≈ 25
Hence, the value of test statistics is 25.
please help with this one
Answer:
2
Step-by-step explanation:
y-intercept is where x = 0, and that point is (0,2), so it's 2
Find the value of X to the nearest tenth.
Choices are: 3, 6, 9, 12
Answer:
Here, we have BC // ST, by applying Thales theorem:
UB/US = UC/UT
=>UB = UC x US/UT =6 x 12/(6 + 18) = 3
=> x = US - UB = 12 - 3 = 9
=> Option C is correct.
Hope this helps!
:)
the price increase of a set of golf clubs is from $250 to $750. What is the percent increase?
Answer:
Positive increase of 200%
Step-by-step explanation:
Answer:
Step-by-step explanation:
percentage increase =increase /original *100
=750-250/250×100
=500/250×100
=200%
hope this helps
plzz mark me brainliest
On a coordinate plane, a graph has number of hours on the x-axis and number of haircuts on the y-axis. A line goes through points (2, 1), (4, 2), and (6, 3).
The graph represents the number of haircuts, y, a hair stylist can give over time, x. Use the graph to find the constant of proportionality and write an equation.
The constant of proportionality is .
The equation that represents the number of haircuts the stylist can give in an hour is .
The proportionality constant is 1/2 (0.5) and the equation of the line will be given as y = 0.5x.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more than two variables.
On a coordinate plane, a graph has a number of hours on the x-axis and a number of haircuts on the y-axis. A line goes through points (2, 1), (4, 2), and (6, 3).
We know that the equation of the line passing through the two-point is given as
[tex]\rm (y-y_1)=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Then we have
[tex]\rm y-1 = \dfrac{2-1}{4-2} \times (x-2)\\\\y = \dfrac{1}{2}\ x - 1+1 \\\\y = \dfrac{1}{2}\ x[/tex]
The proportionality constant is 1/2 (0.5) and the equation of the line will be given as y = 0.5x.
More about the linear system link is given below.
https://brainly.com/question/20379472
Answer:
first one is 1/2 second one is y = 1/2 x
Hope it helps!!!
what is (2x - 4) - (6x + 6)
Answer:
Step-by-step explanation: (2x-4)-(6x+6)
= 2x -4 - 6x - 6 [ opening brackets]
= 2x-6x -4-6 [ bringing the same variables and numbers together]
= -4x-10
=2(2x-5)
Answer:
-4x-10
The 6x + 6 becomes negative due to the negative sign before the parenthesis. You then subtract 6x and 6 from 2x and -4 to get -4x-10
What is the difference between the circumference and area of a circle?
Answer
The circumference of a circle is the length of its side, the area is the amount of space within it.
Step-by-step explanation:
The circumference of a circle represents the distance around the circle's boundary, while the area represents the surface area enclosed by the circle.
The difference between the circumference and area of a circle lies in their respective measurements and what they represent.
Circumference: The circumference of a circle is the measurement of the distance around the outer boundary of the circle. It is essentially the perimeter of the circle. The circumference is calculated using the formula:
Circumference = 2πr or πd
Where r represents the radius of the circle and d represents the diameter. It is a linear measurement and is typically expressed in units such as centimeters, inches, or meters.
Area: The area of a circle is the measurement of the region enclosed by the circle's boundary. It represents the total surface area within the circle. The area of a circle is calculated using the formula:
Area = πr²
Where r represents the radius of the circle. The area is a two-dimensional measurement and is typically expressed in square units such as square centimeters, square inches, or square meters.
To know more about distance here
https://brainly.com/question/13034462
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Two solution of salt water contain 0.03% and 0.23 salt respectively. A lab technician
wants to make 1 liter of Solution which contains
0.18% salt. How much of each solution should
She use?
Amount of 0.3% solution-milliliter
Amount of 0.23% solution - Milliliter
Answer:
750 mL of 0.23% solution250 mL of 0.03% solutionStep-by-step explanation:
Let x represent the quantity (in liters) of the higher percentage solution, the 0.23% solution. Then 1-x will be the quantity of 0.03% solution. The amount of salt in the mix is ...
0.23%·x +0.03%·(1 -x) = 0.18%·1
Multiply by 100% and subtract 3:
20x = 15
x = 15/20 = 0.75 . . . . liters of 0.23% solution
1-x = 1-0.75 = 0.25 . . liters of 0.03% solution
The lab tech needs 750 mL of 0.23% solution and 250 mL of 0.03% solution.
Point A is (-7, 5) and point M is at (0, 4)
Point M is the midpoint of point A and Point B
What are the coordinates of point B
Answer: (7,3)
Step-by-step explanation:
The coordinates of point B(7, 3).
What is Section Formula?The formula below gives the coordinates of the point A(x, y), which internally splits the line segment between the points P([tex]x_1[/tex], [tex]y_1[/tex]) and Q([tex]x_2[/tex], [tex]y_2[/tex]) in the ratio [tex]m_1[/tex]: [tex]m_2[/tex],
A (x, y) = [tex]((m_1 x_2 + m_2 x_1) / ( m_1 + m_2), \;\; (m_1 y_2 + m_2 y_1) / ( m_1 + m_2)[/tex]
Given:
Point A is (-7, 5) and point M is at (0, 4).
and, Point M is the midpoint of point A and Point B.
A (x, y) = [tex](m_1 x_2 + m_2 x_1) / ( m_1 + m_2)[/tex]
So, x= [tex](m_1 x_2 + m_2 x_1) / ( m_1 + m_2)[/tex]
0 = ( 1 x [tex]x_2[/tex] + 1 x (-7)) / (1 + 1)
0 = [tex]x_2[/tex] - 7
[tex]x_2[/tex] =7
and, y= [tex](m_1 y_2 + m_2 y_1) / ( m_1 + m_2)[/tex]
4= ( 1 x [tex]y_2[/tex] + 1 x 5)/ 2
8 = [tex]y_2[/tex] + 5
[tex]y_2[/tex] = 3
Hence, the coordinates of B(7, 3).
Learn more about Section formula here:
https://brainly.com/question/11888968
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Which two values are greater then 3/5
Answer:
4/5 and 1
Step-by-step explanation:
4/5 is greater then 3/5 and 5/5=1 whole which is greater than 3/5, 4/5 and 1 is greater than 3/5 and 1 1/5, 1 2/5 so on and so on it could go forever but 4/5, and 1 is the only ones that our after 3/5 so those are the two greatest ones in this quistion.
Hope this helps.
The two values are 4 by 5 and 1
The following information should be considered:
4 by 5 is greater then 3 by 5 and 5 by 5 = 1 whole which is more than 3 by 5, 4 by 5 and 1 is greater than 3 by 5 and 1 1 by 5.However 4 by 5, and 1 is the only ones that after 3 by 5 so those are the two greatest ones in this given question.Learn more:
https://brainly.com/question/17429689?referrer=searchResults
A student was asked to find a 95% confidence interval for widget width using data from a random sample of size n = 21. Which of the following is a correct interpretation of the interval 10.6 < μ < 29.1? Check all that are correct.
A. With 95% confidence, the mean width of all widgets is between 10.6 and 29.1.
B. With 95% confidence, the mean width of a randomly selected widget will be between 10.6 and 29.1.
C. The mean width of all widgets is between 10.6 and 29.1, 95% of the time.
D. We know this is true because the mean of our sample is between 10.6 and 29.1.
E. There is a 95% chance that the mean of the population is between 10.6 and 29.1.
F. There is a 95% chance that the mean of a sample of 21 widgets will be between 10.6 and 29.1.
Answer:
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean. A 95% confidence interval does not mean 95% probability. It is used to express how confident we are that the true population parameter lies within the confidence interval.
With a lower limit of 10.6 and an upper limit of 29.1, and confidence interval of 95%, the correct option is
With 95% confidence, the mean width of a randomly selected widget will be between 10.6 and 29.1.
Final answer:
The 95% confidence interval represents the range within which the true mean of all widgets is likely to fall, not the individual sample mean.
Explanation:
A 95% confidence interval for widget width of 10.6 < μ < 29.1 means:
With 95% confidence, the mean width of all widgets is between 10.6 and 29.1.
There is not a 95% chance that the mean of a sample of 21 widgets will be between 10.6 and 29.1.
Therefore, the correct interpretations are A and F.
Quiana has 7 times more text messages from Yolanda than from Pierre. Quiana has 56 text messages from Yolanda. Which equation can be used to find how many text messages Quiana has from Pierre, p?
Answer:
Quiana has 8 text messages from Pierre.
Step-by-step explanation:
This question can be solved using a rule of three.
Quiana has 7 times more text messages from Yolanda than from Pierre.
This means that for each message that she receives from Pierre, she receives 7 from Yolanda.
She received 56 from Yolanda.
So
7 messages from Yolanda - 1 messages from Pierre
56 messages from Yolanda - x messages from Pierre
[tex]7x = 56[/tex]
[tex]x = \frac{56}{7}[/tex]
[tex]x = 8[/tex]
Quiana has 8 text messages from Pierre.
Quiana has 8 text messages from Pierre.
To find how many text messages Quiana has from Pierre, represented as p, given that Quiana has 7 times more text messages from Yolanda than from Pierre, and she received 56 text messages from Yolanda, we can set up the following equation:
p × 7 = 56
To solve for p, we divide both sides of the equation by 7:
p = 56 ÷ 7
p = 8
So, Quiana has 8 text messages from Pierre.
is the relationship between the variables in the table a direct variation, an inverse variation, both, or neither? If it is direct or inverse write a function to model it.
x 2 5 20 40
y 40 20 5 2
Answer:
Neither
Step-by-step explanation:
In direct variation, as one number increases, the other number also increases and as one number decreases, the other number also decreases. In inverse variation, as one number increases, the other number decreases and as as one number decreases, the other number increases.
For direct variation, [tex]y=kx[/tex] and for indirect variation, [tex]y=\frac{k}{x}[/tex] where k is a constant.
x 2 5 20 40
y 40 20 5 2
Here,
[tex]\frac{2}{40}=\frac{1}{20}\\ \frac{5}{20}=\frac{1}{4}\\ \frac{20}{5}=4 \\\frac{40}{2} =20[/tex]
So, this is neither a direct variation nor an indirect variation.
It is said that happy and healthy workers are efficient and productive. A company that manufactures exercising machines wanted to know the percentage of large companies that provide on-site health club facilities. A sample of 240 such companies showed that 96 of them provide such facilities. Construct a 97% confidence interval for the percentage of all such companies that provide such facilities on-site. What is the margin of error for this estimate
Answer:
The 97% confidence interval for the percentage of all such companies that provide such facilities on-site is (0.3314, 0.4686). The margin of error is of 0.0686 = 6.86 percentage points.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
The absolute value of the subtraction of one of the bounds by the estimate [tex]\pi[/tex]
For this problem, we have that:
[tex]n = 240, \pi = \frac{96}{240} = 0.4[/tex]
97% confidence level
So [tex]\alpha = 0.03[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.03}{2} = 0.985[/tex], so [tex]Z = 2.17[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 2.17\sqrt{\frac{0.4*0.6}{240}} = 0.3314[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 2.17\sqrt{\frac{0.4*0.6}{240}} = 0.4686[/tex]
0.4686 - 0.4 = 0.0686
The 97% confidence interval for the percentage of all such companies that provide such facilities on-site is (0.3314, 0.4686). The margin of error is of 0.0686 = 6.86 percentage points.
Final answer:
To construct a 97% confidence interval for the percentage of large companies that provide on-site health club facilities, the proportion p is calculated from the sample data and then substituted into the formula. The margin of error is also calculated using the formula.
Explanation:
To construct a 97% confidence interval for the percentage of large companies that provide on-site health club facilities, we can use the formula:
CI = p ± z*(√(p(1-p)/n))
Where:
p is the proportion of companies in the sample that provide on-site health club facilitiesz is the z-value corresponding to the desired confidence level (in this case, 97%)n is the sample sizeFirst, we calculate the proportion p = 96/240 = 0.4
Next, we find the z-value using a standard normal distribution table. For a 97% confidence level, the z-value is approximately 1.88
Finally, substituting the values into the formula:
CI = 0.4 ± 1.88*(√((0.4*(1-0.4))/240))
Calculating the margin of error:
ME = z*(√(p(1-p)/n))
ME = 1.88*(√((0.4*(1-0.4))/240))
ME ≈ 0.036
Therefore, the 97% confidence interval for the percentage of all such companies that provide on-site health club facilities is approximately 0.364 to 0.436. The margin of error for this estimate is approximately ±0.036.
Suppose that Adam rolls a fair six-sided die and a fair four-sided die simultaneously. Let AAA be the event that the six-sided die is an even number and BBB be the event that the four-sided die is an odd number. Using the sample space of possible outcomes below, answer each of the following questions. What is P(A)P(A)P, (, A, ), the probability that the six-sided die is an even num
Answer:
0.5
Step-by-step explanation:
The sample space of a fair six-sided die and a fair four-sided die rolled simultaneously is given below:
[tex](1,1),(1,2),(1,3),(1,4),(1,5),(1,6)\\(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\\(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)\\(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)\\[/tex]
where in each pair (x,y), x represents the four-sided die and y represents the six sided die.
Total Number of Possible Outcomes =24
Event A is the event that the six-sided die is an even number.
n(A)=12
Therefore, the probability that the six-sided die is an even number:
P(A)=12/24=0.5
what’s the answer this question?
Answer:
(x-1)(x-42) or (x-1) x (x-42) <-----(they're basically the same thing)
Step-by-step explanation:
1. x^2-43x+42 2. x^2-x-42x+42 3. x(x-1)-42x+42 4. x(x-1)-42(x-1) 5. (x-1)(x-42)
6. answer is (x-1)(x-42)
(((HELP ASAP)))
Graph the line your equations using the slope of the line and y-intercept taken from the slope intercept form of the equation. Find the intersection of the two graphs. Check that your solution is correct. Watch your place and minus slopes! In y=mx+b, m Is the slope of the line and b is the y-intercept.
Answer: (-2,3)
Step-by-step explanation:
A market surveyor wishes to know how many energy drinks teenagers drink each week. They want to construct a 95% confidence interval with an error of no more than 0.06. A consultant has informed them that a previous study found the mean to be 7.3 energy drinks per week and found the standard deviation to be 1.3. What is the minimum sample size required to create the specified confidence interval? Round your answer up to the next integer.
Answer:
The minimum sample size required to create the specified confidence interval is 1804.
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{1-0.95}{2} = 0.025[/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]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/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.
Minimum sample size for a margin of error of 0.06:
This sample size is n.
n is found when [tex]M = 0.06, \sigma = 1.3[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.06 = 1.96*\frac{1.3}{\sqrt{n}}[/tex]
[tex]0.06\sqrt{n} = 1.96*1.3[/tex]
[tex]\sqrt{n} = \frac{1.96*1.3}{0.06}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96*1.3}{0.06})^{2}[/tex]
[tex]n = 1803.41[/tex]
Rounding up to the next integer
The minimum sample size required to create the specified confidence interval is 1804.
The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.
Price in Dollars 25 33 34 45 48
Number of Bids 2 3 4 5 7
Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.
Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.Step 3 of 6: Find the estimated value of y when x = 34. Round your answer to three decimal places.Step 4 of 6: Determine the value of the dependent variable yˆ at x = 0.Step 5 of 6: Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable yˆ.Step 6 of 6: Find the value of the coefficient of determination.
Answer:
1) b1=5.831
2) b0=12.510
3) y(34)=210.764
4) y(0)=12.510
5) y=12.510+5.831x
6) R^2=0.85
Step-by-step explanation:
We have the linear regression model [tex]y=b_0+b_1 x[/tex].
We start by calculating the all the parameters needed to define the model:
- Mean of x:
[tex]\bar x=\dfrac{1}{5}\sum_{i=1}^{5}(2+3+4+5+7)=\dfrac{21}{5}=4.2[/tex]
- Uncorrected standard deviation of x:
[tex]s_x=\sqrt{\dfrac{1}{n}\sum_{i=1}^{5}(x_i-\bar x)^2}\\\\\\s_x=\sqrt{\dfrac{1}{5}\cdot [(2-4.2)^2+(3-4.2)^2+(4-4.2)^2+(5-4.2)^2+(7-4.2)^2]}\\\\\\ s_x=\sqrt{\dfrac{1}{5}\cdot [(4.84)+(1.44)+(0.04)+(0.64)+(7.84)]}\\\\\\ s_x=\sqrt{\dfrac{14.8}{5}}=\sqrt{2.96}\\\\\\s_x=1.72[/tex]
- Mean of y:
[tex]\bar y=\dfrac{1}{5}\sum_{i=1}^{5}(25+33+34+45+48)=\dfrac{185}{5}=37[/tex]
- Standard deviation of y:
[tex]s_y=\sqrt{\dfrac{1}{n}\sum_{i=1}^{5}(y_i-\bar y)^2}\\\\\\s_y=\sqrt{\dfrac{1}{5}\cdot [(25-37)^2+(33-37)^2+(34-37)^2+(45-37)^2+(48-37)^2]}\\\\\\ s_y=\sqrt{\dfrac{1}{5}\cdot [(144)+(16)+(9)+(64)+(121)]}\\\\\\ s_y=\sqrt{\dfrac{354}{5}}=\sqrt{70.8}\\\\\\s_y=8.414[/tex]
- Sample correlation coefficient
[tex]r_{xy}=\sum_{i=1}^5\dfrac{(x_i-\bar x)(y_i-\bar y)}{(n-1)s_xs_y}\\\\\\r_{xy}=\dfrac{(2-4.2)(25-37)+(3-4.2)(33-37)+...+(7-4.2)(48-37)}{4\cdot 1.72\cdot 8.414}\\\\\\r_{xy}=\dfrac{69}{57.888}=1.192[/tex]
Step 1
The slope b1 can be calculated as:
[tex]b_1=r_{xy}\dfrac{s_y}{s_x}=1.192\cdot\dfrac{8.414}{1.72}=5.831[/tex]
Step 2
The y-intercept b0 can now be calculated as:
[tex]b_o=\bar y-b_1\bar x=37-5.831\cdot 4.2=37-24.490=12.510[/tex]
Step 3
The estimated value of y when x=34 is:
[tex]y(34)=12.510+5.831\cdot(34)=12.510+198.254=210.764[/tex]
Step 4
At x=0, the estimated y takes the value of the y-intercept, by definition.
[tex]y(0)=12.510+5.831\cdot(0)=12.510+0=12.510[/tex]
Step 5
The linear model becomes
[tex]y=12.510+5.831x[/tex]
Step 6
The coefficient of determination can be calculated as:
[tex]R^2=1-\dfrac{SS_{res}}{SS_{tot}}=1-\dfrac{\sum(y_i-f_i)}{ns_y^2}\\\\\\\sum(y_i-f_i)=(25-24.17)^2+(33-30)^2+(34-35.83)^2+(45-41.67)^2+(48-53.33)^2\\\\\sum(y_i-f_i)=0.69+ 8.98+ 3.36+ 11.12+ 28.38=52.53\\\\\\ ns_y^2=5\cdot 8.414^2=353.98\\\\\\R^2=1-\dfrac{52.53}{353.98}=1-0.15=0.85[/tex]
Six pyramids are shown inside of a cube. The height of the cube is h units.
Six identical square pyramids can fill the same volume as a cube with the same base. If the height of the cube is h units, what is true about the height of each pyramid?
The height of each pyramid is One-halfh units.
The height of each pyramid is One-thirdh units.
The height of each pyramid is One-sixthh units.
The height of each pyramid is h units.
Answer:
its the 1st answer on edg
Step-by-step explanation:
I just took it
The height of each pyramid is One-half h units, so that the 6 pyramids can be placed in the cube
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables
The volume of the cube = h unit * h unit * h unit = h³ unit³
Volume of each pyramid = (1/6) * h³ = (1/3) * base² * height
(1/6) * h³ = (1/3) * base² * height
(1/3) * h² * (1/2)h = (1/3) * base² * height
The height of each pyramid is One-half h units, so that the 6 pyramids can be placed in the cube.
Find out more on equation at: https://brainly.com/question/2972832
The City of Decatur finds that salaries for residents working in the technology sector follow an approximately normal distribution with a mean of $42,800 and a standard deviation of $8,365.
To the nearest hundredth, what Z-Score would be used to determine the percentage of residents working in the technology sector who earn more than $30,000?
Answer:
- 1. 15
Step-by-step explanation:
Z score is used in statistic to calculate deviation of an observed value from mean value of sample of observation.
Mathematically it is given by
[tex]z = observed \ value - mean\ value/ standard\ deviation[/tex]
using the above formula and substituting the value of of
mean = $42,800
standard deviation = $8,365
observed value =$30,000
Z = (8,365 - 42,800) / $30,000
= - 34,435/ 30,000 = - 1. 14783
= - 1. 15 ( to the nearest hundredth)
- 1. 15 Z-Score would be used to determine the percentage of residents working in the technology sector who earn more than $30,000
During a recent election, a clerk was responsible for the placement of candidates names on election ballots for a particular voting precinct. Party A candidates were selected for the first position in 30 of 40 ballots. Because the clerk was supposed to use a method of random selection, Party B claimed that instead of using randomness, the clerk used a method favoring Party A. Use a 0.05 significance level to test the claim that the method favored Party A. [Note: Favored means a proportion greater than 50%.]
Answer:
Null hypothesis: H0 = 0.50
Alternative hypothesis: Ha > 0.50
z = 3.16
P value = P(Z>3.16) = 0.0008
Decision: we reject the null hypothesis and accept the alternative hypothesis. That is, the clerk used a method favoring Party A.
Rule
If;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
Z score > Z(at 95% confidence interval) ---- reject Null hypothesis
Z score < Z(at 95% confidence interval) ------ accept Null hypothesis
Step-by-step explanation:
Given;
n = 40 represent the number of samples taken
Null hypothesis: H0 = 0.50
Alternative hypothesis: Ha > 0.50
Test statistic z score can be calculated with the formula below;
z = (p^−po)/√{po(1−po)/n}
Where,
z= Test statistics
n = Sample size = 40
po = Null hypothesized value = 0.50
p^ = Observed proportion = 30/40 = 0.75
Substituting the values we have
z = (0.75-0.50)/√(0.50(1-0.50)/40)
z = 3.16227766
z = 3.16
To determine the p value (test statistic) at 0.05 significance level, using a one tailed hypothesis.
P value = P(Z>3.16) = 0.0008
Since z at 0.05 significance level is between -1.96 and +1.96 and the z score for the test (z = 3.16) which doesn't falls with the region bounded by Z at 0.05 significance level. And also the one-tailed hypothesis P-value is 0.0008 which is lower than 0.05. Then we can conclude that we have enough evidence to FAIL or reject the null hypothesis, and we can say that at 5% significance level the null hypothesis is invalid, therefore we accept the alternative hypothesis.
The 99.7% confidence interval for the mean length of frog jumps is (12.64 cm, 14.44 cm). Which of the following statements is a correct interpretation of 99.7% confidence? 99.7% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm. There's a 99.7% chance that any particular frog I catch can jump between 12.64 cm and 14.44 cm. There's a 99.7% chance that the the mean length of frog jumps falls between 12.64 cm and 14.44 cm. If we were to repeat this sampling many times, 99.7% of the confidence intervals we could construct would contain the true population mean.
Answer:
99.7% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm.
True that's the correct interpretation for this case since if we repeat the measures with this sample size we will got a similar result.
Step-by-step explanation:
For this case we need to remember that the confidence interval for the true mean is given by this formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]
And for this case the 99.7 % confidence interval for the true mean is (12.64cm , 14.44cm) we analyze one by one the possible options in order to select one:
99.7% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm.
True that's the correct interpretation for this case since if we repeat the measures with this sample size we will got a similar result.
There's a 99.7% chance that any particular frog I catch can jump between 12.64 cm and 14.44 cm.
False the confidence interval can't be interpreted as a chance
There's a 99.7% chance that the the mean length of frog jumps falls between 12.64 cm and 14.44 cm.
False the confidence interval can't be interpreted as a chance
If we were to repeat this sampling many times, 99.7% of the confidence intervals we could construct would contain the true population mean.
False always the confidence interval contain the mean since is the middle value.
Final answer:
The correct interpretation of a 99.7% confidence interval for mean length of frog jumps is that if we repeat the sampling many times, 99.7% of the constructed confidence intervals would contain the true population mean. This emphasizes the methodology's reliability over repeated sampling rather than assuring specifics of individual outcomes.
Explanation:
The correct interpretation of a 99.7% confidence interval, like the one provided for the mean length of frog jumps (12.64 cm, 14.44 cm), is that if we were to repeat this sampling process many times, 99.7% of the confidence intervals we construct would contain the true population mean. The other statements provided misinterpret the concept of confidence intervals by implying a probability about individual measurements or the certainty of the mean falling within a specific interval, which is not accurate.
Confidence intervals are about the process of estimation rather than specifics about single outcomes. They provide a range in which we are certain to a specified level (in this case, 99.7%) that the true population mean lies, assuming the sampling and calculations are correct. The correct interpretation underscores the reliability of the methodology over repeated sampling rather than guaranteeing specifics of individual outcomes or the exact location of the population mean.