Answers
Answer:
Step-by-step explanation:
PQ=24
PS=19
PR=42
TQ=10
QR=19
SR=24
PT=21
SQ=20
m∠QRS=180-m∠PQR=180-106=74°
m∠PQS=m∠QSR=49°
m∠RPS=m∠PRQ=m∠QRS-m∠PRS=74-35=39°
m∠PSQ=m∠RQS=m∠PQR-m∠PQS=106-49=57°
m∠PQR=106°
m∠ QSR=49°
M∠PRS=35°
Related Questions
Suppose a basketball player is practicing shooting, and has a prob-ability .95 of making each of his shots. Also assume that his shots are in-dependent of one another. Using the Poisson distribution, approximate theprobability that there are at most 2 misses in the first 100 attempts
Answers
Answer:
0.082
Step-by-step explanation:
Number of attempts = n = 100
Since there are only two outcomes and in-dependent of each other, the probability of missing a shot = 1 - Probability of making each shot
p = 1 - 0.95 = 0.05
Possion Ratio (λ) = np where n is the number of events and p is the probability of the shot missing
λ = 100 x 0.05 = 5
Define X such that X = Number of misses and X ≅ Poisson (λ = 5)
P [X ≤ 2] = P [X = 0] + P [X = 1] + P [X = 2]
P [X ≤ 2] = e⁻⁵ + e⁻⁵ x 5 + e⁻⁵ x 5²/2!
P [X ≤ 2] = e⁻⁵ [1 + 5 + 5²/2!]
P [X ≤ 2] = e⁻⁵ x 12.25 = 0.082
The required probability that there are at most 2 misses in the first 100 attempts is 0.082
In simple regression analysis, if the correlation coefficient is a positive value, then Select one:
A. the slope of the regression line must also be positive.
B. the least squares regression equation could have either a positive or a negative slope.
C. the y-intercept must also be a positive value.
D. the coefficient of determination can be either positive or negative, depending on the value of the slope.
E. the standard error of estimate can have either a positive or a negative value.
Answers
Final answer:
In simple regression analysis, a positive correlation coefficient means that the slope of the regression line must also be positive, as both the dependent and independent variables increase or decrease together.
Explanation:
In simple regression analysis, the correlation coefficient's sign (positive or negative) informs us about the direction of the relationship between the two variables.
A positive correlation coefficient indicates that the variables move in the same direction: as one increases, so does the other, and as one decreases, so does the other. This characteristic of correlation directs us to the correct answer to the student's question.
Considering the options provided:
A. The slope of the regression line must also be positive. B. The least squares regression equation could have either a positive or a negative slope. C. The y-intercept must also be a positive value. D. The coefficient of determination can be either positive or negative, depending on the value of the slope. E. The standard error of estimate can have either a positive or a negative value.The slope of the regression line is directly determined by the correlation coefficient in the context of simple linear regression. Given that the correlation coefficient is positive, the slope of the regression line (which represents the change in the dependent variable for a unit change in the independent variable) must also be positive.
Therefore, option A is correct.
Suppose that in a bowling league, the scores among all bowlers are normally distributed with mean µ = 182 points and standard deviation σ = 14 points. A trophy is given to each player whose score is at or above the 97th percentile. What is the minimum score needed for a bowler to receive a trophy?
Answers
Answer:
209 points
Step-by-step explanation:
Mean points scored (μ) = 182 points
Standard deviation (σ) = 14 points
The z-score for any given game score 'X' is defined as:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
At, the 97th percentile of a normal distribution, the z-score, according to a z-score table, is 1.881.
Therefore, the minimum score, X, needed for a bowler to receive a trophy is:
[tex]1.881=\frac{X-182}{14}\\X=208.334[/tex]
Since only whole point scores are possible, X=209 points.
To find the minimum score at the 97th percentile for bowlers in a league, one must calculate the z-score for the 97th percentile and then apply the formula Score = μ + (z * σ) using the league's mean and standard deviation.
Explanation:To find the minimum score needed for a bowler to receive a trophy (which is at or above the 97th percentile), we need to use the normal distribution properties. With a mean (μ) of 182 points and a standard deviation (σ) of 14 points, we can find the z-score corresponding to the 97th percentile using a z-table or a calculator with normal distribution functions. Once we have the z-score, we can use the formula:
Score = μ + (z * σ)
to calculate the score that corresponds to the 97th percentile.
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A deck of cards contains 52 cards. They are divided into four suits: spades, diamonds, clubs and hearts. Each suit has 13 cards: ace through 10, and three picture cards: Jack, Queen, and King. Two suits are red in color: hearts and diamonds. Two suits are black in color: clubs and spades.
Use this information to compute the probabilities asked for below and leave them in fraction form. All events are in the context that three cards are dealt from a well-shuffled deck without replacement.
a. The first and second cards are both hearts.
b. The third card is an eight.
c. None of the three cards is an ace.
Answers
Answer:
a) 13/52 and the second 12/51
b) Two solutions:
b.1 if we did not picked up an eight in the first two cards 4/50
b.2 there is an eight i the two previous 3/59
c ) (48/52)*(47/51)*(46/50)
Step-by-step explanation:
Condition: Cards are taken out without replacement
a) Probability of first card is heart
There are 52 cards and 4 suits with the same probability , so you can compute this probability in two ways
we have 13 heart cards and 52 cards then probability of one heart card is 13/52 = 0.25
or you have 4 suits, to pick up one specific suit the probability is 1/4 = 0,25
Now we have a deck of 51 card with 12 hearts, the probability of take one heart is : 12/51
b) There are 4 eight (one for each suit ) P = 4/50 if neither the first nor the second card was an eight of heart, if in a) previous we had an eight, then this probability change to 3/50
c) The probability of the first card different from an ace is 48/52 , the probability of the second one different of an ace is 47/51 and for the thirsd card is 46/50. The probability of none of the three cards is an ace is
(48/52)*(47/51)*(46/50)
Need help
6n - 3(2n - 5)
SHOW ALL WORK!
Answers
6n - 3(2n-5)
mutiply the bracket by -3
(-3)(2n)= -6n
(-3)(-5)= 15
6n-6n+15
0+15
answer:
15
6n-(6n-15)
6n-6n+15
(6n-6n)+15
=15
There are 25 dogs playing in the dog park. You are a "dog" person and wonder which dog will be the first to come up to you when you enter the park. There are 15 golden retrievers, 5 pugs, 4 pomeranians, and 1 terrier. What is the probability that the first dog to come over to you will be a pug?
I chose 5/25
2. One Psyc 317 class has 10 people in it; another has 50 people in it. The average grade in the 10-person class is 72% (high probability of getting a C); the average grade in the 50-person class is 85% (high probability of getting a B). Which class average is the most reliable?
a. the 10 person class
b. 50 person class
c. cannot determine with this information
d. both equally
I chose the 50 person class.
Answers
The probability of a pug approaching first in a park of 25 dogs is 5/25 or 1/5. The average grade of a larger class is typically a more reliable representation of the group's performance than that of a smaller one.
Explanation:For the first question, the probability of a pug being the first dog to approach you in a park with 25 dogs, 5 of them being pugs, is indeed 5/25, or 1/5. This fraction represents the ratio of the desired outcome (a pug approaching you first) to the total number of possible outcomes (any of the 25 dogs in the park could potentially be the first to approach).
For the second part of the question - determining the more reliable average grade between two classes - the class with 50 students is the better choice. This conclusion is based on statistical reasoning. A larger sample size (in this case, the larger class) generally provides a more reliable average than a smaller sample size.
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A production process fills containers by weight. Weights of containers are approximately normally distributed. Historically, the standard deviation of weights is 5.5 ounces. (This standard deviation is therefore known.) A quality control expert selects n containers at random. How large a sample would be required in order for the 99% confidence interval for to have a length of 2 ounces?
a. n 15
b. n 16
c. n 201
d. n 226
Answers
Answer:
option (c) n = 201
Step-by-step explanation:
Data provided in the question:
Standard deviation, s = 5.5 ounce
Confidence level = 99%
Length of confidence interval = 2 ounces
Therefore,
margin of error, E = (Length of confidence interval ) ÷ 2
= 2 ÷ 2
= 1 ounce
Now,
E = [tex]\frac{zs}{\sqrt n}[/tex]
here,
z = 2.58 for 99% confidence interval
n = sample size
thus,
1 = [tex]\frac{2.58\times5.5}{\sqrt n}[/tex]
or
n = (2.58 × 5.5)²
or
n = 201.3561 ≈ 201
Hence,
option (c) n = 201
A Common Measure of Student Achievement, The National Assessment of Educational Progress (NAEP) is the only assessment that measures what U.S. students know and can do in various subjects across the nation, states, and in some urban districts. Also known as The Nation's Report Card, NAEP has provided important information about how students are performing academically since 1969. NAEP is a congressionally mandated project administered by the National Center for Education Statistics (NCES) within the U.S. Department of Education and the Institute of Education Sciences (IES). NAEP is given to a representative sample of students across the country. Results are reported for groups of students with similar characteristics (e.g., gender, race and ethnicity, school location), not individual students. National results are available for all subjects assessed by NAEP. In the most recent year, The NAEP sample of 1077 young women had mean quantitative score of 275. Individual NAEP scores have a Normal distribution with standard deviation of 60. (This is indicating that the population standard deviation σσ is 60) Find a 99% Confidence Interval for the mean quantitative scores for young women. a) Check that the normality assumptions are met. ? b) What is the 99% confidence interval for the mean quantitative scores for young women? ____ ≤μ≤ _____ c) Interpret the confidence interval obtained in previous question
Answers
Answer:
a) By the central limit theorem we know that if the random variable X="quantitative scores for young women", and we know that this distribution is normal.
[tex]X \sim N(\mu, \sigma=60)[/tex]
And we are interested on the distribution for the sample mean [tex]\bar X[/tex], we know that distribution for the sample mean is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And with that we have the assumptions required to apply the normal distribution to create the confidence interval since the distribution for [tex]\bar X[/tex] is normal.
b) [tex]270.283\leq \mu \leq 279.717[/tex]
c) We are confident (99%) that the true mean for the quantitative scores for young women is between (270.283;3279.717)
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=275[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma=60[/tex] represent the population standard deviation
n=1077 represent the sample size
Part a
By the central limit theorem we know that if the random variable X="quantitative scores for young women", and we know that this distribution is normal.
[tex]X \sim N(\mu, \sigma=60)[/tex]
And we are interested on the distribution for the sample mean [tex]\bar X[/tex], we know that distribution for the sample mean is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And with that we have the assumptions required to apply the normal distribution to create the confidence interval since the distribution for [tex]\bar X[/tex] is normal.
Part b
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
Since the Confidence is 0.99 or 99%, the value of [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that [tex]z_{\alpha/2}=2.58[/tex]
Now we have everything in order to replace into formula (1):
[tex]275-2.58\frac{60}{\sqrt{1077}}=270.283[/tex]
[tex]275+2.58\frac{60}{\sqrt{1077}}=279.717[/tex]
So on this case the 99% confidence interval would be given by (270.283;3279.717)
[tex]270.283\leq \mu \leq 279.717[/tex]
Part c
We are confident (99%) that the true mean for the quantitative scores for young women is between (270.283;3279.717)
Final answer:
A 99% confidence interval for the mean quantitative scores for young women, based on the NAEP data, is found to be between 270.27 and 279.73. We can state with 99% confidence that the true mean quantitative score for young women falls within this range.
Explanation:
We are asked to find a 99% confidence interval for the mean quantitative scores for young women, based on the National Assessment of Educational Progress (NAEP) sample data.
a) Check that the normality assumptions are met.
The normality assumption is met because individual NAEP scores are given to have a Normal distribution. Additionally, with a large sample size (more than 30), the Central Limit Theorem ensures the sampling distribution of the mean is approximately normal, regardless of the distribution of the population from which the sample is drawn.
b) What is the 99% confidence interval for the mean quantitative scores for young women?
Using the given data, the sample mean, \\bar{x}\, is 275 and the population standard deviation, \(\sigma\), is 60. Since the population standard deviation is given and the sample size is large (1077), we will use the z-distribution to find the 99% confidence interval.
The z-score corresponding to a 99% confidence level is approximately 2.576. Therefore, the margin of error (ME) can be calculated as:
ME = z * [tex](\(\sigma/\sqrt{n}\))[/tex]
ME = 2.576 * [tex](60/\sqrt{1077})[/tex] \approx 4.73
The 99% confidence interval is:
Lower limit =[tex]\(\bar{x}\)[/tex] - ME = 275 - 4.73 = 270.27
Upper limit =[tex]\(\bar{x}\)[/tex] + ME = 275 + 4.73 = 279.73
The 99% confidence interval for the mean quantitative scores for young women is 270.27 ≤ μ ≤ 279.73.
c) Interpret the confidence interval obtained in previous question
The interpretation of this confidence interval is that we are 99% confident that the true mean quantitative score for young women falls between 270.27 and 279.73.
f(1)=-3
f(n)=-5*f(n-1)-7
f(2)=?
pls help lol.
Answers
Answer:
f(2)=8
Step-by-step explanation:
f(2)=(-5)*f(1)-7=
(-5)*(-3)-7=8
f(2)=8
In the word balloons the ratio of vowels consonants is
Answers
Answer:
3 : 5
Step-by-step explanation:
vowels: a o o (3 of them)
consonants: b l l n s (5 of them)
The ratio of vowels to consonants is 3 : 5.
A random sample of 10 shipments of stick-on labels showed the following order sizes.10,520 56,910 52,454 17,902 25,914 56,607 21,861 25,039 25,983 46,929PictureClick here for the Excel Data File(a) Construct a 95 percent confidence interval for the true mean order size. (Round your answers to the nearest whole number.) The 95 percent confidence interval to
Answers
Answer:
Confidence Interval: (21596,46428)
Step-by-step explanation:
We are given the following data set:
10520, 56910, 52454, 17902, 25914, 56607, 21861, 25039, 25983, 46929
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{340119}{10} = 34011.9[/tex]
Sum of squares of differences = 551869365.6 + 524322983.6 + 340111052.4 + 259528878 + 65575984.41 + 510538544 + 147644370.8 + 80512934.41 + 64463235.21 + 166851472.4 = 2711418821
[tex]S.D = \sqrt{\frac{2711418821}{9}} = 17357.09[/tex]
Confidence interval:
[tex]\mu \pm t_{critical}\frac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]t_{critical}\text{ at degree of freedom 9 and}~\alpha_{0.05} = \pm 2.2621[/tex]
[tex]34011.9 \pm 2.2621(\frac{17357.09}{\sqrt{10}} ) = 34011.9 \pm 12416.20 = (21595.7,46428.1) \approx (21596,46428)[/tex]
About 20,000 steel cans are recycled every minute in the United States. Expressed in scientific notation, about how many cans are recycled in 48 hours?
Answers
Answer:
57,600,000
Step-by-step explanation:
Which function has (2,8) on its graph
Answers
Answer:
y = 2x^2
Step-by-step explanation:
The the coordinates (2,8) are expressed in terms of (x,y). Substitute the x with 2 and y with 8 and plug them into the formulas. The one that has the two sides equal to each other is the function that has (2,8) on its line.
You believe that the mean BMI for college students is less than 25. The population standard deviation of BMI is unknown. You select a sample of size 30 and compute the sample mean to be 23.9 with a sample standard deviation of 3. What are the appropriate hypotheses? A. Null Hypothesis: μ< 25 Alt Hypothesis: μ= 25 B. Null Hypothesis: μ=23.9 Alt Hypothesis: μ < 23.9 C. Null Hypothesis: μ=25 Alt Hypothesis: μ>25 D. Null Hypothesis:μ=25 Alt Hypothesis:μ < 25
Answers
Answer:
D. Null Hypothesis:μ=25 Alt Hypothesis:μ < 25
Step-by-step explanation:
Previous concepts and notation
A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".
The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".
The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".
[tex]\bar X= 23.9[/tex] represent the sample mean
[tex]s=3[/tex] represent the sample standard deviation
n=25 represent the sample selected
Solution
The claim that we want to test is that: "You believe that the mean BMI for college students is less than 25". So this statement needs to be on the Alternative hypothesis ([tex]\mu <25[/tex]) and the Null hypothesis would be the complement ([tex]\mu =25[/tex]) or ([tex]\mu \geq 25[/tex]).
So the best option on this case is:
D. Null Hypothesis:μ=25 Alt Hypothesis:μ < 25
Louise is collecting can tabs for charity. She already has 35 collected and intends to collect 4 every week. The equation for the number of can tabs y she has collected is y = 4x + 35, where x is the number of weeks. What do the slope and y-intercept represent?
Answers
Answer:
Step-by-step explanation:
The equation for the number of can tabs y that she has collected is
y = 4x + 35
where x is the number of weeks. To plot the graph, values for different number of weeks are inputted to get the corresponding y values.
Comparing the equation with the slope intercept form,
y = mx + c,
m represents slope.
So slope of the equation is 4. It represents the rate at which the total number of can tabs that she has collected is increasing with respect to the increase in the number of weeks. So the total number increases by 4 each week
The y intercept is the point at x = 0
It is equal to 35. It represents the number of can tabs that she had initially collected before she started collecting 4 can tabs weekly. At this point, her weekly collection is 0
Evaluate the integral Integral ∫ from (1,2,3 ) to (5, 7,-2 ) y dx + x dy + 4 dz by finding parametric equations for the line segment from (1,2,3) to (5,7,- 2) and evaluating the line integral of of F = yi + x j+ 3k along the segment. Since F is conservative, the integral is independent of the path.
Answers
[tex]\vec F(x,y,z)=y\,\vec\imath+x\,\vec\jmath+3\,\vec k[/tex]
is conservative if there is a scalar function [tex]f(x,y,z)[/tex] such that [tex]\nabla f=\vec F[/tex]. This would require
[tex]\dfrac{\partial f}{\partial x}=y[/tex]
[tex]\dfrac{\partial f}{\partial y}=x[/tex]
[tex]\dfrac{\partial f}{\partial z}=3[/tex]
(or perhaps the last partial derivative should be 4 to match up with the integral?)
From these equations we find
[tex]f(x,y,z)=xy+g(y,z)[/tex]
[tex]\dfrac{\partial f}{\partial y}=x=x+\dfrac{\partial g}{\partial y}\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)[/tex]
[tex]f(x,y,z)=xy+h(z)[/tex]
[tex]\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=3z+C[/tex]
[tex]f(x,y,z)=xy+3z+C[/tex]
so [tex]\vec F[/tex] is indeed conservative, and the gradient theorem (a.k.a. fundamental theorem of calculus for line integrals) applies. The value of the line integral depends only the endpoints:
[tex]\displaystyle\int_{(1,2,3)}^{(5,7,-2)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz=\int_{(1,2,3)}^{(5,7,-2)}\nabla f(x,y,z)\cdot\mathrm d\vec r[/tex]
[tex]=f(5,7,-2)-f(1,2,3)=\boxed{18}[/tex]
Cadmium, a heavy metal, is toxic to animals. Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. The Czech and Slovak governments have set a safety limit for cadmium in dry vegetables at 0.5 ppm. Below are cadmium levels for a random sample of the edible mushroom Boletus pinicoloa.0.24 0.92 0.59 0.19 0.62 0.330.16 0.25 0.77 0.59 1.33 0.32a) Perform a hypothesis test at the 5% significance level to determine if the meancadmium level in the population of Boletus pinicoloa mushrooms is greater than thegovernment’s recommended limit of 0.5 ppm. Suppose that the standard deviation ofthis population’s cadmium levels is o( = 0.37 ppm. Note that the sum of the data is 6.31 ppm. For this problem, be sure to: State your hypotheses, compute your test statistic, give the critical value.(b) Find the p-value for the test.
Answers
Answer:
hi
Step-by-step explanation:
Stainless steels are frequently used in chemical plants to handle corrosive fluids, however, these steels are especially susceptible to stress corrosion cracking in certain environments. In a sample of 295 steel alloy failures that occurred in oil refineries and petrochemical plants in Japan over the last 10 tears, 118 were caused by stress corrosion cracking and corrosion fatigue (Materials Performance, 1981). Construct a 95% confidence interval for the true proportion of alloy failures caused by stress corrosion cracking.
Answers
Answer: 95% confidence interval would be (0.344,0.456).
Step-by-step explanation:
Since we have given that
n = 295
x = 118
so, [tex]\hat{p}=\dfrac{x}{n}=\dfrac{118}{295}=0.4[/tex]
At 95% confidence, z = 1.96
So, margin of error would be
[tex]z\times \sqrt{\dfrac{p(1-p)}{n}}\\\\=1.96\times \sqrt{\dfrac{0.4\times 0.6}{295}}\\\\=0.056[/tex]
so, 95% confidence interval would be
[tex]\hat{p}\pm \text{margin of error}\\\\=0.4\pm 0.056\\\\=(0.4-0.056,0.4+0.056)\\\\ =(0.344,0.456)[/tex]
Hence, 95% confidence interval would be (0.344,0.456).
Answer:
95% confidence interval would be (0.344,0.456).Step-by-step explanation:
A news vendor sells newspapers and tries to maximize profits. The number of papers sold each day is a random variable. However, analysis of the past month's data shows the distribution of daily demand in Table 16. A paper costs the vendor 20C. The vendor sells the paper for 30C. Any unsold papers are returned to the publisher for a credit of IOC. Any unsatisfied demand is estimated to cost IOC in goodwill and lost profit. If the policy is to order a quantity equal to the preceding day's demand, determine the average daily profit of the news vendor by simulating this system. Assume that the demand for day 0 is equal to 32. Demand per day Probability30 .0531 .1532 .2233 .3834 .1435 .06
Answers
Let C be the positively oriented square with vertices (0,0), (1,0), (1,1), (0,1). Use Green's Theorem to evaluate the line integral ∫C7y2xdx+8x2ydy.
Answers
Answer:
1/2
Step-by-step explanation:
The interior of the square is the region D = { (x,y) : 0 ≤ x,y ≤1 }. We call L(x,y) = 7y²x, M(x,y) = 8x²y. Since C is positively oriented, Green Theorem states that
[tex]\int\limits_C {L(x,y)} \, dx + {M(x,y)} \, dy = \int\limits^1_0\int\limits^1_0 {(Mx - Ly)} \, dxdy[/tex]
Lets calculate the partial derivates of M and L, Mx and Ly. They can be computed by taking the derivate of the respective value, treating the other variable as a constant.
Mx(x,y) = d/dx 8x²y = 16xyLy(x,y) = d/dy 7y²x = 14xyThus, Mx(x,y) - Ly(x,y) = 2xy, and therefore, the line ntegral is equal to the double integral
[tex] \int\limits^1_0\int\limits^1_0 {2xy} \, dxdy[/tex]
We can compute the double integral by applying the Barrow's Rule, a primitive of 2xy under the variable x is x²y, thus the double integral can be computed as follows
[tex]\int\limits^1_0\int\limits^1_0 {2xy} \, dxdy = \int\limits^1_0 {x^2y} |^1_0 \,dy = \int\limits^1_0 {y} \, dy = \frac{y^2}{2} \, |^1_0 = 1/2[/tex]
We conclude that the line integral is 1/2
To evaluate the line integral using Green's Theorem, we need to find the curl of the vector field and the area enclosed by the square. The line integral of the vector field along the square is equal to the double integral of the curl over the region enclosed by the square. Using this method, we can find the value of the line integral to be 1/3.
Explanation:To evaluate the line integral using Green's Theorem, we first need to find the curl of the vector field. In this case, the vector field is F(x, y) = 7y^2x i + 8x^2y j. Taking the partial derivatives of its components with respect to x and y, we get curl(F) = (8x^2 - 14xy^2) k.
Next, we need to find the area enclosed by the square C, which is 1 unit^2. Using Green's Theorem, the line integral of F along C is equal to the double integral of curl(F) over the region D enclosed by C. Integrating curl(F) with respect to y, we get -7xy^2 + 6x^2y. Integrating this with respect to x over the given limits, we find the value of the line integral to be 1/3.
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A poll showed that 48 out of 120 randomly chosen graduates of California medical schools last year intended to specialize in family practice. What is the width of a 90 percent confidence interval for the proportion that plan to specialize in family practice? Select one:a. ± .0736b. ± .0447c. ± .0876d. ± .0894
Answers
Answer:
± 0.0736
Step-by-step explanation:
Data provided in the question:
randomly chosen graduates of California medical schools last year intended to specialize in family practice, p = [tex]\frac{48}{120}[/tex] = 0.4
Confidence level = 90%
sample size, n = 120
Now,
For 90% confidence level , z-value = 1.645
Width of the confidence interval = ± Margin of error
= ± [tex]z\times\sqrt\frac{p\times(1-p)}{n}[/tex]
= ± [tex]1.645\times\sqrt\frac{0.4\times(1-0.4)}{120}[/tex]
= ± 0.07356 ≈ ± 0.0736
Hence,
The correct answer is option ± 0.0736
The correct option is a. [tex]\±0.0736.[/tex] The width of a [tex]90\%[/tex] confidence interval for the proportion that plan to specialize in family practice
To find the width of a confidence interval for a proportion, we can use the formula:
[tex]\[ \text{Width} = Z \times \sqrt{\frac{p(1-p)}{n}} \][/tex]
where:
[tex]\( Z \)[/tex] is the Z-score corresponding to the desired confidence level,
[tex]\( p \)[/tex] is the sample proportion,
[tex]\( n \)[/tex] is the sample size.
Given:
[tex]Sample\ proportion \( p = \frac{48}{120} = \frac{2}{5} = 0.4 \)[/tex],
[tex]Sample\ size \( n = 120 \)[/tex]
[tex]Confidence \ level = 90\%[/tex], which corresponds to a Z-score of approximately [tex]1.645.[/tex]
Substitute the values into the formula:
[tex]\[ \text{Width} = 1.645 \times \sqrt{\frac{0.4 \times 0.6}{120}} \][/tex]
[tex]\[ \text{Width} = 1.645 \times \sqrt{\frac{0.24}{120}} \][/tex]
[tex]\[ \text{Width} = 1.645 \times \sqrt{0.002} \][/tex]
[tex]\[ \text{Width} = 1.645 \times 0.0447 \][/tex]
[tex]\[ \text{Width} = 0.0736 \][/tex]
How would you describe the difference between the graphs of f(x) = x ^ 2 + 4 and g(y) = y ^ 2 + 4 OA. g(y) is a reflection of f(x) ) over the line y = 1 . O O B. g(y) is a reflection of f(x) ) over the line y=x 1 g(y) is a reflection of f(x) over the x-axis OD. g(y) is a reflection of f(x) over the .
Answers
x is replaced with Y, so it is a reflection across the line y = x
Answer:
y=x
Step-by-step explanation:
The Martian Colonies elect their government through a lottery. There are100,000 people living on Mars, and every year, a council of 99 co-equalleaders is randomly selected from the population. In how many ways canthe leadership be elected? Give your answer in terms of permutations orcombinations and explain your choice. You do not have to evaluate.
Answers
Answer:
The answer is a 100,000-choose-99 (a combination.)
[tex]P(100000, 99) = \displaystyle \left( \begin{array}{c}100000\cr 99\end{array}\right)[/tex].
Step-by-step explanation:
A combination [tex]C(n, r)[/tex] or equivalently [tex]\displaystyle \left(\begin{array}{c}n \cr r\end{array}\right)[/tex] gives the number of ways to choose [tex]r[/tex] out of [tex]n[/tex] elements.
A permutation [tex]P(n, r)[/tex] also gives the number of ways to choose [tex]r[/tex] out of [tex]n[/tex] elements. On top of that, it accounts for the order of the elements. Two elements in different order counts twice in a permutation, but only once in a combination.
The question emphasize that the council members are "co-equal." That implies that the order of the members don't really matter. Hence a combination with [tex]n = 100000[/tex] and [tex]r = 99[/tex] would be a more suitable choice.
Find the absolute maximum and absolute minimum values of f on the given interval.
a) f(t)= t sqrt(36-t^2) [-1,6]
absolute max=
absolute min=
b) f(t)= 2 cos t + sin 2t [0,pi/2]
absolute max=
absolute min=
Answers
Answer:
absolute max= (4.243,18)
absolute min =(-1,-5.916)
absolute max=(pi/6, 2.598)
absolute min = (pi/2,0)
Step-by-step explanation:
a) [tex]f(t) = t\sqrt{36-t^2} \\[/tex]
To find max and minima in the given interval let us take log and differentiate
[tex]log f(t) = log t + 0.5 log (36-t^2)\\Y(t) = log t + 0.5 log (36-t^2)[/tex]
It is sufficient to find max or min of Y
[tex]y'(t) = \frac{1}{t} -\frac{t}{36-t^2} \\\\y'=0 gives\\36-t^2 -t^2 =0\\t^2 =18\\t = 4.243,-4.243[/tex]
In the given interval only 4.243 lies
And we find this is maximum hence maximum at (4.243,18)
Minimum value is only when x = -1 i.e. -5.916
b) [tex]f(t) = 2cost +sin 2t\\f'(t) = -2sint +2cos2t\\f"(t) = -2cost-4sin2t\\[/tex]
Equate I derivative to 0
-2sint +1-2sin^2 t=0
sint = 1/2 only satisfies I quadrant.
So when t = pi/6 we have maximum
Minimum is absolute mini in the interval i.e. (pi/2,0)
A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature.
Construct the 95 % confidence interval for the true proportion of all voters in the state who favor approval.
A) 0.435 < p < 0.508
B) 0.444 < p < 0.500
C) 0.471 < p < 0.472
D) 0.438 < p < 0.505
Answers
Answer: D) 0.438 < p < 0.505
Step-by-step explanation:
We know that the confidence interval for population proportion is given by :-
[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
, where n= sample size
[tex]\hat{p}[/tex] = Sample proportion.
z* = critical value.
Given : A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature.
i.e. n= 865
[tex]\hat{p}=\dfrac{408}{865}\approx0.4717[/tex]
Two-tailed critical avlue for 95% confidence interval : z* = 1.96
Then, the 95 % confidence interval for the true proportion of all voters in the state who favor approval will be :-
[tex]0.4717\pm (1.96)\sqrt{\dfrac{0.4717(1-0.4717)}{865}}\\\\\approx0.4717\pm 0.03327\\\\=(0.4717-0.03327,\ 0.4717+0.03327)=(0.43843,\ 0.50497)\approx(0.438,\ 0.505)[/tex]
Thus, the required 95% confidence interval : (0.438, 0.505)
Hence, the correct answer is D) 0.438 < p < 0.505
The average price of homes sold in the U.S. in the past year was $220,000. A random sample of 81 homes sold this year showed a sample mean price of $210,000. It is known that the standard deviation of the population is $36,000. Using a 1% level of significance, test to determine if there has been a significant decrease in the average price homes. Use the p value approach. Make sure to show all parts of the test, including hypotheses, test statistic, decision rule, decision and conclusion.
Answers
Final answer:
To test if there has been a significant decrease in the average price of homes sold in the U.S., we will conduct a hypothesis test using the p-value approach. We will define the null and alternative hypotheses, calculate the Z-test statistic, compare the p-value to the significance level, and make a conclusion based on the results.
Explanation:
To test if there has been a significant decrease in the average price of homes sold in the U.S., we will conduct a hypothesis test using the p-value approach. Let's define our hypotheses:
Null hypothesis (H0): The average price of homes sold in the U.S. is not significantly different from $220,000.
Alternative hypothesis (Ha): The average price of homes sold in the U.S. is significantly less than $220,000.
Next, we need to calculate the test statistic. Since the population standard deviation is known, we can use a Z-test. The formula for the Z-test statistic is:
Z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
In this case, the sample mean is $210,000, the population mean is $220,000, the population standard deviation is $36,000, and the sample size is 81. Plugging these values into the formula:
Z = (210,000 - 220,000) / (36,000 / sqrt(81))
Calculating this gives us a Z-statistic of -1.6875.
The final step is to compare the p-value of the test statistic to the significance level. Since the significance level is 1%, the critical value is 0.01. We can use a Z-table or calculator to find the p-value corresponding to a Z-statistic of -1.6875. The p-value is approximately 0.0466.
Since the p-value is less than the significance level of 0.01, we reject the null hypothesis. This means that there is sufficient evidence to conclude that there has been a significant decrease in the average price of homes sold in the U.S.
The position vector for particle A is cos(t)i, and the position vector for particle B is sin(t)j. What is the difference in acceleration (i.e. the relative acceleration) between particle A and B at any time t? The acceleration vector of a particle moving in space is the second derivative of the position vector
Answers
Answer:
sin(t)j - cos(t)i
Step-by-step explanation:
Let's start with A:
Position vector = cos(t)i
Velocity vector = -sin(t)i (differentiating the position vector)
acceleration vector = -cos(t)i (differentiating the velocity vector)
Then we go to B:
Position vector = sin(t)j
Velocity vector = cos(t)j
acceleration vector = -sin(t)j
Relative acceleration = -cos(t)i - (-sin(t)j) = sin(t)j - cos(t)i
For the given function, determine consecutive values of x between which each real zero is located. f(x) = –11x^4 – 5x^3 – 9x^2 + 12x + 10
Answers
Answer:
[-1, 0][0, 1]Step-by-step explanation:
Descartes' rule of signs tells you this function, with its signs {- - - + +}, having one sign change, will have one positive real root.
When odd-degree terms have their signs changed, the signs {- + - - +} have three changes, so there will be 1 or 3 negative real roots.
The constant term (10) tells us the y-intercept is positive. The sum of coefficients is -11 -5 -9 +12 +10 = -3, so f(1) < 0 and there is a root between 0 and 1.
When odd-degree coefficients change sign, the sum becomes -11 +5 -9 -12+10 = -17, so there is a root between -1 and 0.
__
Synthetic division by (x+1) gives a quotient of -11x^3 +6x^2 -15x +27 -17/(x+1), which has alternating signs, indicating -1 is a lower bound on real roots.
Real roots are located in the intervals [-1, 0] and [0, 1].
_____
The remaining roots are complex. All roots are irrational.
The attached graph confirms that roots are in the intervals listed here. Newton's method iteration is used to refine these to calculator precision. Dividing them from f(x) gives a quadratic with irrational coefficients and complex roots.
One method for measuring air pollution is to measure the concentration of carbon monoxide, or CO, in the air. Suppose Nina, an environmental scientist, wishes to estimate the CO concentration in Budapest, Hungary. She randomly selects 48 locations throughout the city measures the CO concentration at each location. Based on her 48 samples, she computes the margin of error for a 95% t-confidence interval for the mean concentration of CO in Budapest, in g/m3, to be 4.28 What would happen to the margin of error if Nina decreases the confidence level to 90%? Nina increases the confidence level to 99%? Nina decreases the sample size to 34 locations? Nina increases the sample size to 70 locations? Answer Bank Decrease Stay the sameIncrease
Answers
Answer:
a) Nina decreases the confidence level to 90%? (Decrease)
b) Nina decreases the sample size to 34 locations? (Increase)
c) Nina increases the sample size to 70 locations? (Decrease)
Step-by-step explanation:
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)
s represent the sample standard deviation
n=48 represent the original sample size
Confidence =95% or 0.95
ME=4.28 represent the margin of error.
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the mean and the sample deviation we can use the following formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
And the margin of error is given by the following expression:
[tex]ME= t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (4)
Based on the formula (4) we can answer all the questions involved:
a) Nina decreases the confidence level to 90%?
On this case the value for [tex]t_{\alpha/2}[/tex] will also decrease so the margin of error would decrease.
b) Nina decreases the sample size to 34 locations?
If we analyze the original sample size of 48 we see that if we reduce the value of n to 34, the margin of error would increase, because n is on the denominator of the margin of error.
c) Nina increases the sample size to 70 locations?
If we analyze the original sample size of 48 we see that if we increase the value of n to 70, the margin of error would decrease, because n is on the denominator of the margin of error.
For each of the following scenarios state whether H0 should be rejected or not. State any assumptions that you make beyond the information that is given.
(a) H0 : µ = 4, H1 : µ 6= 4, n = 15, X = 3.4, S = 1.5, α = .05.
(b) H0 : µ = 21, H1 : µ < 21, n = 75, X = 20.12, S = 2.1, α = .10.
(c) H0 : µ = 10, H1 : µ 6= 10, n = 36, p-value = 0.061.
Answers
Answer:
a)[tex]H_0 :\mu = 4\\ H_1 : \mu \neq 4[/tex] , n = 15 , X=3.4 , S=1.5 , α = .05
Formula : [tex]t = \frac{x-\mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{3.4-4}{\frac{1.5}{\sqrt{15}}}[/tex]
[tex]t =-1.549[/tex]
p- value = 0.607(using calculator)
α = .05
p- value > α
So, we failed to reject null hypothesis
b)[tex]H_0 :\mu = 21\\ H_1 : \mu < 21[/tex] , n =75 , X=20.12 , S=2.1 , α = .10
Formula : [tex]t = \frac{x-\mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{20.12-21}{\frac{2.1}{\sqrt{75}}}[/tex]
[tex]t =-3.6290[/tex]
p- value = 0.000412(using calculator)
α = .1
p- value< α
So, we reject null hypothesis
(c) [tex]H_0 :\mu = 10\\ H_1 : \mu \neq 10[/tex], n = 36, p-value = 0.061.
Assume α = .05
p-value = 0.061.
p- value > α
So, we failed to reject null hypothesis
The decision to reject the null hypothesis in each scenario depends on comparing calculated test statistics (or given p-value) to critical values associated with the significance level. In (a) and (c), we may not reject H0, and in (b) we would reject H0 if our test statistic is larger than the critical value.
Explanation:In hypothesis testing, we compare the test statistic, often a t-value, to the critical value determined by our chosen significance level, α. If the test statistic is greater, we reject the null hypothesis (H0).
(a) In the first scenario, we must calculate the test statistic: t = (X - µ) / (S/√n) = (3.4 - 4) / (1.5/√15); if this absolute value is less than our critical value associated with α = .05 and degrees of freedom = 14, we do not reject H0.
(b) For the second, the test statistic would be (20.12 - 21) / (2.1/√75); compare its value to the critical value associated with α = .10 and degrees of freedom = 74. If it is larger, we reject H0 due to the lower tail test in this scenario.
(c) In the third scenario, the p-value is given. Since our p-value = 0.061 is larger than our α = .05, we would not reject H0.
Learn more about Hypothesis Testing here:https://brainly.com/question/34171008
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