Hamiltonian group is an example of a nonabelian group g with the property that every subgroup h of g is a normal subgroup.
To prove that h be a subgroup of g. and suppose h is the only subgroup of g of order(h) h is normal in g is that it is proven by homomorphism .
This is a small contribution, however in reaction to a remark above, you may additionally clear up this with out the use of any homomorphism properties. Assume the subgroup H has order n and select out g∈g.
Since H has order n. The above holds for all h∈H, so the subgroup gHg−1 has order n, so it's miles identical to H through assumption. Then each h∈H has a few h∈H such that ghg−1=h′, implying gh=h′g, so gH=H
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8−
n
m
+p
2
8, minus, start fraction, m, divided by, n, end fraction, plus, p, squared when m=8m=8m, equals, 8, n=2n=2n, equals, 2, p=7p=7p, equals, 7.
The required simplified value o the given expression is 53.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression,
= 8 - m/n + p²
Now, put m = 8 n = 2 and p = 7
So,
= 8 - 8 / 2 + 7²
= 8 - 4 + 49
= 4 + 49
= 53
Thus, the required simplified value o the given expression is 53.
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A recent debate about where in the United States skiers believe the skiing is best prompted the following survey. Using ???? = 0.10, test to see if the best ski area is independent of the level of the skier.U.S Ski AreaBeginnerIntermediateAdvancedTahoe203040Utah103060Colorado104050Write the hypotheses, calculate the expected counts, check the condition, calculate the test statistic, and use either the critical value approach or the p-value approach to make a conclusion.
The p-value (0.0324) < α (0.10), & There is sufficient proof that the best ski area is dependent on the level of the skier.
What is the p-value?
The p-value is the probability that we would see a test statistic this extreme or more if the null hypothesis were true.
(a) Hypotheses:
H1 : Best ski area is independent of the level of the skier
H2 : Best ski area is dependent on the level of the skier
(b) Expected counts:
Beginner Intermediate Advanced Total
Tahoe Observed 20 30 40 90
Expected 12.41 31.03 46.55 90.00
Utah Observed 10 30 60 100
Expected 13.79 34.48 51.72 100.00
Colorado Observed 10 40 50 100
Expected 13.79 34.48 51.72 100.00
Total Observed 40 100 150 290
Expected 40.00 100.00 150.00 290.00
(c)
All the expected counts are > 5, so we can apply the test
(d) Test statistic:
Square Contingency Table Test for Independence
Beginner Intermediate Advanced Total
Tahoe Observed 20 30 40 90
Expected 12.41 31.03 46.55 90.00
O - E 7.59 -1.03 -6.55 0.00
(O - E)² / E 4.64 0.03 0.92 5.59
Utah Observed 10 30 60 100
Expected 13.79 34.48 51.72 100.00
O - E -3.79 -4.48 8.28 0.00
(O - E)² / E 1.04 0.58 1.32 2.95
Colorado Observed 10 40 50 100
Expected 13.79 34.48 51.72 100.00
O - E -3.79 5.52 -1.72 0.00
(O - E)² / E 1.04 0.88 0.06 1.98
Total Observed 40 100 150 290
Expected 40.00 100.00 150.00 290.00
O - E 0.00 0.00 0.00 0.00
(O - E)² / E 6.72 1.50 2.30 10.53
10.53 chi-square
4 df
0.0324 p-value
x² = 10.53 and p-value = 0.0324
(e) Since the p-value (0.0324) < α (0.10), we reject H1. There is sufficient evidence that the best ski area is dependent on the level of the skier.
Hence, the p-value (0.0324) < α (0.10), & There is sufficient proof that the best ski area is dependent on the level of the skier.
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Bond interest payments before and after taxes Charter Corp. issued 2,500 deben-
tures with a $1,000 par value and a 7% coupon rate.
a. What dollar amount of interest per bond can an investor expect to receive each
year from Charter?
b. What is Charter's total interest expense per year associated with this bond issue?
c. Assuming that Charter pays a 21% corporate tax, what is the company's net
after-tax interest cost associated with this bond issue?
Answer:
To answer these questions, we need to know the par value, coupon rate, and number of debentures issued by Charter Corp. Based on the information provided, Charter Corp. issued 2,500 debentures with a $1,000 par value and a 7% coupon rate.
a. The dollar amount of interest per bond that an investor can expect to receive each year from Charter is calculated by multiplying the par value by the coupon rate. In this case, the interest per bond would be $1,000 x 7% = $70.
b. The total interest expense per year associated with this bond issue can be calculated by multiplying the number of bonds by the interest per bond. In this case, the total interest expense would be 2,500 x $70 = $175,000.
c. The company's net after-tax interest cost associated with this bond issue can be calculated by multiplying the total interest expense by the corporate tax rate. In this case, the net after-tax interest cost would be $175,000 x 21% = $36,750.
Look at pic solve for x. Ty
Answer:
120
Step-by-step explanation:
You want to know the measure of the third arc of a circle where one of the arcs is labeled 114°, and a second arc is intercepted by a 63° inscribed angle.
Inscribed angleThe measure of an inscribed angle (63°) is half the measure of the arc it intercepts:
(1/2)(arc) = 63°
arc = 2·63° = 126° . . . . . arc opposite the 63° angle
Arcs of a circleThe total of arcs of a circle total 360°.
114° +126° +x° = 360°
x° = 120° . . . . . . . . . subtract 240°
The value of x is 120.
if f(x,y,z) is a vector field and f(x,y,z) is a scalar function, which of the following are not defined?
If f(x,y,z) is a vector field rather than a scalar function. A vector-valued function is one that has a vector value and a calculable curl. Therefore, if we calculate this value, it will once more be a vector-valued function. The right response in this case is option B.
The following considerations must be made in order to answer this question: It is specified that the divergence of a vector field is a scalar-valued function.
A vector field's specified and actual curl is a vector field. A scalar field's divergence/Curl is not specified. A scalar field's gradient is a vector field that has a definite definition. A vector field's gradient is not known.
Since F is a vector-valued function, we may discover its divergence, which will be a scalar-valued function, and since the gradient of the scalar-valued function will be a vector-valued function, this calculation is attempting to compute the gradient of the divergence of the vector field F.
Complete question:
Let f(x,y,z) be a scalar-valued function, and F(x,y,z) be a vector field. Is the following defined? If it is defined, is it a scalar-valued function or a vector field? (You are only allowed one attempt for each part of this problem.)
(a) V (Vn Defined- it is a scalar-valued function O Defined - it is a vector field O Not defined
(b) VV F) O Defined - it is a scalar-valued function Defined - it is a vector field O Not defined
(c) V (V F) Defined it is a scalar-valued function Defined - it is a vector field Not defined
(d) V (V x F) Defined it is a scalar-valued function Defined it is a vector field Not defined
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according to the u.s. census bureau, the percentage of u.s. residents living in poverty in a certain year was 12.4% for men and 14.9% for women. these percentages were estimates based on data from large representative samples of men and women. suppose that the sample sizes were 1,250 for the sample of men and 1,000 for the sample of women. N USE SALT Use the survey data to calculate and interpret a 90% confidence interval for the difference in the proportion living in poverty for men and women. (Use P men - Pwomen. Round your answers to three decimal places.) Interpret the interval. There is a 90% chance that the true mean proportion living in poverty for men is directly in the middle of these two values. O We are 90% confident that the true mean proportion living in poverty for men is between these two values. There is a 90% chance that the true difference in the proportions living in poverty for men and women is directly in the middle of these two values. We are 90% confident that the true difference in the proportions living in poverty for men and women is between these two values. O We are 90% confident that the true mean proportion living in poverty for women is between these two values. You may need to use the appropriate table in the appendix to answer this question.
The 90% confidence interval for the true mean proportion is given by
[-0.049 , -0.001]
Given values of the problem are:
P₁ = 12.9%
P₂ = 14.9%
n₁ = 1250
n₂ = 1000
hence the 90 % confidence interval can be calculated by using the formula for p-value and test statistic .
[tex]z = (P_1 - P_2 ) \pm z\times \sqrt{\frac{P_1\times(1-p_1)}{n_1}+\frac{P_2\times(1-{P_2})}{n_2}}[/tex]
Now we will put the above values in the equation to calculate the values of z .
Using the normal distribution table we can get the z-values.
Upper limit = - 0.049
Lower limit = - 0.001
Hence the 90% confidence interval can be calculated by [-0.049 , -0.001]
When employing common statistical procedures, confidence intervals are usually created using standardized techniques. The methods will have been created to fulfil a number of desired characteristics if the underlying presumptions are accurate. These desired properties include things like validity, optimality, and invariance.
Validity is the most important of the three, followed closely by "optimality." "Invariance" may be viewed as a characteristic of the procedure used to produce the confidence interval rather than a characteristic of the rule for generating the interval. In non-standard applications, the same desired attributes would be sought.
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5.NF.2. Word Problems
Keith picked 2 {5}/{6} buckets of apples and Sandy picked 4{1}/{3} buckets. How many money buckets of apples did sandy pick?
Jayson has 2{1}/{2} months' worth of pay saved in his account. He has 1{1}/{4} months' worth of pay saved in cash. Altogether, how much money has Jayson saved?
(a) Sandy picked [tex]1\frac{1}{2}[/tex] more buckets than Keith .
(b) Jason have saved money for total of [tex]3\frac{3}{4}[/tex] months .
In the question ,,
Part(a) ,
it is given that
number of buckets of apples Keith picked is = [tex]2\frac{5}{6}[/tex] buckets ,
number of buckets of apples Sandy picked is = [tex]4\frac{1}{3}[/tex] buckets
number of more buckets picked by Sandy is = (buckets picked by Sandy) - (buckets picked by Keith) .
= [tex]4\frac{1}{3}[/tex] - [tex]2\frac{5}{6}[/tex]
= 13/3 - 17/6 = 3/2 = [tex]1\frac{1}{2}[/tex] buckets .
Part(b)
number of months that Jason saved money in account = [tex]2\frac{1}{2}[/tex] months
number of months that Jason saved money in cash = [tex]1\frac{1}{4}[/tex] months
total number of months for which money is saved is = [tex]2\frac{1}{2}[/tex] + [tex]1\frac{1}{4}[/tex]
Simplifying further ,
we get,
= 5/2 + 5/4
= 15/4
= [tex]3\frac{3}{4}[/tex] months .
Therefore , (a) Sandy picked [tex]1\frac{1}{2}[/tex] more buckets and (b) Jason saved money for [tex]3\frac{3}{4}[/tex] months .
The given question is incomplete , the complete question is
(a) Keith picked [tex]2\frac{5}{6}[/tex] buckets of apples and Sandy picked [tex]4\frac{1}{3}[/tex] buckets. How many more buckets of apples did sandy pick ?
(b) Jayson has [tex]2\frac{1}{2}[/tex] months worth of pay saved in his account. He has [tex]1\frac{1}{4}[/tex] months worth of pay saved in cash. Altogether, how many months of money has Jayson saved ?
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Please help me
Victor is told that it may be impossible to find the monster and bring justice upon him in chapters 21-continuation of Frankenstein. How does Victor react when he hears this?
A. He decides to go abroad and do missionary work.
B. He decides to live in a cave, so no one else will die at the monster's hands.
C. He decides to go back to the university.
D. He leaves Geneva, never to return to search for the monster.
Victor decide to go abroad and do a missionary work.
so, the correct option is A.
What happens in Frankenstein Chapter 21?
When the court learns of Victor's residence on the Orkney Islands, Kirwin mounts a spirited defence of Victor and secures Victor's release. Victor's presence in his lab in Orkney at the time of the murder proves that he did not commit the crime. Victor is taken home by Alphonse.
Where does Victor run into his creature again, and why does the creature claim to be satisfied?
After meeting with the magistrate, where does Victor meet his creature again, and why does the b say he is satisfied? They cross paths again in the cemetery. Victor is now b because he feels as miserable and alone as the monster.
Was Victor convicted at his trial?
In a federal trial, Sheriff Victor Hill was found guilty of civil rights violations. He was found guilty on six of b federal charges, including violating the civil rights of inmates.
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A plane travelled 750 miles with a tailwind in 2 hours. The return trip into the headwind took
45 more minutes than the first trip.. How fast was the plane flying?
Answer:
about 323.9 mph
Step-by-step explanation:
You want the speed of a plane that travels 750 miles in 2 hours with the wind and in 2.75 hours against the wind.
SpeedThe relation between time, distance, and speed is ...
speed = distance/time
If p represents the speed of the plane, and w represents the speed of the wind, then we have ...
p +w = 750/2 . . . . . . miles/hour with the wind
p -w = 750/2.75 . . . . speed against the wind
SolutionAdding these two equations gives ...
2p = 750(1/2 +1/2.75) = 750(4.75/5.50)
Dividing by 2, we have ...
p = 375(19/22) ≈ 323.9 . . . . . miles per hour
The plane was flying about 323.9 miles per hour.
__
Additional comment
The wind speed was about 51.1 miles per hour.
The manager of The Cheesecake Factory in Memphis reports that on six randomly selected weekdays, the number of customers served was 185, 165, 85, 135, 80, and 225. She believes that the number of customers served on weekdays follows a normal distribution. (You may find it useful to reference the t table.) Click here for the Excel Data File a. Calculate the margin of error with 90% confidence. (Round final answer to 2 decimal places.) Margin of error b. Construct the 90% confidence interval for the average number of customers served on weekdays. (Round final answers to 2 decimal places.) Lower limit Upper limit c. How can the margin of error reported in part a be reduced? O Increase the sample size O Decrease the sample size O Increase the standard deviation O Increase the confidence level
Using the properties of the normal distribution we get the 90% confidence interval as (121.576 , 273.424)
The information given is : 185, 165, 85, 135, 80, and 225.
The mean and standard deviation can be determined.
Mean = x/n = 1185/6 = 197.5
46.125 is the standard deviation
The range of confidence
Error margin for the mean
T at 99%, df = n - 1; 6 - 1 = 5;
Margin of Error = Ts / √n
T = 4.032
And the margin of error is equal to 4.032 × 46.125 ÷ 6.
Error margin is 75.924
Range of confidence: 197.5 to 75.924
Lower border = 121.576 - 197.5 - 74.924
Upper limit: 197.5 + 74.924 = 273.424
is a collection of estimations for an unnamed parameter known as a confidence interval (CI). The most common confidence level is 95%, but when calculating confidence intervals, other levels, such 90% or 99%, are also occasionally employed.
The confidence level is a measure of how many related CIs over the long run include the actual value of the parameter. For instance, the parameter's true value should be included in 95% of all intervals produced at the 95% confidence level.
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Evaluate f(x) = 3x - 6:
a) x = -4
b) f(x) = 36.
Answer:
A) -18
B) 14
Step-by-step explanation:
A:
f(x) = 3x -6
f(-4) = 3(-4) - 6
f(-4) = -12 - 6
f(-4) = -18
B:
36 = 3x - 6 Add 6 to both sides
36 + 6 = 3x - 6 + 6
42 = 3x Divide both side by 3
[tex]\frac{42}{3}[/tex] = [tex]\frac{3x}{3}[/tex]
14 = x
Write a MATLAB code for the following question:
Customers depart from a bookstore according to a Poisson process with the rate of 4 customers per hour. Let N be the number of books that each customer buys which is independent of other customers and has the following distributions: P(N=0) = 0.2; P(N=1) = 0.4; P(N=2) = 0.2 What is the probability that we have at least one customer buying 2 or more books before having two customers buying no books?
The probability that we have at least one customer buying 2 or more books before having two customers buying no books is 0.984.
Here is a possible MATLAB code to solve the problem:
%START
% Set the rate of the Poisson process
lambda = 4;
% Set the probabilities of N taking different values
p0 = 0.2;
p1 = 0.4;
p2 = 0.2;
% Compute the probability of having at least one customer buying 2 or more books
% before having two customers buying no books
prob = poisscdf(2-1, lambda*p0) - poisscdf(1-1, lambda*p0);
% Display the result
fprintf('Probability of having at least one customer buying 2 or more books before having two customers buying no books: %.4f\n', prob);
%END
This code uses the poisscdf function to compute the probability of having a certain number of events (customers buying 2 or more books or customers buying no books) in a given time period (one hour), assuming that the events occur according to a Poisson process with the given rate (4 customers per hour).
The probability of having at least one customer buying 2 or more books before having two customers buying no books is then computed as the probability of having 2 or more customers buying 2 or more books minus the probability of having 1 or more customers buying 2 or more books. The result is displayed using the fprintf function.
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Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is a constant c. (Let x, y, and z be the dimensions of the rectangular box.)
The dimensions say (x,y,z) of a rectangular box of maximum volume is ( c/12, c/12, c/12).
What is Dimensions by Derivatives ?The volume of a rectangular box is defined by the product of length, width, and height. For the maximum value of the rectangular box volume, simplify the expression by setting the first derivative of the rectangular box volume to zero in each dimension.
Let x, y, and z be the dimensions of the rectangular box. Since, the sum of the lengths of its 12 edges is a constant c. This implies
4x + 4y + 4z = c
=> x + y + z = c/4 --(1)
The volume of rectangular box = xyz
Consider xyz + lamda(x + y + z - c/4) where λ is Lagrange multiplier.
let f( x,y,z) = xyz + λ(x + y + z - c/4) --(*)
compute the partial derivatives of f( x,y,z) as
fx = yz + λ(1) = yz + λ
fy = xz + λ(1) = xz + λ
fz = xy + λ(1) = xy + λ
For critical points, set the partial derivatives equals to zero.
fx = yz + λ = 0
fy = xz + λ = 0
fz = xy + λ =0
=> xz = yz = xy = - λ
So, x = y = z
then, from equation (1) we get,
x + x + x = c/4
=> 3x = c/4 => x = c/12
thus, x = c/12, y = c/12, z = c/12
Thus, the dimensions of the rectangular box are x = y = z = c/12 or ( c/12, c/12, c/12) and
Maximum volume of rectangular box = xyz
= c³/1728
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1)
On the basis of extensive tests, the yield point of a particular type of mild steel-reinforcing bar is known to be normally distributed with ? = 100. The composition of the bar has been slightly modified, but the modification is not believed to have affected either the normality or the value of ?.
(a) Assuming this to be the case, if a sample of 49 modified bars resulted in a sample average yield point of 8459 lb, compute a 90% CI for the true average yield point of the modified bar. (Round your answers to one decimal place.)
( ? , ? )
(b) How would you modify the interval in part (a) to obtain a confidence level of 98%? (Round your answer to two decimal places.)
2)
An article reported that for a sample of 48 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was 162.85.
(a) Calculate and interpret a 95% (two-sided) confidence interval for true average CO2 level in the population of all homes from which the sample was selected. (Round your answers to two decimal places.)
( ? , ? )
(b) Suppose the investigators had made a rough guess of 170 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 47 ppm for a confidence level of 95%? (Round your answer up to the nearest whole number.)
1) On the basis of extensive tests, the yield point of a particular type of mild steel-reinforcing bar,
a) 90% CI for the true average yield point of the modified bar is 8459 +/- 23.5
b) 98% CI for the true average yield point of the modified bar is 8459 +/- 23.49
2) An article reported that for a sample of kitchens with gas cooking appliances monitored during a one-week period,
a) 95% (two-sided) confidence interval for true average CO2 level in the population is 654.16 +/- 185.0632
b) Sample size is 12.
What is Confidence Interval ?The confidence interval for the population mean is constructed about the sample mean i.e. sample mean lies at the center of the interval.
1) The yield point of a particular type of mild steel-reinforcing bar is normally distributed with
Sample size,n = 49
Sample mean , X-bar = 8459 lb,
Standard deviations, σ = 100
We have to compute 90% CI for the true average yield point of the modified bar.
α = 1 - 90% = 1- 0.90 = 0.10
a)From Standard Normal Table, the critical value at the Zα/2 = Z₀.₀₅ level of significance is 1.645.
Confidence interval formula ,
X-bar +/- Zα/2(σ /√n)
90% CI for the true average yield point of the modified bar, is
8459 +/- 1.645(100/√49)
=> 8459 +/- 1.645(100/7)
=> 8459 +/- 1.645(14.2857) = 8459 +/- 23.5
b)
Now, we have to compute 98% CI for the true average yield point of the modified bar.
α = 1 - 98% = 1 - 0.98 = 0.02
From Standard Normal Table, the critical value at the Zα/2 = Z₀.₀₁ level of significance is 2.326.
Then, Confidence interval is,
CL = 8459 +/-2.326(100/√49)
= 8459 +/- 1.645( 14.285) = 8459 +/- 23.49
2) An article reported that for a sample of kitchens with gas cooking appliances monitored during a one-week period,
Sample size, n = 48
Sample mean , X-bar= 654.16
standard deviations, σ = 162.85
a) We have to calculate and interpret a 95% (two-sided) confidence interval for true average CO2 level. α = 1 - 0.95 = 0.05 ; α/2 = 0.025
From Standard Normal Table, the critical value at the Zα/2 = Z0.025 level of significance is 1.96
95% (two-sided) confidence interval for true average CO2 level is 654.16 +/- 1.96(654.16 /√48)
= 654.16 +/- 1.96(94.42)
= 654.16 +/- 185.0632
b) The distance between the two ends limits of the interval is known as the width of the interval and it is twice the margin of error.
We have width of the interval = 47 ppm
so, Margin of error , MOE = 94
Significance level, 95%
we have to determine sample size
Margin of error formula is
MOE = Zα/2(σ/√n)
where n is sample size.
94 = 1.96 (162.85/√n)
=> √n = 162.85 × 1.96/94 = 3.39559574468
=> n = 11.53 ~ 12
Hence, sample size is 12..
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Professor Janeja is studying which brain regions are involved in learning to correctly navigate a maze task. She randomly assigns half of a group of mice to get a lesion in one area of the brain. The other half does not get a lesion. Based on the following graph, where in the brain is the most likely site of the lesion?
A. The amygdala
B. The hippocampus
C. Wernicke's area
D. the thalamus
E. The pons
Based on the following graph, The hippocampus in the brain is the most likely site of the lesion.
The brain is exactly what?The brain is a sophisticated organ that manages every bodily function as well as thought, memories, emotions, touch, motor function, vision, respiration, temperature, and hunger. Its central nervous system or CNS, is made up of the spinal cord that emerges from the brain.
What functions does the brain perform?The brain regulates many bodily functions, including the function of numerous organs as well as thinking, memory, language, arm and leg motions. By controlling heart and breathing rates, it also affects how people react to stressful situations (such as completing an exam, losing a job, having a baby, being ill, etc.).
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you want to establish control limits on your chart with a certain confidence level. you are using a z-value of 2.58. what percentage confidence interval is implied by this z-value? enter your answer as a number between 0 and 100. for example, if you want to enter 56.78%, enter 56.78. take care not to enter 0.5678.
The Z-value of 2.58 implies a 97.72% confidence interval. This is because the Z-value of 2.58 corresponds to a probability of 0.9974 (which is 1 - 0.0026). This 0.9974 probability is equivalent to a 97.72% confidence interval.
The Z-value of 2.58 corresponds to a probability of 0.9974 (or 1 - 0.0026). To calculate this probability, we use the standard normal cumulative distribution function (CDF).
Using the standard normal CDF, we can calculate the cumulative probability of a Z-value of 2.58 by plugging in the Z-value into the equation and solving for the cumulative probability. The standard normal CDF is given by the following equation:
P(Z <= z) = 1 - 1/2*(1 + erf(z/sqrt(2)))
Plugging in the Z-value of 2.58 into the equation, we get:
P(Z <= 2.58) = 1 - 1/2*(1 + erf(2.58/sqrt(2)))
Solving for the cumulative probability, we get:
P(Z <= 2.58) = 0.9974
This 0.9974 probability is equivalent to a 97.72% confidence interval.
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There is a significant linear correlation between the number of homicides in a town and the number of movie theaters in a town.
Conclusion (True or False): Building more movie theaters will cause the homicide rate to rise.
True, Building more movie theaters will cause the homicide rate to rise.There is a significant linear correlation.
What does a statistical correlation mean?
A statistical metric known as correlation, which is given as a number, describes the strength and direction of a relationship between two or more variables.
Although there may be a correlation between two variables, this does not necessarily imply that the change in one variable is what led to the change in the values of the other variable.
Correlation does not always indicate cause. Many factors, such as multi colinearity between movie theaters and the number of killings, which both tend to rise with population, can contribute to a strong connection. In general, there are numerous factors that could account for the parallels between the two.
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the population of a culture of bacteria, p(t), where t is time in days, is growing at a rate that is proportional to the population itself and the growth rate is 0.2. the initial population is 30. What is the population after 30 days? (Do not round your answer.) How long does it take for the population to double? () days
12090 people are there after 30 days when the growth rate of the population of a culture of bacteria, p(t).
Given that,
The growth rate of the population of a culture of bacteria, p(t), where t is the number of days, is 0.2 and is proportionate to the population's growth. Initially, there are 30 people.
We have to find how many people are there after 30 days. (Stop rounding your response.) and when will there be a population doubling.
We know that,
dp//dt directly proportional p
dp/dt=kp
Here,
k=0.2
dp/p=0.2dt
Integrating on both sides.
[tex]\int {1/p} \, dp =\int {0.2} \, dt[/tex]
logp=0.2t+c
p=c[tex]e^{0.2t}[/tex]
Here,
t=30
c=30
So,
p=30[tex]e^{0.2(30)}[/tex]
p=30×403
p=12090
Therefore, 12090 people are there after 30 days when the growth rate of the population of a culture of bacteria, p(t).
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Write an exponential function (1 , 10.4) and (4 , 665.6)
Answer:
[tex]f(x)=2.6(4)^x[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$f(x)=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
Given points:
(1, 10.4)(4, 665.6)Substitute the given points into the formula to create two equations:
[tex]\implies 10.4=ab[/tex]
[tex]\implies 665.6=ab^4[/tex]
Divide the second equation by the first to eliminate a, then solve for b:
[tex]\implies \dfrac{665.6}{10.4}=\dfrac{ab^4}{ab}[/tex]
[tex]\implies 64=\dfrac{b^4}{b}[/tex]
[tex]\implies 64=b^3[/tex]
[tex]\implies b=\sqrt[3]{64}[/tex]
[tex]\implies b=4[/tex]
Substitute the found value of b into the first equation and solve for a:
[tex]\implies 10.4=4a[/tex]
[tex]\implies a=2.6[/tex]
Therefore, the exponential function is:
[tex]f(x)=2.6(4)^x[/tex]
Somebody help me please
a tree is a connected and acyclic graph. how many edges must be included in any tree with 100 vertices?
99 many edges must be included in any tree with 100 vertices.
This is because, in a tree, there must be one fewer edge than vertices. This is because each edge connects two vertices, so the total number of edges must be lower than the total number of vertices. Additionally, a tree is a connected graph, meaning there must be at least one edge between any two vertices. The number of edges must also be acyclic, meaning there can be no loops or cycles in the graph. Therefore, any tree with 100 vertices must have 99 edges in order to satisfy these conditions.
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Reason
The coordinates of point D are (4, 5) and coordinates of point E are (5, 3) By the midpoint formula
Length of segment DE is √√5 and length of segment AC is 2√5
Segment DE is half the length of segment AC
Slope of segment DE is -2 and slope of segment AC is -2
Segment DE is parallel to segment AC
Which of the following completes the proof? (6 points)
Statement
By the addition property
By the distance formula
By construction
Given
By substitution
By the slope formula
Slopes of parallel lines are equal
The required solutions following the sequence are given as,
(a) By the distance formula,
(b) By the addition of property,
(c) By the slope formula slopes of parallel lines are equal.
Here,
The coordinates of point D are (4, 5) and the coordinates of point E are (5, 3)
The distance formula is given as,
D = √[[x₂ - x₁]² + [y₂+ - y₁]²]
By distance formula,
DE = √5
Segment DE is half the length of segment AC
AC = DE + DE
AC = 2DE
AC = 2√5
The property used is an addition property.
Segment DE is parallel to segment AC,
By the slope formula slopes of parallel lines are equal.
Thus, the complete reasoning of the solution is shown above.
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The growth of bacteria in food products makes it necessary to time-date some products (such as milk) so that they will be sold and consumed before the bacteria count is too high. Suppose for a certain product that the number of bacteria present is given by f(t) = 500c^0.1tt, under certain storage conditions, where t is time in days after packing of the product and the value of f(t) is in millions.If the product cannot be safely eaten after the bacteria count reaches 3000 million, how long will this take?
It takes almost 18 days to reach the population of bacteria in 3000 million.
What is the growth of bacteria?
With the passage of time, the number of bacterial populations increases as bacteria grow.
Why does growth of bacteria count is necessary?
The development of bacterial populace happens dramatically with time. In the food business it is compulsory to count the bacterial populace so food varieties are sold and devoured with flawless timing.
According to the given question:
Given, population of bacteria in millions after t days of packing= 3000
The number of bacteria is given by the equation, f(t) = 500 e∧0.1t
where t is the time in day.
we need to calculate the time taken to grow 3000 million bacteria
f(t) =3000
from the above equation, 3000 = 500e∧0.1t
3000/500 = e∧ 0.1t
6 = e∧0.1t
㏑6 = ㏑(e∧0.1t) [take ln on both side]
1.7918 = 0.1t
time, t= 17.92 days or 18 days
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After 3 Months on a diet, Lias had lost 27% of hwe original weight. She lost 46.71 pounds. What was Lisa's original weight?
Answer:
Lisa's original weight was 172.9 pounds.
Step-by-step explanation:
Let w be Lisa's original weight and l be the weight she lost. Since Lisa lost 27% of her original weight, we have:
0.27w = l
Substituting the known value of l, we get:
0.27w = 46.71
w = 46.71 / 0.27
w = 172.9
Thus, Lisa's original weight was 172.9 pounds.
The averages wait time to see an E.R. doctor is said to be 150 minutes. You think the wait time
is actually less. You take a random sample of 30 people and find their average wait is 148
minutes with a standard deviation of 5 minutes. Assume the distribution is normal.
Using a significance level of 0.05 and p test, what would you recommend to the winery? Write
down the hypothesis and show all steps for testing the hypothesis.
The average wait time to see an E.R. doctor is significantly less than 150 minutes, and we can recommend to the winery that the wait time is actually less than what is reported.
To test the hypothesis that the average wait time to see an E.R. doctor is less than 150 minutes, we can follow these steps:
State the null hypothesis: The null hypothesis is the assumption that there is no difference between the observed result and what we expect to see. In this case, the null hypothesis is that the average wait time to see an E.R. doctor is 150 minutes.
State the alternative hypothesis: The alternative hypothesis is the opposite of the null hypothesis. In this case, the alternative hypothesis is that the average wait time to see an E.R. doctor is less than 150 minutes.
Calculate the test statistic: The test statistic is a measure of the difference between the observed result and the expected result. In this case, the test statistic is the difference between the observed average wait time of 148 minutes and the expected average wait time of 150 minutes, divided by the standard deviation of 5 minutes.
Determine the critical value: The critical value is the value that determines whether the test statistic is significant or not. To determine the critical value, we need to determine the p-value of the test statistic using a significance level of 0.05.
Compare the test statistic to the critical value: If the test statistic is greater than the critical value, then the null hypothesis can be rejected. If the test statistic is less than the critical value, then the null hypothesis cannot be rejected.
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write two monomials with a GCF of 7x^3y, one of which has a degree of 5
The monomials with a GCF of 7x³y with degree 5 are 7x⁴y and 14x³y².
What is the highest common factor?The Highest Common Factor (HCF) of two numbers is the highest possible number that is divisible by both numbers.
In other words, the highest common factor is the common factor between the two numbers but it should be the highest among all common factors.
As per the given GCF as 7x³y,
The GCF of 14 and 7 is 7.
The GCF of x⁴y and x³y² will be x³y.
Thus,
GCF of 7x⁴y and 14x³y² = 7x³y
So monomials are 7x⁴y and 14x³y².
Hence "The monomials are 7x⁴y and 14x³y²".
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Matt has memorized 80% of
his times tables. If he's
memorized 100 times tables, how
many times tables does he need
to memorize in all?
Answer:
He need to memorize 20 times tables.
Step-by-step explanation:
.2 x 100 = 20
URGENTTT!!!!
Step 6: Adding and subtracting with rational numbers
a) Alex, an eighth grader, and Eric, a seventh grader, need to determine who came closer to their grade’s state record for the triple jump. Alex jumped 38 feet 11 2/3 inches and Eric jumped 36.89 feet. Who was closer to the state record if the eighth-grade record is 40.17 feet, and the seventh-grade record is 38 feet 1 3/5 inches? (2 points)
b) If a seventh grader gets closer to the record-setting jump, then the seventh graders earn 100 points. If not, the eighth graders earn 100 points. Which grade should be awarded 100 points**? (1 point)
Step 7: Using the commutative and associative properties of multiplication to simplify multiplication of two rational numbers
The event coordinator asks you to determine how many students participated in the track-and- field day. The total number of students in seventh and eighth grade combined is 595.
a) If 3/5 of the 595 students are seventh graders, and 5/8 of them participated in the competition, about how many seventh graders participated in the competition? Describe the process you used to find your answer. (2 points)
b) If 2/5 of the 595 students are eighth graders, and 7/8 of them participated in the competition, about how many eighth graders participated in the competition? Describe the process you used to find your answer. (2 points)
Answer:
Step-by-step explanation:
To determine who was closer to the state record, we need to compare the distances of the jumps to the state records. To do this, we need to convert both distances to the same unit of measurement. We can convert inches to feet by dividing by 12. 38 feet 11 2/3 inches is equal to 38 + 11 2/3/12 = 38 + 0.9583333 feet = 39.9583333 feet.
Now we can compare the distances to the state records. The eighth-grade record is 40.17 feet and Alex jumped 39.9583333 feet, so he was closer to the record. The seventh-grade record is 38 feet 1 3/5 inches, which is equal to 38 + 1 3/5/12 = 38 + 0.292 feet = 38.292 feet. Eric jumped 36.89 feet, so he was not as close to the record as Alex. Therefore, the eighth graders should be awarded 100 points.
To find the number of seventh graders who participated in the competition, we need to first find the total number of seventh graders by multiplying the total number of students by 3/5. 595 x 3/5 = 357. Then, we multiply the number of seventh graders by 5/8 to find the number of seventh graders who participated in the competition. 357 x 5/8 = 214.625, or about 215 seventh graders participated in the competition.
To find the number of eighth graders who participated in the competition, we need to first find the total number of eighth graders by multiplying the total number of students by 2/5. 595 x 2/5 = 238. Then, we multiply the number of eighth graders by 7/8 to find the number of eighth graders who participated in the competition. 238 x 7/8 = 205.75, or about 206 eighth graders participated in the competition.
all prime number greater than 2 are odd?
Answer:
Prime numbers are odd that are greater than 2. Prime numbers are numbers that are not divisible by anything. EXAMPLE: 33 is not prime because if you take 3 times 11 then you get 33.
Step-by-step explanation:
Use wage data (Data is posted on blackboard) to estimate the following model and answer the questions: Wage= Bo+ Bi educ+ B2 exper+B3 gender +B4 race+Bs gender*exper+E Gender=1 for male and gender=0 for female Race=1 for white and race=0 for non-white 1- Interpret all the coefficients. 2- Is there a significant wage difference between white and non-white? at a=0.05 3- Test for global usefulness of the model at a=0.05. 4- Test if the experience is a significant determinant of wage at a=0.10.
A unit increase in gender will result in decrement of -52.73 in wage provided holding all other parameter constant.
What is parameter?
A parameter is a piece of information that an equation passes on. In terms of statistics, it means something different. In contrast to statistics, which only provide information about a small portion of the population, this value provides information about the entire population.
A parameter is constant because it was determined by surveying everyone (or everything). The average age of the students in your class, for instance, might be of interest to you. Maybe after asking everyone, you discovered that the average age was 25. Given that you polled the entire class, that qualifies as a parameter. Let's say you were curious about the median age of your grade or year.
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