The proportion of people with a score between 60 and 70 in the given normal distribution is approximately 0.0236.
False. Jack and Jill do not have the same x-score.
We have,
To calculate the proportion of people with a score between 60 and 70 in a normal distribution, we need to use the Z-score formula and find the corresponding probabilities.
Given:
Mean (μ) = 40
Standard deviation (σ) = 157
First, we need to calculate the Z-scores for the values 60 and 70 using the formula:
Z = (X - μ) / σ
For 60:
Z1 = (60 - 40) / 157 ≈ 0.1274
For 70:
Z2 = (70 - 40) / 157 ≈ 0.1911
Next, we can use a Z-table or statistical software to find the corresponding probabilities for these Z-scores.
Using a Z-table or a calculator, the probability associated with Z1 is approximately 0.5517, and the probability associated with Z2 is approximately 0.5753.
To find the proportion between 60 and 70, we subtract the probability of Z1 from the probability of Z2:
Proportion = P(Z1 < Z < Z2)
= P(Z2) - P(Z1)
≈ 0.5753 - 0.5517
≈ 0.0236
Rounding to the fourth decimal place, the proportion of people with a score between 60 and 70 in the given normal distribution is approximately 0.0236.
The second question:
False. Jack and Jill do not have the same x-score.
Thus,
The proportion of people with a score between 60 and 70 in the given normal distribution is approximately 0.0236.
False. Jack and Jill do not have the same x-score.
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The altitude perpendicular to the hypotenuse of a right triangle is 12 cm. Express the length of the hypotenuse as a function of the perimeter.
Let's denote the lengths of the legs of the right triangle as a and b, and the length of the hypotenuse as c. We are given that the altitude perpendicular to the hypotenuse is 12 cm.
Using the Pythagorean theorem, we have:
[tex]a^2 + b^2 = c^2[/tex]
The perimeter of the right triangle is given by:
Perimeter = a + b + c
We want to express the length of the hypotenuse (c) as a function of the perimeter.
Rearranging the equation for the perimeter, we have:
c = Perimeter - (a + b)
Substituting the equation for c into the Pythagorean theorem equation, we get:
[tex]a^2 + b^2[/tex] = (Perimeter - [tex](a + b))^2[/tex]
Expanding and simplifying, we have:
[tex]a^2 + b^2[/tex]= [tex]Perimeter^2[/tex] - 2Perimeter(a + b) +[tex](a + b)^2[/tex]
Simplifying further:
[tex]a^2 + b^2[/tex]= [tex]Perimeter^2[/tex]- 2Perimeter(a + b) + a^2 + 2ab + b^2
The terms with [tex]a^2[/tex] and [tex]b^2[/tex]cancel out, giving:
[tex]2ab = Perimeter^2 - 2Perimeter(a + b)[/tex]
Dividing both sides by 2, we have:
[tex]ab = (Perimeter^2 - 2Perimeter(a + b))/2[/tex]
[tex]ab = (Perimeter^2 - 2Perimeter(a + b))/2[/tex]
Now, since we are given that the altitude perpendicular to the hypotenuse is 12 cm, we know that:
ab = [tex]12^2 = 144[/tex]
We can solve this equation for either a or b, and then substitute the value into the expression for the hypotenuse (c):
For example, let's solve for a:
a = 144/b
Substituting this into the expression for c
c = Perimeter - (a + b)
c = Perimeter - (144/b + b)
Therefore, the length of the hypotenuse (c) can be expressed as a function of the perimeter.
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SOCCER PRACTICE BEGAN AT 2:30 P.M 3:30 P.M THROUGH WHAT FRACTION OF A CIRCLE DID THE MINUTE HAND TURN HOW MANY DEGREES DID THE MINUTE HAND TURN
Answer:
1 /1 ; 360°
Step-by-step explanation:
Start time = 2:30 pm
Stop time = 3:30 pm
Minute hand makes a complete revolution per hour ;
This means that the minutes hand revolves round the whole circle in one hour, hence fraction of the circle covered by the minute hand between 2:30 pm - 3:30 pm is 1/1 = 1
The angle turned by the minutes hand :
1 complete revolution = 360°
A circle covers 360°
1 /1 fraction of a circle = 1/1 * 360° = 360°
Hence, angle turned by the minute hand = 360°
if m < c = 147 , determine m < e
a) 147
b) 57
c) 33
d) 180
Answer:
c) 33
Step-by-step explanation:
We can calculate supplementary angles by subtracting the given angle from 180°. To find the other angle (in your case, ∠e), use the ∠y = 180° – ∠x where ∠x is the given angle.
Answer:
c)33
Step-by-step explanation:
Find the slope of each line joining each pair of points:
Find the slope of each line joining each pair of points: (4,6) and (1,2)
The slope of the line joining the given pair of points is 4/3.
The slope of the line joining the points (4, 6) and (1, 2) can be found using the formula:
slope = (y2 - y1) / (x2 - x1).
Substituting the coordinates of the two points into the formula:
slope = (2 - 6) / (1 - 4)
Calculating this expression:
slope = -4 / -3
Simplifying the fraction:
slope = 4/3
Therefore, the slope of the line joining the points (4, 6) and (1, 2) is 4/3.
To evaluate the slope of a line joining two points, we use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, we substitute the coordinates (4, 6) and (1, 2) into the formula and calculate the expression.
Simplifying the fraction, we find that the slope of the line is 4/3. This means that for every 3 units of horizontal change (x-axis), the line rises by 4 units (y-axis).
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Laney bought some candy from the bulk food store. She bought a 290 gram bag of gummy worms, a 450 gram bag of sour keys, and 670 gram bag of chocolate covered almonds. What is the total weight in kilograms?
Answer:
1.41 kilograms
Step-by-step explanation:
Given data
290-gram bag of gummy worms
450-gram bag of sour keys
670-gram bag of chocolate-covered almonds
In all, she bought
=290+450+670
=1410grams of candy
Now let us convert from grams to kilograms
1000grams is equal to 1 kilogram
hence 1410 grams will be x
cross multiply
1000x= 1410
x= 1410/1000
x= 1.41 kilograms
Check for a significant change over first-time composite scores when a group of 30 high school seniors retake the Miller Analogies Test (MAT) after completing a Test Preparation Workshop; note that each student will have taken the MAT twice, once before and once following the workshop, and the scores are on a ratio scale.
The preparation workshop’s impact on first-time composite scores can be assessed by evaluating the scores of a group of 30 high school seniors who retake the Miller Analogies Test (MAT) after attending the workshop.
The MAT is taken twice by each student: once before the workshop and once after it. The scores are reported on a ratio scale.
To check if there has been a significant change in scores, the following steps can be followed:
Step 1: To determine the change in scores, subtract the scores obtained before the workshop from the scores obtained after the workshop.
Step 2: Calculate the average score change for the group of 30 students by dividing the sum of score changes by 30.
Step 3: Calculate the standard deviation of the score change by using the following formula:
SD = √[∑ (Xi - X)2 / (n - 1)]
where Xi is the individual score change, X is the average score change, and n is the number of students.
Step 4: Use a t-test to determine if the change in scores is statistically significant. If the t-value is greater than the critical value (using a 5% significance level and 29 degrees of freedom), then the change in scores is significant.
Thus, by following these steps, the impact of the preparation workshop on first-time composite scores of the MAT can be assessed.
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The paired t-test is the appropriate statistical analysis to use for this type of data.
The first step to check for a significant change over first-time composite scores when a group of 30 high school seniors retake the Miller Analogies Test (MAT) after completing a Test Preparation Workshop, note that each student will have taken the MAT twice, once before and once following the workshop, and the scores are on a ratio scale is to compute the ratio of the scores before and after the workshop for each student.
Then, calculate the mean and standard deviation of the ratios.
Finally, conduct a paired t-test to determine if the mean ratio is significantly different from 1 at the 0.05 level of significance.
The paired t-test is the appropriate statistical analysis to use for this type of data.
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HELPPPPPPPPPPPPPPPPPPPP
Simplify: 2(x+3)+5(2x-1)
(no files please)
In a data set with a, b, c, d, e, and f numeric variables, given there are strong correlation of these pairs (f, a), (f, c), (d, e), (a, d), we can set up a regression model as:
Of-a + c Of-a + b + c + d + e Of-a + C + d + e Of-a + C + e
Given two predictor variables with correlation at 0.32879, we should expect there is multicollinearity between them.
Given two predictor variables with a correlation of 0.32879, we should expect there to be multicollinearity between them.
In a data set with a, b, c, d, e, and f numeric variables, given there is a strong correlation of these pairs (f, a), (f, c), (d, e), (a, d), we can set up a regression model as
Of-a + c Of-a + b + c + d + e Of-a + C + d + e Of-a + C + e.
Given two predictor variables with a correlation of 0.32879, we should expect there is multicollinearity between them.
The statement that is true regarding the given two predictor variables with a correlation of 0.32879 is:
we should expect there to be multicollinearity between them.
Multicollinearity is a situation in which two or more predictor variables in a multiple regression model are highly correlated with one another. Multicollinearity complicates the understanding of which predictor variables are significant in the regression model's estimation.
Therefore, given two predictor variables with a correlation of 0.32879, we should expect there to be multicollinearity between them.
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Voting in Seaside's annual school board elections has been going down by 10% from one election to the next. If 990 parents voted this year, how many will vote 4 years from now?
If necessary, round your answer to the nearest whole number.
Answer:
FV= 676
Step-by-step explanation:
Giving the following formula:
Present value (PV)= 990 parents
Decrease rate (d)= 10% = 0.1 per year
Number of periods (n)= 4
To calculate the future value of votes, we need to use the following formula:
FV= PV / (1 + d)^n
FV= 990 / (1.1^4)
FV= 676
The sales tax on a $500 purse is 7%. What is the total cost of the purse?
Answer:
$535
Step-by-step explanation:
First step is figure out what's 7% of 500, and then you can add the numbers together. To make it simpler, you can multiple 500 by 1.07, which would include the sales tax and the 500 altogether to get the answer.
Find the volume of a right circular cone that has a radius of 4 inches and a height of 12 inches. A. 36 in. B. 48 in. C. 52 in. D. 64 in.
Answer:
A) 36 inches
36 Incheon is the correct answer
Answer:
D.) 64pi in.³
Step-by-step explanation:
I got it right in quiz, trust me.
I hope this helps! ^^
What is x abc def
A. 45
B. 60
C. 75
D. 30
Answer:
C
Step-by-step explanation:
An amusement park sold 38 discount tickets and 12 full-price tickets. What percentage of the tickets sold were discount tickets?
i don’t know the answer please help
The (m = 4, n = 7) Hamming code is described by the following matrices: n = (i) Generator matrix 1 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1101001 (ii) Parity check matrix 0 0 0 1 1 1 1 0110011 1 0 1 0 1 0 1 Assuming that no more than one error occurs during transmission, what was the transmitted codeword vector when (a) (5%) 0100110 is received? (b) (5%) 0001111 is received?
(a) The transmitted codeword vector when 0100110 is received is 0100110.
To determine the transmitted codeword vector, we need to find the syndrome of the received vector and check if it corresponds to any error patterns. If the syndrome is zero, it means no error occurred during transmission.
Let's calculate the syndrome for the received vector 0100110 using the parity check matrix:
Received vector: r = 0 1 0 0 1 1 0
Parity check matrix: H = 0 0 0 1 1 1 1
0 1 0 1 0 1 0
1 0 1 0 1 0 1
To calculate the syndrome, we multiply the received vector by the transpose of the parity check matrix:
Syndrome = r * H^T
= 0 1 0 0 1 1 0 * 0 0 1
0 1 0
1 0 1
1 0 1
0 1 0
1 0 1
0 1 0
= 0 1 0 * 0 1 0
1 0 1
0 1 0
1 0 1
0 1 0
1 0 1
0 1 0
= 0 0 0
The resulting syndrome is 0 0 0, which indicates that no error occurred during transmission. Therefore, the transmitted codeword vector is the same as the received vector: 0100110.
(b) The transmitted codeword vector when 0001111 is received is 1001111.
Following the same process as in part (a), let's calculate the syndrome for the received vector 0001111 using the parity check matrix:
Received vector: r = 0 0 0 1 1 1 1
Parity check matrix: H = 0 0 0 1 1 1 1
0 1 0 1 0 1 0
1 0 1 0 1 0 1
Syndrome = r * H^T
= 0 0 0 1 1 1 1 * 0 0 1
0 1 0
1 0 1
1 0 1
0 1 0
1 0 1
0 1 0
= 0 1 1 * 0 1 0
1 0 1
1 0 1
0 1 0
1 0 1
0 1 0
1 0 1
= 0 1 1
The resulting syndrome is 0 1 1, which indicates an error occurred during transmission. To correct the error, we need to locate the error bit. The syndrome corresponds to the position of the error bit in the received vector.
The error bit is in position 3, so we flip the value of the bit in position 3 in the received vector:
Received vector (after error correction): 1001111
Since we assumed that no more than one error occurred during transmission, we can conclude that the transmitted cod
eword vector is 1001111.
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Internet Viewing A researcher wishes to estimate the average number of minutes per day a person spends on the Internet. How large a sample must she select if she wishes to be 90% confident that the population mean is within 13 minutes of the sample mean? Assume the population standard deviation is 46 minutes. Round your final answer up to the next whole number. The researcher needs a sample of at least people. Work Time Lost due to Accidents At a large company, the Director of Research found that the average work time lost by employees due to accidents was 98 hours per year. She used a random sample of 18 employees. The standard deviation of the sample was 5.2 hours. Estimate the population mean for the number of hours lost due to accidents for the company, using a 99% confidence interval. Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final answers to the nearest whole number. Doctoral Student Salaries Full-time Ph.D. students receive an average of $12,837 per year. If the average salaries are normally distributed with a standard deviation of $1500, find the probabilities. Use a TI-83 Plus/TI-84 Plus calculator and round the answer to at least four decimal places. Part: 0/2 Part 1 of 2 (a) The student makes more than $17,000. P(X>17,000)-
Using the z-distribution, as we have the population standard deviation, it is found that a sample of 83 people must be taken.
Given,
Estimation of number of minutes per day a person spends on the internet .
Margin of error in Z distribution,
M = z σ/[tex]\sqrt{n}[/tex]
In which:
z is the critical value.
σ is the population standard deviation.
n is the sample size.
Here,
We have 90% confidence level ,
Thus ,
[tex]\alpha[/tex] = 0.9
z is the value of Z that has a p-value
(1+0.9) / 2
= 0.95
so the critical value is z = 2.575
Also we have
standard deviation = 46 minutes
Population mean = 13 minutes
To find minimum sample size solve for n
M = z σ/[tex]\sqrt{n}[/tex]
13 = 2.575 (46/[tex]\sqrt{n}[/tex])
n = 83 .30
Rounding up, a sample of 83 people must be taken.
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What is the value of f(x) = 4x -9
Answer:
F= 1 /4 y+ 9 /4
Step-by-step explanation:
brainliest?
Find the value of x in the picture below. (round to nearest tenth if needed) THANK YOU FOR HELPING ME:)
Answer:
x ≈ 9.6
Step-by-step explanation:
Using Pythagoras' identity in the right triangle, that is
x² + 14² = 17²
x² + 196 = 289 ( subtract 196 from both sides )
x² = 93 ( take the square root of both sides )
x = [tex]\sqrt{93}[/tex] ≈ 9.6 (to the nearest tenth )
Make a bowl of Pho wit 3 ingredients that cost 14.50.
Will choose brainliest
Answer: $8 bowl, noodles, bean sprouts, beef
Step-by-step explanation:
Look at the number line below. Tyhe number 2 is between 1 and 4 since 1 =1 and 4=2, that means that 2 must be between what two integers?
Answer: i dont know
Step-by-step explanation:
Charlotte started soccer practice at 5:30 pm. Practice lasted for 1 hour and 45 minutes. What time was practice over?
Answer:
7: 15
Step-by-step explanation:
An item is priced at $13.75. If the sales tax is 7%, what does the item cost including sales tax?
Answer:
divide 7/100 which is 0.07
multiply that by 13.75, and you get 0.96
13.75+0.96= $13.20
(this is including sales tax)
Answer:
$12.78
Step-by-step explanation:
I THINK you are supposed to multiply the original price (13.75) by the sales tax as a decimal (0.07) and then subtract that answer from, the original, amount.
The city of İzmir is prone to three main types of natural hazards: earthquakes, winds and floods. Each of these can be modelled as a Poisson process. The mean annual occurrence rates for earthquakes and floods are 0.1 and 0.25 damaging events, respectively. The wind is considered as a hazard when the speed exceeds 40m/s. The probability distribution for the annual wind speed is known to be lognormal with a median of 30m/s and a coefficient of variation 0.2. All the three hazardous events occur independently of each other, and each can cause damages with an approximate cost of 2M TL. For proper budgeting, the municipality of İzmir needs to calculate the expected monetary loss from natural hazards, and approximately estimates the loss as a product of the number of hazardous events and the related cost. Based on this data, find out: a) What is the return period of a hazardous wind? b) What is the probability that more than 3 hazardous events in total can happen within a year? c) What is the probability that no hazardous events can happen within 5 years? d) Provide estimates for the mean and standard deviation of expected annual monetary losses so as to have an idea about how much budget the municipality should allocate for natural hazards.
The return period of a hazardous wind can be calculated by finding the inverse of its cumulative distribution function (CDF) at a certain threshold value.
a) To determine the return period of a hazardous wind, we need to find the threshold wind speed that corresponds to a specific return period. Since the wind speed follows a lognormal distribution with a known median and coefficient of variation, we can calculate the corresponding quantile using the inverse of the lognormal CDF.
b) The probability of more than 3 hazardous events in the total happening within a year can be calculated using the Poisson distribution. We sum the probabilities of having 4, 5, 6, and so on hazardous events in a year.
c) The probability of no hazardous events happening within 5 years can also be calculated using the Poisson distribution. We calculate the probability of zero hazardous events in one year and then raise it to the power of 5.
d) To estimate the mean and standard deviation of expected annual monetary losses, we multiply the mean number of hazardous events for each type by the cost per event. Since the three hazardous events occur independently, we can sum the expected losses for each type.
The standard deviation of the expected losses can be calculated using the properties of independent random variables. By calculating the mean and standard deviation of expected annual monetary losses, the municipality can have an idea of the budget allocation required to mitigate the impact of natural hazards in Izmir.
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Kristin boards a Ferris wheel at the 3-o’clock position and rides the Ferris wheel CCW for one full rotation. The Ferris wheel has a radius of 8 meters and the center of the Ferris wheel is 12 meters above the ground. Imagine an angle with its vertex at the center of the Ferris wheel that subtends the path Kristin travels.
Answer the following questions.
a.If Kristin has traveled 4 meters along the path of the Ferris wheel then the angle has swept out _________radians. b.If Kristin has traveled 45 meters along the path of the Ferris wheel then the angle has swept out ___________radians. c. Write a formula that expresses the number of radians θ the angle has swept out in terms of the number of meters d Kristin has traveled since the ride started.
a) If Kristin has traveled 4 meters along the path of the Ferris wheel then the angle has swept out 0.5 radians.
b) If Kristin has traveled 45 meters along the path of the Ferris wheel then the angle has swept out 5.625 radians.
c) The formula that expresses the number of radians θ the angle has swept out in terms of the number of meters is θ = s / r.
a. To determine the angle in radians, we can use the arc length formula for a circle. The formula is given by θ = s / r, where θ is the angle in radians, s is the arc length, and r is the radius of the circle.
In this case, Kristin has traveled 4 meters along the path of the Ferris wheel, and the radius is 8 meters.
Thus, the angle swept out is
θ = 4 / 8 = 0.5 radians.
b. Following the same approach, if Kristin has traveled 45 meters along the path of the Ferris wheel, the angle swept out is
θ = 45 / 8 ≈ 5.625 radians.
c. The formula that expresses the number of radians θ the angle has swept out in terms of the number of meters Kristin has traveled since the ride started is given by
θ = s / r,
where θ is the angle in radians, s is the arc length traveled by Kristin, and r is the radius of the Ferris wheel.
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Help meee helppp meee help
what is this answer to these questions no links 30 points
Answer:
do i need to answer them for me or just basically?
1. This is NOT a statistical question since you don't need data or mathematical data, or collection of nothing to come to a conclusion because it's a question for any person in the world and we know it's Donald Trump; we don't need math, collection of data or analysis to know this.
2. This is a statistical question because you need to use math to know this; you need to collect a lot of cupcakes, describe their types and size, you need to analyze and count how many you can eat, and see the results or side effects, you might even have to do this more than one so you can gather all your quantitative to come to a conclusion.
3. This is NOT a statistical question. This is a yes or no question where you can ask anyone in your family if they speak another language, this doesn't require math or gathered data to come to a conclusion; the question would be statistical if it was, "How many people in your family speak another language COMPARED to the other people in your family? This would be an example of a statistical question given this scenario.
helppp plss i need to find the range,mean,mode and median but I don't know how
(1 point) Find the square root of 8-2i so that the real part of your answer is positive. The square root is
The square root of 8 - 2i, with the real part of the answer being positive, is approximately 2.34 + 0.52i.
To find the square root of 8 - 2i, we can represent the complex number in its polar form and then apply the square root operation.
First, we calculate the magnitude (r) and argument (θ) of the complex number 8 - 2i:
Magnitude: |8 - 2i| = √([tex]8^2[/tex] + (-2[tex])^2[/tex]) = √(64 + 4) = √68 = 2√17
Argument: θ = arctan(-2/8) = arctan(-1/4) ≈ -0.24498 radians
Next, we express the complex number in polar form:
8 - 2i = 2√17 * (cos(-0.24498) + isin(-0.24498))
To find the square root, we take the square root of the magnitude and divide the argument by 2:
√(8 - 2i) ≈ √(2√17) * (cos(-0.24498/2) + isin(-0.24498/2))
Simplifying the expression:
√(8 - 2i) ≈ √(2√17) * (cos(-0.12249) + isin(-0.12249))
≈ 2.34 + 0.52i
Therefore, the square root of 8 - 2i, with the real part of the answer being positive, is approximately 2.34 + 0.52i.
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Suppose that you take a sample of 1400 adults and find that 320
work more than 40 hours per week. What is the margin of error?
The calculated value of the margin of error is 0.022
How to calculate the margin of error?From the question, we have the following parameters that can be used in our computation:
Sample, n = 1400
The proportion is calculated as
p = 320/1400
So, we have
p = 0.2286
Next, we calculate the standard error using
E = √[(p * (1 - p)) / n]
So, we have
E = √[(0.2286 * (1 - 0.2286)) / 1400]
Evaluate
E = 0.0112
The margin of error is then calculated using
Margin of Error = z * E
Using z at 95% CI, we have
M = 1.96 * 0.0112
Evaluate
M = 0.022
Hence, the margin of error is 0.022
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