The 95% confidence interval for the average number of units that students in their college are enrolled in is approximately 11.66 to 12.54 units. This means that we are 95% confident that the true population mean lies within this interval.
Here,
To calculate the 95% confidence interval for the average number of units that students in their college are enrolled in, we can use the formula for a confidence interval for a population mean when the population standard deviation is unknown but can be estimated using the sample standard deviation.
The formula for the confidence interval is given by:
Confidence Interval = Sample Mean ± (Critical Value) * (Standard Error)
where:
Sample Mean (x) is the mean of the sample (12.1 units in this case).
Critical Value is the value from the t-distribution corresponding to the desired confidence level and the sample size.
For a 95% confidence level and a sample size of 45, the critical value is approximately 2.013 (you can look this up in a t-table or use a calculator).
Standard Error is the standard deviation of the sample mean, which is calculated as the sample standard deviation divided by the square root of the sample size.
Given the information in the problem:
Sample Mean (x) = 12.1 units
Sample Standard Deviation (s) = 1.5 units
Sample Size (n) = 45
Confidence Level = 95%
Critical Value ≈ 2.013
Now, let's calculate the standard error:
Standard Error = s / √n
Standard Error = 1.5 / √45 ≈ 0.2236
Now, calculate the confidence interval:
Lower bound of the confidence interval:
12.1 - (2.013 * 0.2236) ≈ 11.66
Upper bound of the confidence interval:
12.1 + (2.013 * 0.2236) ≈ 12.54
So, the 95% confidence interval for the average number of units that students in their college are enrolled in is approximately 11.66 to 12.54 units. This means that we are 95% confident that the true population mean lies within this interval.
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A camp program charges a registration fee and a daily amount.
The total bill for 12 days is $338. The total bill for 19 days is
$506. Slope can be represented by cost per day. Use x as the
number of days and y as the total cost to represent this
situation.
a. Find the slope for this situation. What does it represent?
b. Write a linear equation that models this situation.
Using the information given, it is found that:
a) The slope is of 24, which means that for each day, the total bill increases by $24.b) The linear equation is: [tex]y = 24x + 50[/tex]Linear functions:A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.Item a:
The total bill for 12 days is $338.The total bill for 19 days is $506.The slope is given by the change in y(total bill) divided by the change in x(number of days), hence:
[tex]m = \frac{506 - 338}{19 - 12} = 24[/tex]
The slope is of 24, which means that for each day, the total bill increases by $24.
Item b:
The total bill for 12 days is $338, hence, when [tex]x = 12, y = 338[/tex], and this is used to find b.[tex]y = 24x + b[/tex]
[tex]338 = 24(12) + b[/tex]
[tex]b = 50[/tex]
Hence, the linear equation is: [tex]y = 24x + 50[/tex]
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The distance between city a and city b is 200 miles. A length of 1.7 feet represents this distance on a certain wall map. City c and city d are 2.55 feet apart on this map. What is the actual distance between city c and city d
Answer:
510
Step-by-step explanation:
200×2.55=510 this is the answer
23 + 7 + 15 =
Simplify each expression. Justify each step
Type the correct answer in each box.
Consider the expressions shown below.
А.
B
C с
-872
-
3.5 + 4812
3r + 8 8r2 + 3r
4
Complete each of the following statements with the letter that represents the expression.
-
(3x2 7x + 14) + (5x2 + 41 6) is equivalent to expression
(2x2 – 5x – 3) + (-10x2 + 2x + 7) is equivalent to expression
(12t2 – 2x – 13) + (-4x2 + 5x + 9) is equivalent to expression
Answer/Step-by-step explanation:
✔️(3x² - 7x + 14) + (5x² + 4x - 6)
3x² - 7x + 14 + 5x² + 4x - 6 (distributive property)
Add like terms
3x² + 5x² - 7x + 4x + 14 - 6
8x² - 3x + 8
Therefore:
✅(3x² - 7x + 14) + (5x² + 4x - 6) is equivalent to expression 8x² - 3x + 8.
✔️(2x² - 5x - 3) + (-10x² + 2x + 7)
2x² - 5x - 3 - 10x² + 2x + 7 (distributive property)
Add like terms
2x² - 10x² - 5x + 2x - 3 + 7
-8x² - 3x + 4
Therefore:
✅(2x² - 5x - 3) + (-10x² + 2x + 7) is equivalent expression to -8x² - 3x + 4
✔️(12x² - 2x - 13) + (-4x² + 5x + 9)
12x² - 2x - 13 - 4x² + 5x + 9
12x² - 4x² - 2x + 5x - 13 + 9
8x² + 3x - 4
Therefore:
✅(12x² - 2x - 13) + (-4x² + 5x + 9) is equivalent expression to 8x² + 3x - 4
Answer:
B, A, C
Step-by-step explanation:
Someone help me please!
Answer:
ACD
Step-by-step explanation:
PLZZ mark brainliest!!
Answer:
D i think i havent done this in a while
Step-by-step explanation:
Find X for the solution
Step-by-step explanation:
good lucks
3.(06.01 LC) Which point on the scatter plot is an outlier? (5 points) у 70 B 60 50 A 40 30 20 10 0 2 4 6 8 10 12 14 Point A Point B Point C Point D
Answer:
point b
Step-by-step explanation:
What is 21+G as an algebraic expression?
Answer:
i dont know
Step-by-step explanation:
lol
Answer:
(20 + 1) + G
Step-by-step explanation:
please help asap !!! Which of the following points is a solution to the system of equations shown in the graph above?
A.(-2, 1)
B.(0, 0)
C.(0, 3)
D.(1, -2)
Answer:
a
Step-by-step explanation:
Suppose John is a high school statistics teacher who believes that watching many hours of TV leads to lower test scores. Immediately after giving the most recent test, he surveyed each of the 24 students in his class and asked them how many hours of TV they watched that week. He then matched each student's test grade with his or her survey response. After compiling the data, he used hours of TV watched to predict each student's test score. He found the least-squares regression line to be
This question is incomplete, the complete question is;
Suppose John is a high school statistics teacher who believes that watching many hours of TV leads to lower test scores. Immediately after giving the most recent test, he surveyed each of the 24 students in his class and asked them how many hours of TV they watched that week. He then matched each student's test grade with his or her survey response. After compiling the data, he used hours of TV watched to predict each student's test score. He found the least-squares regression line to be y" = -1.5x + 85.
He also calculated that the value of r, the correlation, was -0.61.
what is the correct value of the coefficient of determination R² and give a correct interpretation of its meaning
Answer:
Interpretation of coefficient of determination R² = 0.3721
R² = 0.3721, meaning 37.21% of the total variation in test scores can be explained by the least square regression line
Step-by-step explanation:
Given the data in the question;
the least square regression line is;
y" = -1.5x + 85
the correlation coefficient r = -0.61
Now, the coefficient of determination R² is square of correlation coefficient r
R² = -61²
R² = 0.3721
A sample of radium has a weight of 1.5 mg and a half-life of approximately 6 years.
How much of the sample will remain after 1 year?
Answer:
Step-by-step explanation:
1.5×0.5^(⅙) ≅ 1.3 mg
Nathan needs to order some new supplies for the restaurant where he works. The restaurant needs at least 571 forks. There are currently 361 forks. If each set on sale contains 10 forks, use the drop-down menu below to write an inequality representing
Answer:
Nathan must order 21 sets of forks for the restaurant.
Step-by-step explanation:
Since Nathan needs to order some new supplies for the restaurant where he works, and the restaurant needs at least 571 forks since there are currently 361 forks, if each set on sale contains 10 forks, to determine the number of sets to buy you must perform the following calculation:
(571 - 361) / 10 = X
210/10 = X
21 = X
So Nathan must order 21 sets of forks for the restaurant.
Which expression is equivalent to 7u+4u?
Answer:
11u
Step-by-step explanation:
Add 7u and 4u
Hope this helps! :)
Identifying a binomial experiment In a study conducted by the sponsoring organization of an academic conference, attendees were classified during registration into one of three categories according to their field of interest: General, Applied, or Theoretical. Of the 400 people in attendance, 200 were classified as General, 60 were classified as Applied, and 140 were classified as Theoretical. You randomly select three registration cards (with replacement) of attendees of the conference and record their fields of interest.
This experiment _________ binomial experiment.
When you select a registration card, the probabilities associated with each outcome are:
Outcome Probability
General 0.35
Applied 0.45
Theoretical 0.20
binomial random variable with mean E(X) = and Let X be the number of card selections with outcome "General." Then X is a standard deviation o =________
Answer:
1, this is a binomial experiment.
Step-by-step explanation:
this is a binomial experiment. Since it is general outcome, the probability of success is 0.50, that is 50 percent.
we have that X follows the binomial distribution
X ~ Binomial(n = 3, p = 0.50)
we have 3 outcomes( general, applied, theoretical).
mean = E(X)
= np
= 3(0.5)
= 1.5
standard deviation = σ = √np(1-p)
= √3(0.5)(1-0.5)
= √1.5(0.50)
= √0.75
= 0.8660
the mean = 1.5
the standard deviation = 0.8660
An automobile manufacturer claims that its van has a 40.3 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 250 vans, they found a mean MPG of 39.9. Assume the standard deviation is known to be 2.4. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to 2 decimal places.
Answer:
The value of the test statistic is -2.64.
Step-by-step explanation:
The test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the expected(claimed) mean, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
An automobile manufacturer claims that its van has a 40.3 miles/gallon (MPG) rating.
This means that [tex]\mu = 40.3[/tex]
After testing 250 vans, they found a mean MPG of 39.9. Assume the standard deviation is known to be 2.4.
This means, respectively, that:
[tex]n = 250, X = 39.9, \sigma = 2.4[/tex]
So
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{39.9 - 40.3}{\frac{2.4}{\sqrt{250}}}[/tex]
[tex]t = -2.64[/tex]
The value of the test statistic is -2.64.
Helllllllpppppp please help me
Answer:
i think maybe j that is what I think
g^4+ 5h
when g=2 & h=4
Answer: 36
Step-by-step explanation:
g^4+5h
2^4+5(4)
16+20
36
Extra Points and brainliest! Question below
Answer:
14 one fourths
Step-by-step explanation:
First, we convert 7/2 into a fraction with the denominator of a four. To do this, we multiply the top and bottom by 2. 7*2 is 14, and 2*2 is 4, which gives us 14/4. This means that there are 14 one fourths in 7/2. Hope this helps!
Answer:
14 fourths
Step-by-step explanation:
Hey There!
So to solve this problem we need to divide 7/2 by 1/4
[tex]\frac{7}{2}divided by\frac{1}{4} =14[/tex]
Therefore 14 fourths can go into 7/2
HELP ASAP WHAT IS THIS ANSWER
Answer:
Step-by-step explanation:
x = 1/2 ( a + b)
x = 1/2 (129 + 71)
x = 1/2 (200)
x = 100 °
you just have to remember that formula
A checking account contains 6,274.54.how much is left after withdrawing $385.79
Answer:
$5888.21
Step-by-step explanation:
when you see the words withdrawing remember that u always are subtracting so the equation will be 6274.54 - 385.79.
Can you help me on question 12?!
Answer:
A) 8/27
Step-by-step explanation:
(2/3)³ = 8/27
Find the length of the third side. If necessary, round to the nearest tenth
Answer:
x=14.28
Step-by-step explanation:
24^2+x^2=28^2, Pythagorean theorem
x^2=28^2-24^2
x^2=(28+24)(28-24)
x^2=52*4
x^2=204
x is around 14.28
Which figure could be the result of dilating this triangle with a scale factor greater than 1? On a coordinate plane, a triangle has points (0, 0, (0, 3), (6, 0). On a coordinate plane, a triangle has points (0, 0), (0, 3), (9, 0). On a coordinate plane, a triangle has points (0, 0), (0, 1), (6, 0). On a coordinate plane, a triangle has points (0, 0), (0, 5), (10, 0). On a coordinate plane, a triangle has points (0, 0), (0, 2), (4, 0).
Answer:
C
Step-by-step explanation:
Edge
The required figure has been attached below could be the result of dilating a given triangle with a scale factor greater than 1. The correct answer would be an option (C).
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The triangle has points (0, 0), (0, 3), and (6, 0) which are given in the question.
As per option (C), we have
On a coordinate plane, a triangle has points (0, 0), (0, 5), and (10, 0).
This result of dilating a given triangle with a scale factor greater than 1.
The required figure has been attached below which represents the dilation.
The correct answer would be an option (C).
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10) Julio rented a bike from Bill's Bikes. It
cost $20 plus $6 per hour. If Julio paid
$50, then he rented the bike for how many
hours?
what is the volume if this rectangular prism
Answer:
24.2^3cm is the correct answer .
Lori has $450 in her bank account. She withdraws $20 a month for
her gym membership. Construct a linear equation to model Lori’s
bank balance for any given month.
Answer:
I cant give you a linear graph but i can give you the equation and you can graph it. y=20x+450
Step-by-step explanation:
Answer:
Y = -20x + 450.
Step-by-step explanation:
What is the value of p when the expression 2(4 + x) is equivalent to 2(x + p)?
Answer:
p = 4
Step-by-step explanation:
[tex]2(x+p)=2(4+x)\\x+p=4+x\\p=4[/tex]
......................
Answer:
[tex]-1/x^2[/tex]
Step-by-step explanation:
First, let's simplify the expression on the right:
[tex]1/\sqrt{x^2}=1/x[/tex]
Next, rewriting 1/x as x⁻¹, we can use the power rule to differentiate both sides with respect to x:
[tex]y=x^{-1}\\dy/dx=d/dx(x^{-1})\\dy/dx=-x^{-2}=-1/x^2[/tex]
Write the percent as a fraction or mixed number in lowest term 74 3/8%
Answer:
222/2 = 111
8/2 = 4
74 /1
Step-by-step explanation:
Help me pls i don't got a lot of time
Answer:
true
Step-by-step explanation:
I swear I know
i know it