The 95% confidence interval estimate of the mean wake time is equal to (62.61, 88.39).
Given the following data:
Mean wake time = 75.5 min.Standard deviation = 24.2 min. Number of sample, n = 16.How to construct a 95% confidence interval?Mathematically, a confidence interval of 95% is given by;
α = 1 - 0.95
α = 0.05.
α/2 = 0.05/2 = 0.025.
Also, the degrees of freedom (df) is given by:
Degrees of freedom (df) = n - 1
Degrees of freedom (df) = 16 - 1
Degrees of freedom (df) = 15.
From the Student's t-distribution table, a critical value at t₀.₀₂₅, ₁₅ = 2.131.
Mathematically, the confidence interval for mean is given by:
Mean ± (t-critical × (standard deviation/√(sample size)))
75.5 ± (2.131 × (24.2/√(16))
75.5 ± (2.131 × 6.05)
For the upper end, we have:
75.5 + 12.89 = 88.39
For the lower end, we have:
75.5 - 12.89 = 62.61.
In conclusion, we can deduce that there isn't a significant difference between the mean wake time before and after treatment and as such, this drug isn't effective at the significance level of 0.05.
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A rectangular deck has a length of 12 feet and a perimeter of 36 feet. What is the deck's width and area?
Answer:
Deck's width is 6 feet.The area is 72 sq. ft.Step-by-step explanation:
First, label it out:
Length: 12 ft.Width: ?Area: ?Perimeter: 36 ft.Then, we add up 12 twice (Since the length is on 2 sides):
12 + 12 = 2436 - 24 = 1212 - ? = ?Now, we write down a 6 in the ?:
12 - 6 = 6.Width = 6.
We are not done!
Now, we have to solve for area.
12 * 6= 72Answers are:Area = 72 sq. ft.Width = 6 ft.The diameter of a semicircle is 6 kilometres. What is the semicircle's radius?
Answer:
3km
Step-by-step explanation:
d = 2r so r = 1/2 * d = 1/2 * 6 = 3km
6x³ + 3x
how do you factor out the GCF in this question??
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We are asked to factor out the GCF in the expression
[tex]\star~\star\mathrm{6x^3+3x}~\star~\star[/tex]
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Divide every single term of the expression by the GCF (Greatest Common Factor).So let's divide.
But first. we should work out the GCF.
Both terms have 3x in common, so we divide both terms by 3x:
[tex]\mathrm{6x^3+3x}[/tex]
[tex]\mathrm{3x(2x^2+1)}[/tex]
To ensure that we've factored correctly, we can always use the distributive property, distribute 3x and see whether or not we end up with [tex]\mathtt{6x^3+3x}[/tex].
So the answer is
[tex]\mathrm{3x(2x^2+1)}[/tex]
Notice I put parentheses around 2x²+1. This indicates that 3x is multiplied times both 2x² and 1.
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A small plane flew 808 miles in 4 hours with the wind. Then on the return trip flying against the wind it travels only 488 miles in 4 hours. What were the wind velocity and speed of the plane?
Answer:
Step-by-step explanation:
let wind velocity=x
speed of plane=y
(x+y)*4=808
x+y=808/4=202 ...(1)
(y-x)*4=488
y-x=122 ...(2)
add (1) and (2)
2y=202+122=324
y=324/2=162
from (1)
x+162=202
x=202-162=40
wind velocity=40 m/hr
speed of plane=162 m/hr
PLEASE HELP!!! DSFVAGETRYHUJ
Answer: Remeber 2+2=5 and
Step-by-step explanation: if yur on fire stop drop and roll do it and your awesome. Another thing is if someones taking forever drinking water when your behind them sing 123 can you hurry up please 456 imma hit you with a brick 789 imma spit this sick ryme
Which statements describe one of the transformations performed on f(x) = x^2 to create g(x) = (x - 2)^2 + 5? Choose all that apply.
A. A translation of 5 units up
B. A translation of 2 units to the right
C. A translation of 2 units to the left
D. A translation of 5 units down
Verify that (cos²a) (2 + tan² a) = 2 - sin² a....
Trigonometric Formula's:
[tex]\boxed{\sf \ \sf \sin^2 \theta + \cos^2 \theta = 1}[/tex]
[tex]\boxed{ \sf tan\theta = \frac{sin\theta}{cos\theta} }[/tex]
Given to verify the following:
[tex]\bf (cos^2a) (2 + tan^2 a) = 2 - sin^2 a[/tex]
[tex]\texttt{\underline{rewrite the equation}:}[/tex]
[tex]\rightarrow \sf (cos^2a) (2 + \dfrac{sin^2 a}{cos^2 a} )[/tex]
[tex]\texttt{\underline{apply distributive method}:}[/tex]
[tex]\rightarrow \sf 2 (cos^2a) + (\dfrac{sin^2 a}{cos^2 a} ) (cos^2a)[/tex]
[tex]\texttt{\underline{simplify the following}:}[/tex]
[tex]\rightarrow \sf 2cos^2 a + sin^2 a[/tex]
[tex]\texttt{\underline{rewrite the equation}:}[/tex]
[tex]\rightarrow \sf 2(1 - sin^2a ) + sin^2 a[/tex]
[tex]\texttt{\underline{distribute inside the parenthesis}:}[/tex]
[tex]\rightarrow \sf 2 - 2sin^2a + sin^2 a[/tex]
[tex]\texttt{\underline{simplify the following}} :[/tex]
[tex]\rightarrow \sf 2 - sin^2a[/tex]
Hence, verified the trigonometric identity.
Answer:
See below ~
Step-by-step explanation:
Identities used :
⇒ cos²a = 1 - sin²a
⇒ tan²a = sin²a / cos²a
============================================================
Solving :
⇒ (cos²a) (2 + tan² a)
⇒ 2cos²a + (cos²a)(tan²a)
⇒ 2(1 - sin²a) + sin²a
⇒ 2 - 2sin²a + sin²a
⇒ 2 - sin²a [∴ Proved √]
please help me fast write the answer in picture
Step-by-step explanation:
hope you can understand
Based on past experience, a building contractor sets the
probability of winning a contract at 0.10. The contract is
worth $75,000 and the cost to prepare the contract proposal
is $10000. What is the expected value of the contract
proposal?
A. $2500
B. $22600
C. $22600
D. $2500
Based on the cost of the contract and the probability to win it, the total expected value of the contract proposal is -$2500.
How to calculate the expected value of a contract proposal?The general formula to calculate the expected value is:
Expected value: possibility of winnind the contract x the amount when winning - possibility of loing the contract x possible lossPossibility of winning the contract= 0.10Possibility of losing the contract = 0.90Gain: $65000Loss: $10000What is the expected value of the contract?Expected value: 0.10 x 65000 - 0.90 x 10000Expected value: 6500 - 9000Expected value: -$2500Learn more about contract in: https://brainly.com/question/2669219
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City there are 244,000 48-year-olds. Based on the table below how
many are not expected to be alive in a year?
Answer:
405
Step-by-step explanation:
It tells in the table.
A point that is exterior to an angle is found on the acute side of the angle. true of false?
A point that is exterior to an angle is found on the acute side of the angle which is true.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
We know that the sum of the exterior angle and interior angle is equal to 180 degrees.
"If one of the exterior angles is an acute angle, then the corresponding interior angle is an obtuse angle."
A point that is exterior to an angle is found on the acute side of the angle which is true.
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interest on 2000 at 10% per 4years
Answer:
2,800
A = 2000(1 + (0.1 × 4)) = 2800
A = $2,800.00
Find the rule, and type the missing number in the sequence.
96, 192, ____, 384
Answer:
Missing number is 288, and the rule is +96
Step-by-step explanation:
First subtract 96 from 192, which is 96
then add that to 192 and the missing value is 288
you should also add 96 to 288 just to make sure it gets you to the last number which is 384.
WHAT IS THE VOLUME HELPPP!!!!!
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's find the volume of the given figure ~
[tex]\qquad \sf \dashrightarrow \:Volume_{(cuboid)}= length \cdot width \cdot height [/tex]
[tex]\qquad \sf \dashrightarrow \:Volume_{(cuboid)}= 4 \cdot x \cdot x [/tex]
[tex]\qquad \sf \dashrightarrow \:Volume_{(cuboid)}= 4 {x}^{2} [/tex]
So, the correct choice is ~ C
Volume
LBH4(x)(x)4x²Option C
Find the area of a regular
polygon with 8 sides that has a
the side length of 4 inches and an
apothem of 5 inches.
Area = [?]in2
Answer:
80 in²
Step-by-step explanation:
When side length and apothem of a regular polygon are given, the applicable area formula is ...
A = 1/2Pa
where P is the perimeter of the polygon, and 'a' is its apothem.
__
The perimeter of a regular 8-sided polygon will be 8 times the side length, so the area is ...
A = 1/2(8×4 in)(5 in) = 80 in²
The Father of the Bride flips out when he realizes that the hot dogs and buns don't
match. There are 8 hot dogs in a package and 12 buns in a package. How many
packs of hot dogs and how many packs of buns do you need to purchase in order to
have the exact same number of each?
Using the least common multiple, it is found that you need to buy 3 packs of hot dogs and 2 packs of buns to have the exact same number of each.
How to find the number of packs needed?First, we need to find the total number of each element, finding the least common multiple of the sizes of each package, that is, 8 and 12.
The lcm is found factoring them by prime factors, hence:
8 - 12|2
4 - 6|2
2 - 3|2
1 - 3|3
1 - 1
Hence, lcm(8,12) = 2³ x 3 = 24.
Then:
24/8 = 3.24/12 = 2.Which means that you need to buy 3 packs of hot dogs and 2 packs of buns to have the exact same number of each.
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Situation:
Tina wants to save money for school.
Tina invests $400 in an account that
pays an interest rate of 8%.
A = P(1+r)¹
P= amount of money invested
r = interest rate percentage in decimal form
t = time in years
A = total money in the account at timet
How many years will it take for the account to
reach $5,500? Round your answer to the nearest
hundredth.
Enter the correct answer.
DONE
It will take 4 year for the account to reach $5,500.
How to find the amount?The formula we use to calculate the amount is
A = P(1+r)¹
Where, P= amount of money invested
r = interest rate percentage in decimal form
t = time in years
A = total money in the account at time
Tina wants to save money for school.
Tina invests $400 in an account that pays an interest rate of 8%.
A = P(1+r)¹
5500 = 400(( 1 + 0.08)^t
5500/ 400 = ( 1 + 0.08)^t
55/ 4 = (1.08)^t
13.75 = (1.08)^t
t = 4
It will take 4 year for the account to reach $5,500.
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1
Select the correct answer.
Can triangle A be mapped onto triangle B using rigid transformations?
B
A
Answer: A
Step-by-step explanation:
Since the triangles are congruent by HL, we know that there is a sequence of rigid motions.
By inspection, we know this sequence involves rotating triangle A 90 degrees clockwise and then translating it right.
if1(2) at the level 20= 0.94770 and 1(2) at the level 21= 096020 find the required level of mortality for the estimated value of 1(2)* =0.95656.
Answer:
Step-by-step explanation
Sorry but your answer is a fake question which I can't answer
This list shows the age at which 43 U.S. Presidents began their terms.
57
61
50
54
54
54
56
54
61
54
48
49
42
51
61
57
68
65
50
51
60
52
57
51
52
47
56
62
69
58
49
56
55
55
43
64
57
64
46
55
51
55
46
Before you can make a frequency table, you need to decide how to set up the age intervals. What is the BEST way to group these ages into six intervals?
a.
Age of Start Term. 20 to 30, 30 to 40, 40 to 50, 50 to 60, 60 to 70, 70 to 80.
c.
Age of Start Term. 40 to 44, 45 to 49, 50 to 54, 55 to 59, 60 to 64, 65 to 69.
b.
Age of Start Term. 20 to 29, 30 to 39, 40 to 49, 50 to 59, 60 to 69, 70 to 79.
d.
Age of Start Term. 40 to 45, 45 to 50, 50 to 55, 55 to 60, 60 to 65, 65 to 70.
Please select the best answer from the choices provided
A
B
C
D
The best intervals would be 41-45, 46-50, 51-55, 56-60, 61-65, and 69-70.
The best way to decide the appropriate interval would be to find the range of the numbers.
We have given a data set,
What is the smallest value in the data?The minimum is the smallest value in the data set. The maximum is the largest value in the data set.
What is the largest minus the smallest?This would be 69-42=27.
If you need six intervals you would need to round 27 up to 30 to be able to divide it out evenly and include all of the data.
The best intervals would be 41-45, 46-50, 51-55, 56-60, 61-65, and 69-70.
This way you are one over and one under the highest and lowest values.
Therefore, The best intervals would be 41-45, 46-50, 51-55, 56-60, 61-65, and 69-70.
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Is √13 + 4 rational or irrational?
Answer:
irrational
Step-by-step explanation:
what are rational numbers ?
every number that can be expressed as a/b, with a and b being integer numbers, and b different to 0.
the square root of any number that is not a squared rational number is then an irrational number.
I am not sure, if the expression here is
sqrt(13) + 4
or
sqrt(13 + 4), which would then be sqrt(17).
but in both cases we are creating the square root of a not- squared rational number.
neither 13 nor 17 are the result of a multiplication of a rational number with itself.
in fact, 13 and 17 are prime numbers with no other factors than either 1 or themselves.
so, both, sqrt(13) and sqrt(17) are irrational numbers.
adding or subtracting rational numbers to irrational numbers result again in irrational numbers.
Hi student, let me help you out! :)
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We are asked to find out if [tex]\pmb{\sqrt{13} +4}[/tex] is rational or irrational.
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Irrational numbers cannot be expressed as fractions (in [tex]\pmb{\cfrac{p}{q}}[/tex] form).So, can we write [tex]\pmb{\sqrt{13} +4}[/tex] as a fraction? We can write 4 as a fraction, but we cannot write [tex]\pmb{\sqrt{13}}[/tex] as a fraction, because this number has infinitely many digits after the decimal point, and they never repeat; there's no pattern at all!
And even if we add 4, which is a rational number, to [tex]\pmb{\sqrt{13}}[/tex], we'll still get an irrational number.
Thus, [tex]\pmb{\sqrt{13}+4}[/tex] is irrational.
Hope it helps you out! :D
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which choices are in the solution set of the equation below check all that apply 4x=30
The choice in the solution set of the equation 4x = 30 is x = 7.5
How to determine the solution set?The equation is given as:
4x = 30
Divide both sides of the equation by 4
4x/4 = 30/4
Evaluate the quotients
x = 7.5
Hence, the choice in the solution set of the equation 4x = 30 is x = 7.5
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For questions 1 and 2, multiple answers may be selected
1. Circle the data that represents discrete data: The weight of cows The number of books in your apartment The color of your hair The ounces of water that you drink each day.
2. Circle the data that represents continuous data: The weight of cows The number of books in your apartment The color of your hair The ounces of water that you drink each day
The discrete data is (b) while the continuous data are (a) and (d)
What are discrete data?These are data that can be represented using positive whole numbers.
Using the above definition as a guide, the discrete data is (b) The number of books in your apartment
What are continuous data?These are data that can be represented using decimal numbers.
Using the above definition as a guide, the continuous data are (a) The weight of cows and (d) The ounces of water that you drink each day
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please answer asap!!!
A timer is started and a few moments later a swimmer dives into the water and then comes back up. The swimmer's depth (in feet) as
a function of time (in seconds after the timer was started) is given by the equation h(x) = ² - 14t+40.
4
Rewrite the formula in factored form and select each true statement below.
The swimmer dives to a depth of 14 feet.
The swimmer dives into the water 4 seconds after the timer was started.
The swimmer dives to a depth of 40 feet.
The swimmer comes back up 10 seconds after the timer was started.
The swimmer comes back up 40 seconds after the timer was started.
The true statement about the equations include:
The swimmer dives to a depth of 14 feet.The swimmer comes back up 10 seconds after the timer was started.How to solve the equation?The equation given is h(t) = t² - 14t + 40. We'll factorize to get the value of t. This will be:
= t² - 14t + 40
= t² - 10t - 4t + 40
= t(t - 10) - 4(t - 10)
(t - 10) = 0.
t = 0 + 10
t = 10
In this case, the swimmer dives to a depth of 14 feet and then comes back up 10 seconds after the timer was started.
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Answer:
The swimmer comes back up 10 seconds after the timer was started.
The swimmer dives into the water 4 seconds after the timer was started.
Step-by-step explanation:
The guy above me ruined my test score, thanks.
Best of luck to all who find this
These are the correct answers
As a preliminary measure, you want to review only the top 25% of applicants on the basis of of standardized test scores. How does calculating the z-score provide additional information regarding how each subject did overall. Provide specific examples of how you would use the information and interpret the scores
Calculating the z-score provides additional information regarding how each subject did overall as the z-score takes dispersion into account.
What is a z score?Z-score indicates how much a given value differs from the standard deviation. For example, the mean of a test could be a 73 and if a student scored an 85, that's great.
However, if the data is not spread out, that 85 could be the highest in the class by 10 points. That's much more information than just 15 points above the mean. This way you can tell when someone not only did well but did exceptionally well in comparison to his or her peers.
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Which number line shows the solution set for 1h-21 = 4?
Answer: Option 2
Step-by-step explanation:
[tex]|h-2|=4\\\\h-2=\pm 4\\\\h=-2, 6[/tex]
There are 10000 people living in a certain city. Suppose that the rate of population growth in the city is proportional to the number of inhabitants. Suppose that 10% of the original amount increase in 30 years, how much will the population in the city after 60 years?
Answer:
.............30000.............
What are two points on the line
Answer:
(0, 3) (3, 0)
03 - Describe the set S = {x : | ½x − 3| > 4} in terms of intervals.
Answer:
Hi,
Step-by-step explanation:
a)
[tex]if\ \dfrac{x}{2}-3\ > \ 0\ then\ |\dfrac{x}{2}-3|=\dfrac{x}{2}-3\\\\\dfrac{x}{2}-3 > 4\\\\\dfrac{x}{2} > 7\\\\x > 14\\[/tex]
b)
[tex]if\ \dfrac{x}{2}-3\ < \0 \ then\ |\dfrac{x}{2}-3|=-(\dfrac{x}{2}-3)=-\dfrac{x}{2}+3\\\\-\dfrac{x}{2}+3\ > \ 4\\\\-\dfrac{x}{2}\ > \ 4-3\\\\-\dfrac{x}{2}\ > \ 1\\\\\dfrac{x}{2}\ < \ -1\\\\x\ < \ -2\\[/tex]
[tex]S=\{x\in\mathbb{R}\ :\ |\dfrac{x}{2}-3|\ > \ 4\}=(-\infty,-2[\ \cup\ ]14,\infty)\\[/tex]
Daryl was prescribed 14 antibiotic take one tablet daily for 14 days there's 8 pills left what fraction of the prescription has he taken
Answer:
3/7
Step-by-step explanation:
He took 6 out of 14 so that is 6/14 then simplify it to 3/7