. Construct and Interpret a 95% confidence level. 5 poin One study claims students get 8 hours of sleep a night, on average. One professor asks a random sample of 32 students, "How much sleep did you get last night?" Here are the data in hours) 9 6 6 7.5 6 6 5 8.5 6 5.5 6.5 6 4 8 6 6.5 7 7 4 4.5 3 6 5 7 10 8 9 7 7 9
Answers
Using a mean and standard deviation calculator we can see that
\(\text{ the sample mean }\bar{x}=6.75\)\(\text{ the sample standard deviation }s=1.8184\)We now calculate the standard error
\(\begin{gathered} \text{ standard error }=\frac{s}{\sqrt[]{n}} \\ \text{Where} \\ s=\text{ the sample standard deviation} \\ n=\text{ the sample size} \end{gathered}\)In this case,
n = 32,
\(\text{standard error = }\frac{1.8184}{\sqrt[\square]{32}}=\text{ 0.3215}\)We now calculate the critical probability p*
\(\text{ critical probability }=1-\frac{\alpha}{2}\)\(\begin{gathered} \alpha=0.05 \\ \text{ Therefore} \\ \text{ critical probability }=1-\frac{0.05}{2}=0.975 \end{gathered}\)Next, we find the degree of freedom df
\(df=32-1=31\)We can now find the critical value. The critical value is the t value having degrees of freedom equal to df and a cumulative probability equal to the critical probability (p*).
Using a t-score calculator, we find that the critical value is 2.040
We will now find the margin of error (ME)
\(\begin{gathered} ME\text{ = critical value x stansard error} \\ ME\text{ = }2.040\text{ x }0.3215\text{ = 0.6559} \end{gathered}\)confidence interval is = mean
\(\text{confidence interval = mean}\pm\text{ margin of error= }6.75\pm0.6559\text{ }\)Confidence interval is (6,75-0.6559, 6,75+0.6559)
Confidence interval is (6.0941, 7.4059).
This means that the professor is 95% certain that the average hour of sleep of each student falls within the interval (6.0941, 7.4059).
Related Questions
what is the simplified form of (2-^6)(5)(2^3x5)^2
Answers
Answer:
\(( {2}^{ - 6} )(5)( {2}^{3} \times 5) {}^{2} \\ \\ = 2 {}^{( - 6 + (3 \times 2))} \times {5}^{(1 + 2)} \\ \\ = {2}^{0} \times {5}^{3} \\ \\ = 1 \times {5}^{3} \\ \\ = {5}^{3} \)
Write the standard equation of the circle with the center (-14,-5) that passes through the point (-7,5).
Answers
equation: (x + 14)² + (y + 5)² = 149
Given:
centre : (-14,-5)point (-7,5)=============
Formula's:
(x-h)² + (y-k)² = r²centre : (h, k)radius : rdistance between points : \(\sf \sqrt{(x2-x1)^2 + (y2-y1)^2}\)Find the radius:
\(\rightarrow \sf \sqrt{(-7-(-14))^2 + (5-(-5))^2}\)
\(\sf \rightarrow \sqrt{\left(-7+14\right)^2+\left(5+5\right)^2}\)
\(\sf \rightarrow \sqrt{149}\)
Equation of circle:
(x-h)² + (y-k)² = r²(x-(-14))² + (y-(-5))² = (√149)²(x + 14)² + (y + 5)² = 149Graph for clarification:
Answer:
\(\sf (x+14)^2+(y+5)^2=149\)
Step-by-step explanation:
Standard equation of a circle: \(\sf (x-a)^2+(y-b)^2=r^2\)
(where (a, b) is the center and r is the radius of the circle)
Substitute the given center (-14, -5) into the equation:
\(\sf \implies (x-(-14))^2+(y-(-5))^2=r^2\)
\(\sf \implies (x+14)^2+(y+5)^2=r^2\)
Now substitute the point (-7, 5) into the equation to find r²:
\(\sf \implies ((-7)+14)^2+(5+5)^2=r^2\)
\(\sf \implies (7)^2+(10)^2=r^2\)
\(\sf \implies 149=r^2\)
Final equation:
\(\sf (x+14)^2+(y+5)^2=149\)
(i) Write the zeroes of the polynomial by using above graph.
(ii)Form a quadratic polynomial for above graph.
(iii)If a,1/a are the zeroes of polynomial 2x² -x +8k, then find the value of k.
please answer
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Answers
There is no real Value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.
(i) Zeroes of the polynomial:
In the graph, we have two points where the curve intersects the x-axis: one is at (-1,0), and the other is at (2,0).The corresponding values of x are -1 and 2, and they are the zeros of the polynomial. Therefore, the zeros of the polynomial are -1 and 2.(ii) Forming the quadratic polynomial:
From the graph, we can observe that the curve intersects the y-axis at the point (0,5), implying that the constant term of the polynomial is 5.
We can use the formula to find the quadratic polynomial if we have two zeros and one constant term. Thus, the quadratic polynomial is given by:(x + 1)(x - 2) = x² - x - 2x + 2 = x² - 3x + 2. Therefore, the quadratic polynomial is x² - 3x + 2.(iii) Value of k if a, 1/a are the zeroes of the polynomial 2x² - x + 8k:
We know that a and 1/a are the zeroes of the polynomial 2x² - x + 8k. Therefore, we can find the sum and product of the roots and use them to determine the value of k.
The sum of the roots is a + 1/a, and their product is a(1/a) = 1. Using the sum and product of the roots, we can write: a + 1/a = 1/2 (1/2 is the coefficient of x)Substituting a with 1/a in the above equation, we get: 1/a + a = 1/2Multiplying both sides of the equation by 2a, we get: 2 + 2a² = a
Simplifying the equation, we get: 2a² - a + 2 = 0Multiplying both sides by 2,
we get: 4a² - 2a + 4 = 0Dividing both sides by 2, we get: 2a² - a + 2 = 0
Using the quadratic formula, we get: a = [1 ± √(1 - 4(2)(2))]/(2(2))
Simplifying, we get: a = [1 ± √(-31)]/4Since the discriminant of the quadratic formula is negative, the roots are imaginary. Therefore, there is no real value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.
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Evaluate the expression x + 23, when x = 17
Answers
Answer:
40
Step-by-step explanation:
If we have to evaluate an expression, we spsolve for whatever variable there is, and simplify. Here, we know x is 17, so we can plug it into the original expression.
17 + 23 = 40
Which of the following shows a 90° counterclockwise rotation of the blue figure
Answers
Which graph has the same end behavior as f (x) = StartFraction negative 6 x Superscript 5 Baseline minus x cubed + 7 x Over 2 x squared + 1 EndFraction
Answers
The graph with the same end behavior is the one in option C.
Which graph has the same end behavior?The given function has a numerator with a negative leading coefficient and an odd degree, while the denominator is a quadratic polynomial.
It will mean that as x tends to negative infinity, the function tends to infinity, and as x tends to positive infinity, the function tends to negative infinty, that is the end behavior of the given function.
The graph with that end behavior is the same one than in option C.
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please answer! giving brainliest
Answers
Answer:
d .
x=11
Step-by-step explanation:
ML and JK are chords of the circle
MN*LN=JN*KN
(x-7)*(x+21)=(x+5)*(x-3)
x^2+21x-7x-7*21=x^2-3x+5x-5*3
x^2+14x-147=x^2+2x-15
x^2-x^2+14x-2x=147-15
12x=132
x=132/12=11
When defining a topic for an informative essay, what's the first question you must ask yourself?
O How long should my essay be?
O What do I want to write about?
O Where does my essay take place?
O When do I want to begin my essay?
Answers
The Simple interest on $160
for 6 month's at 5% per
annum
Answers
Answer:4$
Step-by-step explanation:
How do I turn 2/19 into a %
Answers
ANSWER
2/19 = 10.53%
EXPLANATION
To turn a fraction into a percentage we have to multiply the fraction by 100:
\(\text{ \%}=\frac{2}{19}\times100\approx10.53\text{ \%}\)(rounded to the nearest hundredth)
Josh used 3 packages of spaghetti to make dinner for 19 guests. How much did
each guest have?
Answers
Answer:
6.3
Step-by-step explanation:
19/3=6.3 repeating so i just shortened it to 6.3.
final answer: 6.3
Is (–3, –2) a solution to the equation y = x + –1?
Answers
Answer:
No.
Step-by-step explanation:
We plug in the coordinates and that gives us -2=-3+-1, that is not true, therefore your answer is no.
Brainliest would be appreciated! :-)
Suppose this hose reel system were used to model a DNA molecule, a
chromosome, and a gene.
Which part of the model would best represent a gene?
A. The handle that turns the reel
B. The entire length of hose
C. The reel holding the coiled-up hose
D. A specific section of the hose
W
Answers
The correct answer is option B.
The entire length of hose
What is a Hose ?Since the early 17th century, primrose and cowslip have been cultivated as Hose in Hose mutants, which exhibit strong homeotic sepal to petal conversion. The S locus, which regulates floral heteromorphy in Primula species, is linked to the phenotypic, which exhibits varying penetrance and expressivity. Here, we show that the primrose B-function MADS box genes PvDef and PvGlo are upregulated in the first floral whorl in association with the homeotic conversion of sepals to petals in Hose in Hose. We have found and characterized a retrotransposon insertion in the PvGlo promoter that is connected to the up-regulated expression of PvGlo, as well as a restriction fragment length polymorphism linked with PvGlo that cosegregates with the Hose in Hose phenotype.
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For the question of total area of the cuboid is 200cm^.
I understand where we divide 150 by 4.
But why do I need to multiply by 5, when there are 6 faces.
Answers
You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.
When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.
A cuboid has six faces, but each face has a pair that is identical in size and shape.
Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.
To find the surface area of a cuboid, you can add up the areas of all its faces.
However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:
(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.
By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.
Essentially, you are considering one face from each pair and then summing their areas.
Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.
When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.
Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.
Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.
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identify which equations have one solution, infinitely many solutions, or no solution 3u+40+2u=6u-30-u
Answers
Answer:
I did the math there is no answer
Graph h(x)=3cos(2x)−1.
Use 3.14 for π.
Answers
Step-by-step explanation:
the answer is in the attachment
Answer:
The right answer is in yellow.
Step-by-step explanation:
Took the quiz :)
the doubling period of a bacteria culture is 15 minutes initially the culture has 5000 bacteria determine the number of bacteria there will be after 1.5 hours
Answers
The number of bacteria after 1.5 hours is 320,000.
Given,
The doubling period of a bacteria culture is 15 minutes.
Initially, the culture has 5000 bacteria.
We need to determine the number of bacteria there will be after 1.5 hours.
We have,
The number of bacteria gets double every 15 minutes.
Number of bacteria at initial stage = 5000
In 1.5 hours we have 90 minutes.
1.5 hours = 1 hour and 30 minutes
1 hour = 60 minutes
1.5 hours = 90 minutes.
In 90 minutes we have 6 times 15 minutes.
First 15 minutes,
The number of bacteria would be = 2 x 5000 = 10,000
Now next 15 minutes,
10,000 x 2 = 20,000
Next 15 minutes,
20,000 x 2 = 40,000
Next 15 minutes,
40,000 x 2 = 80,000
Next 15 minutes,
80,000 x 2 = 160,000
Next 15 minutes,
160,000 x 2 = 320,000
We can also write it as 5000 x 2^6 = 320,000
Thus the number of bacteria after 1.5 hours is 320,000.
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please help on this question i give brainliest
Answers
Answer:
1. 9 bounds of carbon dioxide
2. 27 bounds of carbon dioxide
Step-by-step explanation:
So let's find a unit rate: 1 to 9
"Why is it 1:9?"
If I can find divide 72 pounds into 8 hours? What would I find? You would find the pounds for each other
Example: 72/8=9. So If 9 carbon dioxide per hour. I can do 3 hours is 27 pounds of carbon dioxide.
So to sum it up, 72/8=9 so 1:9 can be used to figure out any amount of pounds used in a certain number of hours. So If 3 hours, then 27 pounds.
Answer:
1. 9 pounds of carbon dioxide
2. 27 pounds of carbon dioxide
Step-by-step explanation:
Well, I just know it.
Which ordered pairs make both inequalities true? Select two options.
y One-halfx + 1
On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (negative 2, 0) and (0, 1). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, negative 3) and (0, 2). Everything to the right of the line is shaded.
(–1, 3)
A. (0, 2)
B. (1, 2)
C. (2, –1)
D. (2, 2)
Answers
Answer:
d
Step-by-step explanation:
i took the test
Answer:
I just did this test, its 1,2 and 2,2
Step-by-step explanation:
If the slope between the points (-5,7) and (4,x) is 1, then
what is the value of x?
Answers
9514 1404 393
Answer:
16
Step-by-step explanation:
The equation of a line with slope m=1 through the point (h, k) = (-5, 7) will be ...
y -k = m(x -h)
y -7 = x +5
y = x +12
Then for x = 4, the value of y is ...
y = 4 +12 = 16
The point is (4, x) = (4, 16), so x = 16.
Answer:
16
Step-by-step explanation:
Given that the slope of the line is 1 . And it passes through the points (-5,7) and (4,x) .We know that slope is difference of ordinate by difference of abssica . So that ,
\(\implies Slope =\dfrac{y_2-y_1}{x_2-x_1}\\\\\implies 1 =\dfrac{ 7-x}{-5-4} \\\\\implies 1 \times -9 = 7-x \\\\\implies -9 -7 = -x \\\\\implies \underline{\underline{ x = 16 }}\)
Hence the required answer is 16 .
PLEASE HELP ANSWER THISS!!! I NEED THIS PLEASE!!! AND NO LINKS EITHER PLSS!!
Answers
It doesn't change because to add fractions, you need a common denominator. To find it, they multiplied 1/3 by 2 to make 2/6, to add to the 3/6.
College level Trigonometry any help will do thanks!
Answers
The hill makes an angle of approximately 11.98 degrees with the horizontal.
How to calculate the angleFrom the information, a force of 5 lb is required to hold a 24-lb crate on a hill and we want to know the angle that the hill make with the horizontal.
F = W * sin(θ)
where sin(θ) is the sine of the angle θ.
Solving for sin(θ), we get:
sin(θ) = F / W
= 5 lb / 24 lb
≈ 0.2083
θ = arcsin(0.2083)
≈ 11.98 degrees
Therefore, the hill makes an angle of approximately 11.98 degrees with the horizontal.
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PLEASE HELP!!!!ASAP!!!!
Answers
Answer:
2.4m
Step-by-step explanation:
area=50 x 25 =1250
pool depth=3000÷1250
=2.4m
I NEED URGENT HELP PLSS
Answers
Answer:
try b or c hop this help have a good day
Answer:
D
Step-by-step explanation:
the answer is D.. nothing to say step by step
m/ABD is a straight angle.
m/CBD = 8x+16°
m/ABC = 6x - 60°
Find m/ABC:
Answers
Answer:
Solution in attached photo.
Step-by-step explanation:
SolutionThe solution is attached as a photo. This Question tests on the concept of Angle Properties.
Properties required:
1) Angles in a straight line sums up to 180°.
BELE
What is the slope of the line represented by the equation y = -- 5x?
-5
Nm nm is
Answers
The mean of 4 numbers is 8 if three numbers are 4,5,10 find the fourth number
Answers
The fοurth number οf a series whοse mean is 8 wiII be 13.
What is mean?By dividing the sum οf the prοvided numbers by the tοtaI number οf numbers, the mean—the average οf the given numbers—is determined.
We can use the fοrmuIa fοr the mean (average) οf a set οf numbers tο sοIve fοr the fοurth number:
mean = (sum οf aII numbers) / (number οf numbers)
In this case, we knοw that the mean οf the fοur numbers is 8 and three οf the numbers are 4, 5, and 10. Let's caII the fοurth number x. Then, we can set up the equatiοn:
8 = (4 + 5 + 10 + x) / 4
MuItipIying bοth sides by 4, we get:
32 = 19 + x
Subtracting 19 frοm bοth sides, we get:
13 = x
Therefοre, the fοurth number is 13.
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The figure below is a net for a right rectangular prism.
10 in
13 in
10 in
5 in
10 in
10 in
What is the surface area of the right rectangular prism, in square inches?
Answers
The surface area of a rectangular prism is 490 in² by the area of each face and then add them up.
Why is it named a rectangular prism ?We refer to the prism as a rectangular prism since each face is shaped like a rectangle. A cuboid, which has six rectangular faces, and each opposite rectangular face is equal to and parallel to another rectangular face is known to have a similar shape.
To find the surface area of the right rectangular prism, we need to find the area of each face and then add them up.
Looking at the net, we can see that there are 6 faces, each with its own dimensions:
The top and bottom faces are both rectangles with dimensions 10 in by 13 in, so each has an area of 10 in × 13 in = 130 in².
The front and back faces are both rectangles with dimensions 10 in by 5 in, so each has an area of 10 in × 5 in = 50 in².
The left and right faces are both rectangles with dimensions 13 in by 5 in, so each has an area of 13 in × 5 in = 65 in².
Therefore, the total surface area of the right rectangular prism is:
2(130 in²) + 2(50 in²) + 2(65 in²) = 260 in² + 100 in² + 130 in² = 490 in²
So, the surface area of the right rectangular prism is 490 square inches.
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PLEASE HELP ME SOLVE THIS
Answers
416 square feet
\(\bold{EXPLANATIONS:}\)
What is the value of f(-5)?
Answers
Answer:
None
Step-by-step explanation:
Cant solve it without an X value