Your question is not complete, however, I have provided answers to it by suggesting that the question goes like this;
Twelve different video games showing drug use were observed. The duration times of drug use (in seconds) were recorded. When using this sample for a t test of the claim that the population mean is greater than 85sec, what does df denote, and what is its value
Answer:
df denote degree of freedom.
degree of freedom df is 11.
Step-by-step explanation:
what does df denote?
df denote degree of freedom
To find it value,
we have twelve different video games showing drug use, then, it means that the sample size "n" is 12
the degree of freedom is 1 < n ( i.e, one less than sample size)
df = n -1 = 12 -1 = 11
So, degree of freedom df is 11.
Note; use your sample size to solve the question as I don't know the exact value you were given. Thanks.
15. Over what range of angles does the value of sin(O) consistently increase?
A. 45° to 135°
B. 90° to 180°
C. 0° to 180°
D. 0° to 90°
Answer:
D. 0° to 90°
Step-by-step explanation:
If we see curve of sin(o) on coordinate, we will notice that value of sin curve increases from 0 to 90 degrees and then decreases from 90 to 180 degrees.
Hence option D is correct.
Alternatively
we see that
sin 0 = 0
sin 30 = 1/2
sin 45 = 1/[tex]\sqrt{2}[/tex]
sin 60 = [tex]\sqrt{3} /2[/tex]
sin 90 = 1
Thus, we see that value of sin is increasing from 0 to 90
now lets see value of sin from 90 to 180
sin 90 = 1
sin 120 = [tex]\sqrt{3} /2[/tex]
sin 135 = 1/[tex]\sqrt{2}[/tex]
sin 150 = 1/2
sin 180 = 0
Thus, we see that value of sin is decreasing from 90 to 180.
The area of a circle is given as 24π. What is its radius?
Answer:
4.9 units
Step-by-step explanation:
The area of a circle is πr².
πr² = 24π
Cancel π on both sides.
r² = 24
Take the square root on both sides.
r = √24
r ≈ 4.898979
The radius is 4.9 units.
Answer: The radius is 4.9
A certain shampoo is available in two sizes. A 13.5 ounces bottle cost $2.98. A 29.2 ounce bottle cost $6.12. Find the Unit price for each size. Then state which size is the better buy based on the unit price. Round your answer to the nearest cent
Answer:
9.2 ounce bottle cost $6.12 is better buy with unit price of $0.22
Step-by-step explanation:
Unit price of any product is given by
unit price = weight of product/ price of product
Given sizes
A
13.5 ounces bottle cost $2.98
cost of 1 ounce of shampoo for this size = cost price/weight of shampoo
cost of 1 ounce of shampoo for this size =2.98/13.5 = $0.22
Unit price for this size is $.022
B
9.2 ounce bottle cost $6.12
cost of 1 ounce of shampoo for this size = cost price/weight of shampoo
cost of 1 ounce of shampoo for this size =6.12/9.2 = 0.66
Unit price for this size is $0.66
As $0.22 is less than $0.66 thus,
9.2 ounce bottle cost $6.12 is better buy.
Tony used a photocopier to dilate the design for a monorail track system. The figure below shows the design and its photocopy
A
10 m
B
F
E
8 m
D
D
С
G
Design
Photocopy
The ratio of CD:GH is 2:3. What is the length, in meters, of side EH on the photocopied image? (5 points)
Answer:
12 m
Step-by-step explanation:
Given that the design, ABCD, was dilated to get a photocopy, EFGH, a scale factor or ratio was multiplied by the original lengths of the design to get the new measurement of the photocopy.
Thus, we are given the ratio, CD:GH = 2:3.
This means, any of the corresponding lengths of both figures would be in that same ratio.
Using the ratio of the design to the photocopy, 2:3, we can find the length of side EH of the photocopy.
The corresponding side of EH in the design is AD = 8m. Thus, AD to EH = ⅔
[tex] \frac{AD}{EH} = \frac{2}{3} [/tex]
[tex] \frac{8}{EH} = \frac{2}{3} [/tex]
Cross multiply
[tex] 3*8 = 2*EH [/tex]
[tex] 24 = 2*EH [/tex]
Divide both sides by 2 to make EH the subject of formula
[tex] \frac{24}{2} = \frac{2*EH}{2} [/tex]
[tex] 12 = EH [/tex]
The length of side EH = 12 m
g A 5 foot tall man walks at 10 ft/s toward a street light that is 20 ft above the ground. What is the rate of change of the length of his shadow when he is 25 ft from the street light
Answer:
[tex]-\frac{10}{3}ft/s[/tex]
Step-by-step explanation:
We are given that
Height of man=5 foot
[tex]\frac{dy}{dt}=-10ft/s[/tex]
Height of street light=20ft
We have to find the rate of change of the length of his shadow when he is 25 ft form the street light.
ABE and CDE are similar triangle because all right triangles are similar.
[tex]\frac{20}{5}=\frac{x+y}{x}[/tex]
[tex]4=\frac{x+y}{x}[/tex]
[tex]4x=x+y[/tex]
[tex]4x-x=y[/tex]
[tex]3x=y[/tex]
[tex]3\frac{dx}{dt}=\frac{dy}{dt}[/tex]
[tex]\frac{dx}{dt}=\frac{1}{3}(-10)=-\frac{10}{3}ft/s=-\frac{10}{3}ft/s[/tex]
Hence, the rate of change of the length of his shadow when he is 25 ft from the street light=[tex]-\frac{10}{3}ft/s[/tex]
Obtain the number 175 in two steps, using the numbers 3, 10 and 25 exactly once. You may use addition, subtraction, or multiplication.
Answer: (10 - 3) x 25 = 175
Step-by-step explanation:
10 - 3 = 7
7 x 25 = 175
A washer and a dryer cost $744 combined, the washer costs $94 more than the dryer, what is the cost of the dryer?
Answer:
$ 325Step-by-step explanation:
Let the cost of washer be ' x '
Let the cost of dryer be ' y '
According to Question,
x + y = 744 -----> equation (i)
x - y = 94 ------> equation (ii)
Adding equation (i) and (ii),
x + y = 744
+ x - y = 94
---------------------
2x = 838
Dividing both sides of the equation by 2
2x/2 = 838/2
Calculate
X = 419
Again,
Putting the value of X in equation (i)
X + y = 744
419 + y = 744
subtract 419 on both sides
y + 419 - 419 = 744 - 419
Calculate:
y = 325
The cost of dryer is $ 325.
Hope this helps...
Good luck on your assignment...
Find the value
a) x^2 when x = 5
Answer:
x²=25 is the answer
Step-by-step explanation:
we have to find the value of x² in the question it is given that
x=5
putting it in x²
x²=5²
x²=5×5
x²=25
i hope this will help you :)
Please Help!! And Fast!! Will give Brainliest to the Best Answers (75 points) --- The historical society hired an artist to restore a stained glass window panel. After studying the original drawings, the artist knows that panel ABCD is square. He also knows that FG is a perpendicular bisector of BC and BC ≅ BE. However, in order to restore the panel to match its original specifications, he needs to know the measure of ∠BED. Given: ABCD is a square FG ⊥ BC BC ≅ BE Step 1: Draw EC on the diagram. Use the given information to explain how you know △EGC ≅ △EGB. Add the appropriate notation to the diagram. (5 points) Step 2: Building on the information from Step 1, use the spaces below to prove that m∠BEC = 60°. Add the appropriate notation to the diagram. (5 points; 4 points for the proof, 1 point for the diagram) Statements Reasons 1. △EGC ≅ △EGB 1. Given 2. EB ≅ EC 3. Given 4. EB ≅ EC ≅ BC 5. m∠BEC = 60° Step 3: Next, use the spaces below to prove the measure of ∠ECD = 30°. Add the appropriate notation to the diagram. (5 points; 4 points for the proof, 1 point for the diagram) Given: ABCD is a square FG ⊥ BC BC ≅ BE △ECG ≅ △EBG △BEC is equilateral m∠BEC = 60° Prove: m∠ECD = 30° Statements Reasons 1. △BEC is equilateral 2. m∠GCE = 60° 3. ABCD is a square 4. Substitution Step 4: Find m∠BED. Show your work and explain your reasoning. Add the appropriate notation to the diagram. (6 points; 4 points for showing work and explaining reasoning; 1 point for final answer; 1 point for diagram) Given: ABCD is a square FG ⊥ BC BC ≅ BE △ECG ≅ △EBG △BEC is equilateral m∠BEC = 60° △ECD is isosceles Find: m∠BED
Answer: I had the same assingment and came here looking for answers myself. When I saw the only anwser was 20 (Which is wrong) I decided I would try my best and If I got it right come back here and share the correct answers for future students.
Just look at the PDF attached below, I somehow got a 50/50.
Step-by-step explanation:
Statements Reasons
1. △EGC ≅ △EGB 1. Given
2. EB ≅ EC Supposition
3. <EGC ≅ <EGB Given
4. Equilateral Triangle EB ≅ EC ≅ BC
5. Equilateral Triangle m∠BEC = 60°
Statements Reasons
1. △BEC is equilateral AAS≅AAS postulate (angle angle side)
2. m∠ GCE = 60° m∠ BEC = 60° Equilateral Triangles
3. FG ⊥ BC & FG ⊥ AD ABCD is a square
4. m∠ECD + m∠ BEC = 30°+60° Substitution (right angles)
m∠DCG = 90° right angles of a square
m∠BED= 135°
Statements Reasons
1. △ECG ≅ △EBG Given
2. ABCD is a square Given
3. BC ≅ BE Given
4. AB ≅ DC ABCD is a square
5. m∠ABE ≅ m∠DCE Outside angles of congruent
triangles △EGB≅ △EGC
5. △AEB≅ △DEC S.S.A ≅ S.S.A. ( side side angle) Postulate
△BEC is equilateral m∠BEC = 60°
△ECD is isosceles m CD= mCE
∠ECD = 30° m∠BEC = 60°
As m∠BEC +∠ECD = 30°+ 60° right angle of the square ABCD
The equal sides of the isosceles triangles are called the legs and the unequal third side is called the base.
Angles opposite to the equal sides of the isosceles triangle must also be equal.
As the third angle is 30° so the other two angles must be 75° each to make a total of 180°.
m∠BED= m∠BEC + m∠CED
= 60° + 75°= 135°
https://brainly.com/question/22140109
An unevenly heated metal plate has temperature T(x,y) in degrees Celsius at a point (x,y). If T(2,1) = 107, Tx(2,1) = 9, and Ty(2,1) = −8, estimate the temperature at the point (2.03,0.95).
Answer: 107.67°C
Step-by-step explanation:
I guess that we could do a Taylor expansion around the point (2, 1)
Remember that a Taylor expansion around the point (a, b) is:
[tex]T(x,y) = T(a, b) + \frac{dT(a,b)}{dx}(x - a) + \frac{dT(a,b)}{dy}(y - b) + .....[/tex]
Where the latter terms need higher orders of the derivates of T, so we can not find them, regardless of that, this expansion will be accurate near the point (a, b),
Then, using this, we can write our expanssion as:
T(x,y) = 107 + 9*(x - 2) - 8*(y - 1)
Now we evaluate this in x = 2.03 and y = 0.95
T(2.03, 0.95) = 107 + 9(2.03 - 2) - 8*(0.95 - 1) = 107.67
Then a good estimation of the temperature at the point (2.03,0.95) is 107.67°C
The estimate of the temperature of the unevenly heated metal plate at temperature at the point (2.03,0.95) is;
T(2.03, 0.95) = 107.67 °C
Formula for taylor expansion around a point (a, b) is given as;
T(x, y) = T(a,b) + [tex]\frac{dT(a,b)}{dx}[/tex](x - a) + [tex]\frac{dT(a,b)}{dy}[/tex](y - b) + ....
We are given;
T(2,1) = 107
T'x(2,1) = [tex]\frac{dT(a,b)}{dx}[/tex] = 9
T'y(2,1) = [tex]\frac{dT(a,b)}{dy}[/tex] = −8
Plugging in the relevant values into our taylor expansion above gives;
T(x, y) = 107 + 9(x - 2) - 8(y - 1)
Now, we want to estimate the temperature at the point (2.03, 0.95).
Thus, we will plug in x = 2.03 and y = 0.95 to get;
T(2.03, 0.95) = 107 + 9(2.03 - 2) - 8(0.95 - 1)
T(2.03, 0.95) = 107 + 0.27 + 0.4
T(2.03, 0.95) = 107.67 °C
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Find f o g and g o f to determine if f and g are inverse functions. If they are not inverses, pick the function that would be the inverse with f(x). f(x) = (-2/x) – 1; g(x) = -2/(x+1)
Choices:
a. g(x) has to be: (1+x)/2
b. g(x) has to be: x/2
c. g(x) has to be: 2 – (1/x)
d. Inverses
Answer:
Step-by-step explanation:
Hello,
[tex]x = (fof^{-1})(x)=f(f^{-1}(x))=\dfrac{-2}{f^{-1}(x)}-1\\\\<=>f^{-1}(x)(x+1)=-2\\\\<=> f^{-1}(x)=\dfrac{-2}{x+1}[/tex]
and this is g(x)
so they are inverses
Hope this helps
which of the following sets of ordered pairs describes a function?
(A) {(2,3),(2,5),(4,7)}
(B) {(2,1),(4,3),(5,7)}
(C) {(3,-2),(2,4),(3,6)}
(D) {(-1,4),(-1,5),(2,5)}
Answer:
(B) {(2,1),(4,3),(5,7)}
Step-by-step explanation:
If the same x value goes to 2 different y values, it is not a function
(A) {(2,3),(2,5),(4,7)} the x value 2 goes to 3 and 5
(B) {(2,1),(4,3),(5,7)}
(C) {(3,-2),(2,4),(3,6)} 3 goes to -2 and 6
(D) {(-1,4),(-1,5),(2,5)}-1 goes to 4 and 5
2.5 – 1.2x < 6.5 – 3.2x?
Answer: x<2 or xϵ(-∞; 2)
Step-by-step explanation:
Add +3.2x to both sides of inequality:
2.5-1.2x+3.2x<6.5-3.2x+3.2x
2.5+2x<6.5
Deduct 2.5 from both sides of inequality:
2.5-2.5+2x<6.5-2.5
2x<4
Divide both sides of inequality by 2
2x/2<4/2
x<2 or xϵ(-∞; 2) ( the answer can be written in 2 ways)
Answer:
2.5 - 1.2x < 6.5 - 3.2x
add 3.2x to both sides;
2.5 + 2x < 6.5
minus 2.5 from both sides;
2x < 4
x < 2
Step-by-step explanation:
This is the exact same as doing a linear equation, so brush up on this skill.
QUICK HELP HURRY! Simplify the expression. [tex]10^{-2} +10^{-1}[/tex]
Answer:
11/100 or 0.11
Step-by-step explanation:
10^-2 is also equal to 1/100
10^-1 is also equal to 1/10
Simply add them now:
1/100+1/10
= 1/100+ 10/100
= 11/100=0.11
Hope this helped!
1. What is a residual?
A. A residual is a value of y -y, which is the difference between an observed value of y and a predicted value of y.
B. A residual is a point that has a strong effect on the regression equation.
C. A residual is a value that is determined exactly, without any error.
D. A residual is the amount that one variable changes when the other variable changes by exactly one unit.
2. In what sense is the regression line the straight line that "best" fits the points in a scatterplot?
The regression line has the property that the______of the residuals is the V possible sum.
Answer:
1. what is a residual?
A. A residual is a value of y -y, which is the difference between an observed value of y and a predicted value of y.
2. The regression line has the property that the_sum of squares_of the residuals is the minimum possible sum.
Step-by-step explanation:
1. What is a residual?
A. A residual is a value of y -y, which is the difference between an observed value of y and a predicted value of y.
2. In what sense is the regression line the straight line that "best" fits the points in a scatterplot?
The regression line has the property that the_sum of squares_of the residuals is the minimum possible sum.
A residual is a value {Δy} that is a difference between an observed value of {y} and a predicted value of {y}.
What is regression line?A regression line is an estimate of the line that describes the true, but unknown, linear relationship between the two variables. Mathematically -
[tex]$Y_i=f(X_i, \beta)+e_i[/tex]
Given is residual.
The residual for each observation is the difference between predicted values of y (dependent variable) and observed values of y. Mathematically -
[tex]r = x-x_{0}[/tex]
Therefore, a residual is a value {Δy} that is a difference between an observed value of {y} and a predicted value of {y}.
To solve more questions on regression line, visit the link below -
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What is the equation of the line ( 1,9 ) ( 0,0 )
Answer:
y = 9x
Step-by-step explanation:
First find the slope
m = (y2-y1)/(x2-x1)
= (0-9)/(0-1)
-9/-1
9
The y intercept is 0 since the y value is 0 when x=0
The slope intercept form is y = mx+b where m is the slope and b is the y intercept
y = 9x +0
y = 9x
find two complex numbers whose sum is 12 and whose product is 37.
Answer:
6 ± i and 6 ± i
Step-by-step explanation:
Let x be the first number.
Let y be the second number.
x + y = 12
x × y = 37
Solve for x in the first equation.
x = 12 - y
Put x as 12-y in the second equation and solve for y.
(12- y)y = 37
12y - y² = 37
- y² + 12y - 37 = 0
y = 6 ± i
Put y as 6 ± i in the first equation and solve for x.
x + 6 ± i = 12
x = 12 - 6 ± i
x = 6 ± i
College students spend $183 more each year on textbooks and course materials than on computer equipment. They spend a total of $819 on textbook and course materials and equipment each year. How much is spent each year on textbooks and course materials and computer equipment?
Answer:
Textbooks: $506Course Materials and Electronics: $323Step-by-step explanation:
First, we need to divide the amount into 2 equal parts:
$819/2 = $414.50
Now, because they spent $183 more on textbooks, we add half of that to $414.50.
$414.50 + $91.50 = $506
$414.50 - $91.50 = $323
To make sure that the amount spent on textbooks is $183 more than the amount spent on course materials and computers, we need to add $183 to $323. If we get $506, our answer is correct.
$323 + $183 = $506 ✅
Textbooks: $506Course Materials and Electronics: $323I'm always happy to helpPick a card from a regular 52-card deck and record the suit, then toss a coin and record heads or tails. Let A be the event a club or spade is picked from a regular 52-card deck. Let B the event a heads appears when the coin is tossed.
(a) determine the sample space for this experiment
(b) Are the events A and B disjoint? Why or why not?
(c) Find P(AUB)
(d) Find P(A intersect B')
Answer:
a) The sample space for this experiment includes
(Clubs, head), (Clubs, tail), (spades, head), (spades, tail), (diamonds, head), (diamonds, tail), (hearts, head), (hearts, tail)
b) The two events are not mutually exclusive or disjoint as both events can occur at the same time and the set of A intersect B is not an empty set and P(A n B) ≠ 0.
c) P(A u B) = (3/4) = 0.75
d) P(A n B') = (1/4) = 0.25
Step-by-step explanation:
Let A be the event a club or spade is picked from a regular 52-card deck.
Let B the event a heads appears when the coin is tossed.
a) A sample space consists of all the possible outcomes of the whole process of picking a random suit and then tossing the coin for heads or tails.
There are 4 suits in a 52 deck card namely, clubs, spades, diamonds and hearts.
And in a toss of a coin, there are only 2 possible outcomes, a head or a tail.
The possible outcomes for the random pick of cards include
{clubs, spades, diamonds, hearts}
And for the second event
{Head, tail}
Combined, the sample space is
(Clubs, head), (Clubs, tail), (spades, head), (spades, tail), (diamonds, head), (diamonds, tail), (hearts, head), (hearts, tail)
Noting that P(A) = probability of a club or a spade being picked = (26/52) = (1/2)
P(A') = Probability that a club or spade will not be picked, that is, a diamond or a heart will be picked = (26/52) = (1/2)
P(B) = Probability of a head turning up from the coin toss = (1/2)
P(B') = Probability of a head not turning up, that is, a tail turning up = (1/2)
b) Disjoint events are events that are mutually exclusive and cannot both occur at the same time. The set of the intersection of the two mutually exclusive/disjoint events is a null set.
Mathematically, mutually exclusive/disjoint events are proven through the relation that P(A n B) = 0.
But from the sample spaces obtained in (a) above, the event
(A n B) = (Clubs, head), (spades, head)
And it isn't a null set.
Since the probability of an event is the number of elements in the event divided by the total number of elements in the sample space.
n(A n B) = 2
n(total sample space) = 8
P(A n B) = (2/8) = (1/4) ≠ 0
Hence, the two events aren't disjoint.
c) P(A u B)
This represents the probability of obtaining a club or spade from the deck of card or getting head from the coin toss.
From the Total sample space, the set (A u B) includes (Clubs, head), (Clubs, tail), (spades, head), (spades, tail), (diamonds, head), (hearts, head)
n(A u B) = 6
n(total sample space) = 8
P(A u B) = (6/8) = (3/4) = 0.75
d) P(A n B')
This represents the probability of obtaining a club or spade from the deck of card and NOT getting a head from the coin toss.
The set (A n B') includes (Clubs, tail), (spades, tail)
n(A n B') = 2
n(total sample space) = 8
P(A n B') = (2/8) = (1/4) = 0.25
Hope this Helps!!!
What is the definition of PEMDAS
Answer:
it's the step by step proceedure you use when solving an equation. Parentethese (do this first)
Exponents (take care of that after parentheses)
Multiplication
Division
Addition
subtraction (always the last step in the problem)
Step-by-step explanation:
Answer:
PEMDAS = ( ), Exponents, Multiplication, Division, Addition, Subtraction
Step-by-step explanation:
essentially, PEMDAS are an order of a rule in which you have to follow.
1. P = Parenthesis/ ( )
2. E= Exponents/ ²
3. M= Multiplication/ x
4. D= Division/ ÷
5. A= Addition/+
6. S= Subtraction/-
Each goes in order, and if there isn't one of the steps included in the math problem you are given, then its better to move on to the next uwu
I hope this was helpful owo
The probability that Hugo is on time for a given class is 71 percent. If there are 57 classes during the semester, what is the best estimate of the number of times out of 57 that Hugo is on time to class? Round your answer to the nearest integer.
Answer:
40
Step-by-step explanation:
P(Hugo is on time for a given class)=71%=0.71
If there are 57 classes during the semester
The number of times Hugo is on time to class during the semester will
=0.71 X 57
=40.47
[tex]\approx 40 $ (correct to the nearest integer.)[/tex]
Hugo is on time to class approximately 40 out of 57 times.
Helppp Please!!!!!!!!!
Answer:
B. 17°.
Step-by-step explanation:
To solve the problem, we can use SOH CAH TOA.
SOH = Sine, Opposite divided by Hypotenuse
CAH = Cosine, Adjacent divided by Hypotenuse
TOA = Tangent, Opposite divided by Hypotenuse
In this case, we are given both the opposite and the hypotenuse, so we will use sine to solve it.
sine(N) = 4 / 14
sine(N) = 2 / 7
N = sec(2/7)
N = 16.6015496, which is about B. 17°.
Hope this helps!
square root of -49 in terms of i
Answer:
7i
Step-by-step explanation:
We know that i = √-1
Then solving the given:
√-49 = √49×(-1) = √49 × √-1 = 7×√-1 = 7iSo the answer is:
√-49 = 7iplease simplify this equation
Answer:
The answer is -24√35
Step-by-step explanation:
-6√7 × 4√5
Using the rules of surds multiply the numbers outside the square root and the ones inside
That's
(-6×4)(√ 7 × √5)
= - 24√7×5
= -24√35
Hope this helps you
Answer:
-24√35
Step-by-step explanation:
-6√7 × 4√5
-6 × √7 × 4 √5
-6 × 4 × √7 × √5
-24 × √(7 × 5)
-24√35
A train leaves Station A traveling west at 60 miles per hour for 7 hours, and then continues to travel west on the same track for 3 hours at 55 miles per hour, where it stops at Station B. How far is Station A from Station B?
Answer: 585 miles
Step-by-step explanation: 60 x 7 for the first 7 hours = 420 miles, then 3 x 55 for the last 3 hours = 165 add them together, 420+265 you get= 585
60 miles per hour x 7 hours = 420 miles
55 miles per hour x 3 hours = 165 miles
Total miles = 420 + 165 = 585 miles
The variance in drug weights is critical in the pharmaceutical industry. For a specific drug, with weights measured in grams, a sample of 18 units provided a sample variance of 0.36. a. Construct a 90% confidence interval estimate of the population variance for the weight of this drug. Show your work. b. Construct a 90% confidence interval estimate of the population standard deviation.
Answer:
a) 0.2218 to 0.7057
b) 0.4710 to 0.8401
Step-by-step explanation:
Given:
sample = n = 18
sample variance = s² = 0.36
To find:
a) 90% confidence interval estimate of the population variance.
b) 90% confidence interval estimate of the population standard deviation.
a)
Compute degree of freedom
degree of freedom = df = n - 1 = 18 - 1 = 17
Compute value of α for a 90% confidence interval
The confidence level for 90% is:
c = 0.90
So
α = 1 - c = 1 - 0.90 = 0.1
α = 0.1
Now use the table of critical values of the chi-square distribution in order to find critical values. Search for the 17th row of table using df = 17 and find the column corresponding to 1 - α/2 i.e. 0.95 of table for upper tail critical values and column corresponding to α /2 i.e. 0.05 of table for lower tail critical values.
Using the table:
[tex]X^{2}_{0.95}[/tex] = 8.672
[tex]X^{2}_{0.05}[/tex] = 27.587
90% Confidence interval estimate of the population variance
The boundaries of CI are computed using formula:
(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex] ≤ σ² ≤ (n−1) s² / [tex]X^{2}_{1-\alpha/2}[/tex]
(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex] = (18-1) 0.36 / 27.587
= (17) 0.36 / 27.587
= 6.12 / 27.587
(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex] = 0.2218
(n−1) s² / [tex]X^{2}_{1-\alpha/2}[/tex] = (18-1) 0.36 / 8.672
= (17) 0.36 / 8.672
= 6.12 / 8.672
= 0.7057
This results in inequalities 0.2218 ≤ σ² ≤ 0.7057 for the variance
b)
90% Confidence interval estimate of the population standard deviation
The boundaries of CI are computed using formula:
√(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex] ≤ σ ≤ √(n−1) s² / [tex]X^{2}_{1-\alpha/2}[/tex]
√(n−1) s² / [tex]X^{2}_{\alpha/2}[/tex] = √((18-1) 0.36 / 27.587)
= √((17) 0.36 / 27.587)
= √(6.12 / 27.587)
= √0.2218
= 0.4709
= 0.4710
√(n−1) s² / [tex]X^{2}_{1-\alpha/2}[/tex] = √((18-1) 0.36 / 8.672)
= √((17) 0.36 / 8.672)
= √ (6.12 / 8.672)
= √0.7057
= 0.8401
0.4710 ≤ σ ≤ 0.8401 for the standard deviation.
In a random sample of high school seniors, the proportion who used text messaging was 0.88. In a random sample of high school freshmen, this proportion was 0.68. Researchers found the difference in proportions to be statistically significant and obtained one of the following numbers for the p-value. Which is it?
a. 1.5
b. 0.02
c. 0.78
d. 0.30
Answer:
Option B - 0.02
Step-by-step explanation:
In this question, the p-value is used to tell us the probability that a difference of (0.88 – 0.68) which is 0.2 or greater would occur in the distribution of simulated differences. This is created done with the assumption that there is no true difference in the two populations.
Due to the fact that the researchers found the difference in proportions to be statistically significant, hence these results would rarely occur due to just the sampling variability and thus the p-value must be small.
Looking at the options, the p-value in Option (B) will be the correct response,l as it indicates that a difference of 0.2 or more would only occur about 2% of the time by chance alone provided the proportion who text were the same in the population of seniors and the population of freshmen. This resonates well with the claim that the difference in proportions is statistically significant.
Thus, Option B is the correct answer.
Find the length of the given segment.
Find LN
Answer:
x+10=1/2*(x+2)
2x+20=x+2
20-2= x-2x
x= -18
now,
LN= X+10
= -18+10
= -8
If the statement shown is rewritten as a conditional statement in if-then form, which best describes the conclusion? When a number is divisible by 9, the number is divisible by 3.
Answer:
when a number is divisible by 9, then the number is divisible by 3.
Step-by-step explanation:
They tell us "When a number is divisible by 9, the number is divisible by 3" we could change it by:
when a number is divisible by 9, then the number is divisible by 3.
Which makes sense because the number 9 is a multiple of the number 3, which means that the 9 can be divided by 3, therefore, if the number can be divided by 9, in the same way it can be divided by 3 .
Answer:
a
Step-by-step explanation:
of the following fractions which is 50% greater than 3/7
Answer:
9/14
Step-by-step explanation:
3/7 + 50%×3/7 =
= 3/7 + 1/2×3/7
= 3/7 + 3/14
= 6/14 + 3/14
= 9/14
The required fraction which 50% grater than 3/7 is 9/14.
Fraction to determine that 50% grater than 3/7.
Fraction of the values is number represent in form of Numerator and denominator.
Here, fraction = 50% grater than 3/7
= 1.5 x 3/7
= 4.5/7
= 45/70
= 9/14
Thus, The required fraction which 50% grater than 3/7 is 9/14.
Learn more about fraction here:
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