A sample of 13 sheets of cardstock is randomly selected and the following thicknesses are measured in millimeters. Give a point estimate for the population standard deviation. Round your answer to three decimal places. 1.96,1.81,1.97,1.83,1.87,1.84,1.85,1.94,1.96,1.81,1.86,1.95,1.89
Answers
===============================================
Explanation:
Add up the values to get
1.96+1.81+1.97+1.83+1.87+1.84+1.85+1.94+1.96+1.81+1.86+1.95+1.89= 24.54
Then divide over 13 (the number of values) to get 24.54/13 = 1.8876923 which is approximate.
So the mean is approximately 1.8876923
---------------------
Now make a spreadsheet as shown below
We have the first column as the x values, which are the original numbers your teacher provided. The second column is of the form (x-M)^2, where M is the mean we computed earlier. We subtract off the mean and square the result.
After we compute that column of (x-M)^2 values, we add them up to get what is shown in the highlighted yellow cell at the bottom of the column.
That sum is approximately 0.04403076924
Next, we divide that over n-1 = 13-1 = 12
0.04403076924 /12 = 0.00366923077
That is the sample variance. Apply the square root to this to get the sample standard deviation. This is the point estimate of the population standard deviation. As the name implies, it works for samples that estimate population parameters.
sqrt(0.00366923077) = 0.06057417576822
This rounds to 0.061 which is the final answer.
Related Questions
If f(x) = 4x + 5 and fog(x) = 8x + 13 then find g(x).
Answers
Answer:
given
f(x).4x+5
fog(x).8x+13
now
fog(x):8x+13
4x+5(g(x)):: 8x+13
g(x):: 8x+13/4x+5
Answer:
g(x) = 2x + 2
Step-by-step explanation:
One is given the following information:
f(x) = 4x + 5f o g (x) = 8x + 13One is asked to find the following:
g(x)Remember, (f o g (x)) is another way of representing a composite function. A more visual way of representing this composite function is the following (f(g(x)). In essence, one substitutes the function (g(x)) into the function (f(x)) in places of the varaible (x). Thus, represent this in the form of an equation:
f(g(x)) = 8x + 13
Substitute the given infromation into the equation:
4(g(x)) + 5 = 8x + 13
Solve for (g(x)) in terms of (x). Remember to treat (g(x)) as a single parameter:
4(g(x)) + 5 = 8x + 13
Inverse operations,
4(g(x)) + 5 = 8x + 13
4(g(x)) = 8x + 8
g(x) = (8x + 8) ÷ 4
g(x) = 2x + 2
Suppose the volume of the cone is 324pi Find dy/dx when x=6 and y=27
Answers
Answer:
[tex]\displaystyle \frac{dy}{dx} \bigg| \limits_{x = 6} = -9[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityCalculus
Differentiation
DerivativesDerivative NotationBasic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle V = \frac{1}{3} \pi x^2y[/tex]
[tex]\displaystyle V = 324 \pi[/tex]
[tex]\displaystyle x = 6[/tex]
[tex]\displaystyle y = 27[/tex]
Step 2: Differentiate
Substitute in volume [Volume Formula]: [tex]\displaystyle 324 \pi = \frac{1}{3} \pi x^2y[/tex][Equality Properties] Rewrite: [tex]\displaystyle y = \frac{972}{x^2}[/tex]Quotient Rule: [tex]\displaystyle \frac{dy}{dx} = \frac{(972)'x^2 - (x^2)'972}{(x^2)^2}[/tex]Basic Power Rule: [tex]\displaystyle \frac{dy}{dx} = \frac{0x^2 - (2x)972}{(x^2)^2}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = \frac{-1944x}{x^4}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = \frac{-1944}{x^3}[/tex]Step 3: Evaluate
Substitute in variables [Derivative]: [tex]\displaystyle \frac{dy}{dx} \bigg| \limits_{x = 6} = \frac{-1944}{6^3}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} \bigg| \limits_{x = 6} = -9[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
A lady wearing a McDonalds t-shirt with a delicious-looking Big Mac on it asks which fast food restaurant is your favourite. This leads to which type of bias?
a) Response Bias
b) Sampling Bias
c) Measurement Bias
d) Non-response Bias
Answers
what is the answer to EVAULATE 8+-9+-6
Answers
Answer:
11
Step-by-step explanation:
8 + 9 + -6
8 + 9 = 17
17 + (-6) = 11
Answered by Gauthmath
Find the function G defined by G(x) =5x+3 find G(-1)
Answers
Answer:
G(-1) = -2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Functions
Function NotationStep-by-step explanation:
Step 1: Define
Identify
G(x) = 5x + 3
Step 2: Evaluate
Substitute in x [Function G(x)]: G(-1) = 5(-1) + 3Multiply: G(-1) = -5 + 3Add: G(-1) = -2Answer:
G = -2
Step-by-step explanation:
Plug in -1 for x.
5(-1) + 3
-5 + 3
-2
G = -2
HELP NEEDED PLEASE!!!!!
Answers
Answer:
1^1 + 0^1 =1
Step-by-step explanation:
sin^2 theta + cos^2 theta = 1
sin^2 (pi/2) + cos^2 (pi/2) =1
1^1 + 0^1 =1
I need help completing this problem ASAP
Answers
4/(√x - √(x - 2)) × (√x + √(x - 2))/(√x + √(x - 2))
= 4 (√x + √(x - 2)) / ((√x)² - (√(x - 2))²)
= 4 (√x + √(x - 2)) / (x - (x - 2))
= 4 (√x + √(x - 2)) / (x - x + 2)
= 4 (√x + √(x - 2)) / 2
= 2 (√x + √(x - 2))
Mary is thinking of a mystery number. She reduces it by 15% then subtracts 5. The result is 29. Determine the mystery number
Answers
Answer:
40
Step-by-step explanation:
Let x represent the mystery number.
Create an equation to represent the situation, then solve for x:
0.85x - 5 = 29
0.85x = 34
x = 40
So, the mystery number is 40.
12. Convert 30.283° into a degree-minute-second format.
O A. 18° 16' 98"
B. 18° 28' 30"
C. 30° 16' 58"
D. 30° 28' 30"
Answers
Non of the above it’s correct.
The correct answer is 283/60 =4°71’
71-60=1
4°+30°+1°= 35°
Answer 35°01’00”
The angle of 30.283° in a degree-minute-second format will be 30° 16' 58". Then the correct option is C.
What is conversion?Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
The angle is given below.
⇒ 30.283°
Convert 30.283° into a degree-minute-second format. Then we have
⇒ 30° (0.83 x 60')
⇒ 30° 16.98'
⇒ 30° 16' (0.98 x 60'')
⇒ 30° 16' 58"
The angle of 30.283° in a degree-minute-second format will be 30° 16' 58". Then the correct option is C.
More about the conversion link is given below.
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Write an equation in slope-intercept form for the line with slope -3/2
and y-intercept 5.
Answers
Answer: y = -3/2x + 5
Step-by-step explanation:
Slope-intercept form: y = mx + b
m = slope = -3/2b = y-intercept = 5y = -3/2x + 5
Answer:
y = -3/2x + 5 totally
Step-by-step explanation:
What is the shape of the cross section?
Answers
Answer:
Step-by-step explanation:
Triangular cross-section.
Answer:
it is a triangle cross-section
hope this answer helps you
Plz make me a brainlist
Select the correct answer.
Given the following formula, solve for l.
A.
B.
C.
D.
Answers
Answer:
c
Step-by-step explanation:
took the test so i assume its this question
Given the linear function f(x) 2/3x + 6 evaluate f(-6)
Answers
the answer is on the photo
Joes bait shop brought in a gross profit in sales of $4,100.00 in the month of June. During the same month their operating expenses totaled $1990.00. Calculate the net income of the bait shop for the month of June
Answers
Answer:
2110
Step-by-step explanation:
4100-1990=2110
Carol is having a hard time understanding the central limit theorem, so she decides to do her own experiment using the class data survey collected at the beginning of class on the number of hours a student takes during her Spring 2019 BUSI 2305 course. The data file has a total number of 54 students where the average is 10.8 with a standard deviation of 3.15. She sets out to collect the mean on 8 samples of 6 students. Based on this what are the total possible samples that could occur based on the population
Answers
Answer:
25827165
Step-by-step explanation:
from the question that we have here
the total population = 54 students
the sample size = 6 students
So given this information carol has to pick the total samples from the 54 students that we have here
the total ways that she has to do this
= 54 combination 6
= 54C6
= [tex]\frac{54!}{(54-6)!6!}[/tex]
= 25827165
this is the total number of possible samples that could occur given the total population of 54 students.
Help
Plz!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
angle G
sin inverse (21/29) = 46.4
GH
c^2 - b^2 = a^2
29^2 - 21^2 = a^2
a = √(29^2 - 21^2)
GH = 20
therefore ans is B) <G = 46.4º, <I = 43.6º, GH = 20
Rewrite the polynomial in the form ax+by+c and then identify the values of a, b, and c.
x -- 1 -- 2y
Answers
Answer:
a=1, b=-2,c=-1
Step-by-step explanation:
1*(x)+(-2)*y+(-1)*1. a=1, b=-2,c=-1
A swimmer dove off a board that was 50 ft above the water. The swimmer reached a depth of 15 ft in the pool. What number represents the swimmer's original height, in feet?
Answers
9514 1404 393
Answer:
50
Step-by-step explanation:
The number you choose depends on the location you consider to be zero height.
If we consider the surface of the pool to be zero height, and "up" to be the positive direction for measuring height, then the appropriate number for the original 50-ft height is 50.
What is the common ratio for this geometric sequence?
27, 9, 3, 1, ...
Answers
Answer:
1/3
Step-by-step explanation:
common ratio is
9÷27=1/3
3÷9=1/3
1÷3=1/3
therefore common ratio is 1/3
Answer: 1/3
Step-by-step explanation:
Let us confirm that this is a geometric sequence. 9/27 = 1/3 and 3/9 = 1/3. Thus, the common ratio is 1/3.
50% of 80
50% of 48
50% of 15
25% of 120
25% of 90
Answers
2. 24
3. 7.5
4. 30
5. 22.5
Suppose $12,000 is deposited into an account paying 5.5% interest, compounded continuously.
How much money is in the account after five years if no withdrawals or additional deposits are
made?
Answers
Answer:
$15798.4
Step-by-step explanation:
We will have to use this formula A = Peᵃᵇ
A = Final amount
P = Initial amount (12,000)
e = Mathematical constant: 2.7183
a = Interest rate (5.5% or 0.055)
b = Years
So our equation will look like this
A = 12,000e⁵ ⁰·⁵⁵
A = 12,000(2.7183)·²⁷⁵
A = 12,000(1.316533)
A = 15798.396
Which of the following shows the extraneous solution to the logarithmic equation below?
2 log Subscript 5 Baseline (x + 1) = 2
Answers
Answer:
x=4
Step-by-step explanation:
log5(x+1)=1, (x+1)=5, x=4
Answer:
x= -6
Step-by-step explanation:
i got it wrong and the answer is -6
Plz answer asap question in picture
Answers
Answer:
-1 <x < 7
(-1,7)
Step-by-step explanation:
open circle on the left means the number is greater than
-1 <x
Open circle on the right means the number is less than
x < 7
Since both statements are true. we combine them
-1 <x < 7
open circles means parentheses, closed circles mean brackets
From the observation deck of a skyscraper, Isabella measures a 67
angle of depression to a ship in the harbor below. If the observation deck is 824 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest tenth of a foot if necessary.
Answers
The horizontal distance from the base of the skyscraper out to the ship is 349.8feet
Angle of elevation and depressionThe angle situated above the hill is known as the angle of depression
Given the following parameters
Height of the harbor = 824 feet
Angle of depression = 67degrees
According to SOH CAH TOA identity:
tan 67 = opp/adj
tan 67 = 824/d
d = 824/tan67
d = 349.8 feet
Hence the horizontal distance from the base of the skyscraper out to the ship is 349.8feet
Learn more on angle of depression here: https://brainly.com/question/12483071
If (x+2) is a Factor x^3 + 2x^2 + 2x + k then find the value of K.
Answers
Answer:
4
Step-by-step explanation:
if x+2 is a factor of the above expression then,
x=-2
so putting the value of x in above expression we get,
(-2)^3+2×(-2)^2+2×(-2)+k=0
or,-8+8-4+k=0
k=4
Answer:
Step-by-step explanation:
If (x + 2) is a factor of a polynomial then ( - 2 ) is the zero of that polynomial ⇒ ( - 2 )³ + 2( - 2 )² + 2( - 2 ) + k = 0 ⇒ k = - 4
i provided the question
Answers
Answer:
(0, 3)
Step-by-step explanation:
y = 3 is the horizontal tangent to y = x^2+3, and passes the parobala at (0, 3)
Please help‼️
Given O below, if XY and YZ are congruent, what is the measure of chord XY?
Answers
Answer:
11.2
Step-by-step explanation:
yz = 11.2
since the corresponding arc of yz and xy are same, their measures will ba same too
Answered by GAUTHMATH
Answer:
11.2
Step-by-step explanation:
good luck!
Write a 6-digit number that fits the description.
1. The value of its thousands digit is 5,000.
2. The value of its hundreds digit is 700.
3. Its tens digit is 2 less than the thousands digit.
4. Its hundred thousands digit is the same as the hundreds digit.
The number is?
Answers
Answer:
175731 is one of the answers of the 6 digit number
some others are:
275732
375733
475734
575735
675735
775734
875732
The 6-digit number is 175731.
What is the place value strategy?The place value strategies are defined as math strategies that use to assist you in resolving your elementary math problems, use your places values, such as tens and hundreds. It is possible to employ enlarged notation or compensation. Using regrouping techniques, you can make the problem easier by compensating for addition.
Let the number would be ABCDEF
Given the condition that the value of its thousands of digits is 5,000.
So C = 5
Given the condition that the value of its hundreds of digits is 700.
So D = 7
Given the condition that Its tens digit is 2 less than the thousand digits.
So E = 5-2 = 3
Given the condition that Its hundred thousand digits is the same as the hundred digits.
So B = 7
Therefore, all possible answers:
275732
375733
475734
575735
675735
775734
875732
Hence, the 6-digit number is 175731
Learn more about the place value strategy here:
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- 2/3 (2 - 1/5) use distributive property
Answers
Answer:
-6/5
Step-by-step explanation:
- 2/3 (2 - 1/5)
Distribute
-2/3 *2 -2/3 *(-1/5)
-4/3 + 2/15
Get a common denominator
-4/3 *5/5 +2/15
-20/15 +2/15
-18/15
Simplify
-6/5
A one lane highway runs through a tunnel in the shape of one half a sine curve cycle
Answers
The sine curve equation, y = 10·sin(x·π/24), that models the entrance of the
tunnel with a cross section that is the shape of half of a sine curve and the
height of the tunnel at the edge of the road, (approximately 7.07 ft.) are
found by applying the following steps
(a) The equation for the sine curve is y = 10·sin(x·π/24)
(b) The height of the tunnel at the edge of the road is approximately 7.07 feet
The reason for the above answers are presented as follows;
(a) From a similar question posted online, the missing part of the question
is, what is the height of the tunnel at the edge of the road
The known parameters;
The shape of the tunnel = One-half sine curve cycle
The height of the road at its highest point = 10 ft.
The opening of the tunnel at road level = 24 ft.
The unknown parameter;
The equation of the sine curve that fits the opening
Method;
Model the sine curve equation of the tunnel using the general equation of a sine curve;
The general equation of a sine curve is y = A·sin(B·(x - C) + D
Where;
y = The height at point x
A = The amplitude = The distance from the centerline of the sine wave to the top of a crest
Therefore;
The amplitude, A = The height of half the sine wave = The height of the tunnel = 10 ft.
D = 0, C = 0 (The origin, (0, 0) is on the left end, which is the central line)
The period is the distance between successive points where the curve passes through the center line while rising to a crest
Therefore
The period, T = 2·π/B = 2 × Opening at the road level = 2 × 24 ft. = 48 ft.
T = 48 ft.
We get;
48 = 2·π/B
B = 2·π/48 = π/24
By plugging in the values for A, B, C, and D, we get;
y = 10·sin((π/24)·(x - 0) + 0 = 10·sin(x·π/24)
The equation of the sine curve that fits the opening is y = 10·sin(x·π/24)
(b) The height of the tunnel at the edge of the road is given by substituting
the value of x at the edge of the road into the equation for the sine curve
as follows;
The width of the shoulders = 6 feet
∴ At the edge of the road, x = 0 + 6ft = 6 ft., and 6 ft. + 12 ft. = 18 ft.
Therefore, we get;
y = 10 × sin(6·π/24) = 10 × sin(π/4) = 5×√2
y = 10 × sin(18·π/24) = 10 × sin(3·π/4) = 5×√2
The height of the, y, tunnel at the edge of the road where, x = 6, and 18 is y = 5·√2 feet ≈ 7.07 ft.
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