Shape of the distribution of the mean is appropriately normal.
What is sampling distribution ?The sampling distribution for a given population is the frequency distribution of the different outcomes that can occur for a population statistic.
In statistics, the population is the entire pool from which statistical samples are drawn. Population can refer to an entire group of people, things, events, visits, or measurements. Populations can therefore be described as aggregated observations from subjects grouped according to common characteristics.
CalculationFrom the given information
X:- impact force produced
X follows normal distribution with mean 30 and standard deviation of 3
n=3
As we know that when random sample is drawn from normal population then sample mean always follows normal distribution irrespective with sample size.
Shape of the distribution of the mean is appropriately normal.
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calculate a 90% confidence interval for the mean airborne time for flights from san francisco to washington dulles. (round your answers to three decimal places.)
The 90% confidence interval for the mean is (264.6935,275.5065)
What is meant by confidence interval?A confidence interval (CI) in frequentist statistics is a range of estimates for an unknown parameter. A confidence interval is calculated at a specified confidence level; the 95% confidence level is the most frequent, but other levels, such as 90% or 99%, are occasionally used. The confidence level denotes the long-run proportion of related CIs that include the true value of the parameter. For example, 95% of all intervals generated at the 95% level should contain the parameter's true value.
From the given data ,
Sample mean = X = 270.1
Sample standard deviation = s = 9.3268
n = 10
Therefore , the 90% confidence interval for the mean is ,
[tex]\bar{X}[/tex]±[tex]t_{n-1,\alpha /2}[/tex](s/√n)
270.1 ± [tex]t_{10-1.0.10/2}[/tex](9.3268/√10)
270.1 ±1.8331 ×2.9494
270.1 ± 5.4065
(264.6935,275.5065)
Therefore, the 90% confidence interval for the mean is (264.6935,275.5065)
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The complete question is:
"The following are airborne times (in minutes) for 10 randomly selected flights from San Francisco to Washington Dulles airport. 269 255 267 285 274 275 266 258 271 281
(a) Compute a 90% confidence interval for the mean airborne time for flights from San Francisco to Washington Dulles. (Round your answers to three decimal places.)"
which two angles have the same measure?
Answer:
1 and c or 3 I´m not sure what the third angle labeled is
Step-by-step explanation:
The reason why is because they are corresponding angles which makes them equal to each other.
Hope this helped
write equation f the line passing through points (6,-2) (4,10)WILL GIVE BRAINLY PLS HELP
Answer:y=-6x+34
Step-by-step explanation: I hope this helps
if you have 240 meters of fencing and want to enclose a rectangular area up against a long, straight wall, what is the largest area you can enclose?
The largest area that can be enclosed by a fence of 240 m and a wall is 7200m²
It is given that the rectangular area will be fenced up against a long rectangular wall. Therefore, the fencing will be done on just three sides.
Let one side be x
Then the side opposite to it must be x cm as well
The sum of the three sides should be equal to 240 m
Hence the third side must be 240 - 2x m
Therefore the area of the region fenced must be
A = x(240 - 2x)
or, A = 240x - 2x²
Now we need to maximize the above equation
Taking the first derivative zero we get
A' = 0
or, 240 - 4x = 0
or, 60 - x = 0
or, x = 60
Now we will test whether the above output is maximum or not. The second derivative of A is
A'' = -4
Since A'' is a constant function,
Now, A''(60) = -4
Therefore, the maximum side will have lengths of 60 m and 120 m.
Hence the largest area that can be enclosed with the fence is
60 X 120 m²
= 7200 m²
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For a circle with a radius = 4.3, find the following
The circumference is 27.004 and the Area is 58.0586 calculated for the circle with radius of 4.3 and π = 3.14
Circumference and Area of a circleThe circumference of a is the arc length of the circle with the formula 2πr. While the area of a circle is calculated with formula πr²
Given radius r = 4.3 and π = 3.14
circumference = 2 × 3.14 × 4.3
circumference = 27.004
Area of the circle = 3.14 × 4.3²
Area of the circle = 3.14 × 4.3 × 4.3
Area of the circle = 58.0586
Therefore, the circumference and area of the circle with radius of 4.3 is 27.004 and 58.0586 respectively.
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lescribed below.
9. Translate left 12 units, stretch by a factor of 4,
and reflect over the x-axis. Then state the
vertex.
g(x)=
vertex:
Translate left 12 units, stretch by a factor of 4, and reflect over the x-axis. Then state the vertex. g(x)= vertex:
Using the transformation concepts, it is found that:
The rule for g is: [tex]g(x) = -4x^{2}[/tex]
The vertex is: (0,0).
Stretching a function f(x) vertically by a factor of b is given by:
[tex]g(x) - bf(x)[/tex]
Reflecting a function over the x-axis is the equivalent of:
g(x) = -f(x)
The original function is: [tex]f(x) = x^{2}[/tex]
Stretching by a factor of 4 means that the function is multiplied by 4, thus: [tex]g(x) = 4x^{2}[/tex]
Reflecting over the x-axis, that is, multiplying by -1, we have that: [tex]g(x) = -4x^{2}[/tex], which is the rule for g.
From the above equation, added at the end of this answer, the vertex is at (0,0).
Hence the answer is the vertex is at (0,0)
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Suki has placed $800 in an account that pays 4 percent interest compounded quarterly. At the end of two years (eight quarters), the balance in the account will be $. That means suki will have earned $ in interest during that time. (round your answers to the nearest cent. ) what will be the balance in the account at the end of two years (eight quarters)? how much interest will suki have earned during that time? (round your answers to the nearest cent. ).
The account balance at the end of two years (eight quarters) is $866.24.
Suki earned $66.24 interest during that time.
What do you mean by interest rate?
The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number.
According to data in the given question,
We have:
Placed amount= A= $800
Interest rate (quarterly)= r= 4%
Time= t = 2 years
Now, we will using the formula below:
[tex]A=P(1+\frac{r}{n} )^{nt}\\=800(1+\frac{0.04}{4} )^{4*2}\\=800(1+0.01 )^{8}\\=800(1.0828)\\=866.24[/tex]
So, the account balance at the end of two years (eight quarters) is $866.24.
Then, we have to determine the earned interest during that time,
Earned interest= A-P
= 866.24 - 800
= 66.24
Therefore, she earned $66.24 interest during that time.
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A recipe uses 5 cups of flour for every 2 cups of sugar. How much sugar is used for every cup of flour?
A recipe uses 5 cups of flour for every 2 cups of sugar. How much sugar is used for every cup of flour?
2/5 = 0.4
so there is 0.4 cups of sugar used for every one cup of flour.
The quantity of an element is decaying over time such that the amount of material at any time is given by the function G(t)=9000(0.7)^2t. Write an equivalent function of the form G(t)=ab^t
Answer:
see below
Step-by-step explanation:
= 9000 ( .7^2) ^t = 9000 (.49)^t
Answer:
[tex]G(t)=9000(0.49)^{t}[/tex]
Step-by-step explanation:
Given function:
[tex]G(t)=9000(0.7)^{2t}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies G(t)=9000(0.7^2)^{t}[/tex]
Simplify:
[tex]\implies G(t)=9000(0.49)^{t}[/tex]
The area of a sign in the shape of a square is 219 square inches. Which measurement is closest to the side length of this sign in inches?.
The measurement closest to the side of this sign is 15 inch.
Area of Square is a², where 'a' is the length of a side of a square.
The Area of square is 219 in²,
Therefore, a²=219
Adding square roots to both sides..
√a² = √219
a = 14.798
=15 inches (nearest value)
Hence, the closest value of the side is 15 inches.
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according to smith travel research, the average hotel price in the united states in 2009 was $97.00. assume the population standard deviation is $18.00 and that a random sample of 40 hotels was selected. what is the probability that a randomly selected sample mean will be more than $100?
The probability that a randomly selected sample mean will be more than $100 = 0.14082.
We are given that according to a research institution, the average hotel price in a certain year was $97.00.
Assume the population standard deviation is $18.00 and that a random sample of 40 hotels was selected.
Here, Mean = μ = $97.00 and Standard deviation = σ = $18 and n = 40
(a) Standard error of the mean = σ/[tex]\sqrt{n}[/tex] = 18/[tex]\sqrt{40}[/tex] = 2.74
(b) Let X bar = Sample Mean
The z score probability distribution for sample mean is ;
Z = Xbar-μ/ σ/[tex]\sqrt{n}[/tex] ~ N(0,1)
So, Probability that the sample mean will be less than $102 = P(X bar < $102)
P(X bar < 102) = P(Xbar-μ/ σ/[tex]\sqrt{n}[/tex] < 102 - 97.00/ 18/[tex]\sqrt{40}[/tex]) = P(Z < 0.74) = 0.7704
(c) Probability that the sample mean will be more than $104 =P(X bar > $104)
= P(X bar > 104) = P(Xbar-μ/ σ/[tex]\sqrt{n}[/tex] < 104 - 97.00/ 18/[tex]\sqrt{40}[/tex]) = P(Z > 1.47) = 1 - P(Z <= 1.47)
= 1 - 0.92922 = 0.0708
(d) Probability that the sample mean will be between $99 and $100 is given by = P($99 < X bar < $100) = P(X bar < $100) - P(X bar <= $99)
= P(X bar < 100) = P(Xbar-μ/ σ/[tex]\sqrt{n}[/tex] < 100 - 97.00/ 18/[tex]\sqrt{40}[/tex]) = P(Z < 0.01) = 0.50399
= P(X bar <= 99) = P(Xbar-μ/ σ/[tex]\sqrt{n}[/tex] <= 99 - 97.00/ 18/[tex]\sqrt{40}[/tex]) = P(Z <= -0.35) = 1 - P(Z <= 0.35)
= 1 - 0.63683 = 0.36317
Therefore, P($99 < X bar < $100) = 0.50399 - 0.36317 = 0.14082 .
Hence the answer is the probability that a randomly selected sample mean will be more than $100 = 0.14082.
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ASAP
(8.2 x 10^-3) x (2.0 x 10^2)=?
The value of the expression is 1.64.
What is an exponent?The number of times a number is multiplied by itself is referred to as an exponent.
The given expression is (8.2×10⁻³)×(2.0×10²).
Simplify the expression as follows:
(8.2×10⁻³)×(2.0×10²)
=16.4×10⁻³⁺²
= 16.4 × 10⁻¹
= 16.4 × 1/10
= 1.64
Hence, the value of the expression is 1.64.
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Jackon i working two ummer job, making $10 per hour wahing car and $12 per hour landcaping. Lat week Jackon worked a total of 14 hour and earned a total of $152. Determine the number of hour Jackon worked wahing car lat week and the number of hour he worked landcaping lat week
The number of hour Jackon worked washing car last week = 8 hours and no . of hours he spent on landcaping = 6 hours .
Let x be no . of hours spent washing car and y be no . of hours spent in landcaping .
According to question ,
x + y = 14 ....... eqn ( 1 )
( 10 * x ) + ( 12 * y ) = 152
10 x + 12 y = 152 ...... eqn ( 2 )
Solving linear eqn in 2 variable
Mult . eqn ( 1 ) by 10 ,
10 x + 10 y = 140 ....... eqn ( 3 )
Subtracting eqn ( 2 ) from eqn ( 3 ) we get ,
( 10 x + 10 y ) - ( 10 x + 12 y ) = 140 - 152
- 2 y = - 12
y = 6
Substituting value of y in eqn ( 1 )
x = 8
Hence , the no . of hour Jackon worked washing car last week = 8 hours and no . of hours he spent on landcaping = 6 hours .
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g 6. if you had to hike up the top of stone mountain which side would you choose to climb? why? (remember your rules about contour intervals! use the cardinal direction in your description.) 7. you do not have enough information from this map to calculate the slope. what are you missing?
I would choose the western side to climb because it is less steep then others.
What is steepness?In mathematics, a line's steepness is determined by its slope (or gradient). The slope is the ratio of any two points on a line's vertical and horizontal distances. A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope's absolute value serves as a gauge for a line's steepness, incline, or grade. A steeper line is indicated by a slope with a higher absolute value. A line can be drawn with one of four directions: upward, downward, horizontal, or vertical. If a line rises from left to right, it is said to be increasing.
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Prove algebraically that the sum of 1/2n(n+1) and 1/2(n+1)(n+2) is always a square number.
This proves that the sum of 1/2n(n+1) + 1/2(n+1)(n+2) is always a square number.
What is square number?When a number is multiplied by itself, the result is a square number. As an illustration, 25 is a square number as it is composed of 5 groups of 5, or 5 x 5. A square number, sometimes known as a perfect square, is an integer that is the square of another integer, or the result of multiplying another integer by itself. For instance, 9 is a square number as it equals 32 and is represented by the symbols 3.
Here,
Find the sum:
=1/2n(n+1) + 1/2(n+1)(n+2)
=1/2(n² + n) + 1/2(n² + 3n + 2)
=1/2(n² + n + n² + 3n + 2)
=1/2(2n² + 4n + 2)
=n² + 2n + 1
=(n + 1)²
This demonstrates that 1/2n(n+1) + 1/2(n+1)(n+2) is always a square number when added together.
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The density of grape juice is 1.07 grams per cm³.
The density of fruit syrup is 1.6 grams per cm³.
The density of carbonated water is 0.99 grams per cm³.
35 cm³ of grape juice are mixed with 25 cm³ of fruit syrup and
310 cm³ of carbonated water to make a drink with a volume of 370 cm³.
Work out the density of the drink.
Give your answer correct to 2 decimal places.
Answer:
2
Step-by-step explanation:
The density of the drink is approximately 1.04 g/cm³.
What is the density?Density is the ratio of mass and volume.
density = mass/volume
To work out the density of the drink, you will need to calculate the total mass of the drink and then divide it by the volume of the drink.
First, you can calculate the mass of the grape juice by multiplying the density of grape juice by the volume of grape juice:
Mass of grape juice = Density of grape juice x Volume of grape juice
= 1.07 g/cm³ * 35 cm³
= 37.45 grams
Then, you can calculate the mass of the fruit syrup in the same way:
Mass of fruit syrup = Density of fruit syrup x Volume of fruit syrup
= 1.6 g/cm³ x 25 cm³
= 40 grams
Finally, you can calculate the mass of the carbonated water in the same way:
Mass of carbonated water = Density of carbonated water x Volume of carbonated water
= 0.99 g/cm³ * 310 cm³
= 308.9 grams
To find the total mass of the drink, you can add the mass of the grape juice, the mass of the fruit syrup, and the mass of the carbonated water:
Total mass of drink = 37.45 grams + 40 grams + 308.9 grams
= 386.35 grams
To find the density of the drink, you can divide the total mass of the drink by the volume of the drink:
The density of drink = Total mass of drink / Volume of drink
= 386.35 grams / 370 cm³
= 1.04 g/cm³
Therefore, the density of the drink is approximately 1.04 g/cm³.
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sushilava
3 hours ago
Mathematics
High School
You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is 0. How confident can you be that your predicted value will be reasonably close to the actual value?
Responses
I can’t be confident at all; this is about as close to a random guess as you can get.
I can be a little confident; it might be close, or it might be way off.
I can be very confident; it will be close, but it probably won’t be exact.
Answer:
I can’t be confident at all; this is about as close to a random guess as you can get.
Step-by-step explanation:
A correlation coefficient of 0 ⇔ no linear relationship
Felipe is paid $1,000 every month plus an additional bonus for every tractor he sells, x. Write an equation to represent the total amount of money, y, Felipe makes every month
The linear equation representing the total amount of money Felipe makes every month be
y = x + 1000
Given, Felipe is paid $1,000 every month plus an additional bonus for every tractor he sells, x.
Let the total amount of money be, y
as, felipe gets a fixed amount i.e. $1000 every month.
now, let felipe gets 'x' amount as the additional bonus.
So, the linear equation be,
y = 1000 + x
Hence, the linear equation representing the total amount of money Felipe makes every month be
y = x + 1000
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can you guys please answer this? its timed so dont take too long!
The expression equivalent to (5z² + 3z + 2)² is 25x⁴ + 30z³ + 29z² + 12z + 4.
The correct answer option is option D
What is the equivalent expression?(5z² + 3z + 2)²
Expand the expression(5z² + 3z + 2) (5z² + 3z + 2)
= 25z⁴ + 15z³ + 10z² + 15z³ + 9z² + 6z + 10z² + 6z + 4
collect like terms= 25x⁴ + 15z³ + 15z³ + 10z² + 9z² + 10z² + 6z + 6z + 4
= 25x⁴ + 30z³ + 29z² + 12z + 4
In conclusion, the equivalent expression is 25x⁴ + 30z³ + 29z² + 12z + 4.
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factorise 3xsquared+5x+2
The charge of 0.25 quintal to a certain distance is Rs45, how many quintals can be carried for Rs180 to the same direction
1 Quintal can be carried for Rs 180 to the same direction.
Given that the charge of 0.25 quintal to a certain distance is Rs 45.
With Rs 45, 0.25 quintals can be carried.
With Rs 1, 0.25/45 quintals can be carried in same direction.
With Rs 180, (0.25*180)/45 = 1 quintal can be carried in same direction.
Hence 1 Quintal can be carried for Rs 180 to the same direction.
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em.
AWAL
2 Mr. Olin bought 6 sketchbooks for the
students in his art class. Each sketchbook
was on sale for $3 off. If the sketchbooks
cost $18 total before tax, what was the
original price of each sketchbook?what is the two step equation?
The original price of each sketchbook is $6
Mr. Olin bought 6 sketchbooks for the students in his art class.
If the sketchbooks cost $18 total before tax
Each sketchbook was on sale for $3 off
We need to calculate the original price of each sketch book.
If the sketchbooks cost $18 total before tax
Cost of each text book = total cost / number of sketchbooks
= 18/6 = 3
Cost of each sketch book is $3
Each sketchbook was on sale for $3 off
Cost price = original price = discount
3 = original price - 3
original price = 6
Therefore, the original price of each sketchbook is $6
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A group of students was recently polled about the technology they own. Create a vent diagram from the information below
69 own cell phone
45 own a computer
23 own an iPod
4 do not own any of the above three items
34. Own all three, a computer, an iPod , and an cell phone
8 own a cell phone and an iPod but not a computer. How many students were polled?
As per the given data about the group of student, total number of students polled about the technology they own is equal to 99.
As given in the question,
Let 'n(U)' represents the total number of students polled about the technology they own.
Number of students own cell phone = 69
Number of students own a computer = 45
Number of students own a iPod = 23
Number of students own nothing of the above items = 4
Number of students own all three items = 34
Number of students own a cell phone and an iPod but not computer = 8
Total number of students polled
= 69 + 45 + 23 + 4 + 34 - 8
= 99
Therefore, for the given data about the group of student, total number of students polled about the technology they own is equal to 99.
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In machine tool feed rate or dimenional change notation, dimenional ditance i related to rotation or travel change. Three of the more common notation are IPM, IPR, or TPI, In each of thee expreion R=_____, T=_____, and I=_____
A. Rotational, total, inertion
B. Revolution, taper, inche
C. Radiu, turn, increment
D. Radian, taper, inch
The R means Revolution, T means taper and I means inch. The correct option is B.
Given that in machine tool feed rate or dimensional change notation, dimensional distance i related to rotation or travel change.
We want to find the expression R, T and I.
Machining center programmers specify spindle speed in revolutions per minute (RPM). Feedrates per minute are often given in either inches per minute (ipm) or millimeters per minute (mmpm).
From the above definition, we get that R means Revolution, I means inch and T means taper.
Hence, The expressions R means revolution, T means taper and I means inch for the three of the more common notation are IPM, IPR, or TPI.
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suppose 150 returns from this year are selected and analyzed regarding the preparation time. what is the probability that the mean time for the sample of 150 returns for this year is greater than 92?
The probability that the mean time for the sample of 150 returns for this year is greater than 92 is 0.04006.
In the given question,
The mean time to prepare a return is 90 minutes. So μ = 90.
The population standard deviation of this distribution is 14 minutes. So σ=14.
150 returns from this year are selected and analyzed regarding the preparation time. So n = 150.
Then we have to find the probability that the mean time for the sample of 150 returns for this year is greater than 92.
μx = μ = 90
σx = σ/√n = 14 /√150 = 1.14
P (x>92 ) = 1-P(x<92)
= 1 - P[z < (x-μx)/σx]
= 1 - P[z < (92-90)/1.14}
= 1 - P ( z < 1.754)
Using standard normal table
= 1 - 0.95994
= 0.04006
Probability = 0.04006
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The right question is:
Bones Brothers & Associates prepare individual tax returns. Over prior years, Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes, and the population standard deviation of this distribution is 14 minutes. Suppose 150 returns from this year are selected and analyzed regarding the preparation time. What is the probability that the mean time for the sample of 150 returns for this year is greater than 92?
Match the expression on the left with its simplified form on the right. Answer options on the right may be used more
than once.
-(-1)
-|-1|
-|1|
|1|
|-1|
1
-1
The solutions of the expressions -(-1), -|-1|, -|1|, |1|, and |-1| are 1, -1, -1, 1, and 1.
We are given five expressions. An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. The first expression is -(-1). The simplified solution of the first expression is 1. The second expression is -|-1|. The simplified solution of the first expression is -1. The third expression is -|1|. The simplified solution of the first expression is -1. The fourth expression is |1|. The simplified solution of the first expression is 1. The fifth expression is |-1|. The simplified solution of the first expression is 1.
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You work for an electric company and make a base pay of $200 every two weeks. You earn and extra
$15 for each hour you work. Write a function to model this scenario using f(h) for the amount of
money made and h for the hours of worked.
Answer: f=15h+200
Step-by-step explanation:
h=hours
15$ and hour
mutiply hours and dollars add base pay
f for total money made :)
On god I need help with this
Answer:
below
Step-by-step explanation:
Domain is the set of all x values a function can have
this one goes from - inf to the asymtope at x = 2
(-∞, 2) domain
range is the y values the function can have
looks like 0 to - inf
(- ∞, 0] ( but it COULD be ( -∞, 0) <===cannot tell from graph)
What is the image point of (8,4)(8,4) after a translation left 2 units and down 4 units?
The image of point (8,4) after translation is (-6,0).
What is image of a point?
A transformation where a point is moved across a certain line, called the line of reflection, to appear at an equal distance.
Main Body:
Given point is (8,4)
Translation in the point is left 2 units, down 4 units.
so left- right translation is done on x-axis where moving left means subtracting is while up - down translation is done on y- axis where moving down means subtracting.
Which means 2 units will be subtracted from x-axis and 4 units from y-axis
New point = (8-2 ,4-4)
= (6,0)
Image of point (6,0) according to y-axis will be (-6,0).
Hence image point is (-6,0)
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20 POINTS
please use what is provide and converse it simply for my monkey brain
Answer:
Step-by-step explanation:
Inverse matrix:
