the standard deviation of the sample means:
σ(x) = σ/[tex]\sqrt{n}[/tex]
The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement text annotation indicator, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large (usually n > 30). If the population is normal, then the theorem holds true even for samples smaller than 30. In fact, this also holds true even if the population is binomial, provided that min(np, n(1-p))> 5, where n is the sample size and p is the probability of success in the population. This means that we can use the normal probability model to quantify uncertainty when making inferences about a population mean based on the sample mean.
For the random samples we take from the population, we can compute the mean of the sample means:
μ (x) = μ
and the standard deviation of the sample means:
σ(x) = σ/[tex]\sqrt{n}[/tex]
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Out of 168 randomly selected adults in the United States who were surveyed, 89 exercise on a regular basis. Construct a 98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis. Round to three decimal places.
98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis is 0.440 < P < 0.619.
What does a statistical random sampling entail?
A selection of participants from a population are chosen at random by the researcher using simple random sampling, a sort of probability sampling.Every person in the population has the same chance of being chosen. Then, data are gathered from as much of this randomly selected subgroup as possible.P = x/n
= 89/168
= 0.53
α= 0.02
∴ Zc = Zi - α/2
= 2.326
Now, C.I = P ± Zc * √[P(1-P)/n]
= 0.5 ± 2.326 *√[(0.53(1-0.53)) / 168
= (0.440, 0.619)
∴98% C.I. = 0.440 < P < 0.619
Hence, 98 % confidence interval for the proportion of all adults in the United States who exercise on a regular basis is 0.440 < P < 0.619.
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a theater has 20 rows with 28 seats in the first row, 33 in the second row, 38 in the third row, and so forth. how many seats are in the theater?
The number of seats in the theater is 1510.
Here we have to find the number of seats in the theater.
Data given:
Total row = 20
number of seats on the first row = 28
number of seats on the second row = 33
number of seats on the third row = 38
Therefore we get the series as 28, 33, 38......., which is in arithmetic sequence.
The common difference (d) = 5
Here we have to find the sum of the series.
The formula for the sum of n term of the arithmetic sequence:
[tex]S_{n}[/tex] = n/2( 2a + (n-1)d)
= 20/2 ( 2× 28 + (20 -1) 5)
= 10 ( 56 + 19×5)
= 10( 56 + 95)
= 10 ×151
= 1510
Therefore the number of seats is 1510.
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a dog of this breed weighs 48 pounds. what is the dog's z-score? round your answer to the nearest hundredth as needed. z
If the dog has a z-score of -1.09, his weight is 48.46kg but if the dog has a z-score of 1.09, his weight is 61.54kg according to given standard deviation.
What is standard deviation?
Standard Deviation is a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exists. the quality deviation indicates a “typical” deviation from the mean. it's a well-liked live of variability as a result of it returns to the first units of live of the info set.
Main body:
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = x- υ/σ
Given that μ = 55, σ = 6;
For x = 49:
z = 49 - 55/6
z = -1
If the dog has a z-score of -1.09, his weight is:
-1.09 = x -55/6
x - 55 = -6.54
x = 48.46
If the dog has a z-score of 1.09, his weight is:
1.09 = x - 55/6
x -55 = 6.54
x = 61.54
Hence ,If the dog has a z-score of -1.09, his weight is 48.46kg but if the dog has a z-score of 1.09, his weight is 61.54kg
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the number of pollinated flowers as a function of time in days can be represented by the function
f(x)=(3) x/2
what is the average increase in the number of flowers pollinated per day between days 4 and 10
The average increase in the number of flowers pollinated per day between days 4 and 10 is 39.
What is average increase?
Average increase refers to the average rate of growth that a variable experiences within a given period.
According to the given question:
The number of pollinated flowers as a function of time in days is represented by the function f(x) = [tex]3^{(x/2)[/tex]
To find the average increase in the number of flowers pollinated per day between days 4 and 10, we use the formula
{f(10) - f(4)}/{10 - 4}
Now f(10) = [tex]3^{(10/2)[/tex]
= 243
Also f(4) = [tex]3^{(4/2)[/tex]
= 9
Therefore average increase = {f(10) - f(4)}/{10 - 4}
= (243 - 10)/10 - 4
= 234/6
= 39
Thus, the average increase in the number of flowers pollinated per day between days 4 and 10 is 39.
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n interval estimation, as the sample size becomes larger, the interval estimate remains the same, because the mean is not changing. gets closer to 1.96. becomes narrower. becomes wider.
In interval estimation, when the sample size have become larger then the interval estimate then it will becomes narrower. Option (c) is correct.
A large sample of pattern length or decrease variability will bring about a tighter self belief c program interval with a smaller margin of error. A smaller pattern length or a better variability will bring about a much wider self belief c program interval with a bigger margin of error. The stage of self belief additionally impacts the c program interval width. The large your pattern, the greater certain you may be that their solutions genuinely mirror the population.
This suggests that for a given self belief stage, the bigger your pattern length, the smaller your self belief c program language period. The width of the self belief c program interval for an character observe relies upon to a massive volume at the pattern length. Larger research generally tend to provide greater unique estimates of effects (and therefore have narrower self belief intervals) than smaller research.
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Correct Question:
In interval estimation, as the sample size becomes larger, the interval estimate
a). remains the same, because the mean is not changing.
b). gets closer to 1.96.
c). becomes narrower.
d). becomes wider.
A biased coin is tossed 10 times and the probability of obtaining heads is 0. 6. Find the probability of obtaining the following. Round answers to the nearest ten-thousandth.
When a biased coin is tossed ten times, the likelihood of getting at least nine heads is 0.0463.
Explain the term Binomial distribution?This binomial probability distribution makes the assumption that there are two possible outcomes for each trial and that the number of tests is independently distributed.The binomial distribution's PMF is;
P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ
There were 10 trials.0.6 percent chance of receiving a headFollowing are the results of a calculation using a binomial distribution to determine the likelihood of receiving at least 9 heads.
P(X ≥ 9) = P(X = 9) + P(X = 10)
P(X ≥ 9) = ¹⁰C₉. (0.6)⁹ (1 - 0.6)¹ + ¹⁰C₁₀. (0.6)¹⁰ (1 - 0.6)⁹
P(X ≥ 9) = 0.0403 + 0.0060
P(X ≥ 9) = 0.0463
Thus, when a biased coin is tossed ten times, the likelihood of getting at least nine heads is 0.0463.
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The complete question is-
A biased coin is tossed 10 times and the probability of obtaining heads is 0.6.
Find the probability of obtaining at least 9 heads. Round answer to the nearest ten-thousandth.
Cameron earns an hourly wage at his job. He makes a table of the number of hours he works each week and the amount of money he earns. Assume that Cameron works between 2 and 8 hours a day, for 5 days per week. Identify the constraints on the domain. Describe the domain using inequality or set-builder notation
For Cameron's job, the restrictions on the domain are 168 hours for the hourly rate.
Define the term set-builder form?x: Characteristic of x or x | Characteristics of x is the generalized form of such a set-builder notation. Here, the letter x (but other letters, such as y, z, a, b, or c, may also be used) is used to represent a set element, and it is followed by either a colon (":") or a vertical line ("|").The total number of hours affects how much money is made.
This suggests that the amount of money made is the result of the number of hours put in.
A week can only have a total of 168 hours (24 x 7).
Thus, the domain for the hourly wage of Cameron.
24 x 7 < 168
Since 168 hours is the maximum that can be completed in a week, this represents the constraint mostly on domain.
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A pentagon is made up of an equilateral △ABC of side length 2cm on top of a square BCDE. Circumscribe a circle through points, A,D and E. The radius of the circle is
A1+√32
B5−2√3
C 2
D 1+√3
The circle's radius circumscribed through points, A,D and E are 2 units.
Look at the image of the figure attached below for a better understanding of the solution :
From the given figure, we can conclude the following data:
AP = √3/2(a) → 1 length of the median for the triangle of side a.
by putting the value of a. we get:
AP = √3/2(2) = √3
AQ = AP + PQ = √3 + 2
Area of triangle AEΔ = 1/2 × EΔ × AQ = 1/2(2) (√3+2)
AE = AD = √(EQ)² + (AQ)²
= √(1)² + (2+√3)² = √1+4+3+4√3 = √8+4√3
= 2√2+√3
We know that,
R = abc/4Δ
R = 2(2×√2+√3) (2√2+√3) / 4{1/2×2×(√3+2)}
R= 2{4(2+√3)} / 4(√3+2)²
On solving the above equation we get ,
R = 2 units.
As a result, the radius of the circle is 2 units when it is defined by the points A, D, and E.
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what is the equation of the line on the graph?
Answer:y=2x+-1
Step-by-step explanation:
y= slopex + y-intercept, the y-intercept is at the point (0,-1) as the y-intercept is when the x coordinate is 0 and the y coordinate gets touched by the y axis, therefore 2x+-1
What is the answer in standard form?
y=-9+5x
Answer: 9x - y = -5
Step-by-step explanation:
Veronica's birthday was coming up. Her mother bought six packages of cupcake mix. Each package could make 12 cupcakes. 24 people had planned to attend Veronica's party. How many cupcakes would be available for each guest?
Answer:
3 cupcakes per person
Step-by-step explanation:
first we need to find the total number of cupcakes so in order to do that we need to multiply the number of mixes and the number of cupcakes each mix would make so:
total number of cupcakes = 6 * 12 = 72
now we can divide it by the total number of people who attended the party so:
72/24 = 3 cupcakes per person
Brainlist + 100 points if correct and well explained:
Graph the line 2x − 3y = 12.
a: The graph shows a line through the points 0 comma 4 and 6 comma 0.
b: The graph shows a line through the points 0 comma negative 4 and 6 comma 0.
c: The graph shows a line through the points 0 comma 4 and negative 6 comma 0.
d: The graph shows a line through the points 0 comma negative 4 and negative 6 comma 0.
Pretty sure it's C!!! :))))))))))))
what is the even function?
Reason:
Every exponent shown for choice A is an even number, which by extension points us to an even polynomial function.
Choice D has all odd exponents (think of [tex]\text{x}[/tex] as [tex]\text{x}^1[/tex]), which means choice D is an odd polynomial function.
Choices B and C have a mix of even and odd exponents for their terms. This means B and C are neither even nor odd.
Determine if the equations represent lines that are parallel, perpendicular, or neither. Equation 1: 14x=2y-6 Equation 2: 8/7 =y-7x
Answer:
Parallel
Step-by-step explanation
Put into y=mx+b
Equation 1:
14x=2y-6
add 6
14x+6=2y
Divide by 2
7x+3=y
Equation 2:
8/7=y-7x
add 7x
7x+8/7=y
Look at the slope of each equation (the x)
1: 7x and 2. 7x
The slopes are the same so the lines are parallel
Hope this helped!
if the mean of a population is 250 and its standard de- viation is 20, approximately what proportion of obser- vations is in the interval between each pair of values?
Observed proportions (relative frequencies) from a sample are statistics that can be used to estimate probabilities.
a) Thre is 99.73% proportion of observations is in between 190 and 310 .
b)there is 95.44% proportion of observations is in between 210 and 290 .
We have given that,
Mean of population, μ = 250
standard deviations, σ = 20
we have to calculate proportion of observations in the given interval pair.
a) pair of values are 190 and 310
Using Z-score formula,
Z =( x - μ) /σ
=> Z = (190 - 250) / 20 = -3
Similarly, Z = (310 - 250)/20 = 3
So, -3 < z < 3 and from Z score we found p-value
P(190<X<310) = P( 190-u/sd < X-u/sd < 310-u/sd)
= P( X< 310 ) - P(X<190) = P(Z < 3) - P( Z< -3 )
=0.99865 - 0.00135 0.9973 = 99.73%
b) pair is 210 and 290
Z-Score = (210-250)/20 = -2
Z-score = (290-250)/20 = 2
so, -2 < z < 2
From Z score we found p-value
P(210<X<290) = P(X<290) - P(X<210)
= P(Z< 2) - P(Z< -2)
= 0.9772 - 0.0228 = 0.9544 = 95.44%
So, the required proportion are 99.73% and 95.44% proportion of observations in each given pair.
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Complete question:
If the mean of a population is 250 and its standard deviation is 20, approximately what proportion of observations is in the interval between each pair of values? a 190 and 310 b. 210 and 290.
the amount that susan charges per hour for babysitting is directly proportional to the number of children she is watching. she charges $4.50 for 3 kids. how much would she charge to babysit 5 kids? $3.33 $7.50 $6.50 $1.50
Susan would charge $7.50 to babysit 5 kids.
The unitary method is used to calculate the value of a single unit from a given multiple. If the cost of 40 pens is Rs. 400, how do you calculate the value of one pen? The unitary method can be used to accomplish this. Furthermore, once we've determined the value of a single unit, we can multiply that value by the number of units needed.
Given,
Amount charged for 3 kids =$4.50
then,
Amount charged for 1 kid will be [tex]\frac{4.50}{3}=$1.50[/tex]
now, amount charge to babysit 5 kids =1.50*5=$7.50
Thus, Susan would charge $7.50 to babysit five children..
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select all valid relational set operators from the list below. select all that apply. group of answer choices plus union unionize except
The Union of South American Nations (UNASUR) is not a regional alliance.
What is the Union of South American Nations?
The Union of South American Nations was formed in 2008 to further the interests of South American nations. It was an intergovernmental union and that was meant to bring more prosperity to the region.
There are also plans to make UNASUR a single-currency union. The Union of South American Nations was never meant to be a regional alliance however.
complete question is
the union of south american nations (unasur) is considered all of the following except (5 points) group of answer choices a supranational organization an intergovernmental union a single-currency union a regional alliance
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Akeem created a list by correctly putting a group of fraction in percentage and decimals order from least to greatest valve which list could be the one Akeem created
List could be the one Akeem created is option D . 0.21 22% 1/4 0.35 3/8 38%.
Given:
Akeem created a list by correctly putting a group of fraction in percentage and decimals order from least to greatest value.
Least to greatest value:
Option D :
0.21 22% 1/4 0.35 3/8 38%
= 22 %
= 22 / 100
= 0.22
1/4 = 0.25
3/8 = 0.375
38 = 38 / 100
= 0.38
0.21 < 0.22 < 0.25 < 0.35 < 0.375 < 0.38.(least to greatest)
Hence Option D is correct.
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Full question:
Is in the image uploaded.
12 shirts cost $59.36. Find the unit rate.
Answer:
divide 59.36 by 12 to get through cost of one = 4.95
Step-by-step explanation:
unit cost is the cost of one product
11. the measures of the four angles in a quadrilateral have a ratio of 2:3:6:7.2:3:6:7. what is the measure, in degrees, of the largest of these angles?
The measure of the largest angle of quadrilateral is 140°.
We have given that,
the ratio of angles of a quadrilateral is 2:3:6:7.
And we have to find the largest angle of quadrilateral.
We know that the sum of all the interior angles of quadrilaterals 360°.
Let the common multiple of angles be x,
therefore
2x + 3x + 6x + 7x = 360°
18x = 360°
x = [tex]\frac{360}{18}[/tex]
x = 20°
so the angles becomes,
2(20°) = 40°
3(20°) = 60°
6(20°) = 120°
7(20°) = 140°
Hence the largest of these angles is 140°.
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A truck delivers 568 oranges to grocery stores each week. How many oranges will it deliver in 25 weeks?.
how many integers must a set s contain to be certain that at least 35 integers in s have the same remainder when divided by 4?
Set S should contain 137 number of integers so that at least 35 integers in S have same remainder when divided by 4.
What is pigeonhole principle?According to the pigeonhole principle in mathematics, at least one container must hold more than one item if n things are placed into m containers, where n > m. As an illustration, if one has three gloves (none of which are ambidextrous or reversible), at least two of them must be right-handed or left-handed as there are three items but only two categories of handedness to classify them into. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.
Equating pigeonhole principle :Given: Set S = {}, least number of integers having same remainder when divided by 4=35
To find: Number of integers in set S so that at least 35 of the integers in set S have same remainder?As we know, any number when divided by 4 has following remainder = 0, 1, 2, 3.
Least number of integers having same remainder when divided by 4 = 35.
∴ Number of integers in set S = 35×4
= 140
but 3 is to be subtracted from 140 as it is the last different remainder after which the remainders repeat in manner 0, 1, 2 & 3.
∴ Total number of integers in set S = 140-3
= 137
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please help me with my homework Find the values of the variables assuming the figures are parallelograms
Adjacent angles of a parallelogram are supplementary.
[tex]3x+10+8x+5=180 \\ \\ 11x+15=180 \\ \\ 11x=165 \\ \\ \boxed{x=15} \\ \\ \\ \\ 5y+3(15)+10=180 \\ \\ 5y+55=180 \\ \\ 5y=125 \\ \\ \boxed{y=21}[/tex]
Brooklyn is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 23 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 24^{\circ} ∘ , and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 38^{\circ} ∘ . If her eyes are 1.66 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest meter if necessary.
The height of the antenna found using trigonometric ratios is about 8 meters
What are trigonometric ratios?Trigonometric ratios indicates the ratio of the sides of a right triangle, and have values based on the lengths of the sides of a right triangle, drawn on the coordinate plane.
The distance from the building at which Brooklyn stands = 23 meters
Angle of elevation from her eyes to the roof, θ = 24°
Angle of elevation from her eyes to the top of the antenna = 38°
Height of her eyes from the ground = 1.66 meters
[tex]tan(\theta) = \dfrac{Opposite}{Adjacent} = \dfrac{Height}{Horizontal \, distance}[/tex]
Therefore;
Height = Horizontal distance × tan(θ)
Height to the top of the roof, H₁ = Horizontal distance × tan(θ)
Therefore;
H₁ = 23 × tan(24°) ≈ 10.24
Height to the top of the antenna, H₂ = 23 × tan(38°) ≈ 17.97
Height of the antenna ≈ 17.97 - 10.24 ≈ 8
Height of the antenna is about 8 meters
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after a town is abandoned, the concrete parking lots remain empty and inactive for hundreds of years. what is the most likely order of ecological succession in that area?
The correct Option (B). Succession may be defined as the change in the ecological community of the species with respect to time. Two main types of succession are primary succession and secondary succession.
The living things that accumulate in the succession is from the simple organism to the complex organism. First lichens will evade in the land. After lichens grass then shrubs and finally the trees will cover the area and convert into the forest.
Primary succession occurs in basically dead areas—regions where the soil is incapable of supporting life due to causes such as lava flows, newly created sand dunes, or glacier-left boulders.
Pioneer microorganisms, plants (lichens and mosses), grassy stage, smaller shrubs, and trees are all stages of primary succession. When there is food available, animals begin to return. The climax community stage is reached when the ecosystem is fully functional.
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Full Question :
After a town is abandoned, the concrete parking lots remain empty and inactive for hundreds of years. What is the most likely order of ecological succession in that area?
A.grass → trees → lichens → moss
B.lichens → grass → shrubs → trees
C.lichens → grass → trees → shrubs
D.shrubs → grass → trees → lichens
Find the perimeter of a square with a side length of miles 1.25 The perimeter is blankmiles.
The solution is
Answer:
5 miles
Step-by-step explanation:
Perimeter of a square = 4s
Where s = side length
We are given that the square has a side length of 1.25 (so s = 1.25)
Plugging this into the formula we acquire perimeter = 4(1.25) = 5 miles
8) A bowl has four different color balls.
The ratio of orange balls to red balls is 3:7
and the ratio of green balls to yellow balls is
9:21. Are the ratios of orange balls to red
balls and green balls to yellow balls
proportional?
BC IF YOU MULIPLY 3X3=9 AND 7X3=21 so yes its is proprational
Step-by-step explanation:
Hope you have a good day :D
PLEASE HELP 15 POINTS 1. A balloon has a volume of 5.0 L and a temperature of 200 K. What will the volume of the balloon be if the pressure temperature is raised to 373 K? Formula: v1/t1 = v2/t2
2. What was the volume in my tire this morning if I knew the pressure was 80 KPa and now in the afternoon the pressure is 250 KPa and the volume is 3.5 Liters? Formula: p1v1=p2v2
The volume of the balloon will be 9.3 L and the volume of the tire in the morning will be 10.93 L.
What is heat?Heat is the result of the movement of kinetic energy within a material or an item, or from a power source to a material or an object. Three ways exist for such transfer of energy to take place: Convection, radiation, and conduction
As per the given information in the question,
1.
Volume, V1 = 5 L
Temperature, T1 = 200 K and,
Temperature, T2 = 373 K
V1/T1 =V2/T2
5/200 = V2/373
V2 = 9.3 L
2.
Pressure, P1 = 80 KPa
Pressure, P2 = 250 KPa
Volume, V2 = 3.5 L
P1V1 = P2V2
80(V1) = 250(3.5)
V1 = 10.93 L
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Aphids are discovered in a cherry orchard. The Department of Agriculture has determined that the population of aphids t hours after the orchard has been sprayed is approximated by N(t)=1500−3tln(0.1t)−t where 0
Step 2 of 2 :
What is the maximum number of aphids in the cherry orchard? Round to the nearest whole number.
The maximum number of aphids in the cherry orchard is 1508.
What is population growth?
Population growth is the term used to describe the relative increase in population over a period of time. The growth rate is defined as growth per unit of time.
Given, N(t) = 1500-3t*ln(0.1t)-t
For maximum/minimum, [tex]\frac{dN}{dt} =0[/tex]
or, -3*ln(0.1t) - [tex]\frac{3t}{0.1t} *0.1[/tex] - 1 = 0
or, -3*ln(0.1t) = 4
or, ln(0.1t) = -4/3
or, t = 2.64
Then, [tex]\frac{d^{2} N}{dt^{2} } = \frac{-3*0.1}{0.1t} = \frac{-3}{t}[/tex] at t = 2.64
= -1.1381 < 0
Hence, it is maximum.
For the maximum number of Aphids put t = 2.64, we get
N = 1508
Hence, the maximum number of aphids in the cherry orchard is 1508.
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a random sample of size 81 is taken from an infinite population with a mean of 50 and a standard deviation of 9. find an approximate probability that the sample mean is within 48 and 51 (round off to second decimal place).
The approximate probability that the sample mean is within 48 and 51 is 0.82.
How to calculate probability?n = sample size = 81
σ = standard deviation = 9
μ = population mean = 50
Probability is a chance of something event can occur, for this case the probability measure of the chance of sample mean is between 48 and 51 can occur. So, the probability of the sample mean is between 48 and 51 is,
P(48 ≤ x ≤ 51) = P([tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex] ≤ z ≤ [tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex])
= P([tex]\frac{48-50}{\frac{9}{\sqrt{81}}}[/tex]≤ z ≤ [tex]\frac{51-50}{\frac{9}{\sqrt{81}}}[/tex])
= P(-2 ≤ z ≤ 1)
= P(z ≤ 1) - P(z ≤ -2)
using z table and we get,
= 0.8413 - 0.0228
= 0.8185
= 0.82
Thus, the probability is 0.82 for the sample mean is within 48 and 51.
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