Answer:
a) The mean is 18 and the standard deviation is 1.79.
b) The interpretation is that the standard deviation of the sample means of groups of 20 students will be of 1.79, which is the sample error, which is different from the population standard deviation.
c) 0.2005 = 20.05% probability that a sample of 20 students has a mean score of 19.5 or more.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 18 and a standard deviation of 8.
This means that [tex]\mu = 18, \sigma = 8[/tex]
Sample of 20:
This means that [tex]n = 20, s = \frac{8}{\sqrt{20}} = 1.79[/tex]
(a) Calculate the mean and standard deviation of the sampling distribution of x¯.
By the Central Limit Theorem, the mean is 18 and the standard deviation is 1.79.
(b) Interpret the standard deviation from part (a).
The interpretation is that the standard deviation of the sample means of groups of 20 students will be of 1.79, which is the sample error, which is different from the population standard deviation.
(c) Find the probability that a sample of 20 students has a mean score of 19.5 or more.
This is 1 subtracted by the pvalue of Z when X = 19.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{19.5 - 18}{1.79}[/tex]
[tex]Z = 0.84[/tex]
[tex]Z = 0.84[/tex] has a pvalue of 0.7995
1 - 0.7995 = 0.2005
0.2005 = 20.05% probability that a sample of 20 students has a mean score of 19.5 or more.
water has a density of 1.0 g/cm3 a plastic box has a volume of 78 cm and weighs 80 grams will the box sink or float on water
If possible explain thx!
What we'll do:
A method to find whether an object will float or sink in a liquid is to find it's specific gravity with respect to the liquid, The Specific Gravity tells us the percentage of object's mass which will be submerged in water
Finding the Specific Gravity:
Density of Box:
Density = Mass / Volume
Density = 80 grams / 78 cm³
Density = 1.02 grams/cm³
Specific Gravity of Box with respect to water:
Specific Gravity = Density of Box / Density of Water
we know that density of water is 1 gm/cm³, plugging the values
Specific Gravity = 1.02 / 1
Specific Gravity = 1.02
Hence, 102% of the object will be under water
Q. but I've only heard about 100% of something, how can something be more than 100%?
A. The answer is that the extra 2% over the 100% is providing to the object being even deeper underwater
Helpppsppspspspspsp plssss
Answer: About 804.25
Step-by-step explanation:
Do the inverse of the circumference formula and then take the radius and put it into the formula for the area of a circle
An equation is shown: a×b=c. Let c be an irrational number. What can be said about a and b?
Please help
if c is a irrational number that means a or b is also an irrational number or both of them are irrational numbers but they are different then each other
i hope that will help
There are two possible answers:
'a' is irrational and b is rational, OR'a' is rational and b is irrationalYou can only pick one of those two cases. In short, exactly one of the 'a' or b is irrational and the other is rational. Both 'a' and b cannot be rational together, and they both cannot be irrational together.
================================================
Explanation:
For a moment, let's say that 'a' and b are both rational numbers. This means they would be ratios of integers. So,
a = p/q
b = r/s
where p,q,r,s are integers. The denominators q & s cannot be zero.
Multiplying those rational numbers 'a' and b leads to
a*b = (p/q)*(r/s) = (p*r)/(q*s)
We get a result in the form of integer/integer. Recall that multiplying any two integers leads to some other integer. Since (p*r)/(q*s) is a ratio of integers, it is rational and that makes a*b = c to be rational. However, your teacher said that c is irrational which is the opposite of rational.
In short, if both 'a' and b are rational, then a*b = c is rational. This means we know for certain that both 'a' and b cannot be both rational for c to be irrational.
------------------------
Next, we'll consider 'a' and b to both be irrational. Is it possible to have a*b = c to be irrational as well? It depends.
If we have the following
a = sqrt(3)
b = sqrt(12)
then,
a*b = sqrt(3)*sqrt(12) = sqrt(3*12) = sqrt(36) = 6
Showing that a*b is rational because 6 = 6/1 is a ratio of integers. This is a bit strange considering how 'a' and b themselves were irrational, but they led to a rational product.
This doesn't always happen since something like
sqrt(3)*sqrt(5) = sqrt(3*5) = sqrt(15)
is irrational. So if both 'a' and b are irrational together, then a*b could be rational or it could be irrational. We would need more information about the values of 'a' and b.
Therefore, we know that we can rule out the case that 'a' and b are irrational together.
------------------------
Lastly, we'll consider the case when one of 'a' or b is rational while the other is irrational. The order doesn't matter. So we'll make 'a' to be irrational and b to be rational.
Since b is rational, this means b = p/q for some integers p,q where q is nonzero. The value of 'a' cannot be written as a ratio like this because it is irrational.
Multiplying any nonzero rational number with an irrational one always leads to an irrational result. If a*b was rational, then we could say
a*b = r/s
a*(p/q) = r/s
a = (r/s)*(q/p)
a = (r*q)/(s*p)
Showing that 'a' is rational, but this contradicts the fact we made 'a' to be irrational at the top of this section. Therefore, a*b is always irrational if exactly one of 'a' or b is irrational and the other is rational.
In other words, if,
'a' is rational and b is irrational, or'a' is irrational and b is rationalthen a*b = c is irrational
please help meeeeeeeewwewe
Plz hurry.....................
Answer:
figure of cuboid
volume of cuboid=l×b×h
Step-by-step explanation:
(10×3×4)in cube=120incube
NASA launches a test rocket with an initial velocity of 235 meters per second from an initial height of 15 meters above sea-level. Find a quadratic function that models the height of the rocket, in meters above sea-level, as a function of time t , in seconds after the launch. (HINT: 4.9 meters = 16 feet) Use your model to answer the following questions. Assuming that the rocket will splash down into the ocean, how many seconds after launch does splashdown occur? (round to the nearest tenth of one second) The rocket splashes down after seconds. What is the maximum height above sea-level attained by the rocket? (round to the nearest meter) The maximum height is meters above sea-level.
9514 1404 393
Answer:
48.0 seconds2833 metersStep-by-step explanation:
A graphing calculator shows the points of interest nicely.
The rocket splashes down after 48.0 seconds.
The maximum height is 2833 meters above sea level.
__
The equation for the motion is ...
h(t) = -4.9t^2 +235t +15 . . . . launch at 235 m/s from height of 15 m
The vertex (maximum height) is found at ...
t = -(235)/(2(-4.9)) = 235/9.8 ≈ 23.980 . . . seconds
Then the maximum height is ...
h(23.980) = (-4.9(23.980) +235)(23.980) +15 ≈ 2833 . . . meters
The value of t when h(t) = 0 can be found using the quadratic formula.
t = (-235 -√(235² -4(-4.9)(15)))/(2(-4.9)) = (-235 -√55519)/-9.8
t ≈ 48.023 ≈ 48.0 . . . seconds
If r = .15, this indicates
strong negative correlation.
strong positive correlation.
weak negative correlation.
weak positive correlation.
Answer:
Weak Positive Correlation
Step-by-step explanation:
The r value of 0.15 indicates a weak positive correlation value because a weak correlation value is less than 0.3, anything between 0.3 and 0.7 are a moderate correlation, and anything greater than 0.7 would be a string correlation. So, since this is less than 0.3, this is a weak correlation. A positive correlation is a positive value and a negative correlation value is a negative number, so this would be a weak positive correlation value.
A value of r = 0.15 suggests a weak positive correlation, indicating a slight tendency for the variables.
As per the question, the value of r is positive (greater than 0), which suggests a positive correlation between the variables.
However, the value of 0.15 is close to 0 and relatively small, indicating a weak correlation.
This means that there is a weak tendency for the variables to increase or decrease together.
Thus, a value of r = 0.15 suggests a weak positive correlation, indicating a slight tendency for the variables to increase or decrease together, but the relationship is not strong.
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Persons taking a 30-hour review course to prepare for a standardized excam averago a score of 620 on that exam. Persons taking a 70-hour review course average a score of 809. Find a linear function, S(t), which fits this data, and which
expresses score as a function of time. Use this function to predict an average score for persons taking a 42-hour review course. Do not round until the final answer. Then round to the nearest tenth as needed.
Answer:
S(t) = 4.725t + 478.25
S(t) = 4.725(42)+478.25
S(t) = 676.7
Step-by-step explanation:
In the question, score is a function of time, that means time is the x-axis, while score is the y-axis.
Order the pairs to get:
(30,620) and (70, 809)
With these values, you use the the equation [tex]\frac{x2-x1}{y2-y1}[/tex] to get the slope m.
[tex]\frac{70-30}{809-620} = 4.725[/tex]
Use this equation and input any ordered pair to get the final function.
y-y1 = m(x-x1)
y-620 = 4.725x-141.75
y = 4.725x + 478.25
Replace x with t and y with S(t) to fit the x & y axis of the question.
Find the quotient of 10x4 / 5x2.
What is the amount of simple interest saved on a savings deposit of $1,500 for 18 months at an interest rate of 6%?
Answer:
$135
Step-by-step explanation:
Given data
Principal= $1,500
Time= 18 months = 1.5 years
Rate= 6%
The formula for simple interest is given as
SI= PRT/100
Substiute
SI= 1500*6*1.5/100
SI= 13500/100
SI= $135
Hence the simple interest after 18months(1.5 years) is $135
Question 12 (5 points)
Which statement represents the transitive property of equality?
OA) If m ZA= mB, then m
B) If x = y, then y = x.
OC) If WX = XY, then XY = WX.
OD) If WX = XY and XY = YZ, then WX = YZ.
Answer:
D) If WX = XY and XY = YZ, then WX = YZ.
Step-by-step explanation:
The transitive property states that if a=b and b=c, then a=c. So, if two different values equal to the same, separate value, then they are also congruent. The answer choice, d, represents this idea because WX and YZ both equal XY and are shown to be equal.
Answer:
OD) If WX = XY and XY = YZ, then WX = YZ.
Step-by-step explanation:I took the test
In circle H with m \angle GHJ= 104m∠GHJ=104 and GH=15GH=15 units, find the length of arc GJ. Round to the nearest hundredth.
Answer: GJ= 27.23
i dont know how to explain this lol sorry but that answer is right
The length of arc GJ is equivalent to 26π/3 units.
What is Circumferance?Circumferance is defined as the length of the boundary of any two dimensional shape. Mathematically, we can write circumferance as -
C = ∫F(x) dx
Given is that in circle H with m ∠GHJ = 104 and GH = 15 units.
The length of the arc subtending an angle θ at the center is -
L = θ/360 x 2πr
L = 104/360 x 2π x 15
L = 13/45 x 2π x 15
L = 26π/3 units
Therefore, the length of arc GJ is equivalent to 26π/3 units.
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due today! The price of an ice cream cone is $2.75. You buy one for yourself and another for your little brother. How much sales tax will you pay? The sales tax rate is 7.5% How much sales tax will you pay?
Answer:
$0.41
Step-by-step explanation:
1 ice cream cone: $2.75
2 ice cream cones: 2 * $2.75 = $5.50
7.5% of $5.50 =
= 0.075 * $5.50
= $0.4125
Answer: $0.41
A researcher collected data on the speed of vehicles traveling through a construction zone on a state highway, where the posted speed limit was 25mph. The recorded speed of 20 randomly selected vehicles is given below: 2038243927402837293530313219331834213623 Calculate the sample mean, standard deviation, and the median of the above data. (Round to one decimal place
Answer:
[tex]\bar x =29.7[/tex]
[tex]\sigma = 6.81[/tex]
[tex]Median = 30.5[/tex]
Step-by-step explanation:
Given
[tex]Data:20,38,24,39,27,40,28,37,29,35,30,31,32,19,33,18,34,21,36,23[/tex]
[tex]n = 20[/tex]
Solving (a): The sample mean
This is calculated as:
[tex]\bar x =\frac{\sum x}{n}[/tex]
[tex]\bar x =\frac{20+38+24+39+27+40+28+37+29+35+30+31+32+19+33+18+34+21+36+23}{20}[/tex]
[tex]\bar x =\frac{594}{20}[/tex]
[tex]\bar x =29.7[/tex]
Solving (b): The standard deviation
This is calculated as;
[tex]\sigma = \sqrt{\frac{\sum(x-\bar x)^2}{n}}[/tex]
So, we have:
[tex]\sigma = \sqrt{\frac{928.2}{20}}[/tex]
[tex]\sigma = \sqrt{46.41}[/tex]
[tex]\sigma = 6.81[/tex]
Solving (c): The median
First, sort the data in ascending order
[tex]Sorted:18,19,20,21,23,24,27,28,29,30,31,32,33,34,35,36,37,38,39,40[/tex]
The position of the median is calculated as:
[tex]Median = \frac{n+1}{2}[/tex]
[tex]Median = \frac{20+1}{2}[/tex]
[tex]Median = \frac{21}{2}[/tex]
[tex]Median = 10.5th[/tex]
The 10.5th item represents the mean of the 10th and 11th item.
So, median is:
[tex]Median = \frac{30+31}{2}[/tex]
[tex]Median = \frac{61}{2}[/tex]
[tex]Median = 30.5[/tex]
The coordinates of G are
The coordinates of vertex G are (2,0). I did this.
PLS HELP FAST ITS THE LAST DAY TO DO THIS TEST NO LINKSSSS
An electrician charges $40 per hour plus an initial service fee of $75. He charges a customer $195 for 3 hours of work.
When this linear relationship is graphed, which value represents the slope?
A. 3
B. 40
C. 75
D. 195
Answer:
40 because every hour he charges 40 dollas so its 40x+75=y
Step-by-step explanation:
The slope is 40 because every hour he charges 40 dollars so its 40x+75=y
We have given that,
An electrician charges $40 per hour plus an initial service fee of $75. He charges a customer $195 for 3 hours of work.
We have to determine,
When this linear relationship is graphed, which value represents the slope.
What is the slope?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as a rising overrun.
The slope is 40 because every hour he charges 40 dollars so its 40x+75=y
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x + 2 1/2 = 10 what does x equal
Answer:
x = 7 1/2
Step-by-step explanation:
x + 2 1/2 = 10
subtract 2 1/2 from both sides of the equation:
x = 7 1/2
Answer:
x=15/2
Step-by-step explanation:
x+2 1/2=10
x+2×2+1/2=10
x+4+1/2=10
x+5/2=10
x=10-5/2
x=15/2
decimal form: 7.5
6 more than the quotient
of a number and 5
Graph the equation.
y-3= -5(x-1)
Step-by-step explanation:
First you gotta write it in standard form
y - 3 = -5(x-1)
distribute -5(x-1) = -5x + 5
y - 3 = -5x + 5
+3 +3
y = -5x + 8
I used desmos graphing caculator to graph
Jose is going hiking for 5 days. He packed 8 bags of trail mix to eat along the way.
Jose wants to eat all the trail mix without having any left over. He also wants to eat
the same amount every day. Use division to help Jose calculate how much he can
eat every day
Answer:
1.6
Step-by-step explanation:
since it is 5 days and you are splitting the traik mix
divided the amount of trail mix by the day
Answer:
The answer is D
Step-by-step explanation:
plzzzzzzzzzzzzzzzzzzzzzzzzz help me this is a grade
Answer:
1.83
Step-by-step explanation:
Answer:
I'm not good with models and modeling but the answer will be 1.83.
3
13
1
3
Area
-
in?
6
N
1
1
2
3
2
1
6.
2
3
4
5
6
7
8
Enter
Answer:
IF THERE IS A LINK DON'T CLICK ON IT
Step-by-step explanation:
IT IS A COMPUTER TABLET AND PHONE VIRUS
Annette has 1/4 yard of fabric. She cuts it into 3 equal pieces. Each piece of fabric is ____ yard.
Answer:
1/12
Step-by-step explanation:
Simpliy divide 1/4 by 3
(1/4)/3=1/12
f(x)=
2x
2
−x−15
−4x+12
Answer:
f(x) = -x -3
Step-by-step explanation:
Find the probability that a randomly
selected point within the circle falls
in the red shaded area.
r = 4 cm
2.5 cm
3 cm
3 cm
[? ]%
Round to the nearest tenth of a percent.
PLEASE
Answer:
38.8%
Step-by-step explanation:
This is a very famous computer solution called the Monte Carlo Method. It's like throwing darts at an enlarged diagram. You will always be inside the circle.
The red triangle has an area = 1/2 h * b
The red triangle has an area = 1/2 * (2.5 + 4) * (3 + 3)
The red triangle area = 1/2 6.5 * 6
The red triangle area = 19.5
The area of the circle = pi * r^2
pi = 3.14
r = 4
The area of the circle = 3.14 * 4^2
The area of the circle = 50.24
% = (19.5/50.25) * 100
% = 38.8%
If D = {1,3,5}, E={3,4,5}, F={1,5,10}
Find
a) ∪
b) ∩
c) ( ∩ )
d) ( ∪ ) ∩
e) ( ∩ )
Step-by-step explanation:
a)U={1,3,4,5}
b)={1,3,5}
PLS HELP IM CONFUSED
Answer:
D
Step-by-step explanation:
6 and 3 can both be divided by 3, which gives u 2/1
Answer:
D. 2 cups of flour/1 cup of milk.
Step-by-step explanation:
Here's the definition of unit rate:
unit ratethe ratio of two different units, with the denominator as 1. For example, kilometer/hour, meter/sec, miles/hour, salary/month, etc.
Since we need to find the unit rate, find the GCF of 6 & 3 (3). Now divide both values by 3.
(6/3)/(3/3)
2/1
The unit rate between cups of flour to cups of milk is 2:1, which is D.
Plzzzz answer fast..
Answer:
D) LM=12; QP=8
Step-by-step explanation:
12/18=(x-1)/(x+3)
cross multiply
12x+36=18x-18
36+18=18x-12x
54=6x
9=x
LM = x+3 = 9+3 = 12
QP = x-1 = 9-1 = 8
5. In the morning, Kevin's cat eats 1/2 of a can of cat food. In the afternoon, the cat eats 1/4 of a can of food. In the evening, the cat eats 4/5 of a can of food. Which is the most reasonable estimate for the amount of food the cat eats throughout the day: 1 can, 2 cans, or 3 cans?
In just lazy so thanks people who are helping me
Answer:
2 cans
Step-by-step explanation:
1/2 + 1/4 + 4/5 = 1.55
2 is the best answer since we know the cat eats more than 1 and a half cans so the closest thing would be 2 cans
Need answer with full work
Answer:
Step-by-step explanation:
x^2 - 17x - 60
(x - 20)(x + 3)
x^2 + 3x - 20x - 60
x^2 - 17x - 60
(x + 20) is not one of the factors
using F.O.I.L., it would have been
x^2 + 17x - 60