According to the central limit theorem, given a population with mean μ and standard deviation σ, if a suitably large random sample (n ≥ 30) is drawn from the population with permutation, the distribution of the sample mean will be approximately normally distributed. Standard Error is known to be the square root of the variance. if a given variance increases, so its standard error also.
Then the mean of the sample mean is given by
[tex]\mu_ {x} =\mu[/tex]
and the standard deviation of the sample mean is given by
[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} }[/tex]
The standard deviation of the sample mean is inversely proportional to the sample size n
so if n increases, the standard deviation decreases and vice versa.
(a) Sample size increased from 64 to 196.
As mentioned above, the standard deviation decreases as the sample size increases.
Therefore, increasing the value of n from 64 to 196 reduces the standard deviation of the sample mean.
n = 64 sample mean standard deviation:
[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{64} } \\\\\sigma_{x} = 0.7[/tex]
n = 196 sample mean standard deviation:
[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{196} } \\\\\sigma_{x} = 0.4[/tex]
sample mean standard deviation decreased from 0.7 to 0.4 n was 64 When it increased to 196.
Therefore the variance is also decreases.
(b)
decreace the sample size, increase the standard deviation.
Therefore, as the value of n decreases from 784 to 49, the standard deviation of the sample mean increases.
Standard deviation of sample mean for n = 784:
[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{784} } \\\\\sigma_{x} = 0.2[/tex]
Standard deviation of sample mean for n = 49:
[tex]\sigma_{x} = \frac{\sigma}{\sqrt{n} } \\\sigma_{x} = \frac{\ 5.6}{\sqrt{49} } \\\\\sigma_{x} = 0.8[/tex]
Standard deviation of sample mean increased from 0.2 to 0.8 while, n increased from 784 Then 49 decreases.
Therefore, the variance is also increases.
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Actual Unemployment Rate = 12%
Cyclical Unemployment Rate = 7%
What is the Natural Unemployment Rate?
The Natural Unemployment Rate based on the information is 5%.
What is natural rate of unemployment?The natural rate of unemployment is the lowest unemployment rate when inflation is stable, or the unemployment rate when inflation is not accelerating. The natural rate of unemployment (NAIRU) is the rate of unemployment caused by all factors other than changes in aggregate demand. Potential GDP estimates are based on the long-term natural rate.
The unemployment rate is the proportion of the total labor force that is unemployed but actively looking for work and willing to work. Cyclical unemployment is associated with an industry's business cycle. It is a direct result of a drop in consumer demand, which has resulted in a drop in labor demand. If cyclical unemployment rises, it indicates that the economy is slowing, which is not good.
Cyclical unemployment occurs when labor forces are reduced as a result of business cycles or economic fluctuations. If you are cyclically unemployed, it means that your employer has laid you off to save money during a period of slow business.
In this case, the unemployment will be:
= Actual unemployment rate - Cyclical unemployment rate
= 12% - 7%
= 5%
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420.9536 Find the digits in the ones place, in the tenths place, and in the thousandths place for the following number.
Answer:
ones: 0
tenths: 9
thousandths: 3
Step-by-step explanation:
Because 0 is at the beginning of the whole "part" of the number, it is a "one" in place value (confusing right??) for example, in the number 54,743, 3 would be the digit in the ones place.
Because 9 is one decimal place across the example number, it is a tenth - because you would need 10 lots of 0.1 in order to make a whole number.
Because 3 is three decimal places across the example number, it is a thousandth - because you would need 1000 lots of 0.001 to make a whole number.
A good way of remembering these decimal place values is by using the number of zeros after 10, 100, 1,000, 10,000, and so on (one zero is a ten-th, two zeros is a hundred-th, etc, etc.)
Which of the equations below represent a proportional relationship? Choose all that apply.
Answer:
1
3
6
are all the correct answers because they made the most sense and looked the most proportional
the number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 15. a random sample of 430 salespeople was taken and the mean number of cars sold annually was found to be 79. find the 97% confidence interval estimate of the population mean.
At the 97% confidence interval estimate of the population mean is
(80.55, 77.45).
Following are the calculation to the confidence interval :
Given that,
σ = 15
n = 430
X = 79
Here C = 97% = 0.97
⇒ α = 1 -C = 1 - 0.97 = 0.03
∴ Zₙ = Zₙ/2 = Z₀.₀₁₅ = 2.17
Now,
97% confidence interval,
C.I = X ± σ/√n
= 79 ± 2.17 × (15/√430)
= 79 + 2.17 × (15/ 21) [taking round figure of √430=2.0736441]
= 80.55
Now taking the negative sign,
= 79 - 2.17 × (15/√430)
= 79 - 2.17 × (15/ 21)
= 77.45
The final answer is (80.55, 77.45).
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polynomial function
Answer:
[tex]f(x) = (x+1)(x-2)(x+4)[/tex]
[tex]= (x^{2} +x-2x-2)(x+4)\\\\= (x^{2} -x-2)(x+4)\\\\= x^{3}-x^{2}-2x+4x^{2} -4x-8\\\\= x^{3} +3x^{2} -6x-8[/tex]
What is the greatest common divisor of x and y?
The only common factor (different than 1) between x and y is 29, so the greatest common divisor is 29.
How to get the greatest common divisor between x and y?
Here we have two real numbers that are written as a product between their corresponding prime factors.
These numbers are:
x = 2*3*5*7*11*13*17*19*23*29
y = 29*31*37*41*43*47*53*59*61*67
Again, all of these are prime numbers, so the only common divisors between the two numbers are the factors that appear in both numbers.
And we can see that the only common factor between x and y is 29, then the greatest common divisor between x and y is 29.
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pls, hurry!!!!!!!
I will give brainliest to the one who finishes the table!
Answer: 1 is 77 3 is 231 5 is 308 and 7 is 385
Step-by-step explanation:
mia identified a point located at (-5,-8) her directions told her to flip it across the y axis and then across the x axis. mia wrote that the point would now be at (8,5) what was mia's error in her thinking? where would the point be actually located
Mia's error in her thinking was that she interchanged the coordinate of both the x- and y-axis. Also, the point would actually be located at (5, 8).
What is a reflection across the x-axis?In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate would change from positive to negative. Therefore, a reflection across the x-axis is given by this transformation rule:
(x, y) → (x, -y)
In Geometry, a reflection across the y-axis of a graph is given by this transformation rule (x, y) → (-x, y).
(x, y) → (-x, y)
(-5, -8) → (5, -8)
Next, we would apply another reflection across the x-axis of a graph as follows:
(x, y) → (x, -y)
(5, -8) → (5, 8)
In conclusion, we can logically deduce that Mia was wrong in her calculations.
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(x-3)45° find the value of x
Answer:
the value of x is 135 i believe
Step-by-step explanation:
sorry if im wrong
Write the slope-intercept form equation of a line that passes through the points (-1,2) and (4,-8).
Answer: y=-2x
Step-by-step explanation: Use the slope formula
-8-2/4-(-1)
-10/5=-2
y=-2
Answer:
y = - 2x
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 2 ) and (x₂, y₂ ) = (4, - 8 )
m = [tex]\frac{-8-2}{4-(-1)}[/tex] = [tex]\frac{-10}{4+1}[/tex] = [tex]\frac{-10}{5}[/tex] = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (- 1, 2 )
2 = 2 + c ⇒ c = 2 - 2 = 0
y = - 2x + 0 , that is
y = - 2x ← equation of line
help please i really need this done
Solving an equation we will see that x = 13, then the measure of interior angle G is 63°.
How to find the measure of angle G?
Here we have the 3 interior angles of a triangle defined with a variable x.
m∠E = (5x + 6)°
m∠F = (4x - 6)°
m∠G = (5x - 2)°
Now, remember that the sum of the interior angles of a triangle is always equal to 180°.
Then we can write:
(5x + 6)° + (4x - 6)° + (5x - 2)° = 180°
We can solve this for x.
14x - 2 = 180
14x = 180 + 2
x = 182/14 = 13
Now that we know the value of x, we can find the value of angle G.
m∠G = (5x - 2)° = (5*13 - 2)° = (15 - 2)° = 63°
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a 4-sided die is a pyramid whose four faces are labeled with the numbers 1, 2, 3, and 4 (see image). imagine rolling two fair, 4-sided dice and recording the number along the base of each pyramid. (a) what is the sample space for this chance process? (1,1), (1,2), (1,3), (1,4), (2,2), (2,3), (2,4), (3,3), (3,4), (4,4) (1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4). (1,1), (2,2), (3,3), (4,4) (1,1), (1,2), (1,3), (1,4) because the dice are fair, each of the outcomes in the sample space are equally likely. what is the probability of each outcome in the sample space? enter a fraction. (b) define event a as getting a sum of 5. p(a)
The probability of each outcome in the sample space = 1/16
The probability of getting a sum of 5 = 1/4
Step-by-step explanation:
We have been given a four-sided die is a pyramid whose four faces are labeled with the numbers 1, 2, 3 and 4
sample space = {(1,1), (1,2), (1,3), (1,4), (2,1),(2,2), (2,3), (2,4),(3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)}
Two fair 4-sided dices are rolled and all sixteen possible outcomes are equally likely.
The possible outcomes can be deduced by making combinations of different faces with a particular face.
given that each of the outcomes in the sample space is equally likely. So the probability of each outcome in the sample space is the same.
now we find the probability of each of the outcomes in the sample space
(a) when two dices are rolled, we have n(s) = 4*4=16
the chances of getting the outcome as (1,1) n(a) = 1
the probability of getting the outcome as (1,1) p(a)= n(a)/n(b)
p(a) = 1/16
so the probability of each outcome in the sample space = 1/16
(b) P(A) is the probability of getting 5 as a sum
P(A) = Total outcomes with 5 as a sum/Total outcomes
Total outcomes with 5 as sum= 4
Total outcomes= 16
P(A)=4/16=1/4
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Write a recursive formula: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21
Answer:
[tex]a_1=3[/tex]
[tex]a_n=a_n_-_1+2[/tex]
Step-by-step explanation:
Recursive formula : an = a(n-1) + d
where d = common difference , an = nth term, and n = number of terms
Because we are just writing the recursive formula rather than the explicit formula, the only defined term will be "d" or the common difference.
Here, the common difference is +2. This is evident as you must add 2 to get to 5 and then add 2 to get to 7 etc.
So d = 2
Plugging this into the recursive formula we get an = a(n-1) + 2
Also it's very important to state the first term which is 3 so a1 = 3
A scale drawing of a rectangular park had a scale of 1 cm = 90 m. 7.6 cm 9.1 cm- What is the actual area of the park in meters squared?
please answer this quickly this is due by 8pm ;((
Step-by-step explanation:
The drawing has the side dimension of 7.6 cm
since each cm represents 90 m the ACTUAL park is
7.6 x 90 = 684 meters
similarly, the bottom of the drawing has the dimension 9.1 cm which represents 9.1 x 90 = 819 m
the area of the park is then
Area = height x width = 684 m x 819 m = 560 196 m^2
OR in one step:
Area of the actual park is then
(7.6 cm * 90 m / cm ) X ( 9.1 cm * 90 m/cm ) = 560 196 m^2
It takes Oliver 2 hours to wash the windows in his house. It takes his sister 3 hours. Based on this information we can conclude that in one hour, Oliver and his sister would get of the windows washed. This means that it would take hours (which is equal to minutes) for them to get all of the windows washed. Submit Answer attempt 1 out of 5 / problem 1 out of max 1
Answer: 5/6 windows in an hour, 6/5 hours, 72 minutes
Step-by-step explanation: the general formula used is 1/Oliver+1/sister=1/together and you plus in to find the amount of windows in an hour. Once solved, you take the reciprocal of that and that is the hours. Then you solve for the amount of minutes.
Nadia is a stockbroker. She earns 13% commission each week. Last week, she sold $7500 worth of stocks. How much did she make last week in commission? If she averages that same amount each week, how much did she
make in commission in 2011?
Answer:6400 multiplied by 13% (0.13) then multiply that answer by 52 , for weeks in the year.
Step-by-step explanation:
6400*.013= $832.00
832*52= $43264.00
Kiefer service company common stock sells for $36. 84 per share and has a market rate of return of 15. 8 percent. The company just paid an annual dividend of $1. 61 per share. What is the dividend growth rate?.
The dividend growth rate of Kiefer service company is 0.16% . Dividend growth rate can be determined by using the return rate formula.
Dividend growth rate is the annual rate of growth that a particular stock's dividends experience over a specified period of time.
We have given that ,
Common stocks sells or current price = $36.84
Market rate of return (R) = 25.8 %
Annual dividend (D) = $1.61
Rate of return is defined as net gain or loss of। an investments over a specified time period . It is expressed as a percentage of investment initial cost .
Using the formula,
Rate of return = (D1/ current price )+growth rate where,
D1 --> divided of previous year
putting all the values in above formula we get,
15.8 = ( 1.61/36.84) + growth rate
=> growth rate= 15.8 - (1.61/36.84) = 15.756
Hense, the dividend growth rate for Kiefer service company is 0.16%.
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Determine the range of the following graph:
The range of the given function is represented as {y | -5 ≤ y ≤ 5 , y ∈ R} .
Range of a function is defined as the possible values of y or the dependent variable in relation to the values of x.
Here from the graph we can see that the greatest value y achieves is 5.
The lowest value of y from the graph is -5 for all the values of x.
Hence the range will be {-5 ≤ y ≤ 5}
Now the graph is continuous, so we accept all values of y, hence y ∈ R .
Therefore the range will be: {y | -5 ≤ y ≤ 5 , y ∈ R} .
The set of all possible values for the results of the dependent variable, or the entire set of all possible values when the domain is substituted, is the range of a function.
The steps to find the range is:
The range of a function or similar object is the range of all y values, from least to greatest.We determine whether the provided expression of y is positive, negative, or equal to other values by substituting all possible values of x into it.We find the minimum and greatest values of y.To learn more about range visit:
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What’s the value of a?
6x+22=13x-41
1234567890
Answer:
x=9
Step-by-step explanation:
I assume you want me to solve for x.
6x+22=13x-41
Subtract 6x from both sides.
22=7x-41
Add 41 to both sides.
63=7x
Divide both sides by 7.
x=9.
CHECK:
6x+22=54+22=76
13x-41=117-41=76
76=76
So, x=9
A rectangular swimming is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a consistent 2 feet wide and has as area of 196 square feet. What are the dimensions of the pool? If the depth of the pool is 6 feet, how much water can the pool hold if the height of water is 1 foot below the top of the pool?
Convert cubic feet to gallons
The length of the swimming pool is 30 feet
The width of the swimming pool is 15 feet
The volume of the swimming pool is 16875 gallons
Given,
Length of the rectangular swimming pool = 2x
Width of the rectangular swimming pool = x
A small concrete walkway surrounds the pool.
The width of the walkway = 2 feet
The area of the walkway = 196 square feet
We have to find the dimensions of the pool;
Here,
Area of rectangle = length x width
Area of walkways = (4x + 8x) + 4 x 4 = 196
12x + 16 = 196
12x = 196 - 16
12x = 180
x = 180/12
x = 15
That is,
Width of the pool is 15 feet
Length of the pool = 2 × x = 15 x 2 = 30 feet
Now,
If the depth of the pool is 6 feet, we have to find the amount of water that the pool can hold if the height of water is 1 foot below the top of the pool.
That is,
Volume of pool = length x width x depth
Here, depth = 6 - 1 = 5 feet
So,
Volume = 15 x 30 x 5 = 2250 cubic feet
Convert cubic feet to gallons
2250 x 7.5 = 16875 gallons of holding capacity
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What is the value of the expression below when w=4 and x=5
2w+4x
The value of the expression, 2w+4x, is 28 when w = 4 and x = 5.
According to the question,
We have the following expression:
2w+4x
We have the following values of w and x:
w = 4 and x = 5
Now, in order to find the value of the given expression, we will put these values in the expression.
So, we have this:
2*4+4*5
Now, we will first multiply the integers and then we will add the obtained results together:
8+20
28
Hence, the value of the expression, 2w+4x, is 28 when w = 4 and x = 5.
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J(13,-5), K(2, 6), L(-1,-5), M(-4,-2)
J10
L(-3,2
Answer:
is there a graph for this
Step-by-step explanation:
i need a grapg or to know what they wanted to know
Stress, measured in newtons per square meter (N/m^2) is the ratio of force, in newtons (N) to the area, in square meters (m^2) on which that force is acting. Based on the table at left, which object is experiencing the greatest stress?
Object: Object 1, Object 2, Object 3, Object 4
Force (N): 72, 185, 406, 512
Area (m^2): 6.46 * 10^-5, 4.56 * 10^-5, 5.07 * 10^-4, 1.14*10^-3
(^Here is the table^)
A) Object 1
B) Object 2 ***** Correct
C) Object 3
D) Object 4
The greatest stress is experienced by object 2.
How to determine the object experiencing the greatest stress?Stress is defined as force divided by area
Given: the table containing values of force and area for objects
Object 1
Stress = 72/6.46×10⁻⁵ = 1114551.084 N/m²
Object 2
Stress = 185/4.56×10⁻⁵ = 4057017.544 N/m²
Object 3
Stress = 406/5.07×10⁻⁴ = 792899.4083 N/m²
Object 4
Stress = 512/1.14×10⁻³ = 449122.807 N/m²
Therefore, object 2 is experiencing the greatest stress
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a photograph is enlarged into a poster so that the dimensions of the poster are 8 times the dimensions of the photograph. Which statements are true about the perimeter and the area of the poster?
Answer:
I think that the correct answers are C and D. I have questions. how many answers can I choose? what is the original photograph size? don't choose an answer until I get the information that I need
waste management company wants to construct a dumpster in the shape of a rectangular solid with no top whose length is four times its width. its volume is fixed at 25.6 yd3. find the dimensions of the dumpster that will minimize its surface area.
the dimensions of the dumpster that will minimize its surface area
length l = 6.32
width w = 1.58
height h = 0.39
Length = l
width = w
height = h
given that length is four times its width
l = 4w
Now, the formula for the surface area of a cube is;
S = 2lh + 2lw + 2wh
substitute l = 4w in the above equation
S = 2(4w)h+2(4w)w+2wh
S = 8wh+8[tex]w^{2}[/tex]+2wh
S = 10wh + 8[tex]w^{2}[/tex]
formula for the volume of a cube is;
V = lwh
now substitute l=4w in the above equation
V = (4w)wh
V = 4[tex]w^{2}[/tex]h
h = 4[tex]w^{2}[/tex]/V
Put V/2w² for h in the surface area equation to get;
S= 8w² + 10w(V/4w²)
= 8w² + 5V/2w
given that volume V = 25.6 substitute that in the above equation
S = 8w² + 5(25.6)/2w
= 8w² + 128/2w
Since we want to minimize the surface area, let us find the first derivative of S to get;
S' = 16w - 128/2w²
At S' = 0
0 = 16w- 128/2w²
16w = 128/2w²
32w³ = 128
w³ = 128/32
w³ = 4
w = [tex]\sqrt[3]{4}[/tex]
w = 1.58 yds
since l = 4w substitute the value of w in that
l = 4(1.58) = 6.32
h = 4[tex]w^{2}[/tex]/V = 4([tex]1.58^{2}[/tex])/25.6
h = 0.39
the dimensions are
length l = 6.32
width w = 1.58
height h = 0.39
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A chemist has 3 different acidic solutions.
The first solution contains 20% acid, the second contains 35% acid, the third contains 80% acid.
She created 54 liters of a 50% acid mixture, using all 3 solutions. The number of liters of 80% solution used is 2 times the number 35% solution is used
The chemist used_ liters of 20% solution,_35% of solution,_liters of 80% solution.
The volumes of the 20% solution, 35% solution, and 80% solution used by the chemist are 18 liters, 12 liters, and 24 liters, respectively.
The chemist has three different acidic solutions. The first solution contains 20% acid, the second contains 35% acid, and the third contains 80% acid. She created 54 liters of a 50% acid mixture, using all 3 solutions. The number of liters of 80% solution used is 2 times the number of liters of 35% solution used.
Let the amounts of 20% solution, 35% solution, and 80% solution used be x, y, and z. We already know that z = 2y. We can write equations as given below.
The sum of the volumes must be equal to the final volume.
x + y + z = 54
x + y + 2y = 54
x = 54 - 3y
Now we will write the equation using the concentrations of the acid.
50%*54 = 20%*x + 35%*y + 80%*z
27 = 0.2(54 - 3y) + 0.35y + 0.8(2y)
2700 = 20(54 - 3y) + 35y + 80(2y)
2700 = 1080 - 60y + 35y + 160y
1620 = 135y
y = 1620/135 = 12
z = 2y = 2*12 = 24
x = 54 - 3y = 54 - 36 = 18
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Ariel sings a song in 5.92 minutes. Carlos sings the same song in 7.73 minutes. How much longer does it take Carlos to sing the song? Estimate by rounding to the nearest whole number.
HELP
Approximately Carlo takes 2 minutes time to sing the song.
Given that, Ariel sings a song in 5.92 minutes. Carlos sings the same song in 7.73 minutes.
What is the rounding off numbers?Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.
Now,
Difference of singing time = 7.73-5.92
= 1.81 minutes
≈ 2 minutes
Hence, approximately Carlo takes 2 minutes time to sing the song.
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what is the volume of a trunk of a regular quadrangular pyramid where the side of the base is 18cm, the length of the upper side is 7.5cm and the height of the trunk is 20.4cm
The volume of a trunk of a regular quadrangular pyramid is 2754 cubic centimeters.
According to the question,
We have the following information:
The side of the base is 18cm, the length of the upper side is 7.5cm and the height of the trunk is 20.4cm.
Now, we know that the trunk of a regular quadrangular pyramid is in the shape of a cuboid.
And the following formula is used to find the volume of cuboid:
Length*breadth*height
Volume of a trunk of a regular quadrangular pyramid = 7.5*18*20.4
Volume of a trunk of a regular quadrangular pyramid = 2754 cubic centimeters
Hence, the volume of a trunk of a regular quadrangular pyramid is 2754 cubic centimeters.
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construct triangle abc if ac=10cm angle bac=50 degrees and angle bca=50 degrees what type of triangle does this create
Answer:
Angle BAC =50
Step-by-step explanation:
Since O is the circumcenter and angle BOC is the angle subtended by the arc BC at the center and angle BAC is the angle subtended by arc BC