This is a great question!
When we are given ( r - c )( 3 ), we are being asked to take 3 as x in the functions r( x ) and c( x ), taking the difference of each afterwards -
[tex]r( 3 ) = ( 3 )^2 + 5( 3 ) + 14,\\x( 3 ) = ( 3 )^2 - 3( 3 ) + 4[/tex]
____
Let us calculate the value of each function, determine their difference, and multiply by 100, considering r( x ) and c( x ) are measured in hundreds of dollars,
[tex]r( 3 ) = 9 + 15 + 14 = 38,\\x( 3 ) = 9 - 9 + 4 = 0 + 4 = 4\\----------------\\( r - c )( 3 ) = 38 - 4 = 34,\\34 * 100 = 3,400( dollars )\\\\Solution = 3,400( dollars )[/tex]
Therefore, ( r - c )( 3 ) " means " that George's new store will have a profit of $3,400 after it's third month in business, given the following options,
( 1. The new store will have a profit of $3400 after its third month in business.
( 2. The new store will have a profit of $2400 after its third month in business.
( 3. The new store will sell 2400 items in its third month in business.
( 4. The new store will sell 3400 items in its third month in business.
The required answer is , [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.
Substitution:The substitution method is the algebraic method to solve simultaneous linear equations.
Given function is,
[tex]r(x) = x^2+5x+14[/tex]...(1)
And [tex]c(x) = x^2-4x+5[/tex]...(2)
Now, substituting the value into the equation (1) and (2).
[tex]r(5) = (5)^2+5(5)+14=64[/tex]
[tex]c(5) = (5)^2-4(5)+5=10[/tex]
Therefore,
[tex](r-c)(5)=r(5)-c(5)\\=64-10\\=54[/tex]
Now, [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.
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At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.05 for the estimation of a population proportion
Answer:
A sample of 385 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
How large a sample:
We need a sample of n.
n is found when M = 0.05.
We dont know the true proportion, so we work with the worst case scenario, which is [tex]\pi = 0.5[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.05}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96*0.5}{0.05})^{2}[/tex]
[tex]n = 384.16[/tex]
Rounding up
A sample of 385 is needed.
Prepare the journal entries on December 31, 2019, for the 40 extended contracts (the first year of the revised 3-year contract).
This is not the complete question, the complete question is:
P18-1 (LO2,3) (Allocate Transaction Price, Upfront Fees)
Tablet Tailors sells tablet PCs combined with Internet service, which permits the tablet to connect to the Internet anywhere and set up a Wi-Fi hot spot. It offers two bundles with the following terms.
1. Tablet Bundle A sells a tablet with 3 years of Internet service. The price for the tablet and a 3-year Internet connection service contract is $500. The standalone selling price of the tablet is $250 (the cost to Tablet Tailors is $175). Tablet Tailors sells the Internet access service independently for an upfront payment of $300. On January 2, 2017, Tablet Tailors signed 100 contracts, receiving a total of $50,000 in cash.
2. After 2 years of the 3-year contract, Tablet Tailors offers a modified contract and extension incentive. The extended contract services are similar to those provided in the first 2 years of the contract. Signing the extension and paying $90 (which equals the standalone selling of the revised Internet service package) extends access for 2 more years of Internet connection. Forty Tablet Bundle A customers sign up for this offer.
INSTRUCTION
a) Prepare the journal entries when the contract is signed on January 2, 2019, for the 40 extended contracts. Assume the modification does not result in a separate performance obligation.
b) Prepare the journal entries on December 31, 2019, for the 40 extended contracts (the first year of the revised 3-year contract).
Answer:
Step-by-step explanation:
(A)
Date Particulars Debit Credit
2-Jan-19 Cash 3600
Unearned Service Revenue 3600
40 * 90 = 3600
services in the extended period are the same as the services that were provided in the original contract period. As they are not distinct hence the modifications will be considered as part of the original contract.
(B)
Date Particulars Debit Credit
31-Dec-19 Unearned Service Revenue 2413
Service revenue 2413
internet = 300, price = 550, connection service = 500
(300/550) * 500 = 273
so
Original internet service contract = 40 * 273 = 10,920
Revenue recognized in 1st two years = 10,920 * 2/3 = 7280
Remaining service at original rates = 10920 - 7280 = 3640
Extended service = 3600
3640 + 3600 = $7240
7240 / 3 = $2413
HELP ASAP! The number of entertainment websites in 1995 wass 54. By 2004 there were 793 entertainment website..
Approximately, what was the rate of change for the number of the websites for this time period??
=============================================================
How I got that answer:
We have gone from 54 websites to 793 websites. This is a change of 793-54 = 739 new websites. This is over a timespan of 2004-1995 = 9 years.
Since we have 739 new websites over the course of 9 years, this means the rate of change is 739/9 = 82.1111... where the '1's go on forever. Rounding to the nearest whole number gets us roughly 82 websites a year.
----------
You could use the slope formula to get the job done. This is because the slope represents the rise over run
slope = rise/run
The rise is how much the number of websites have gone up or down. The run is the amount of time that has passed by. So slope = rise/run = 739/9 = 82.111...
In a more written out way, the steps would be
slope = rise/run
slope = (y2-y1)/(x2-x1)
slope = (793 - 54)/(2004 - 1995)
slope = 739/9
slope = 82.111....
In a survey, 205 people indicated they prefer cats, 160 indicated they prefer dots, and 40 indicated they don’t enjoy either pet. Find the probability that if a person is chosen at random, they prefer cats
Answer: probability = 0.506
Step-by-step explanation:
The data we have is:
Total people: 205 + 160 + 40 = 405
prefer cats: 205
prefer dogs: 160
neither: 40
The probability that a person chosen at random prefers cats is equal to the number of people that prefer cats divided the total number of people:
p = 205/405 = 0.506
in percent form, this is 50.6%
Which proportion would convert 18 ounces into pounds?
Answer:
16 ounces = 1 pound
Step-by-step explanation:
You would just do 18/16 = 1.125 pounds. There are always 16 ounces in a pound, so it always works like this
¿Cuál serie numérica tiene como regla general Xn = 2n +1?
a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5
Answer:
The series of numbers that correspond to the general rule of [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.
Step-by-step explanation:
We are given with the following series options below;
a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5
And we have to identify what number series has a general rule as [tex]X_n=2n+1[/tex].
For this, we will put the values of n in the above expression and then will see which series is obtained as a result.
So, the given expression is ; [tex]X_n=2n+1[/tex]
If we put n = 1, then;
[tex]X_1=(2\times 1)+1[/tex]
[tex]X_1 = 2+1 = 3[/tex]
If we put n = 2, then;
[tex]X_2=(2\times 2)+1[/tex]
[tex]X_2 = 4+1 = 5[/tex]
If we put n = 3, then;
[tex]X_3=(2\times 3)+1[/tex]
[tex]X_3 = 6+1 = 7[/tex]
If we put n = 4, then;
[tex]X_4=(2\times 4)+1[/tex]
[tex]X_4 = 8+1 = 9[/tex]
Hence, the series of numbers that correspond to the general rule of [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.
The length of a rectangle is 5M more than twice the width and the area of the rectangle is 63M to find the dimension of the rectangle
Answer:
width = 4.5 m
length = 14 m
Step-by-step explanation:
okay so first you right down that L = 5 + 2w
then as you know that Area = length * width so you replace the length with 5 + 2w
so it's A = (5 +2w) * w = 63
then 2 w^2 + 5w - 63 =0
so we solve for w which equals 4.5 after that you solve for length : 5+ 2*4.5 = 14
Brainliest to whoever gets this correct This word problem has too much information. Which fact is not needed to solve the problem? Tanisha tried to sell all her old CDs at a garage sale. She priced them at $2 each. She put 80 CDs in the garage sale, but she sold only 35 of them. How many did she have left? A. All of the information is needed. B. Tanisha sold the CDs for $2 each. C. Tanisha put 80 CDs in the sale. D. Tanisha sold 35 of the CDs.
Answer:
B. Tanisha sold the CDs for $2 each.
Step-by-step explanation:
the ellipse is centered at the origin, has axes of lengths 8 and 4, its major axis is horizontal. how do you write an equation for this ellipse?
Answer:
The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].
Step-by-step explanation:
The standard equation of the ellipse is described by the following expression:
[tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1[/tex]
Where [tex]a[/tex] and [tex]b[/tex] are the horizontal and vertical semi-axes, respectively. Given that major semi-axis is horizontal, [tex]a > b[/tex]. Then, the equation for this ellipse is written in this way: (a = 8, b = 4)
[tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex]
The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].
whats 1/2 + 2/4 - 5/8?
Answer:
3/8
Step-by-step explanation:
Step 1: Find common denominators
1/2 = 4/8
2/4 = 4/8
Step 2: Evaluate
4/8 + 4/8 - 5/8
8/8 - 5/8
3/8
Alternatively, you can just plug this into a calc to evaluate and get your answer.
Answer:
3/8
Step-by-step explanation:
Look at the denominator:
2, 4, 8. The LCM (Lowest Common Multiple) is 8.
So this equation becomes
4/8+4/8-5/8=3/8
Suppose a random variable X is best described by a uniform probability distribution with range 1 to 5. Find the value of that makes the following probability statements true.
a) P(X <-a)= 0.95
b) P(X
c) P(X
d) P(X ->a)= 0.89
e) P(X >a)= 0.31
Answer:
a) 4.8
b) 2.96
c) 4.4
d) 1.44
e) 3.76
Step-by-step explanation:
What we will do is solve point by point, knowing the following:
Fx (x) = P (X <= x) = (x - 1) / 4
a) P (X <-a) = 0.95
Fx (a) = 0.95
(a -1) / 4 = 0.95
a = 1 + 0.95 * 4
a = 4.8
b) P (X <a) = 0.49
Fx (a) = 0.49
(a -1) / 4 = 0.49
a = 1 + 0.49 * 4
a = 2.96
c) P (X <a) = 0.85
Fx (a) = 0.85
(a -1) / 4 = 0.55
a = 1 + 0.85 * 4
a = 4.4
d) P (X> a) = 0.89
P (X <a) = 1 - 0.89 = 0.11
Fx (a) = 0.11
(a -1) / 4 = 0.11
a = 1 + 0.11 * 4
a = 1.44
e) P (X> a) = 0.31
P (X <a) = 1 - 0.31 = 0.69
Fx (a) = 0.69
(a -1) / 4 = 0.69
a = 1 + 0.69 * 4
a = 3.76
1. Growth of Functions (11 points) (1) (4 points) Determine whether each of these functions is O(x 2 ). Proof is not required but it may be good to try to justify it (a) 100x + 1000 (b) 100x 2 + 1000
Answer:
See explanation
Step-by-step explanation:
To determine whether each of these functions is [tex]O(x^2)[/tex], we apply these theorems:
A polynomial is always O(the term containing the highest power of n)Any O(x) function is always [tex]O(x^2)[/tex].(a)Given the function: f(x)=100x+1000
The highest power of n is 1.
Therefore f(x) is O(x).
Since any O(x) function is always [tex]O(x^2)[/tex], 100x+1000 is [tex]O(x^2)[/tex].
[tex](b) f(x)=100x^ 2 + 1000[/tex]
The highest power of n is 2.
Therefore the function is [tex]O(x^2)[/tex].
Answer:
i think its 2000
Step-by-step explanation:
4
The equation of a circle is x2 + y2 + x + Dy+ E= 0. If the radius of the circle is decreased without changing the coordinates of the center point, how are the coefficients CD,
and E affected?
O A CD, and E are unchanged.
Answer:
Step-by-step explanation:
in x²+y²+2gx+2fy+c=0
center=(-g,-f)
radius=√((-g)²+(-f)²-c)
if center is not changed ,then c will change .
Here only coefficients of E will change.
if a varies inversely as the cube root of b and a=1 when b=64, find b
Answer:
b = 64/a³
Step-by-step explanation:
Using the given information, we can only find a relation between a and b. We cannot find any specific value for b.
Since a varies inversely as the cube root of b, we have ...
a = k/∛b
Multiplying by ∛b lets us find the value of k:
k = a·∛b = 1·∛64 = 4
Taking the cube of this equation gives ...
64 = a³b
b = 64/a³ . . . . . divide by a³
The value of b is ...
b = 64/a³
Find the circumference of a circle with a radius of 15 centimeters. Round your answer to the nearest centimeter
Answer:
94 cm
Step-by-step explanation:
The formula for finding the circumference of a circle is;
Circumference = 2πr
where π = [tex]\frac{22}{7}[/tex] or 3.14 and
r = radius
Here radius is 15 cm so;
Circumference = [tex]2 * \frac{22}{7} * 15[/tex]
= [tex]\frac{660}{7}[/tex]cm
= 94.28cm
= 94 cm ( rounded to the nearest centimetre )
I got the answer but I really don’t know if it’s correct or not, please help this is due today
What is the equation of the graphed line written in
standard form?
O 2x - y = -4
O 2x - y = 4
O y = 2x – 4
O y=x-4
Answer:
2x-y=4
Step-by-step explanation:
Standard form of a line: Ax+by=c
Use slope intercept form: y=mx+b
slope= 2
y=2x-4
Add 4 to both sides.
y+4=2x
subtract y from both sides.
4=2x-y
Rotate the equation
2x-y=4
Answer:
2x-y=4
Step-by-step explanation:
y=2x-4 is the slope intercept.
y-2x=-4
-2x+y=-4
2x-y=4
Show all work to solve 3x^2 – 5x – 2 = 0.
Answer:
Step-by-step explanation:
3x2−5x−2=0
For this equation: a=3, b=-5, c=-2
3x2+−5x+−2=0
Step 1: Use quadratic formula with a=3, b=-5, c=-2.
x= (−b±√b2−4ac )2a
x= (−(−5)±√(−5)2−4(3)(−2) )/2(3)
x= (5±√49 )/6
x=2 or x= −1 /3
Answer:
x=2 or x= −1/ 3
The solutions to the equation are x = -1/3 and x = 2.
Here are the steps on how to solve [tex]3x^{2}[/tex] – 5x – 2 = 0:
First, we need to factor the polynomial. The factors of 3 are 1, 3, and the factors of -2 are -1, 2. The coefficient on the x term is -5, so we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).
Next, we set each factor equal to 0 and solve for x.
(3x + 1)(x - 2) = 0
3x + 1 = 0
3x = -1
x = -1/3
x - 2 = 0
x = 2
Therefore, the solutions to the equation [tex]3x^{2}[/tex] – 5x – 2 = 0 are x = -1/3 and x = 2.
Here is the explanation for each of the steps:
Step 1: In order to factor the polynomial, we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).
Step 2: We set each factor equal to 0 and solve for x. When we set 3x + 1 equal to 0, we get x = -1/3. When we set x - 2 equal to 0, we get x = 2. Therefore, the solutions to the equation are x = -1/3 and x = 2.
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2{ 3[9 + 4(7 -5) - 4]}
Answer:
2{3[9+4(7-5)-4]}
2{3[9+4(2)-4]}
2{3[13(2)-4]}
2{3[26-4]}
2{3[22]}
2{66}
132
Step-by-step explanation:
Not sure of how to solve this
Answer:
undefined
Step-by-step explanation:
Using the slope formula
m = (y2-y1)/ (x2-x1)
and the given points
m = ( 8 - -1)/( 2-2)
= (8+1) / 0
We cannot divide by 0 so the slope is undefined
Jeremy makes $57,852 per year at his accounting firm. How much is Jeremy’s monthly salary? (There are 12 months in a year.) How much is Jeremy’s weekly salary? (There are 52 weeks in a year.)
Answer:
Monthly: $4,821
Weekly: $1112.54
Step-by-step explanation:
Monthly
A monthly salary can be found by dividing the yearly salary by the number of months.
salary / months
His salary is $57,852 and there are 12 months in a year.
$57,852/ 12 months
Divide
$4,821 / month
Jeremy makes $4,821 per month.
Weekly
To find the weekly salary, divide the yearly salary by the number of weeks.
salary / weeks
He makes $57,852 each year and there are 52 weeks in one year.
$57,852 / 52 weeks
Divide
$1112.53846 / week
Round to the nearest cent. The 8 in the thousandth place tells use to round the 3 up to a 4 in the hundredth place.
$1112.54 / week
Jeremy makes $1112.54 per week
The width of a casing for a door is normally distributed with a mean of 24 inches and a standard deviation of 1/8 inch. The width of a door is normally distributed with a mean of 23 7/8 inches and a standard deviation of 1/16 inch. Assume independence. a. Determine the mean and standard deviation of the difference between the width of the casing and the width of the door. b. What is the probability that the width of the casing minus the width of the door exceeds 1/4 inch? c. What is the probability that the door does not fit in the casing?
Answer:
a) Mean = 0.125 inch
Standard deviation = 0.13975 inch
b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25) = 0.18673
c) Probability that the door does not fit in the casing = P(X < 0) = 0.18673
Step-by-step explanation:
Let the distribution of the width of the casing be X₁ (μ₁, σ₁²)
Let the distribution of the width of the door be X₂ (μ₂, σ₂²)
The distribution of the difference between the width of the casing and the width of the door = X = X₁ - X₂
when two independent normal distributions are combined in any manner, the resulting distribution is also a normal distribution with
Mean = Σλᵢμᵢ
λᵢ = coefficient of each disteibution in the manner that they are combined
μᵢ = Mean of each distribution
Combined variance = σ² = Σλᵢ²σᵢ²
λ₁ = 1, λ₂ = -1
μ₁ = 24 inches
μ₂ = 23 7/8 inches = 23.875 inches
σ₁² = (1/8)² = (1/64) = 0.015625
σ₂ ² = (1/16)² = (1/256) = 0.00390625
Combined mean = μ = 24 - 23.875 = 0.125 inch
Combined variance = σ² = (1² × 0.015625) + [(-1)² × 0.00390625] = 0.01953125
Standard deviation = √(Variance) = √(0.01953125) = 0.1397542486 = 0.13975 inch
b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25)
This is a normal distribution problem
Mean = μ = 0.125 inch
Standard deviation = σ = 0.13975 inch
We first normalize/standardize 0.25 inch
The standardized score of any value is that value minus the mean divided by the standard deviation.
z = (x - μ)/σ = (0.25 - 0.125)/0.13975 = 0.89
P(X > 0.25) = P(z > 0.89)
Checking the tables
P(x > 0.25) = P(z > 0.89) = 1 - P(z ≤ 0.89) = 1 - 0.81327 = 0.18673
c) Probability that the door does not fit in the casing
If X₂ > X₁, X < 0
P(X < 0)
We first normalize/standardize 0 inch
z = (x - μ)/σ = (0 - 0.125)/0.13975 = -0.89
P(X < 0) = P(z < -0.89)
Checking the tables
P(X < 0) = P(z < -0.89) = 0.18673
Hope this Helps!!!
The problem is: On a Map, 3 inches represents 40 miles, How many inches represents 480 miles?
Given a right triangle with a hypotenuse length of radical 26 and base length of 3. Find the length of the other leg (which is also the height).
Answer:
√17
Step-by-step explanation:
The Pythagorean theorem can be used for the purpose.
hypotenuse² = base² +height²
(√26)² = 3² +height²
26 -9 = height²
height = √17
The length of the other leg is √17.
show that 7 1/2 - 4 2/3 = 2 5/6
Equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex] is true.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex]
We need to check whether the left hand side is equal to right hand side.
These are in the form pf mixed fraction we can convert them to the improper fraction.
[tex]7\frac{1}{2}=15/2[/tex]
[tex]4\frac{2}{3}=\frac{14}{3}[/tex]
So Let us subtract 24/3 from 15/2
15/2-14/3
LCM of 2 and 3 is 6
45-28/6
17/6
This can be written as mixed fraction [tex]2\frac{5}{6}[/tex]
Hence, equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex] is true.
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The mean monthly car payment for 123 residents of the local apartment complex is $624. What is the best point estimate for the mean monthly car payment for all residents of the local apartment complex?
Answer:
The best point estimate for the mean monthly car payment for all residents of the local apartment complex is $624.
Step-by-step explanation:
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].
In this question:
We apply the inverse Central Limit Theorem.
The mean monthy car payment for 123 residents of the local apartment complex is $624.
So, for all residents of the local apartment complex, the best point estimate for the mean monthly car payment is $624.
Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 116 meters
Answer:
Length = 29 m
Width = 29 m
Step-by-step explanation:
Let x and y be the length and width of the rectangle, respectively.
The area and perimeter are given by:
[tex]A=xy\\p=116=2x+2y\\y=58-x[/tex]
Rewriting the area as a function of x:
[tex]A(x) = x(58-x)\\A(x) = 58x-x^2[/tex]
The value of x for which the derivate of the area function is zero, is the length that maximizes the area:
[tex]A(x) = 58x-x^2\\\frac{dA}{dx}=0=58-2x\\ x=29\ m[/tex]
The value of y is:
[tex]y = 58-29\\y=29\ m[/tex]
Length = 29 m
Width = 29 m
. The client was hoping for a likability score of at least 5.2. Use your sample mean and standard deviation identified in the answer to question 1 to complete the following table for the margins of error and confidence intervals at different confidence levels. Note: No further calculations are needed for the sample mean. (6 points: 2 points for each completed row) Confidence Level | Margin of error | Center interval | upper interval | Lower interval 68 95 99.7
Answer:
The 68% confidence interval is (6.3, 6.7).
The 95% confidence interval is (6.1, 6.9).
The 99.7% confidence interval is (5.9, 7.1).
Step-by-step explanation:
The Central Limit Theorem states that if we have a population with mean μ and standard deviation σ and take appropriately huge random-samples (n ≥ 30) from the population with replacement, then the distribution of the sample-means will be approximately normally distributed.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\bar x[/tex]
And the standard deviation of the sample means (also known as the standard error)is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}} \ \text{or}\ \frac{s}{\sqrt{n}}[/tex]
The information provided is:
[tex]n=400\\\\\bar x=6.5\\\\s=4[/tex]
As n = 400 > 30, the sampling distribution of the sample-means will be approximately normally distributed.
(a)
Compute the 68% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 0.9945\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.1989\\\\=(6.3011, 6.6989)\\\\\approx (6.3, 6.7)[/tex]
The 68% confidence interval is (6.3, 6.7).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{6.7-6.3}{2}=0.20[/tex]
(b)
Compute the 95% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 1.96\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(6.108, 6.892)\\\\\approx (6.1, 6.9)[/tex]
The 95% confidence interval is (6.1, 6.9).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{6.9-6.1}{2}=0.40[/tex]
(c)
Compute the 99.7% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 0.594\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(5.906, 7.094)\\\\\approx (5.9, 7.1)[/tex]
The 99.7% confidence interval is (5.9, 7.1).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{7.1-5.9}{2}=0.55[/tex]
Christopher collected data from a random sample of 800 voters in his state asking whether or not they would vote to reelect the current governor. Based on the results, he reports that 54% of the voters in his city would vote to reelect the current governor. Why is this statistic misleading?
Answer:
The statistic is misleading because Christopher collects his sample from a population (voters in his state) and make inferences about another population (voters in his city).
Step-by-step explanation:
The statistic is misleading because Christopher collects his sample from a population (voters in his state) and make inferences about another population (voters in his city).
He should make inferences about the population that is well represented by his sample (voters in his state), or take a sample only from voters from his city to make inferences about them.
Evaluate the expression.........
Answer:
9
Step-by-step explanation:
p^2 -4p +4
Let p = -1
(-1)^1 -4(-1) +4
1 +4+4
9