Question 1 of 10, Step 1 of 1
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An economist wants to estimate the mean per capita Income (in thousands of dollars) for a major city in California. He believes that the mean Income is $21.3, and the
variance is known to be $32.49. How large of a sample would be required in order to estimate the mean per capita income at the 99 % level of confidence with an
error of at most $0.39? Round your answer up to the next integer.
Answers
n=1422 is the sample that would be required in order to estimate the mean per capita income at the 99 % level of confidence with an error of at most $0.39.
What is meant by confidence level?The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The parameter's true value, for instance, should be present in 95% of all intervals computed at the 95% level. The range of values within the 95% confidence interval represents the population's actual mean, with 95% confidence. The sample mean (the center of the CI) will differ between samples due to natural sampling variability. The process itself, not a certain CI, is what inspires confidence. According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, hence to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.
At 99% confidence interval the critical value is \(z_{0.005}\)=2.58
Margin of error=0.39
Or, \(z_{0.005}\)(σ/√n)=0.39
Or, 2.58(5.7/√n)=0.39
Or, n=(2.58×(5.7/0.39)²
Or, n=1422
n=1422 is the sample that would be required in order to estimate the mean per capita income at the 99 % level of confidence with an error of at most $0.39.
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Related Questions
PLEASE HELP ASAP I WILL GIVE BRAINSLET TO THE CORRECT ANSWER!!!!!!!!!!
Answers
Answer:
Therefore has one solution.
explanation:
Given equations:
6x + y = -7
-24x -7y = 25
Make y the subject:
6x + y = -7
y = -7 - 6x ..............equation 1
-24x -7y = 25
-7y = 25 + 24x
y = (25 + 24x)/-7 ..........equation 2
Solve them simultaneously:
(25 + 24x)/-7 = -7 - 6x
25 + 24x = -7 (-7 - 6x)
25 + 24x = 49 + 42x
42x - 24x = 25- 42
18x = -24
x = \(-\frac{4}{3}\)
Then y is:
y = -7 - 6x
y = -7 - 6( \(-\frac{4}{3}\))
y = 1
Has one separate value of x and y: ( \(-\frac{4}{3}\) , 1 ); so it has one solution.
Tell whether the following equation has one,
zero or infinitely many solutions.
3(x - 1) = 2x + 9
O Zero Solutions
O x = 1
O One Solution
O Infinitely Many
will give brainlest!!
Answers
Answer:
3(x-1) = 2x+9
3x-3 = 2x+9
3x-2x = 9+3
x = 12
In a survey of 92 pet owners, 11 said they own a dog, and 39 said they own a cat. 4 said they own both a
dog and a cat. How many owned a cat but not a dog?
Answer =
owners
Answers
Answer:
35 people
Step-by-step explanation:
Factor 4x2 + 24x + 36.
A) 4(x + 3)(x + 3)
B) 4(x + 6)(x – 6)
C) (4x + 3)(x + 3)
D) (2x – 6)(2x – 6)
Answers
Answer:
\(\huge\boxed{\text{A) } 4(x+3)(x+3) }\)
Step-by-step explanation:
In order to factor this, we need to factor out a common term and then solve for x.
We can see that we can factor out a 4 from this entire equation as each term is a multiple of 4.
This leaves us with \(4(x^2+ 6x + 9)\).
We can now solve for x for the expression in the parentheses, \(x^2 +6x + 9\).
To solve for x, we can use the XBOX method. This tells us that:
When the two roots are added, they will equal b (in this case, 6) When the two roots are multiplied, they will equal c (in this case 9)Experimenting with some numbers gets us with 3 and 3 - 3+3 = 6 and 3*3 = 9.
Therefore, our roots will be \((x+3)(x+3)\).
Putting that back into the factorization of our original expression, that leaves us with \(4(x+3)(x+3)\).
Hope this helped!
simplify the radical below
3√x^18
Answers
The radical is 3sqrt(x^18)
18/2=9
so, the radical is
3x^9
3√x^18 simplified would be x^6, hope it helps sorry if it doesn’t tho, have a great day!
HELP ME PLEASE THANKS
Answers
Answer: Answer choice B
Step-by-step explanation:
What is the value of y in the solution to the system of equations?
1/3 x + 1/4y =1
2x - 3y = -30
-8
-3
3
8
Answers
Answer:
y = 8
Step-by-step explanation:
2/3 x+1/2y = 2
2/3 x - y = -10
3/2y = 12
y = 8
I need help on question 27
Answers
A = \(\frac{1}{2}h(b_{1} +b_{2} )\)
If A = 136 when \(b_{1}\) = 7 and h = 16, find \(b_{2}\)
Givens:We are given the equation that we are working with:
A = \(\frac{1}{2}h(b_{1} +b_{2} )\)
We are given certain values that the variables, in this case, are equal to:
A = 136
\(b_{1}\) = 7
h = 16
Steps:Substitute the given variables in the given equation for the corresponding numbers:
A = \(\frac{1}{2}h(b_{1} +b_{2} )\)
136 = \(\frac{1}{2}\) * 16 (7 + \(b_{2}\))
We know all the values in the equation except \(b_{2}\). In order to find \(b_{2}\) we must isolate it on one side of the equation
136 = 8 (7 + \(b_{2}\))
\(\frac{136}{8}\) = \(\frac{8 (7 + b_{2}) }{8}\)
17 = 7 + \(b_{2}\)
17 - 7 = 7 - 7 + \(b_{2}\)
10 = \(b_{2}\)
Check:If \(b_{2}\) is equal to 10 then if we plug it back into the given equation both sides of the equation should equal each other. Remember to use PEMDAS
136 = \(\frac{1}{2}\) * 16 (7 + \(b_{2}\))
136 = \(\frac{1}{2}\) * 16 (7 + 10)
136 = \(\frac{1}{2}\) * 16 (17)
136 = 8 (17)
136 = 136
\(b_{2}\) = 10
Two cars are traveling towards a hotel on the same road. From the edge of the hotel, 600 feet high, Spiderman sits on the rooftop thinking about the depression angle needed to reach each car. If the depression angle to the nearest car is 52 degrees, and the depression angle to the farther car is 46 degrees, how far apart must the two cars be from each other?
Make a sketch, solve the problem, and round your answer to the nearest hundredth of a foot.
Answers
The two cars must be approximately 177.34 feet apart from each other for Spiderman to have different depression angles to each car.
To find the distance between the two cars, we can use trigonometry and the concept of similar triangles. Let's denote the distance between Spiderman and the nearest car as d1 and the distance between Spiderman and the farther car as d2.
In a right triangle formed by Spiderman, the height of the hotel, and the line of sight to the nearest car, the tangent of the depression angle (52 degrees) can be used:
tan(52) = 600 / d1
Rearranging the equation to solve for d1:
d1 = 600 / tan(52)
Similarly, in the right triangle formed by Spiderman, the height of the hotel, and the line of sight to the farther car, the tangent of the depression angle (46 degrees) can be used:
tan(46) = 600 / d2
Rearranging the equation to solve for d2:
d2 = 600 / tan(46)
Using a calculator, we can compute:
d1 ≈ 504.61 feet
d2 ≈ 681.95 feet
The distance between the two cars is the difference between d2 and d1:
Distance = d2 - d1
Plugging in the values, we have:
Distance ≈ 681.95 - 504.61
Distance ≈ 177.34 feet
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A painting was sold for 179.4 million dollars, Write this amount in scientific notation
Answers
Answer:
\(1.794 \times {10}^{2} \)
(in scientific notation)
There are 15 , 000 students attending the community college. Find the percent of students that attend classes in the evening if there are 3 , 750 evening students.
Answers
Identify the amount, base, and percent in the problem:
4.8 is what percent of 12?
A. The amount is 12, the base is 4.8, and the percent is unknown.
B. The amount is 4.8, the base is 12, and the percent is unknown.
C. The amount is unknown, the base is 4.8, and the percent is 12 %
D. The amount is unknown, the base is 12, and the percent is 4.8%
Answers
The amount is 4.8, base is 12 and the precent of the given condition is unknown.
Define base:
In mathematics, the term "base" refers to a fixed number or symbol used as a point of reference for counting, measuring or representing a quantity.
In the decimal system, for example, the base is 10, because there are 10 possible digits (0-9) that can be used to represent a number. In binary system, the base is 2, because there are only 2 possible digits (0 or 1) that can be used to represent a number.
What about precent?
In mathematics, percent is a way of expressing a number as a fraction of 100. The term "percent" means "per hundred," so a number expressed as a percent represents a fraction of 100.
To convert a number to a percent, we multiply it by 100. For example, if we want to express the number 0.25 as a percent, we can multiply it by 100 to get:
⇒ 0.25 x 100 = 25%
According to the given information:
Percent: The precent is the number with the % symbol
Base: The base is the whole amount which in this case is 12.
Amount: The amount based on the precent is 4.8
So, from overall condition we have that option 'a' is correct.
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PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((
Answers
Answer:
2.333333333
Step-by-step explanation:
divide 3 into 7 and it's is repeating
Answer:
Step-by-step explanation:
geometry help pleaseeeee
Answers
Answer:
obtuse triangleStep-by-step explanation:
to understand thisyou need to know about:trianglePEMDASgiven:sides:3,5,6 respectivelytips and formulas:obtuse triangle when c²>a²+b²let's solve:let's justify whether it's right or not
according to Pythagoras theorem
a²+b²=c²
3²+5²=6²
9+25=36
34≠36
therefore it is not right angle triangle
using the formula
34<36
therefore
it obtuse triangle
what’s the answer to 5y-4
Answers
Answer:
y = 0.8
Step-by-step explanation:
what is the place value of 8 in fullowing number? 348000
Answers
Answer: 8000
Step-by-step explanation:
The 8 in the number 348,000 is in the thousands place.
So it represents the value of 8,000 .
The volume of a sphere is 3000 m. What is the surface area of the sphere to the nearst square meter.
Answers
Answer:
113097336
Step-by-step explanation:
(3000^2 x Pi) x 4
113097335.52923
113097336
Classify the following into finite and infinite set
(i) The set of months in a year
(ii)The set of stars in the galaxy
(iii)The set of even integers
(iv)The set of odd integers
(v)The set of alphabets
Answers
i) finite set, ii) infinite set, iii) infinite set, iv) infinite set, and v) finite set are the required solutions.
A Set is a collection of objects with similar properties. There are different types of set two of them are finite and infinite set.
Finite set- A set is called a finite set when the elements inside the set are countable or where we can know the starting and the ending of the elements. For example- A set of players in a cricket team.
Infinite set- A set is called an infinite set when the elements inside the set are uncountable or where the ending of the elements is not known. For Example- A set of positive numbers.
Here in the question the option (i) and (v) are finite sets because the no.of months in the year and no.of alphabets are countable or finite. Option (ii), (iii), and (iv) are infinite sets as no.of stars in the galaxy, even integers, and odd integers are uncountable.
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Answer:
the set of months in a year is finite
the set of star in the Galaxy is finite
the set of even integers is infinite
the set of odd integers is infinite
the set of alphabet is finite
Step-by-step explanation:
1) the set of month in a year is finite because they are limit and we can count them easily
2) the set of star in the galaxy is finite cause there are zillions of stars
3) the set of even integer is infinite because numbers are unlimit or infinite
4) the set of odd integers is infinite cause numbers are infinite ir they have not limit
5) the set of alphabet is finite because we can count them limitedly
Express the given trigonometric functions in terms of the same function of a positive acute angle.sec 948 degrees, cos(-948) degrees
Answers
Given the Trigonometric Functions:
\(\begin{gathered} sec(948\text{\degree}) \\ \\ cos(-948\text{\degree}) \end{gathered}\)Using your calculator you get:
\(sec(948\text{\degree})\approx-1.49\)By definition, Secant is negative in Quadrant III.
Finds its Reference Angle as follows:
\(948\text{\degree}-5\cdot180\text{\degree}=48\text{\degree}\)Because:
\(\frac{948}{180}\approx5\)Then, you get:
\(=-sec\left(48\text{\degree}\right)\)Notice that:
\(cos(-948\text{\degree})\approx-0.67\)Then, you can conclude that it is in Quadrant II.
Therefore its Reference Angle is:
\(5\cdot180\text{\degree}-948\text{\degree}=-48\)So you can set up:
\(=-cos\lparen-48)\)By definition:
\(cos(-\theta)=cos\theta\)Therefore, you can rewrite it in this form:
\(=-cos(48\text{\degree})\)Hence, the answer is:
\(\begin{gathered} sec(48\text{\degree}) \\ \\ -cos(48\text{\degree}) \end{gathered}\)Spencer is working with his finande advisor to create some personal financial goals for the next year. One of his goals is to reduce the amount of debt
he has. Which statement could
his goal specific and timely?
He should focus intust his student loan debt and give himself a deadline of five years.
B. He should ask
end to be his accountability partner and remind him of his goal every two weeks.
le should review.
current finances to determine how much he can allocate to his goal.
He should pay
the minimum payment on his credit card statement each month.
Answers
Answer: A. He should focus on his student loan debt and give himself a deadline of five years. This statement specifies a particular type of debt and sets a time-bound goal, making it both specific and timely.
Step-by-step explanation:
What is the range of f(x) = sin(x)?
the set of all real numbers -2pi≤y≤2pi
the set of all real numbers -1≤y≤1
the set of all real numbers 0≤y≤2pi
the set of all real numbers
Answers
Answer:
the set of all real numbers -1≤y≤1
Step-by-step explanation:
according to the definition of 'sin'-function, the max value of it is '+1' and the min is '-1'. Finally, the correct answer is B. the set of all real numbers -1≤y≤+1.
I need Help ASAP please
Answers
The answers are in the photo
A person invested $880 in an account growing at a rate allowing the money to double every 6 years. How much money would be in the account after 13 years, to the nearest dollar?
Answers
Answer:
$3,951
Step-by-step explanation:
The growth factor for t years is given as 2^(t/6). Then in 13 years, the account will be multiplied by ...
2^(13/6) ≈ 4.489848
Its value will be ...
$880·4.489848 ≈ $3,951
please help it's due tomorrow
Answers
Answer:
B. -414,720 x⁷y⁶
Step-by-step explanation:
To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.
The binomial theorem states that for an expression of the form (a + b)ⁿ:
\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)
For the expression (2x - 3y²)¹⁰:
a = 2xb = -3y²n = 10Therefore, each term in the expression can be calculated using:
\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)
The 4th term is when r = 3. Therefore:
\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)
So the 4th term of the given expansion is:
\(\boxed{-414720\:x^7y^6}\)
If APR on credit card is 17.8% what is the daily percentage rate (DPR)?
Answers
The daily percentage rate (DPR) for the given Annual Percentage Rate (APR) on credit card is 17.8% is equal to 0.048%.
Given the Annual Percentage Rate (APR) on credit card is 17.8%.
Now, we need to find the daily percentage rate (DPR) for the given yearly percentage on credit card.
To find your current annual percentage rate, look at your monthly statements. To determine the daily percentage rate (DPR), divide the annual percentage rate (APR) by 365 (the number of days in a year).
So, given APR = 17.8%
Now, daily percentage rate will be:
⇒ Daily percentage rate = Annual Percentage Rate ÷ 365
⇒ DPR = APR / 365
⇒ DPR = 17.8% ÷ 365
⇒ DPR = 0.048%
Therefore, daily percentage rate (DPR) is equal to 0.048%.
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PLEASE ANSWER ASAP WILL MARK BRAINLIEST!!!!!
Answers
Answer:
y>3
Step-by-step explanation:
All values on the y axis will be greater than 3
Hope this helps :D
1. How is the orientation of the triangie affected by the translation?
Answers
Solution: The orientation is inverted
Explanation:
Given a triangle ABC if we reflect if along a straight line L we get the triangle A'C'B' and now we are going to draw it
Please answer this question ASAP
Answers
Answer:
Budgins.
Step-by-step explanation:
Waitroze is selling the cans of soup for 1.27 more than Budgins. So, therefore, Budgins has a WAY better deal than Waitroze.
solve the file please
Answers
Answer:
z + 4 × 9
Sorry if this is wrong.
FInd the slope of the line graphed.
PLS HELP ME IMPORTANT TEST!!!!!!
Answers
Answer:
2/5
Step-by-step explanation:
rise/run = 2/5