Answer:
a) [tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{2.58})^2}=1849[/tex]
And rounded up we have that n=1849
b) [tex]n=\frac{0.26(1-0.26)}{(\frac{0.03}{2.58})^2}=1422.99[/tex]
And rounded up we have that n=1423
c) For this case we can see that if we have a prior estimate the minimum sample size required for the margin of error desired would be less as we can see in part b we reduce the sample size compared to the part a
Step-by-step explanation:
Part a
The critical value for a confidence level of 99% is for this case [tex]z_{\alpha/2} =2.58[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
Since we don't know any estimate for the true proportion we can use [tex]\hat p =0.5[/tex] as a godd estimator. And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{2.58})^2}=1849[/tex]
And rounded up we have that n=1849
Part b
For this case we have a prior estimate [tex]\hat p =0.26[/tex] and replacing we got:
[tex]n=\frac{0.26(1-0.26)}{(\frac{0.03}{2.58})^2}=1422.99[/tex]
And rounded up we have that n=1423
Part c
For this case we can see that if we have a prior estimate the minimum sample size required for the margin of error desired would be less as we can see in part b we reduce the sample size compared to the part a
Can someone plz help ne
Answer:
38.5
Step-by-step explanation:
The perimeter is found by
P = 2( l+w)
We know the width is 23, we are looking for the length
P = 2 (23+l)
The perimeter is 123
123= 2 (23+l)
Divide each side by 2
123/2 = 23+l
61.5 = 23+l
Subtract 23 from each side
61.5 -23 = l
38.5 = l
The length of AB = 38.5
How to round to the nearest degree
Answer:
to the nearest whole degree means that you look at the first decimal place. if it is less than 5, you keep the whole number and eliminate the decimal. if otherwise, the decimal is ≥5, you round up the whole number and eliminate the decimal.
Scientists researching amphibians put tags on 30 frogs in a wetland area. Later, the scientists captured 520 frogs, of which 12 had tags. To the nearest whole number, what is the best estimate for the frog population?
Final answer:
The best estimate for the frog population, calculated using the mark-recapture method where 30 frogs were initially tagged and later 12 tagged frogs were found in a sample of 520, is approximately 208 frogs.
Explanation:
The question involves estimating the total population of frogs in a wetland area based on a mark-recapture study. The calculation is based on a proportion set up by the initial number of tagged frogs to the total initial tagging, compared with the number of tagged frogs found in a later sample to the size of that sample. This is a classic example of a capture-recapture method used in ecology for estimating population sizes.
The initial number of tagged frogs is 30, and later, from a sample of 520 frogs, 12 are found to be tagged. To estimate the total population (N), we set up the proportion as follows:
30 tagged frogs / N total population = 12 tagged frogs / 520 sample size
Now we cross-multiply and solve for N:
30N = 12 × 520
N = (12 × 520) / 30
N = 6240 / 30
N = 208
Therefore, the best estimate for the total frog population is approximately 208 frogs, rounded to the nearest whole number.
Which word describes the slope of the line?
positive
negative
zero
undefined
Answer:
If it is horizontal then it is zero, if it is vertical then it is undefined
Step-by-step explanation:
horizontal= <------------->
^
vertical=| (up and down)
v
Answer:
undefined
Step-by-step explanation:
Allison's cinema has 100 seats. One day, Allison notices that her cinema is full, and she has taken exactly £100. The prices where: adult=£3.50, pensioner= £1, child=£0.85. she knows not everyone in the audience is a pensioner. Howmmany adults, children and pensioners where there?
Answer:
So starting with what we already know, £100 was paid in all, all 100 seats were taken. Adults pay £3.50, Children pay $0.85 and the Pensioners pay $1.00. I basicaly started off by trying it so all adults, children and pensioners are the exact same number. 33 adult tickets would cost them £115.50. Crossing that suggestion out; I tried again, but this time, with 3 adults, 50 children and the 47 that were left, i put as pensioners. So, now there is 100 people and this is kind of working out:
3 adults= £10.50, 50 children= £42.50, 47 pensioners= £47.00 Total £100
Step-by-step explanation:
As per the given data number of adults [tex]=3[/tex] , number of children [tex]= 50[/tex] and number of pensioner [tex]= 47[/tex].
What is number?" Number is defined as the count of the given quantity."
According to the question,
Total number of seats [tex]=100[/tex]
Total amount of full seats [tex]= \£100[/tex]
Price of adult ticket [tex]= \£ 3.50[/tex]
Price of children ticket [tex]= \£ .85[/tex]
Price of adult ticket [tex]= \£ 1[/tex]
[tex]'x'[/tex]represents the number of adults
[tex]'y'[/tex] reprsents the number of children
[tex]'z'[/tex] represents the number of pensioner
As per given condition we have,
[tex]x + y + z = 100\\\\\£3.50x + \£0.85y + \£1z = \£ 100[/tex]
Using trial and error method we get,
[tex]x = 3 ,\\\\y= 50\\\\z= 47[/tex]
For total number of tickets
[tex]3 + 50 + 47 = 100[/tex]
Left hand side = Right hand side
Substitute in left hand side of total cost we get,
[tex]\£3.50(3) + \£0.85(50) + \£1(47) \\\\= \£10.50 + \£42.50 + \£47[/tex]
[tex]= \£ 100[/tex]
= Right hand side
Hence, as per the given data number of adults [tex]=3[/tex] , number of children [tex]= 50[/tex] and number of pensioner [tex]= 47[/tex].
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URGENT!!!
Graph: -4x+2y=8
Answer:
Step-by-step explanation:
Which of the following is the coordinate for the image of point M(3, –7) after a 90° clockwise rotation? a.)M’(–7, –3) b.)M’(7, –3) c.)M’(7, 3) d.)M’(–7, 3)
M,(-7, -3)
Step-by-step explanation:
Answer:
M,(-7, -3) i took the quiz liker 5 seconds ago
Ned scored 84 points in the first 6 games of the basketball season . How many points per game has Ned scored ?
Answer:
he scored 14 points per game :)
Step-by-step explanation:
Simplify the following algebraic expression:
10xy - 5ab - 15yx + 9ba
Answer:
- 5xy + 4ab
Step-by-step explanation:
Please answer i will mark brainliest Plato stores his Pokémon cards in a shoe box measuring eight inches by 14 inches by six
inches. Socrates stores his Magic cards in a cake box measuring one foot by one foot by
five inches. Whose container has the greater capacity?
Answer:
Socrates' box is 48 sq inches larger than Plato's.
Step-by-step explanation:
14x8x6=672
12x12x5=720
happy to help ya :)
m∠QPS=40
m∠RPS=8x+7
m∠QPR=9x+16
find m∠QPR
Answer:
25
Step-by-step explanation:
from the information given, we know that rps + qpr = qps.
so, (8x+7)+(9x+16) = 40.
simplify to get 17x + 23 = 40.
17x = 17.
x = 1.
plug in: 9+16 = 25.
Benjamin started her walk from the front door of her ground floor apartment. She walked 6 meters to the corner of the building and then turned the corner and walked 10 meters to her friend's apartment.
Answer:
4 meters.
Step-by-step explanation:
Benjamin has walked two legs of a right triangle, so you can connect her two movements with a line if you were sketching the situation.. The displacement is the objects overall change in position in relation to its origin, so in your case, Benjamin's apartment. While the total distance adds up regardless of her position.
So, the total distance Benjamin walked is 10m + 6m = 16m
Her displacement can be found by your best friends, the Pythagorean Theorem: 10m ^2 + 6m ^2 = delta x^2 (or displacement squared).. giving you a displacement of 11.66, or 12 m.
The difference between the distance she walked and her displacement is 4 meters.
I hope this helps. If you have any more questions, please feel free to post them and someone will be able to help you, whether it's myself or others. Please leave a like, rating, and if possible, Brainliest. Have a great day!
Answer the following questions about the problem above. Write in complete sentences to get full credit.
1. What is the slope for section "b" of Mrs. Washington's commute.
2. What is the slope for section "c" of Mrs Washington's commute?
3. Explain the difference in "b" and "c" in context of Mrs. Washing driving home.
4. How far does Mrs. Washington live from her work?
Answer:
1. -1
2. -1/4
3. As the line nears closer to y = 0, Mrs. Washington is getting closer to her house. As such, the line represents miles driven per minute, representing speed. As the slope of the line becomes steeper, as it does during section B of the commute, Mrs. Washington is driving one mile per minute, or 60 miles per hour. As she drives through section C, she only drove 1 mile after 4 minutes, or 15 miles per hour.
4. She lives 20 miles from her office.
Step-by-step explanation:
1. You can find the slope for section B of the commute by taking two points in section B and using them to find the slope.
I will take (10, 13) and (14, 9) as my points.
You can use [tex]\frac{y2-y1}{x2-x1}[/tex] to find the slope:
[tex]\frac{13-9}{10-14} \\\\\frac{4}{-4}[/tex]
The slope for section b is -1.
2. You can find the slope for section C using the same method.
I will use the points (16, 7) and (20, 6):
[tex]\frac{7-6}{16-20} \\\\\frac{1}{-4}[/tex]
The slope for section c is -1/4.
3. As the line nears closer to y = 0, Mrs. Washington is getting closer to her house. As such, the line represents miles driven per minute, representing speed. As the slope of the line becomes steeper, as it does during section B of the commute, Mrs. Washington is driving one mile per minute, or 60 miles per hour. As she drives through section C, she only drove 1 mile after 4 minutes, or 15 miles per hour.
4. She lives 20 miles from her office. This is stated in the question itself.
Answer:
1. Speed = 1 mph
2. ¼ mph
3. She's driving at 4 times faster speed in b than c
4. 20 miles
Step-by-step explanation:
1. Slope of a distance time graph is the speed
(15-7)/(16-8)
8/8
1 mph
2. Speed = (7-6)/(20-16)
1/4 mph
3. Speed in b is greater than c
1 = 4(¼)
4. Distance from 20 to 0, is 20 miles
Popular culture may include changing trends in all of the following categories except __________. A. clothing styles B. history C. music D. art
Answer:
B. History
Step-by-step explanation:
Because cultures have certain clothing styles on cations, they listen to one or more types of music in certain lands, and they have art that is so pretty.
Popular culture may include changing trends in all of the following categories except history. Then the correct option is B.
What is history?History is the study of an event that is done in the past.
Examples - The British empire, Hitler's torture, world wars, political interference, etc.
Popular culture may include changing trends in all of the following categories except history.
Thus, the correct option is B.
More about the history link is given below.
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Mr. John borrows $10,000 to remodel his kitchen; he borrows the money for 5 years, and has to pay a simple interest rate of 4.5% per year.
A) Since there are 12 months in the year, how many total months does Mr. John have to pay back this loan?
B) What will be the amount of Mr. john's monthly payment to the bank?
Answer:
A) 60
B)450
Step-by-step explanation:
A) you multiply 5x12
B)10,000(the whole) divided by 100(the 4.5% comes from 100%)is 100.Now instead of trying to divide the missing number,(you cant cause its not there) you instead multiply.You multiply 4.5% by the hundred that you got earlier.
What is the area of the following circle?
Either enter an exact answer in terms of it or use 3.14 for IT and enter your answer as a decimal.
r = 7
Answer:
A =153.86
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
We know pi = 3.14 and the radius is 7
A = 3.14 * 7^2
A =153.86
Anyone know how to go this ?
Answer:
the first one
P= 34
A= 66
----------------------------
the second one
P= 40
A= 120
----------------------------
the third one
P= 40
A= 81
the fourth one
if that's a 4
P= 12
if that's a 9
P=27
A=?
Rylee shopped at a clothing store, where she spent $36.50 plus 8% tax. Then, she spent $25 to refuel her car at the gas station. Finally, she bought groceries worth $23.50. At the grocery checkout, she handed over a coupon for a 20% discount on her purchase. what is her net change
Rylee's total spending was $39.42 for clothing (including tax), $25 for gas, and $18.80 for groceries (after applying a 20% discount). Summing these up, her total expenditure for all purchases was $83.22.
Explanation:This is a question involving basic arithmetic and percentage operations. In total, Rylee made three different purchases. She shopped for clothing costing $36.50 and paid 8% tax on it, which amounts to $36.50 * 0.08 = $2.92. Therefore, her total expenditure at the clothing store was $36.50 + $2.92 = $39.42. She then spent $25 to refuel her car.
Lastly, she bought groceries worth $23.50, but had a 20% discount coupon so she only paid 80% of the price, which is $23.50 * 0.80 = $18.80. If we add these expenditures together, we can find that Rylee's total spending was $39.42 (clothing) + $25 (gas) + $18.80 (groceries) = $83.22.
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What is the scale factor in the dilation?
Examine the diagram. It is not drawn to scale.
A triangle has angles A, C, 57 degrees. The exterior angle to angle A is B and the exterior angle to angle C is 118 degrees.
Use the measurements provided in the diagram to determine the measure of AngleB.
mAngleB =
°
E DGENUITY
Answer: 119
Step-by-step explanation: got it right
In the given figure, measure of angle A is 61°, measure of angle B is 119° and measure of angle C is 62°.
From the given triangle triangle, exterior angle to the angle C is 118°.
We know that, sum of two adjacent angles is 180°.
Here, ∠C+118°=180°
∠C=180°-118°
∠C=62°
By using exterior angle theorem of triangle, we get
∠A+57°=118°
∠A=118°-57°
∠A=61°
So, ∠A+∠B=180° (Adjacent angles)
61°+∠B=180°
∠B=180°-61°
∠B=119°
Therefore, in the given figure, measure of angle A is 61°, measure of angle B is 119° and measure of angle C is 62°.
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See below! Thanks Durtle!
Answer:
(6,7)
Step-by-step explanation:
The length of the new vector is [tex]\sqrt{85}[/tex], with side lengths 7 and 6. Therefore, the new coordinates are (6,7). Hope this helps!
9515 1404 393
Answer:
<6, 7>
Step-by-step explanation:
The sum of two vectors is found by summing their corresponding components.
a + b = <4, 1> + <2, 6> = <4+2, 1+6>
a + b = <6, 7>
Audrey grabs a meal with her two co-workers. If everyone paid an equal amount of $8.50 then how much would the total be
Answer:
$25.50
Step-by-step explanation:
There three people- Audrey and two co-workers
Each pay $8.50
Then the total is:
$8.50*3 = $25.50which set is closed under subtraction?
Answer:
The rational numbers are "closed" under addition, subtraction, and multiplication. Under division, we run into the problem of division by 0, which makes the statement that "the rationals are closed under division" false.
Step-by-step explanation:
A rectangle has a height of 4x ^ 3 width of x ^ 3 + 3x ^ 2 + 2x . Express the area of the entire rectangle .
Answer:
[tex]4x^6+12x^5+8x^4[/tex]
Step-by-step explanation:
To find the area of a triangle, you need to multiply the width by the height. In this case:
[tex](4x^3)(x^3+3x^2+2x)=\\4x^6+12x^5+8x^4[/tex]
Hope this helps!
5. Solve: (2n – 5)^2= 81
Answer:
(n -7)(4n + 8) = 0
Step-by-step explanation:
(a -b)² = a² - 2ab + b²
(2n - 5)² = 81
(2n)² - 2*2n*5 + 5² = 81
4n² - 20n + 25 = 81
4n² - 20n + 25 - 81 = 0
4n² - 20n - 56 = 0
4n² - 28n + 8n - 8*7 = 0
4n*(n -7) + 8*(n - 7) = 0
(n -7)(4n + 8) = 0
Can someone please explain this?
Answer:
-pi
Step-by-step explanation:
as x equals zero, g(x) = -3.14 = -pi
Your answer would be the second option, -π.
This is because as x approaches 0, cos(x + π) approaches cos(π) = -1. On top, x + π as x approaches 0 will tend to π, so you end up with π/-1. This simplifies to -π.
I hope this helps! Let me know if you have any questions :)
The polynomial p(x)=x^3-7x-6 has a non-factor of (x+1) rewrite p(x) as a product of linear factors.
Answer:
Using synthetic division suffices to answer your question:
Step-by-step explanation:
Synthetic division is the process by one reduces a large polynomial in your case [tex]x^3-7x-6[/tex] by a binomial in your case [tex](x+1)[/tex].
To do so one does the following:
[tex]\begin{array}{cccccc}-1|& 1&0&-7&-6\\ & &-1&1&6 \\& 1&-1&-6&0 \end{array}[/tex]
Since we divided by a linear binomial it reduces the power by one which produces the following quadratic:
[tex](x^2-x-6)[/tex]
Which can be factored in the following, and I will provide the complete factorization as well:
[tex]p(x)=(x+1)(x-3)(x+2)[/tex]
The 53 students go to a nearby Italian restaurant for lunch. Each table holds 5 people. How many tables will the group need
Answer:
They will need 11 tables
Step-by-step explanation:
The first 10 will seat 5, the 11th will seat the final 3.
Answer:
The group will need 11 tables.
Step-by-step explanation:
Think: How many times does 5 go into 53?
We know that 5 goes into 50, 10 times. The extra 3 students must sit at a seperate table. That means they need 10 tables plus another. Therefore, the group will need 11 tables.
The function f(x)=2.5x can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the multiplicative rate of change of the function?
Answer:
The answer is 5.
Step-by-step explanation:
Multiplicative rate of change can be described as the rate change based on a original amount or point.
If we look at the given points for the function f(x) = 2.5x, we can see that the x coordinates increase by one while the y coordinate is increasing by 5 times it's value for the previous point.
So we can say that the multiplicative rate of change is 5 for the function f(x) = 2.5x.
I hope this answer helps.
the answer is(b) 5 got it right on the test
How can you determine if a function is odd?
Answer:
Its easy !
Step-by-step explanation:
Test to determine if a function y=f(x) is even, odd or neither: Replace x with -x and compare the result to f(x). If f(-x) = f(x), the function is even. If f(-x) = - f(x), the function is odd.