Answer:
0.12 ± 1.96 * √(0.12(0.88) / 100)
Step-by-step explanation:
Confidence interval :
Phat ± Zcritical * √(phat(1 -phat) / n)
Phat = 12/100 = 0.12
1 - phat = 0.88
Zcritical at 95% = 1.96
Hence, we have :
0.12 ± 1.96 * √(0.12(0.88) / 100)
0.12 ± 1.96 * 0.0324961
0.12 ± 0.0636924
Lower boundary = (0.12 - 0.0636924) = 0.0563
Upper boundary = 0.12 + 0.0636924 = 0.1837
The calculations for 95% confidence interval for this case is given as: [tex]CI = 0.12 \pm 1.96 \times \sqrt{\dfrac{0.12(1 - 0.12)}{100}}[/tex]
How to find the confidence interval for proportion with large sample ?For large enough sample( size > 30), let the population proportion of a quantity be denoted by random variable [tex]p[/tex]
Then, we get:
[tex]p \sim N(\hat{p}, \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}})[/tex]
where
[tex]\hat{p}[/tex] = estimated(mean value) proportion of that quantity
and n = size of sample drawn.
It is visible that as we increase the value of n, the standard deviation decreases, therefore, forcing the values of population proportion to be closer to the estimated proportion.
Margin of error is the distance between the mean and one of the end point of the confidence interval(assuming its equal on both the sides of the mean). The margin of error with level of significance [tex]\alpha[/tex] is calculated as:
[tex]MOE = Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
where [tex]Z_{\alpha/2}[/tex] is the critical value of the test statistic for level of significance [tex]\alpha[/tex]
The confidence interval is then calculated as:
[tex]CI = \hat{p} \pm MOE[/tex]
For the considered case,
the confidence interval is to be found for 95% confidence, therefore,
level of significance = 100% - 95% = 5% = 0.05
At this level of significance, the critical value of test statistic Z is 1.96The sample size given is n = 100The estimated proportion of defective chips estimated from sample is:
[tex]\hat{p}[/tex] = Fraction of defective chips to total chips = 12/100 = 0.12Thus, we get the confidence interval for this case as:
[tex]CI = \hat{p} \pm Z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\CI = 0.12 \pm 1.96 \times \sqrt{\dfrac{0.12(1 - 0.12)}{100}}[/tex]
Thus, the calculations for 95% confidence interval for this case is given as: [tex]CI = 0.12 \pm 1.96 \times \sqrt{\dfrac{0.12(1 - 0.12)}{100}}[/tex]
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Help just help please. !!!
Answer: The maximum value is -3.75
Note: -3.75 = -15/4
=============================================================
Explanation:
The given quadratic is in the form y = ax^2 + bx + c, where,
a = -1b = 1c = -4We'll plug the values of 'a' and b into the formula below
h = -b/(2a)
h = -1/(2(-1))
h = 1/2
h = 0.5
This represents the x coordinate of the vertex. Recall the vertex is (h,k).
Plug this x value into the function to find its corresponding y coordinate
y = -x^2 + x - 4
y = -(0.5)^2 + 0.5 - 4
y = -3.75
The vertex is located at (0.5, -3.75)
Since a < 0, this means the parabola opens downward and that the vertex is the highest point on the parabola. Therefore, the largest y can get is y = -3.75 which we consider the maximum.
The graph visually helps confirm this (see image attachment).
Side note: -3.75 = -15/4
-------------------
Here's another way we can find the vertex (h,k). We'll complete the square to get the function into vertex form
y = -x^2 + x - 4
y + 4 = -x^2 + x
y + 4 = -(x^2 - x)
y + 4 = -(x^2 - x + 0)
y + 4 = -(x^2 - x + 0.25 - 0.25) .... see note below
y + 4 = -(x^2 - x + 0.25) -(-0.25)
y + 4 = -(x^2 - x + 0.25) + 0.25
y + 4 = -(x - 0.5)^2 + 0.25
y = -(x - 0.5)^2 + 0.25 - 4
y = -(x - 0.5)^2 - 3.75
This is in the form y = a(x-h)^2 + k where (h,k) = (0.5, -3.75).
Note: The x coefficient is -1 which cuts in half to -0.5, then that squares to 0.25
please help the will get a brilliantaal
Two friends decided to open up bank accounts. Israel deposited $1000 into an account with a growth rate of 15%, and Dameon deposited $3,000 into an account with a growth rate of 2%. After 10 years, who will have more money in their account?
Answer:
Isreal
Step-by-step explanation:
15% of 1000 is 150x10=1500
2% of 3000 is 60x10=600
What is 777778978734*79980324768762378945569723
Phoenix and Stella found a box with a total of 216
books that needed to be shelved.Phoenix said he can
arrange all the books on 18 shelves with 12 books on
each shelf. Stella says she can arrange all the books
on 9 shelves with 24 books on each shelf. Who is?
Answer:
432
Step-by-step explanation:
216 + 216
= 432
Hope this helps!
Please mark me Brainliest!
Have a nice day
What is the speed if the distance is 234 MI and time is 3 hrs
Answer:
speed = 78 miles per hour
Step-by-step explanation:
Speed is distance divided by time
speed = 234 miles / 3 hours
speed = 78 miles per hour
what is the factored from of the polynomial function f(x)=x3-6x2+11x-6
Answer:
[tex]f(x) =(x-1)(x-2)(x-3)[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^3-6x^2+11x-6[/tex]
Required
The factored form
[tex]f(x) = x^3-6x^2+11x-6[/tex]
Split
[tex]f(x) =x^3 -3x^2- 3x^2 +2x +9x -6[/tex]
Rearrange as:
[tex]f(x) = x^3 -3x^2 +2x - 3x^2+9x -6[/tex]
Factorize
[tex]f(x) = x(x^2 - 3x + 2) - 3(x^2 - 3x + 2)[/tex]
Factor out [tex]x^2 - 3x + 2[/tex]
[tex]f(x) = (x^2 - 3x + 2)(x - 3)[/tex]
Expand
[tex]f(x) = (x^2 - 2x - x + 2)(x - 3)[/tex]
Factorize
[tex]f(x) = (x(x - 2) - 1(x - 2))(x - 3)[/tex]
Factor out [tex]x - 2[/tex]
[tex]f(x) = (x - 1) (x - 2)(x - 3)[/tex]
Kate thought she could only run for 12 minutes, but she actually ran for 25 minutes. What is the percent error?
Answer:
[tex]108\frac{1}{3}[/tex] %
Step-by-step explanation:
[tex]\frac{25}{12} :\frac{y}{100}[/tex]
12 · y = 25 · 100
12y = 2500
12y ÷ 12 = 2500 ÷ 12
[tex]y=208\frac{1}{3}[/tex]
[tex]208\frac{1}{3} - 100 = 108\frac{1}{3}[/tex]
What is the volume of a regular cylinder whose base has a radius of 14cm and has a height of 6 cm
Answer:
3692.64 cm³
Step-by-step explanation:
What is the answer? Thank you for those that answer!
9514 1404 393
Answer:
2. Given
4. SAS postulate
Step-by-step explanation:
Reason 2: Statement 2 is one of the Given statements.
Reason 4: You have shown that two sides and the angle between them are congruent. The Side-Angle-Side (SAS) congruence postulate applies.
Use the Law of Cosines to find the measure of ∠A. Round to the nearest degree.
a = 12, b = 5, c = 9
Use: a² = b² + c² – 2bc cos A
Answer:
Solution given:
a = 12, b = 5, c = 9
We have
: a² = b² + c² – 2bc cos A
12²=5²+9²-2×5×9 cos A
12²-25-81=-90 cos A
cos A=38/-90
A=cos -1(-19/45)
A=115°
is a required answer.
Practice
what is sin(-30*) ? Sketch a graph to help determine the answer.
a. 0.5
b. -0.5
c. 1
d. 0
Please select the best answer from the choices provided
Answer:
B. -0.5
Step-by-step explanation:
I calculated it logically
Plz help me well mark brainliest if correct.....??
Answer:
C
Step-by-step explanation:
I think it’s C because under the numbers it says pets they own so the x has to be the fourth graders
Answer:
C
Step-by-step explanation:
It says it below the number line!! hoped this helped
2.1x 10^8 is how many times the value of 4.2 x 10^2?
A 5.0 x 10^5
B 5.0 x 10^6
C 2.1 x 10^5
D 2.1 x 10^6
Answer:
Step-by-step explanation:
If you want to find out how many times larger something is than something else, you have to divide. We will set up a problem that looks like this:
[tex]\frac{2.1*10^8}{4.2*10^2}[/tex]
Diving 2.1 by 4.2 gives us .5; to divide the exponents, we remember that if we divide like bases we have to subtract the exponents. 10 is our base in both cases, so 8 - 2 gives us 6, resulting in:
[tex].5*10^6[/tex]
However, this isn't in scientific notation. We need to move the decimal one more place to the right, which in trn reduces the exponent by 1:
[tex]5*10^5[/tex]
A shopkeeper earns a profit of rupees 300 on Monday, a loss of rupees 150 on Tuesday, than a loss of rupees 200 on Wednesday and profit of rupees 50 and rupees 75 on thursday and friday respectively.Find his net profit or loss in 5 days.
Answer:
75 rupees in net profit
Step-by-step explanation:
Loss indicates subtraction, and profit indicates addition
300-150-200+50+75=75
HELP ME PLEASEEEEEEEEEEEEEEEEEEE
Answer:
the last one
Step-by-step explanation:
Answer:
The 2nd one (the one you chose) is right thats the answer
Step-by-step explanation:
Consider the following question: How many years has each person played on the soccer team? Which best describes the question? It is a statistical question because the data may vary for each player. It is a statistical question because the data will all be the same. It is not a statistical question because the answers are all whole numbers. It is not a statistical question because there is only one answer per person.
Answer:
Its the first one
Step-by-step explanation:
It is a statistical question because the data may vary for each player. :)
How can you get a good credit score?
Pay credit card and loan payments late.
Don't apply for credit.
Pay your loan payments on time, every time.
Go above your credit limit.
Answer:
Pay your loan payments on time, every time.
Step-by-step explanation:
The other answers either hurt or have no effect on your credit score.
The option 2 and 3 is right get a good credit score. Avoid the options 1 and 4.
To get a good credit score, you should follow these steps:
Pay your loan payments on time, every time: Timely payments are one of the most crucial factors in building a good credit score. Consistently paying your bills and loans on or before the due date shows lenders that you are a responsible borrower.
Don't apply for credit excessively: Each time you apply for new credit, a hard inquiry is made on your credit report, which can temporarily lower your score. Applying for multiple credit accounts in a short period may signal financial instability to lenders.
Avoid options 1 and 4:
Paying credit card and loan payments late: Late payments negatively impact your credit score and show a lack of responsibility in managing credit.
Going above your credit limit: Maxing out your credit cards or going above the credit limit can harm your credit score as it indicates a higher risk of defaulting on your debts.
Hence, the option 2 and 3 is right get a good credit score. Avoid the options 1 and 4.
Learn more about Loan here:
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what's the slope for coordinates (-5,-5) (5,3)?
Answer:
4/5
Step-by-step explanation:
slope = (difference in y)/(difference in x)
slope = (-5 - 3)/(-5 - 5)
slope = -8/(-10)
slope = 4/5
in an inverse variation, x=2 when y=-4. what is the value of y when x=16
Answer:
y = -1/2
Step-by-step explanation:
Use the inverse variation equation, y = [tex]\frac{k}{x}[/tex]
Plug in 2 as x and -4 as y, then solve for k:
y = [tex]\frac{k}{x}[/tex]
-4 = [tex]\frac{k}{2}[/tex]
-8 = k
So, the equation is y = [tex]\frac{-8}{x}[/tex]
Plug in 16 as x and solve for y:
y = [tex]\frac{-8}{x}[/tex]
y = [tex]\frac{-8}{16}[/tex]
y = -1/2
So, when x = 16, y = -1/2
Sarah pays $80 for 5
piano lessons. What is
the cost per lesson?
HELPP IF WRONG ILL REPROT
A store employee conducted a survey of 590 randomly selected customers. According to the survey, 177 of the customers often use coupons.
How many people would you expect to use a coupon if all 5,000 people in the community visited the store?
Question 7 options:
5,310 people
1,250 people
3,750 people
1,500 people
Answer:
Solution given
:total n[U]=590
customers using coupon n[C]=177
the percentage of all customers who often use coupons=177/590×100%=30%.
If n[U]=5000
no of customer using coupon be x
we have
30% of 5000=x
x=30/100×5000
x=1500
So1500 people would you expect to use a coupon if all 5,000 people in the community visited the store.Reflect P (-5,10) over the x-axis. What are the coordinates of the reflected point? What quadrant is the reflected point in?
Answer:
I need the answer 2 QwQ....PLEASE HELP I WILL GIVE BRAINLIEST!!!
Josephine is taking a college course, and her professor bases the course grade on the average of 2 tests taken in the semester. She wants to know what she needs to earn on the last test to maintain her grade. Rearrange the following equation for b, where C is the average of 2 test scores, a and b.
C equals the quantity a plus b all over two
b equals two times C over a
b = 2C + a
b = 2C − a
b = 2C(a)
Answer:
Hi i know im very late answering this question but i believe the correct option is: b = 2C - a
Step-by-step explanation:
I believe this is the answer because:
2C = the average of 2 test scores combined
A and B = the two scores
were trying to solve for b so what we would do to figure that out is have the average of both test scores and then subtract A which will leave you with only B. therefor the answer is B = 2C - a
hope this helped.
Find the perimeter of a quadrilateral with vertices at C (-2, 1), D. (2, 4), E (5,0), and. F (1, -3)
12 units
O 16 units
O 20 units
O 24 units
Ms. Lin’s son likes to lift weights. He was lifting 125 pounds last year. This year he can lift 35 more pounds. How much weight can he lift this year?
Answer:
He can lift 160 pounds
Step-by-step explanation:
125 (from last year) + 35 (more pounds) = 160 (total pounds)
125 + 35 = 160
I need help, please !
Answer: the answer is 8 because
Step-by-step explanation:
What is the answer for 1/2 + 1/2?
Answer:
1 is the answer to 1/2+1/2
Answer:
1
Step-by-step explanation:
if you add 1/2 and 1/2, you get 2/2 which is also equal to 1.
Trying to finish this test at 3:30 am plz help
Given:
The given sum is:
[tex]\sum _{k=4}^9(5k+3)[/tex]
To find:
The expanded form and find the sum.
Solution:
We have,
[tex]\sum _{k=4}^9(5k+3)[/tex]
The expanded form of given sum is:
[tex]\sum _{k=4}^9(5k+3)=(5(4)+3)+(5(5)+3)+(5(6)+3)+(5(7)+3)+(5(8)+3)+(5(9)+3)[/tex]
[tex]\sum _{k=4}^9(5k+3)=(20+3)+(25+3)+(30+3)+(35+3)+(4+3)+(45+3)[/tex]
[tex]\sum _{k=4}^9(5k+3)=23+28+33+38+43+48[/tex]
[tex]\sum _{k=4}^9(5k+3)=213[/tex]
Therefore, the correct option is C.
A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1070 and a standard deviation of 204. Scores on the ACT test are normally distributed with a mean of 19.1 and a standard deviation of 5.2. It is assumed that the two tests measure the same aptitude, but use different scales.
(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score. Round answer to a whole number. SAT score =
(B) What would be the equivalent ACT score for this student? Round answer to 1 decimal place. ACT score =
(C) If a student gets an SAT score of 1417, find the equivalent ACT score. Round answer to 1 decimal place. ACT score =
Answer:
a) SAT score = 1075
b) ACT score = 19.2.
c) ACT score = 27.9.
Step-by-step explanation:
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.
(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score
SAT scores have mean 1070 and standard deviation 204, so [tex]\mu = 1070, \sigma = 204[/tex]
51th percentile means that Z has a p-value of 0.51, so Z = 0.025. The score is X. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.025 = \frac{X - 1070}{204}[/tex]
[tex]X - 1070 = 0.025*204[/tex]
[tex]X = 1075[/tex]
SAT score = 1075.
(B) What would be the equivalent ACT score for this student?
ACT scores have mean of 19.1 and standard deviation of 5.2, which means that [tex]\mu = 19.1, \sigma = 5.2[/tex]. The equivalent score is X when Z = 0.025. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.025 = \frac{X - 19.1}{5.2}[/tex]
[tex]X - 19.1 = 0.025*5.2[/tex]
[tex]X = 19.2[/tex]
ACT score = 19.2.
(C) If a student gets an SAT score of 1417, find the equivalent ACT score.
Z-score for the SAT:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1417 - 1070}{204}[/tex]
[tex]Z = 1.7[/tex]
Equivalent score on the ACT:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.7 = \frac{X - 19.1}{5.2}[/tex]
[tex]X - 19.1 = 1.7*5.2[/tex]
[tex]X = 27.9[/tex]
ACT score = 27.9.
(PLZ HELP DUE IN 10 MIN)
Eber can mow 4 lawns in one hour. The equation l = 4h can be used to determine the number of lawns, 1. Eber can
mow in h hours. Create a graph to represent the number of lawns Eber can mow in 0 to 5 hours. Click on the
coordinate plane to place the points in the correct locations.
Answer:
See attachment for plot
Step-by-step explanation:
Given
[tex]l = 4h[/tex]
Required
Represent the scenario on a graph
When h = 0
[tex]l = 4h= 4 * 0 = 0[/tex]
When h = 1
[tex]l = 4 * 1 = 4[/tex]
When h = 2
[tex]l = 4 * 2 = 8[/tex]
When h = 3
[tex]l = 4 * 3 = 12[/tex]
When h = 4
[tex]l = 4 * 4 = 16[/tex]
When h = 5
[tex]l = 4 * 5 = 20[/tex]
So, we have:
[tex](h,l) = (0,0)[/tex]
[tex](h,l) = (1,4)[/tex]
[tex](h,l) = (2,8)[/tex]
[tex](h,l) = (3,12)[/tex]
[tex](h,l)= (4,16)[/tex]
[tex](h,l)= (5,20)[/tex]
See attachment for plot