Step-by-step explanation:
let us keep the price of pants as x
and price of necklace as y
Simultaneous equations comes as follows:
4x + 3y = 216 for Alexis
7x + 2y = 300 for Jess
we'll make either x or y equal
here let's make y equal
2 ( 4x + 3y = 216)
3 ( 7x + 2y = 300)
8x + 6y = 432
21x + 6y = 900
21x - 8x = 900 - 432
13x = 468
x = $36
so a pant costs $36
And
3y = 72
y = $ 24
so a necklace costs $36
if there are about 3.346x10^26 molecules of water in a liter of water and the ocean is about 1.26x10^21 liters in volume, how many water molecules are there in the ocean?
Answer: 4.21596 x 10⁴⁷
Step-by-step explanation:
(3.346 x 10²⁶) (1.26 x 10²¹)
= (3.346 x 1.26) x 10²⁶⁺²¹
= 4.21596 x 10⁴⁷
Simple linear equations
Check Whether the value given in the brackets is the root of the given equation or not (nessessary steps is needed)
a) 4x = -4 [x=-1]
b) 2(x-3) =-12 [x=3]
c) 8x - 4x = 24 [x = 1/2]
d) 9x - 4x = 24 [x=18]
Answer: Evaluate the Function, right?
Hello!
~~~~~~~~~~~~~~~~~~
A) 4x = -4 [x=-1] =
4x = -4 =
x = -1 = x = -1
( The steps : Substitute the given value into the function and evaluate.)
B) 2(x-3) =-12 [x=3] =
2 ( x - 3) = -12 = x = -3
x = 3 = x = 3
( The steps : Substitute the given value into the function and evaluate.)
C) 8x - 4x = 24 [x = 1/2] =
8x - 4x = 24 = x = 6
x = 1/2 = x = 1/2
( The steps : Substitute the given value into the function and evaluate.)
D) 9x - 4x = 24 [x=18] =
9x - 4x = 24 = x = 24/5
x = 18 = x = 18
( The steps : Substitute the given value into the function and evaluate.)
~~~~~~~~~~~~~~~~~~
Step-by-step explanation: All the steps are the same. Substitute the given value into the function and evaluate.
Hope this helped you!
No one is helping me :( Can someone please give me a hand? :(
Which statement best describes the graph of x^3 – 3x^2
- X + 3?
A.It starts down on the left and goes up on the right
and intersects the x-axis at x = -1, 2, and 3.
B.It starts down on the left and goes up on the right
and intersects the x-axis at x = -1, 1, and 3.
C.It starts up on the left and goes down on the right
and intersects the x-axis at x = -1, 2, and 3.
D.It starts up on the left and goes down on the right
and intersects the x-axis at x = -1, 1, and 3.
Solve for y: |6y - 3| + 8 = 35 Select one: a. y = -5 b. y = 5 or y = -4 c. =5=−203 y = 5 o r y = − 20 3 d. y = 5
Answer:
y=5 or y=-4
Step-by-step explanation:
6y - 3| + 8 = 35
|6y-3|=35-8
|6y-3|=27
either 6y-3=-27 then 6y=27+3
y=30/6=5
or 6y-3=-27
6y=-27+3
y=-24/6
y=-4
how do you mathematically write 6 inches and 4 1/2 inches
I’m not exactly sure what this means.
But you can use “ to abbreviate the labels.
So it would be 6” and 4.5”
Answer:
Step-by-step explanation:
There is some ambiguity in this question. I think you want 4.5 + 6 = 10.5 inches.
Arrange in ascending order. 8/13, 2/9,28/29
Step-by-step explanation:
he operation of sorting fractions in ascending order: 18/46, 28/41, 29/38, 29/44, 32/30 ... terms equivalents: 18/46=(2×3^2)/(2×23)=((2×3^2)÷2)/((2×23)÷2)=9/23; 28/41 already reduced to ... by the largest exponents: LCM (9, 28, 29)=2^2×3^2× 7×29=7308 Calculate LCM, the least ... /10 </13 </19
Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he is able to buy 5 packages of paper and 6 staplers for $62. How much does a package of paper cost? How much does a stapler cost?
Answer:
paper = $4 and stapler = $7
Step-by-step explanation:
let p represent paper and s represent stapler, then
3p + 4s = 40 → (1)
5p + 6s = 62 → (2)
Multiplying (1) by 5 and (2) by - 3 and adding will eliminate p
15p + 20s = 200 → (3)
- 15p - 18s = - 186 → (4)
Add (3) and (4) term by term to eliminate p
2s = 14 ( divide both sides by 2 )
s = 7
Substitute s = 7 into either of the 2 equations and evaluate for p
Substituting into (1)
3p + 4(7) = 40
3p + 28 = 40 ( subtract 28 from both sides )
3p = 12 ( divide both sides by 3 )
p = 4
Thus package of paper costs $4 and stapler costs $7
PLEASE HELP ASAP!!! A toy store has 10 stores all about the same size in a city the graph shows sales for one of the stores last month. Which statement is best supported by the information in the graph?
Answer:
The first one
Step-by-step explanation:
Took the test
Answer: 1/10 of the store's total sales last month were in appliances (lower right corner)
Step-by-step explanation:
Let's go through the four possible answers
In the upper left corner it says "Total mobile phone sales is likely 27,000" which is a paraphrase of what is given. The chart gives 9000 as the phone sales for that one particular store. If all stores are identical in performance, then we have 4*9000 = 36000 in total mobile phone sales. Of course, it's impossible to know for sure how the other stores did. So we can eliminate this as one of the answers.
In the upper right corner, it says "13% of the stores sales was in car electronics" (also paraphrased). We have 13 thousand in car electronics out of 17+13+6+9+15 = 60 thousand total. Divide the two values: 13/60 = 0.2167 = 21.67% approximately. So we can eliminate this as an answer.
In the lower left corner, it says "the total sales is likely greater than $300,000" but we don't know for sure because again we don't have the other charts for the three other stores. Assuming the four stores perform the same, then we'd have 4*60 = 240 thousand as the total and not 300 thousand. It's safe to say we can eliminate this as an answer.
In the lower right corner, it says "1/10 of the stores sales were appliances". This statement is true. Why? Because 6 thousand is the sales figure for appliances out of 60 thousand total. Divide the values: 6/60 = 1/10. So this is why the lower right corner is the answer.
What is coefficient of the term of degree of degree 5 in the polynomial below 3x^6+5-x^2+4x^5-9 which one is the right answer A. 3 B. 4 C. 6 D. 5
Answer:
B. 4
Step-by-step explanation:
We are looking for the coefficient of the term x⁵. When we see it in the polynomial as 4x⁵, our coefficient and answer would then be 4.
I flip a fair coin 17 times. Answer the following questions:
a. What is the probability of getting 9 heads?
b. What is the probability of getting 2 heads?
c.. What is the probability of getting 1 tail?
d. What is the probability of getting 14 or more heads?
e. What is the probability of getting 17 tails?
Answer:
A) 0.1855
B) 0.0010376
C) 0.0001297
D) 0.006363
E) 0.000007629
Step-by-step explanation:
In calculation of a probability, we normally take the ratio of the number of ways to meet a certain condition (i.e. the numerator) divided by the number of ways to pick from a pool (i.e. the denominator).
So what are the number of ways the flip of a coin 17 times can come out?
A coin has a head and tail, so each toss will have two possible results. If we toss once, we have 2 possible results. If we toss, twice we have 2² = 4 possible results.
If we toss thrice, we have 2³ = 8 possible results, etc.
Thus, for 17 tosses, we will have 2^(17) = 131072 possible results.
A) To achieve the probability of getting 9 heads, we will use combination formula;
C(n, k) = n! / (k!(n - k)!)
In this case, n = 17 and k = 9
So,
P(9 heads) = 17! / (9!(17 - 9)!) = 24310
Thus,
P(9 heads in 17 tosses of a fair coin) = 24310/131072 = 0.1855
B) Similar to A above;
P(2 heads) = 17! / (2!(17 - 2)!) = 136
Thus,
P(2 heads in 17 tosses of a fair coin) = 136/131072 = 0.0010376
C) Similar to A above;
P(1 tail) = 17! / (1!(17 - 1)!) = 17
Thus,
P(1 tail in 17 tosses of a fair coin) = 17/131072 = 0.0001297
D) probability of getting 14 or more heads?
Since, there are 17 tosses, this will be;
P(14 or more heads in 17 tosses) = P(14 heads in 17 tosses) + P(15 heads in 17 tosses) + P(16 heads in 17 tosses) + P(17 heads in 17 tosses)
P(14 heads) = 17! / (14!(17 - 14)!) = 680
P(15 heads) = 17! / (15!(17 - 15)!) = 136
P(16 heads) = 17! / (16!(17 - 16)!) = 17
P(17 heads) = 17! / (1!(17 - 17)!) = 1
Thus;
P(14 heads in 17 tosses) = 680/131072 = 0.005188
P(15 heads in 17 tosses) = 136/131072 = 0.0010376
P(16 heads in 17 tosses) = 17/131072 = 0.0001297
P(1 head in 17 tosses) = 1/131072 = 0.00000763
P(14 or more heads in 17 tosses) = 0.005188 + 0.0010376 + 0.0001297 + 0.00000763 = 0.006363
E) Similar to A above;
P(17 tails) = 17! / (17!(17 - 17)!) = 1
Thus,
P(17 tails in 17 tosses of a fair coin) = 1/131072 = 0.000007629
You just purchased two coins at a price of $1,030 each. Because one of the coins is more collectible, you believe that its value will increase at a rate of 7.7 percent per year, while you believe the second coin will only increase at 7.1 percent per year. If you are correct, how much more will the first coin be worth in 20 years
Answer:4541(Rounded) 4541.99779(Unrounded)
Step-by-step explanation:
A= P(1 + r)^T
A= answer
P=principle(amount of money)
r=Rate(percent / 100)
T=Time(Annually)
1030(1 + .077)^20
Brainliest would be appericiated!
Mary Jo spends $2,690 to buy stock in two companies. She pays $24 a share to one of the companies and $25 a share to the other. If she ends up with a total of 110 shares, how many shares did she buy at $24 a share and how many did she buy at $25 a share?
Answer:
60 of 24 dollars each and 50 of 25 dollars
Step-by-step explanation:
x= 24 dollars
110 shares, total x at 24 dollars each
110-x at 25 dollars each
24x+25 (110-x)=2690
24x+ 2750 - 25x= 2690
-1x= -60
x= 60
24 multiplied by 60 =1440
2690-1440 =1250
1250 / 25 = 50
can u vote me as brainliest ?
The shape on the left is transformed to the shape on the right. Figure A B C D is rotated to form figure A prime B prime C prime D prime. Which of the following statements describes the transformation? A B C D right-arrow A prime B prime C prime D prime A prime B prime C prime D prime right-arrow A B C D A B C D right-arrow D prime A prime C prime B prime D prime B prime C prime A prime right-arrow C A D B
Answer:
A
Step-by-step explanation:
I did the test and it is the only one that makes sense
Answer:
a
Step-by-step explanation:
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
You wish to accumulate $14,580 in 6 years. Payments are made at the end of every six-month period into an account earning 7.2% compounded semi-annually. Find the required payment amount to accomplish your goal.
What is the greatest common factor of 48 and 32?
Answer:
GCF - 16
Step-by-step explanation:
48 - 1, 2, 3, 4, 6, 8, 12, 16
32 - 1, 2, 4, 8, 16
Hope this helps! :)
Answer:
16
Step-by-step explanation:
48=3*16
32=2*16
While the Pareto distributions are continuous, they tend to be used to model discrete data in humanities and actuarial sciences. Moreover, with its roots in power functions, Pareto distributions may be used in the growing popularity of the studies of networks. The probability density function (PDF) for a Pareto distribution is
Answer:
Step-by-step explanation:
While the pareto distributions are continuous in nature, they are sometimes used to model discrete data in fields such as Social Sciences, Humanities, Geophysics, and Actuarial Sciences.
The Pareto Distribution is a power-law probability distribution used in studies of observable phenomena.
The probability density function (PDF) for a Pareto Distribution is:
Xn = 1
for various Alpha levels
Where Xn is the probability value of X
As Alpha tends to infinity, the pareto distribution tends to ¶ [X-Xn]
Where ¶ is the Dirac Delta function.
g The p-value of a test is the probability of obtaining a result as or more extreme as the one obtained in the sample, assuming the null hypothesis is false
Answer:
The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.
Step-by-step explanation:
The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.
We reject the null hypothesis if the p-value of a statistic is lower than the level of significance α.
And we fail to eject the null hypothesis if the p-value of a statistic is greater than the level of significance α.
A lower p-value indicates that the result is statistically significant.
And a higher p-value indicates that the result is not statistically significant.
Given that (0,0) is on the graph of f(x), find the
corresponding point for the function
f(x) – 5.
Answer:
(0, -5)
Step-by-step explanation:
You have (x, f(x)) = (0, 0) and you want (x, f(x) -5).
That would be ...
(x, f(x) -5) = (0, 0 -5) = (0, -5)
The mean weight of an adult is 6767 kilograms with a variance of 121121. If 164164 adults are randomly selected, what is the probability that the sample mean would be greater than 64.864.8 kilograms
Answer:
99.48% probability that the sample mean would be greater than 64.8 kilograms.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
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].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 67, \sigma = \sqrt{121} = 11, n = 164, s = \frac{11}{\sqrt{164}} = 0.86[/tex]
What is the probability that the sample mean would be greater than 64.8 kilograms?
This is 1 subtracted by the pvalue of Z when X = 64.8.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{64.8 - 67}{0.86}[/tex]
[tex]Z = -2.56[/tex]
[tex]Z = -2.56[/tex] has a pvalue of 0.0052
1 - 0.0052 = 0.9948
99.48% probability that the sample mean would be greater than 64.8 kilograms.
help with this I don't know how to solve
Answer:
86.53
Step-by-step explanation:
Area of Triangle Formula: A = 1/2bh
Pythagorean Theorem: a² + b² = c²
Step 1: Draw altitude and label numbers
If we draw a line down the middle, we can see that we get a perpendicular bisector and that we get 2 right triangles with a hypotenuse of 29 and a leg of 3. We need to find h using Pythagorean Theorem in order to use area formula:
3² + b² = 29²
b² = 29² - 3²
b = √832 = h
Step 2: Plug in known variables into area formula:
A = 1/2(√832)(6)
A = 3√832
A = 86.5332
www.g A bag contains 3 white counters, 10 black counters, and 4 green counters. What is the probability of drawing (a) a white counter or a green counter
Answer:
41.18% probability of drawing a white counter or a green counter
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
There are 3+10+4 = 17 counters.
Of those, 3+4 = 7 are white or green
7/17 = 0.4118
41.18% probability of drawing a white counter or a green counter
Beginning three months from now, you want to be able to withdraw $2,300 each quarter from your back account to cover college expenses over the next four years. If the account pays .45 percent interest per quarter, how much do you need to have in your bank account today to meet your expense needs over the next four years?
Answer:
$36,450.46
Step-by-step explanation:
The amortization formula can be used to figure this. For quarterly payment A, the principal invested must be P for interest rate r and compounding n times per year for t years.
A = P(r/n)/(1 -(1 +r/n)^(-nt))
2300 = P(0.0045/4)/(1 -(1 +0.0045/4)^(-4·4))
2300 = P·0.06309934
P = 2300/0.06309934 = 36450.46
You need $36,450.46 in your account today so that you can withdraw $2300 quarterly for 4 years.
I NEED HELP ASAP,THANKS! :)
Roland’s Boat Tours sells deluxe and economy seats for each tour it conducts. In order to complete a tour, at least 1 economy seats must be sold and at least 6 deluxe seats must be sold. The maximum number of passengers allowed on each boat is 30 Roland’s Boat Tours makes $40 profit for each economy seat sold and $35 profit for each deluxe seat sold. What is the maximum profit from one tour? Show work.
Answer:
$1170
Step-by-step explanation:
Let x and y represent the numbers of economy and deluxe seats sold. The constraints are ...
x ≥ 1y ≥ 6x +y ≤ 30And the objective function we want to maximize is ...
p = 40x +35y
__
I find it convenient to graph the equations and locate the objective function line as far from the origin as possible. The graph is shown, along with the solution.
Here, it's even simpler than that. The profit per seat is the greatest for economy seats, so Roland's should sell as many of those as they can. The only limit is that 6 seats must be deluxe. The remaining 30-6=24 can be economy. So, the profit will be maximized for ...
24 economy seats and 6 deluxe seats
The corresponding profit will be ...
24(40) +6(35) = 1170
The maximum profit from one tour is $1170.
Use ￢, →, ∧ and ∨ to express the following declarative sentences in propositional logic; in each case state what your respective propositional atoms p, q, etc. a) If interest rates go up, share prices go down. b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. c) Today it will rain or shine, but not both. d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. e) My sister wants a black and white cat.
Answer:
a) If interest rates go up, share prices go down : this will be assigned p→q
b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r)
c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q)
d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. P → (q∨r)
e) My sister wants a black and white cat. p∧q
Step-by-step explanation:
A statement is said to be propositionally logical if the statement that can be assigned either true or false.
∧and
∨or
¬not
→implies
a) If interest rates go up, share prices go down : this will be assigned p→q implies because the occurrence of event (share prices go down) depends on the possibility of the other event happening.
b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨￢r) : either of the two of the other events (i.e. he has sold his car or he has not paid his mortgage ) can only occur if the first event occur
c) Today it will rain or shine, but not both:(p∨q) ∨ ￢(p∧q) : either of the events can occur but not both i.e. they are mutually exclusive
d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. P → (q∨r) either of the two of the other events (i.e. they had a cup of coffee together or they took a walk in the park ) can only occur if the first event (Sam met Jane yesterday) occur
e) My sister wants a black and white cat. p∧q : both events can only occur together
Graph the equation y = 1/8x-7
Answer:
[tex]slope:1/8y-intercept:-7\\COORDINATES(x,-7)\\\\(56,0)[/tex]
Step-by-step explanation:
Box A contains 5green and 7 red balls. Box B contains 3green, 3 red and 6 yellow balls. A box is sleeted at random and a ball is drawn at random from it. What is the probability that the drawn ball is green?
Answer:
5/48Step-by-step explanation:
Given
the sample space for box A
green balls = 5
red balls= 7
sample size= 5+7= 12
the sample space for box B
green balls = 3
red balls= 3
yellow balls= 6
sample size= 3+3+6= 12
The probability of drawing a green ball from box A= 5/12
The probability of drawing a green ball from box B= 3/12= 1/4
Therefore the probability of picking a green ball from either of the boxes at random is =[tex]=\frac{5}{12} *\frac{1}{4}[/tex][tex]=\frac{5}{48}[/tex]
Find the values of x and y in these equations. (x + yi) + (4 + 6i) = 7 − 2i (equation A) (x + yi) − (-8 + 11i) = 5 + 9i (equation B)
Answer:
Step-by-step explanation:
(x+yi)+4+6i=7-2i
x+yi=7-2i-4-6i
x+yi=3-8i
equating real and imaginary parts
x=3,y=-8
B.
x+yi=5+9i+(-8+11i)
x+yi=5+9i-8-11i
x+yi=-3-2i
equating real ,and imaginary parts
x=-3
y=-2
The value of x and y for equation A is
[tex]x=3, y=-8[/tex]
The value of x and y for equation B is
[tex]x=-3 , y=20[/tex]
Given :
[tex](x + yi) + (4 + 6i) = 7 - 2i[/tex]
find the value of x and y in the given equation
Lets open the parenthesis and combine like terms
Equate the real and imaginary part to solve for x and y
[tex]\left(x+4\right)+\left(y+6\right)i=7-2i\\x+4=7\\x=3\\\\y+6=-2\\y=-2-6\\y=-8[/tex]
The value of x=3 and y=-8
Now we do the same with second equation
[tex](x + yi) - (-8 + 11i) = 5 + 9i\\\\x+8+yi-11i=5+9i\\\left(x+8\right)+\left(y-11\right)i=5+9i\\x+8=5\\x=-3\\\\y-11=9\\y=9+11\\y=20[/tex]
The value of x and y is x=-3 and y=20
Learn more : brainly.com/question/18552411
During a 5 5 -day period, a florist served a different number of customers at a flower shop each day. The mean number of daily customers served during this period was 17 17 . In the following month, during another 5 5 -day period, the florist served 16 16 customers per day for four of the days, but served 25 25 customers on the fifth day. What is the difference between the mean number of customers the florist served during each of the two five-day periods?
Answer:
0.8
Step-by-step explanation:
Mean for the first 5 day period = 17
Mean for the second 5 day period = 17.8
Difference 17.8 - 17 = 0.8
The difference between the mean number of customers the florist served during each of the two five-day periods is of 0.8.
-------------------------------
The mean of a data-set is the sum of all values in the data-set divided by the number of values.
-------------------------------
First period:
5 days, mean of 17.
-------------------------------
Second period:
First four days, mean of 16, thus total of [tex]4 \times 16 = 64[/tex]Fifth day, 25 customers.Thus, 64 + 25 = 89 customers in 5 days, and the mean is:
[tex]M = \frac{89}{5} = 17.8[/tex]
-------------------------------
Difference:
17.8 - 17 = 0.8
The difference between the mean number of customers the florist served during each of the two five-day periods is of 0.8.
A similar question is given at https://brainly.com/question/10235056
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.