Answer:
a) A sample of 385 must be taken.
b) The 95% confidence interval for the proportion of workers who have changed jobs within the past year is (0.1216, 0.2784).
c) A sample of 246 is needed.
Step-by-step explanation:
Question a:
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]
Absence of preliminary data:
This means that we use [tex]\pi = 0.5[/tex], which is when the largest sample will be needed.
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 must be taken to ensure that a 95% confidence interval will specify the proportion to within ±0.05?
A sample of n must be taken.
n is found when [tex]M = 0.05[/tex]. So
[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]
Dividing both sides by 0.05
[tex]\sqrt{n} = 1.96*10[/tex]
[tex](\sqrt{n})^2 = (19.6)^2[/tex]
[tex]n = 384.16[/tex]
Rounding up,
A sample of 385 must be taken.
Question b:
In a sample of 100 workers, 20 of them had changed jobs within the past year.
This means that [tex]n = 100, \pi = \frac{20}{100} = 0.2[/tex]
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2 - 1.96\sqrt{\frac{0.2*0.8}{100}} = 0.1216[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2 + 1.96\sqrt{\frac{0.2*0.8}{100}} = 0.2784[/tex]
The 95% confidence interval for the proportion of workers who have changed jobs within the past year is (0.1216, 0.2784).
Question c:
Same procedure as question a, just with [tex]\pi = 0.2[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.2*0.8}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96\sqrt{0.2*0.8}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.2*0.8}}{0.05}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.2*0.8}}{0.05})^2[/tex]
[tex]n = 245.8[/tex]
Rounding up
A sample of 246 is needed.
You are cutting pieces of fabric for a craft project. You need three pieces that measure 6 2/3 inches, 4 1/2inches, and 3 5/8inches.
What is the total length of fabric that you need ?
Answer:
Step-by-step explanation:
14/19/24
Solve for x.
3/4(8x-12)=2(4x+1)-4
What are the step to this equation.
Kei buys a table and 12 chairs. Each chair cost the same price. The table cost $165. The total cost for the table and 12 chairs is $ 465. What is the cost of one chair?
Answer:
$38.75
Step-by-step explanation:
$465/12=$38.75
For the following set of data, find the mean, median and mode.
age of children Danielle babysits:
6,9,2,4,3,6,5
(3 Points)
Mean = 4 years old
Mean = 5 year old
Mean = 9 years old
Mode = 2 years old
Mode = 6 years old
Mode = 9 years old
Median = 4 years old
Median = 4.5 years old
Median = 5 years old
What is the value of x if x+15=38 ?
Answer:
x=23
Step-by-step explanation:
x+15=38 (we subtract 15 from both sides to get x alone on one side)
x=23
Answer:
23
Step-by-step explanation:
Subtract 15 by both sides to get X by itself and you get your answer!
Eva earns $500 per month plus $3 for every sale she makes which inequality can she use to find how much she must sale to earn at least $1,200 in a month
Answer:
500 + 3(s) ≥ 1200
Step-by-step explanation:
Ok so the goal is to earn 1,200 / month
We know that she already earns 500/month
So lets do some subtraction
Because she needs to make ATLEAST 1,200, well use either ≤ or ≥
Lets call (s) the number of sales she makes
Lets form the inequality
500 + 3(s) ≥ 1200
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Emily grows flowers on part of her 2-acre farm. Her house
and barn cover half an acre, her vegetable gardens cover
1 1/4 acres, and her flower garden covers the rest of her
farm. She divides the flower garden into 16 equal-sized
plots and puts 4 kinds of flowers in each plot.
How large is each plot of flowers in Emily's garden?
Answer:
1/64 for each type f flowe
Step-by-step explanation:
6. cory gets paid every two weeks. he works 40 hours per week at $7.75 per hour. cory has the following deductions: 8% for medical insurance, 12% for federal and state taxes, and 10% for retirement. cory's net pay will be $________.
Answer:
$434
Step-by-step explanation:
Gross Pay
$7.75 per hour40 hours per weekPay received every 2 weeks⇒ Total gross pay = 7.75 × 40 × 2 = $620
Deductions
Medical insurance = 8%Taxes = 12%Retirement = 10%⇒ Total deductions = 8% + 12% + 10% = 30%
Net Pay
Net Pay = Total Gross Pay - Total deductions
= $620 - (30% of $620)
= $620 - (0.3 × $620)
= $620 - $186
= $434
Therefore, Cory's net pay will be $434.
Which numbers between 10 and 20 do not appear in the table at all?
Why don’t they appear?
Answer:
the answer is 11, 13, 17
Step-by-step explanation:
this is because they do not have any even number that multiplies into them.
3. What is the axis of symmetry of the graph of function f(x) = x² - 6x – 1
Answer:
guihnijiop;kl;lkm
Step-by-step explanation:
Answer:
A parabola has an axis of symmetry at x = 3 if the x-value of the vertex is 3.
f(x) = x^2 + 3x + 1 = x^2 + 3x + 9/4 - 5/4 = (x + 3/2)^2 - 5/4 => vertex = (-3/2, -5/4)
f(x) = x^2 - 3x - 3 = x^2 - 3x + 9/4 - 21/4 = (x - 3/2)^2 - 21/4 => vertex = (3/2, -21/4)
f(x) = x^2 + 6x + 3 = x^2 + 6x + 9 - 6 = (x + 3)^2 - 6 => vertex = (-3, -6)
f(x) = x^2 - 6x - 1 = x^2 - 6x + 9 - 10 = (x - 3)^2 - 10 => vertex = (3, -10)
Therefore, f(x) = x^2 - 6x - 1 has an axis of symmetry at x = 3.
Step-by-step explanation:
plz mark me as brainlist
ASAP PLEASE HELP!!! Given the cylinder with the given dimensions, match the measures of the radius, circumference, and area of the base.
Answer:
Radius of cylinder = 4.5 inch
Circumference of Base = 9π inch
Area of base = 20.25π
Step-by-step explanation:
Given:
Diameter of cylinder = 9 inch
Height of cylinder = 22 inch
Find:
Radius of cylinder
Circumference of Base
Area of base
Computation:
Radius of cylinder = Diameter of cylinder / 2
Radius of cylinder = 9 / 2
Radius of cylinder = 4.5 inch
Circumference of Base = 2πr
Circumference of Base = 2π(4.5)
Circumference of Base = 9π inch
Area of base = πr²
Area of base = π(4.5)²
Area of base = 20.25π
Help SOMEONE???? MATH IS SO HARD!!!
Answer:
16. 70%
17. 100%
Step-by-step explanation:
16. As seen here, there are 10 marbles in total. Out of those marbles, there are 7 green marbles.
We can set up a "part to whole" fraction such as 7/10
Then we just find the % value by finding an equivalent "x to 100" ratio (percentages go up to 100)
7/10 = x/100
1000 = 7x
70 = x
17. Fortunately, there doesn't seem to need too much math involved as the only possible marbles are red and green. Therefore, you have a 100% chance of getting a green or red marble.
Hope that helps a bit!
A train arrives at a station and waits 3.5 minutes before departing. Another train arrives at the station 16 minutes later, repeating the cycle. Identify the probability that a train will not be at the station when you arrive.
Step-by-step explanation:
so we can safely say that one train will be there for 3.5 minutes and it will be gone for 16 minutes before another train comes and repeats the cycle.
we want how many minutes that the train will not be there over the total time that is possible so that would be
16/(16+3.5)
16/19.5
32/39
Hope that helps :)
The probability of the train not being at the station on arrival would be:
0.82
Find the probabilityGiven that,
The duration for which the train makes = 3.5 minutes
The time at which the second train arrives = 16 minutes later
We know that this cycle is repeated.
The duration for which the train is not there would be:
[tex]= 16/(16+3.5)[/tex]
[tex]= 16/19.5[/tex]
[tex]= 32/39[/tex]
[tex]= 0.82[/tex]
Thus, 0.82 is the probability.
Learn more about "Probability" here:
brainly.com/question/8069952
Two closets can store 16
chairs. How many chairs
can 8 closets store?
Answer:
64
Step-by-step explanation:
Find the surface area.
Answer:
do you want to me to find it for all or just 1
Answer:
88 [tex]m^{2}[/tex]
Step-by-step explanation:
The surface are is the total area of all the faces
Opposite faces have the same area
Label each side either l, h or w
SA of a cuboid = 2lw + 2lh + 2hw
(2 x 4 x 6) + (2 x 4 x 2) + (2 x 6 x 2) = 8
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
Answer:
I believe its c
Step-by-step explanation:
Answer:
(4, -11)
Explanation:
The coordinate's signs just change (negative becomes positive and vise versa)
What is the sum of 4 3/10 + 3 6/10 =
Answer:
The sum is 10 times 11Step-by-step explanation:
Answer:
I just put it into my calculator, but if you don't have one here's how to solve this by hand.
First, figure out what 4 3/10 is. Once you figured that out, you should've gotten 43/10 = 4 3/10. Next do 3 6/10, you should get 18/5 = 3 6/10. This may seem like a useless part but it can help if you have a different learning method or thinking than others. How I found the 43/10 and 18/10 was that if you add the whole number and denominator and add the numerator then you get your sum fraction(s). 43/10 and 18/5.
Since both the original fractions above have a denominator of 10, the final sum will also have a denominator of 10. If you take your calculator and put in 43/10 + 18/5 and hit the = button, you should get 79/10 = 7 9/10.
Step-by-step explanation:
Hope that this helps! :)
Have a great rest of your day/night!
PLEASE HELPPP
Given △ABC and altitude AH, decide whether each statement is necessarily true about △AHC. Select Yes or No for A − C.
ge80512
A. AH < HC
A Yes B No
B. AH < AC
A Yes B No
C. △AHC ≅ △AHB
Answer:
(a) AH < HC is No
(b) AH < AC is Yes
(c) △AHC ≅ △AHB is Yes
Step-by-step explanation:
Given
See attachment for triangle
Solving (a): AH < HC
Line AH divides the triangle into two equal right-angled triangles which are: ABH and ACH (both right-angled at H).
To get the lengths of AH and HC, we need to first determine the measure of angles HAC and ACH. The largest of those angles will determine the longest of AH and HC. Since the measure of the angles are unknown, then we can not say for sure that AH < HC because the possible relationship between both lines are: AH < HC, AH = HC and AH > HC
Hence: AH < HC is No
Solving (b): AH < AC
Length AC represents the hypotenuse of triangle ACH, hence it is the longest length of ACH.
This means that:
AH < AC is Yes
Solving (c): △AHC ≅ △AHB
This has been addresed in (a);
Hence:
△AHC ≅ △AHB is Yes
1. Tiffany bought a phone for $350. If the value of the phone depreciates at a rate of 6%
per year, what would you pay for the phone after 3 years?
Answer:
Amount of phone after 3 year = $290.7 (Approx.)
Step-by-step explanation:
Given:
Amount of phone = $350
Depreciation rate = 6% = 0.06
Find:
Amount of phone after 3 year
Computation:
A = p[1-r]ⁿ
Amount of phone after 3 year = Amount of phone[1-Depreciation rate]ⁿ
Amount of phone after 3 year = 350[1-0.06]³
Amount of phone after 3 year = 350[0.94]³
Amount of phone after 3 year = 350[0.83054]
Amount of phone after 3 year = $290.7 (Approx.)
Given the trapezoid below, Peter and
Christine each wrote different expressions to
find its perimeter.
w+2
4
4
6
Peter's expression: 6 + 4+ (w + 2) + 4
Christine's expression:
W + 16
Who is correct? Explain.
O Only Christine is correct.
O Only Peter is correct.
Both Christine and Peter are correct.
O Neither Christine or Peter is correct.
Vi
Answer:
Both.
Step-by-step explanation:
The perimeter of a trapezuun is given by : a + b + c + d ; where a, b, c, d are the lengtb of the sides of the trapezium.
The perimeter of the trapezium Given below is :
(4 + 6 + 4 + w + 2)
Evaluating both expressions :
Peter = 6 + 4 + (w + 2) + 4
Christine's expression = w + 16
From the expression, we can see that Peter's expression is correct s he wrote the sum of all the four sides
As for Christine's expression, it is also right ; as she added all the sides to obtain a reduced term
Hence, both are correct
Answer:
both of them are correct
Step-by-step explanation:
Bob has $2,500 in a savings account that earns 3 % annually. How much will he earn in interest in 1 year?
Use the formula = , where is the interest earned, is the principal (starting amount), is the interest rate expressed as a decimal, and is the time in years.
Answer:
the answer is 2575 I believe
Step-by-step explanation:
(2500x3x1/100)
(2500+75)
Find the Mean Absolute Deviation: (MAD)
10, 9, 3, 8, 10.
Answer: Hey there !! The answer is 2.
Step-by-step explanation:
The mean absolute deviation of a dataset is the average distance between each data point and the mean.
The absolute mean deviation is 2.
What is mean absolute deviation?The mean absolute deviation of a dataset is the average distance between each data point and the mean.
We have,
10, 9, 3, 8, 10
We first find the mean of 10, 9, 3, 8, 10
Mean = (10 + 9 + 3 + 8 + 10) / 5
Mean = 40 /5 = 8
Data sets
10 | 10 - 8 | 2
9 | 9 - 8 | 1
3 | 3 - 8 | 5
8 | 8 - 8 | 0
10 | 10 - 8 | 2
Mean absolute deviation
= (2 + 1 + 5 + 0 + 2) / 5
= 10 / 5
= 2
Thus the absolute mean deviation is 2.
Learn more about absolute mean deviation here:
https://brainly.com/question/10528201
#SPJ1
explain how the diagram can help find the area of a circle
Answer:
Step-by-step explanation:
This is a really famous diagram! The circle has been divided into many wedges (think slices of pizza!). The wedges have been colored alternately blue and yellow, then the wedges were rearranged to form a "rectangle" -- well, it's approximately a rectangle because the wedges have arcs (pieces of a circle) on them. See how the bottom and top edges of the rectangle look bumpy?
The area of the "rectangle" is approximately [tex]\pi r^2[/tex] . The reason is that the height of the rectangle is r , the radius of the circle. And the length of the rectangle is about [tex]\pi r[/tex] -- half the circumference of the circle. It's half because the circumference is in the bumpy parts of the wedges--half blue, half yellow.
The approximation improves as the number of wedges increases. In fact, as the number of slices (sorry, pizza again) gets larger, the length of the rectangle gets closer and closer to half the circumference. In other words, making more wedges makes the rectangle less bumpy!
what is 21 5/8% as a decimal
Answer: 21.625
Step-by-step explanation:
The percentage of 21 (5/8)% in decimal form is 173/800.
We have,
The percentage means the required value out of 100.
It is calculated by dividing the required value by the total value and multiplying by 100.
The given percentage expression.
21(5/8) %
Divide by 100 to remove the %.
This can be written as,
21(5/8) / 100
Now,
21(5/8)
= (21 x 8 + 5) / 8
Simply the fraction.
= 173/8
Now,
173/8 / 100
Simplify the fraction.
= 173/800
Thus,
The percentage of 21 (5/8)% in decimal form is 173/800.
Learn more about percentages here:
https://brainly.com/question/11403063
#SPJ4
Help please and why
solve plsssssssssssss
Answer:
7/24 is x and 24/25 is y :)
Step-by-step explanation:
hopefully that helped
If I get paid $5 for every 10 minutes, how much do I get paid an hour?
Step-by-step explanation:
30$ hope it helped I don't know if its correct though let me know if I'm wrong
I need help please help
Answer:
B (340)
Step-by-step explanation:
this is new information to me
Wendy is making potato salad for a picnic. One sack of potatoes weighs 14 pounds.What is the weight of a sack of potatoes in ounces
Answer:
224 ounces
Step-by-step explanation:
1 pound is 16 ounces, 14 multiplied by 16 is 224
every pound equal 16 ounces so 14 × 16 = 224